WorldWideScience

Sample records for perturbative transport numerical

  1. Two-scale approach to oscillatory singularly perturbed transport equations

    CERN Document Server

    Frénod, Emmanuel

    2017-01-01

    This book presents the classical results of the two-scale convergence theory and explains – using several figures – why it works. It then shows how to use this theory to homogenize ordinary differential equations with oscillating coefficients as well as oscillatory singularly perturbed ordinary differential equations. In addition, it explores the homogenization of hyperbolic partial differential equations with oscillating coefficients and linear oscillatory singularly perturbed hyperbolic partial differential equations. Further, it introduces readers to the two-scale numerical methods that can be built from the previous approaches to solve oscillatory singularly perturbed transport equations (ODE and hyperbolic PDE) and demonstrates how they can be used efficiently. This book appeals to master’s and PhD students interested in homogenization and numerics, as well as to the Iter community.

  2. Numerical solution of singularity-perturbed two-point boundary-value problems

    International Nuclear Information System (INIS)

    Masenge, R.W.P.

    1993-07-01

    Physical processes which involve transportation of slowly diffusing substances in a fast-flowing medium are mathematically modelled by so-called singularly-perturbed second order convection diffusion differential equations in which the convective first order terms dominate over the diffusive second order terms. In general, analytical solutions of such equations are characterized by having sharp solution fronts in some sections of the interior and/or the boundary of the domain of solution. The presence of these (usually very narrow) layer regions in the solution domain makes the task of globally approximating such solutions by standard numerical techniques very difficult. In this expository paper we use a simple one-dimensional prototype problem as a vehicle for analysing the nature of the numerical approximation difficulties involved. In the sequel we present, without detailed derivation, two practical numerical schemes which succeed in varying degrees in numerically resolving the layer of the solution to the prototype problem. (author). 3 refs, 1 fig., 1 tab

  3. Models and numerical methods for time- and energy-dependent particle transport

    Energy Technology Data Exchange (ETDEWEB)

    Olbrant, Edgar

    2012-04-13

    Particles passing through a medium can be described by the Boltzmann transport equation. Therein, all physical interactions of particles with matter are given by cross sections. We compare different analytical models of cross sections for photons, electrons and protons to state-of-the-art databases. The large dimensionality of the transport equation and its integro-differential form make it analytically difficult and computationally costly to solve. In this work, we focus on the following approximative models to the linear Boltzmann equation: (i) the time-dependent simplified P{sub N} (SP{sub N}) equations, (ii) the M{sub 1} model derived from entropy-based closures and (iii) a new perturbed M{sub 1} model derived from a perturbative entropy closure. In particular, an asymptotic analysis for SP{sub N} equations is presented and confirmed by numerical computations in 2D. Moreover, we design an explicit Runge-Kutta discontinuous Galerkin (RKDG) method to the M{sub 1} model of radiative transfer in slab geometry and construct a scheme ensuring the realizability of the moment variables. Among other things, M{sub 1} numerical results are compared with an analytical solution in a Riemann problem and the Marshak wave problem is considered. Additionally, we rigorously derive a new hierarchy of kinetic moment models in the context of grey photon transport in one spatial dimension. For the perturbed M{sub 1} model, we present numerical results known as the two beam instability or the analytical benchmark due to Su and Olson and compare them to the standard M{sub 1} as well as transport solutions.

  4. Transport of energetic ions by low-n magnetic perturbations

    International Nuclear Information System (INIS)

    Mynick, H.E.

    1992-10-01

    The stochastic transport of MeV ions induced by low-n magnetic perturbations is studied, focussing chiefly on the stochastic mechanism operative for passing particles in low frequency perturbations. Beginning with a single-harmonic form for the perturbing field, it iii first shown numerically and analytically that the stochastic threshold of energetic particles can be much lower than that of the magnetic field, contrary to earlier expectations, so that MHD perturbations could cause appreciable loss of energetic ions without destroying the bulk confinement. The analytic theory is then extended in a number of directions, to darity the relation of the present stochaistic mechanism to instances already found, to allow for more complex perturbations, and to consider the more general relationship between the stochasticity of magnetic fields, and that of particles of differing energies (and pitch angles) moving in those fields. It is shown that the stochastic threshold is in general a nonmonotonic function of energy, whose form can to some extent be tailored to achieve desired goals (e.g., burn control or ash removal) by a judicious choice of the perturbation. Illustrative perturbations are exhibited which are stochastic for low but not for high-energy ions, for high but not for low-energy ions, and for intermediate-energy ions, but not for low or high energy. The second possibility is the behavior needed for burn control; the third provides a possible mechanism for ash removal

  5. Numerical stochastic perturbation theory in the Schroedinger functional

    International Nuclear Information System (INIS)

    Brambilla, Michele; Di Renzo, Francesco; Hesse, Dirk; Dalla Brida, Mattia; Sint, Stefan; Deutsches Elektronen-Synchrotron

    2013-11-01

    The Schroedinger functional (SF) is a powerful and widely used tool for the treatment of a variety of problems in renormalization and related areas. Albeit offering many conceptual advantages, one major downside of the SF scheme is the fact that perturbative calculations quickly become cumbersome with the inclusion of higher orders in the gauge coupling and hence the use of an automated perturbation theory framework is desirable. We present the implementation of the SF in numerical stochastic perturbation theory (NSPT) and compare first results for the running coupling at two loops in pure SU(3) Yang-Mills theory with the literature.

  6. Numerical stochastic perturbation theory in the Schroedinger functional

    Energy Technology Data Exchange (ETDEWEB)

    Brambilla, Michele; Di Renzo, Francesco; Hesse, Dirk [Parma Univ. (Italy); INFN, Parma (Italy); Dalla Brida, Mattia [Trinity College Dublin (Ireland). School of Mathematics; Sint, Stefan [Trinity College Dublin (Ireland). School of Mathematics; Deutsches Elektronen-Synchrotron (DESY), Zeuthen (Germany). John von Neumann-Inst. fuer Computing NIC

    2013-11-15

    The Schroedinger functional (SF) is a powerful and widely used tool for the treatment of a variety of problems in renormalization and related areas. Albeit offering many conceptual advantages, one major downside of the SF scheme is the fact that perturbative calculations quickly become cumbersome with the inclusion of higher orders in the gauge coupling and hence the use of an automated perturbation theory framework is desirable. We present the implementation of the SF in numerical stochastic perturbation theory (NSPT) and compare first results for the running coupling at two loops in pure SU(3) Yang-Mills theory with the literature.

  7. Optimal perturbations for nonlinear systems using graph-based optimal transport

    Science.gov (United States)

    Grover, Piyush; Elamvazhuthi, Karthik

    2018-06-01

    We formulate and solve a class of finite-time transport and mixing problems in the set-oriented framework. The aim is to obtain optimal discrete-time perturbations in nonlinear dynamical systems to transport a specified initial measure on the phase space to a final measure in finite time. The measure is propagated under system dynamics in between the perturbations via the associated transfer operator. Each perturbation is described by a deterministic map in the measure space that implements a version of Monge-Kantorovich optimal transport with quadratic cost. Hence, the optimal solution minimizes a sum of quadratic costs on phase space transport due to the perturbations applied at specified times. The action of the transport map is approximated by a continuous pseudo-time flow on a graph, resulting in a tractable convex optimization problem. This problem is solved via state-of-the-art solvers to global optimality. We apply this algorithm to a problem of transport between measures supported on two disjoint almost-invariant sets in a chaotic fluid system, and to a finite-time optimal mixing problem by choosing the final measure to be uniform. In both cases, the optimal perturbations are found to exploit the phase space structures, such as lobe dynamics, leading to efficient global transport. As the time-horizon of the problem is increased, the optimal perturbations become increasingly localized. Hence, by combining the transfer operator approach with ideas from the theory of optimal mass transportation, we obtain a discrete-time graph-based algorithm for optimal transport and mixing in nonlinear systems.

  8. Analysis of radionuclide transport through fissured porous media with a perturbation method

    Energy Technology Data Exchange (ETDEWEB)

    Banat, M [JGC Corp., Tokyo (Japan)

    1995-04-01

    This paper presents a specific procedure for obtaining solutions for the transport of radionuclides in a fissured porous media. The concentration profiles are deduced for a wide range of Peclet numbers using a perturbation method with a multiscale of time. Results show clearly that because of an increase of longitudinal dispersion, the radionuclide moves faster with respect to the case of zero dispersion (i.e. an infinite Peclet number). The main purpose of this paper is to demonstrate the practical advantage of the present calculation method with respect to the classical numerical and analytical methods used for radionuclide transport. (author).

  9. Perturbation theory and importance functions in integral transport formulations

    International Nuclear Information System (INIS)

    Greenspan, E.

    1976-01-01

    Perturbation theory expressions for the static reactivity derived from the flux, collision density, birth-rate density, and fission-neutron density formulations of integral transport theory, and from the integro-differential formulation, are intercompared. The physical meaning and relation of the adjoint functions corresponding to each of the five formulations are established. It is found that the first-order approximation of the perturbation expressions depends on the transport theory formulation and on the adjoint function used. The approximations of the integro-differential formulation corresponding to different first-order approximations of the integral transport theory formulations are identified. It is found that the accuracy of all first-order approximations of the integral transport formulations examined is superior to the accuracy of first-order integro-differential perturbation theory

  10. Transport perturbation theory in nuclear reactor analysis

    International Nuclear Information System (INIS)

    Nishigori, Takeo; Takeda, Toshikazu; Selvi, S.

    1985-01-01

    Perturbation theory is formulated on the basis of transport theory to obtain a formula for the reactivity changes due to possible variations of cross sections. Useful applications to cell homogenization are presented for the whole core calculation in transport and in diffusion theories. (author)

  11. Controlled transport of solitons and bubbles using external perturbations

    International Nuclear Information System (INIS)

    Gonzalez, J.A.; Marcano, A.; Mello, B.A.; Trujillo, L.

    2006-01-01

    We investigate generalized soliton-bearing systems in the presence of external perturbations. We show the possibility of the transport of solitons using external waves, provided the waveform and its velocity satisfy certain conditions. We also investigate the stabilization and transport of bubbles using external perturbations in 3D-systems. We also present the results of real experiments with laser-induced vapor bubbles in liquids

  12. Perturbative analysis of transport and fluctuation studies on RFX

    International Nuclear Information System (INIS)

    Martini, S.

    2002-01-01

    On the RFX reversed field pinch different transport mechanisms govern the centre and the edge of the plasma. Core transport is driven by parallel transport in a stochastic magnetic field, giving rise to an outward directed particle convection velocity. At the edge, roughly corresponding to the region outside the toroidal field reversal surface (where q=0), electrostatic fluctuations are an important loss channel, but more than 50% of the power losses have been associated to localized plasma-wall interaction due to the non-axisymmetric magnetic perturbations caused by locked modes. In the paper we present the most recent progress made in the modeling and understanding of the above mechanisms underlying particle and energy transport. The paper also discusses the correlations between core and edge transport phenomena. The main tools are perturbative transport studies by pellet injection and the analysis of the contribution of intermittency processes to particle transport in the edge. (author)

  13. Numerical studies of QCD renormalons in high-order perturbative expansions

    International Nuclear Information System (INIS)

    Bauer, Clemens

    2013-01-01

    Perturbative expansions in four-dimensional non-Abelian gauge theories such as Quantum Chromodynamics (QCD) are expected to be divergent, at best asymptotic. One reason is that it is impossible to strictly exclude from the relevant Feynman diagrams those energy regions in which a perturbative treatment is inapplicable. The divergent nature of the series is then signaled by a rapid (factorial) growth of the perturbative expansion coefficients, commonly referred to as a renormalon. In QCD, the most severe divergences occur in the infrared (IR) limit and therefore they are classified as IR renormalons. Their appearance can be understood within the well-accepted Operator Product Expansion (OPE) framework. According to the OPE, the perturbative calculation of a physical observable must be amended by non-perturbative power corrections that come in the form of condensates, universal characteristics of the rich QCD vacuum structure. Adding up perturbative and non-perturbative contributions, the ambiguity due to the renormalon cancels and the physical observable is well-defined. Although the field has made considerable progress in the last twenty years, a proof of renormalon existence is still pending. It has only been tested assuming strong simplifications or in toy models. The aim of this thesis is to provide the first numerical evidence for renormalon existence in the gauge sector of QCD. We use Numerical Stochastic Perturbation Theory (NSPT) to directly obtain perturbative coefficients within lattice regularization, a means to replace continuum spacetime by a four-dimensional hypercubic lattice. A peculiar feature of NSPT are comparatively low simulation costs when reaching high expansion orders. We examine two distinct observables: the static self-energy of an isolated quark and the elementary plaquette. Following the OPE classification, the static quark self-energy is ideally suited for a renormalon study. Taking into account peculiarities of the lattice approach such

  14. New numerical method for iterative or perturbative solution of quantum field theory

    International Nuclear Information System (INIS)

    Hahn, S.C.; Guralnik, G.S.

    1999-01-01

    A new computational idea for continuum quantum Field theories is outlined. This approach is based on the lattice source Galerkin methods developed by Garcia, Guralnik and Lawson. The method has many promising features including treating fermions on a relatively symmetric footing with bosons. As a spin-off of the technology developed for 'exact' solutions, the numerical methods used have a special case application to perturbation theory. We are in the process of developing an entirely numerical approach to evaluating graphs to high perturbative order. (authors)

  15. Numerical simulation of plasma response to externally applied resonant magnetic perturbation on the J-TEXT tokamak

    Science.gov (United States)

    Bicheng, LI; Zhonghe, JIANG; Jian, LV; Xiang, LI; Bo, RAO; Yonghua, DING

    2018-05-01

    Nonlinear magnetohydrodynamic (MHD) simulations of an equilibrium on the J-TEXT tokamak with applied resonant magnetic perturbations (RMPs) are performed with NIMROD (non-ideal MHD with rotation, open discussion). Numerical simulation of plasma response to RMPs has been developed to investigate magnetic topology, plasma density and rotation profile. The results indicate that the pure applied RMPs can stimulate 2/1 mode as well as 3/1 mode by the toroidal mode coupling, and finally change density profile by particle transport. At the same time, plasma rotation plays an important role during the entire evolution process.

  16. A global numerical solution of the radial Schroedinger equation by second-order perturbation theory

    International Nuclear Information System (INIS)

    Adam, G.

    1979-01-01

    A global numerical method, which uses second-order perturbation theory, is described for the solution of the radial Schroedinger equation. The perturbative numerical (PN) solution is derived in two stages: first, the original potential is approximated by a piecewise continuous parabolic function, and second, the resulting Schroedinger equation is solved on each integration step by second-order perturbation theory, starting with a step function reference approximation for the parabolic potential. We get a manageable PN algorithm, which shows an order of accuracy equal to six in the solution of the original Schroedinger equation, and is very stable against round off errors. (author)

  17. Wilson loops to 20th order numerical stochastic perturbation theory

    Energy Technology Data Exchange (ETDEWEB)

    Horsley, R. [Edinburgh Univ. (United Kingdom). School of Physics; Hotzel, G.; Perlt, H.; Schiller, A. [Leipzig Univ. (Germany). Inst. fuer Theoretische Physik; Ilgenfritz, E.M. [Humboldt-Universitaet, Berlin (Germany). Inst. fuer Physik; Joint Institute for Nuclear Research, VBLHEP, Dubna (Russian Federation); Millo, R.; Rakow, P.E.L. [Liverpool Univ. (Germany). Theoretical Physics Div.; Nakamura, Y. [RIKEN Advanced Institute for Computational Science, Kobe, Hyogo (Japan); Schierholz, G. [Deutsches Elektronen-Synchrotron (DESY), Hamburg (Germany)

    2012-05-15

    We calculate Wilson loops of various sizes up to 20 loops in SU(3) pure lattice gauge theory at different lattice sizes for Wilson gauge action using the technique of numerical stochastic perturbation theory. This allows us to investigate the perturbative series for various Wilson loops at high loop orders. We observe differences in the behavior of those series as function of the loop order. Up to n=20 we do not find evidence for the factorial growth of the expansion coefficients often assumed to characterize an asymptotic series. Based on the actually observed behavior we sum the series in a model parametrized by hypergeometric functions. Alternatively we estimate the total series in boosted perturbation theory using information from the first 14 loops. We introduce generalized ratios of Wilson loops of different sizes. Together with the corresponding Wilson loops from standard Monte Carlo measurements they enable us to assess their non-perturbative parts.

  18. SMD-based numerical stochastic perturbation theory

    Science.gov (United States)

    Dalla Brida, Mattia; Lüscher, Martin

    2017-05-01

    The viability of a variant of numerical stochastic perturbation theory, where the Langevin equation is replaced by the SMD algorithm, is examined. In particular, the convergence of the process to a unique stationary state is rigorously established and the use of higher-order symplectic integration schemes is shown to be highly profitable in this context. For illustration, the gradient-flow coupling in finite volume with Schrödinger functional boundary conditions is computed to two-loop (i.e. NNL) order in the SU(3) gauge theory. The scaling behaviour of the algorithm turns out to be rather favourable in this case, which allows the computations to be driven close to the continuum limit.

  19. SMD-based numerical stochastic perturbation theory

    Energy Technology Data Exchange (ETDEWEB)

    Dalla Brida, Mattia [Universita di Milano-Bicocca, Dipartimento di Fisica, Milan (Italy); INFN, Sezione di Milano-Bicocca (Italy); Luescher, Martin [CERN, Theoretical Physics Department, Geneva (Switzerland); AEC, Institute for Theoretical Physics, University of Bern (Switzerland)

    2017-05-15

    The viability of a variant of numerical stochastic perturbation theory, where the Langevin equation is replaced by the SMD algorithm, is examined. In particular, the convergence of the process to a unique stationary state is rigorously established and the use of higher-order symplectic integration schemes is shown to be highly profitable in this context. For illustration, the gradient-flow coupling in finite volume with Schroedinger functional boundary conditions is computed to two-loop (i.e. NNL) order in the SU(3) gauge theory. The scaling behaviour of the algorithm turns out to be rather favourable in this case, which allows the computations to be driven close to the continuum limit. (orig.)

  20. SMD-based numerical stochastic perturbation theory

    International Nuclear Information System (INIS)

    Dalla Brida, Mattia; Luescher, Martin

    2017-01-01

    The viability of a variant of numerical stochastic perturbation theory, where the Langevin equation is replaced by the SMD algorithm, is examined. In particular, the convergence of the process to a unique stationary state is rigorously established and the use of higher-order symplectic integration schemes is shown to be highly profitable in this context. For illustration, the gradient-flow coupling in finite volume with Schroedinger functional boundary conditions is computed to two-loop (i.e. NNL) order in the SU(3) gauge theory. The scaling behaviour of the algorithm turns out to be rather favourable in this case, which allows the computations to be driven close to the continuum limit. (orig.)

  1. Non-perturbative Heavy-Flavor Transport at RHIC and LHC

    Energy Technology Data Exchange (ETDEWEB)

    He, Min, E-mail: mhe@comp.tamu.edu; Fries, Rainer J.; Rapp, Ralf

    2013-08-15

    We calculate open heavy-flavor (HF) transport in relativistic heavy-ion collisions by applying a strong-coupling treatment in both macro- and microscopic dynamics (hydrodynamics and non-perturbative diffusion interactions). The hydrodynamic medium evolution is quantitatively constrained by bulk and multi-strange hadron spectra and elliptic flow. The heavy quark transport coefficient is evaluated from a non-perturbative T-matrix approach in the Quark–Gluon Plasma which, close to the critical temperature, leads to resonance formation and feeds into the recombination of heavy quarks on a hydrodynamic hypersurface. In the hadronic phase, the diffusion of HF mesons is obtained from effective hadronic theory. We compute observables at RHIC and LHC for non-photonic electrons and HF mesons, respectively.

  2. The joint essential numerical range, compact perturbations, and the Olsen problem

    Czech Academy of Sciences Publication Activity Database

    Müller, Vladimír

    2010-01-01

    Roč. 197, č. 3 (2010), s. 275-290 ISSN 0039-3223 R&D Projects: GA ČR GA201/09/0473; GA AV ČR IAA100190903 Institutional research plan: CEZ:AV0Z10190503 Keywords : joint essential numerical range * joint numerical range * compact perturbation * Olsen's problem Subject RIV: BA - General Mathematics Impact factor: 0.567, year: 2010 http://journals.impan.pl/cgi-bin/doi?sm197-3-5

  3. The SU(3) beta function from numerical stochastic perturbation theory

    Energy Technology Data Exchange (ETDEWEB)

    Horsley, R. [Edinburgh Univ. (United Kingdom). School of Physics and Astronomy; Perlt, H. [Leipzig Univ. (Germany). Inst. fuer Theoretische Physik; Bonn Univ. (Germany). Helmholtz Inst. fuer Strahlen- und Kernphysik; Rakow, P.E.L. [Liverpool Univ. (United Kingdom). Theoretical Physics Div.; Schierholz, G.; Schiller, A. [Deutsches Elektronen-Synchrotron (DESY), Hamburg (Germany)

    2013-09-15

    The SU(3) beta function is derived from Wilson loops computed to 20th order in numerical stochastic perturbation theory. An attempt is made to include massless fermions, whose contribution is known analytically to 4th order. The question whether the theory admits an infrared stable fixed point is addressed.

  4. Nonlocal transport in the presence of transport barriers

    Science.gov (United States)

    Del-Castillo-Negrete, D.

    2013-10-01

    There is experimental, numerical, and theoretical evidence that transport in plasmas can, under certain circumstances, depart from the standard local, diffusive description. Examples include fast pulse propagation phenomena in perturbative experiments, non-diffusive scaling in L-mode plasmas, and non-Gaussian statistics of fluctuations. From the theoretical perspective, non-diffusive transport descriptions follow from the relaxation of the restrictive assumptions (locality, scale separation, and Gaussian/Markovian statistics) at the foundation of diffusive models. We discuss an alternative class of models able to capture some of the observed non-diffusive transport phenomenology. The models are based on a class of nonlocal, integro-differential operators that provide a unifying framework to describe non- Fickian scale-free transport, and non-Markovian (memory) effects. We study the interplay between nonlocality and internal transport barriers (ITBs) in perturbative transport including cold edge pulses and power modulation. Of particular interest in the nonlocal ``tunnelling'' of perturbations through ITBs. Also, flux-gradient diagrams are discussed as diagnostics to detect nonlocal transport processes in numerical simulations and experiments. Work supported by the US Department of Energy.

  5. Local and accumulated truncation errors in a class of perturbative numerical methods

    International Nuclear Information System (INIS)

    Adam, G.; Adam, S.; Corciovei, A.

    1980-01-01

    The approach to the solution of the radial Schroedinger equation using piecewise perturbative theory with a step function reference potential leads to a class of powerful numerical methods, conveniently abridged as SF-PNM(K), where K denotes the order at which the perturbation series was truncated. In the present paper rigorous results are given for the local truncation errors and bounds are derived for the accumulated truncated errors associated to SF-PNM(K), K = 0, 1, 2. They allow us to establish the smoothness conditions which have to be fulfilled by the potential in order to ensure a safe use of SF-PNM(K), and to understand the experimentally observed behaviour of the numerical results with the step size h. (author)

  6. Reactivity perturbation formulation for a discontinuous Galerkin-based transport solver and its use with adaptive mesh refinement

    International Nuclear Information System (INIS)

    Le Tellier, R.; Fournier, D.; Suteau, C.

    2011-01-01

    Within the framework of a Discontinuous Galerkin spatial approximation of the multigroup discrete ordinates transport equation, we present a generalization of the exact standard perturbation formula that takes into account spatial discretization-induced reactivity changes. It encompasses in two separate contributions the nuclear data-induced reactivity change and the reactivity modification induced by two different spatial discretizations. The two potential uses of such a formulation when considering adaptive mesh refinement are discussed, and numerical results on a simple two-group Cartesian two-dimensional benchmark are provided. In particular, such a formulation is shown to be useful to filter out a more accurate estimate of nuclear data-related reactivity effects from initial and perturbed calculations based on independent adaptation processes. (authors)

  7. Study of Heat Flux Threshold and Perturbation Effect on Transport Barrier Formation Based on Bifurcation Model

    International Nuclear Information System (INIS)

    Chatthong, B.; Onjun, T.; Imbeaux, F.; Sarazin, Y.; Strugarek, A.; Picha, R.; Poolyarat, N.

    2011-06-01

    Full text: Formation of transport barrier in fusion plasma is studied using a simple one-field bistable S-curve bifurcation model. This model is characterized by an S-line with two stable branches corresponding to the low (L) and high (H) confinement modes, connected by an unstable branch. Assumptions used in this model are such that the reduction in anomalous transport is caused by v E velocity shear effect and also this velocity shear is proportional to pressure gradient. In this study, analytical and numerical approaches are used to obtain necessary conditions for transport barrier formation, i.e. the ratio of anomalous over neoclassical coefficients and heat flux thresholds which must be exceeded. Several profiles of heat sources are considered in this work including constant, Gaussian, and hyperbolic tangent forms. Moreover, the effect of perturbation in heat flux is investigated with respect to transport barrier formation

  8. Transportation package design using numerical optimization

    International Nuclear Information System (INIS)

    Harding, D.C.; Witkowski, W.R.

    1991-01-01

    The purpose of this overview is twofold: first, to outline the theory and basic elements of numerical optimization; and second, to show how numerical optimization can be applied to the transportation packaging industry and used to increase efficiency and safety of radioactive and hazardous material transportation packages. A more extensive review of numerical optimization and its applications to radioactive material transportation package design was performed previously by the authors (Witkowski and Harding 1992). A proof-of-concept Type B package design is also presented as a simplified example of potential improvements achievable using numerical optimization in the design process

  9. Analysis and Application of High Resolution Numerical Perturbation Algorithm for Convective-Diffusion Equation

    International Nuclear Information System (INIS)

    Gao Zhi; Shen Yi-Qing

    2012-01-01

    The high resolution numerical perturbation (NP) algorithm is analyzed and tested using various convective-diffusion equations. The NP algorithm is constructed by splitting the second order central difference schemes of both convective and diffusion terms of the convective-diffusion equation into upstream and downstream parts, then the perturbation reconstruction functions of the convective coefficient are determined using the power-series of grid interval and eliminating the truncated errors of the modified differential equation. The important nature, i.e. the upwind dominance nature, which is the basis to ensuring that the NP schemes are stable and essentially oscillation free, is firstly presented and verified. Various numerical cases show that the NP schemes are efficient, robust, and more accurate than the original second order central scheme

  10. Generalized perturbation theory using two-dimensional, discrete ordinates transport theory

    International Nuclear Information System (INIS)

    Childs, R.L.

    1979-01-01

    Perturbation theory for changes in linear and bilinear functionals of the forward and adjoint fluxes in a critical reactor has been implemented using two-dimensional discrete ordinates transport theory. The computer program DOT IV was modified to calculate the generalized functions Λ and Λ*. Demonstration calculations were performed for changes in a reaction-rate ratio and a reactivity worth caused by system perturbations. The perturbation theory predictions agreed with direct calculations to within about 2%. A method has been developed for calculating higher lambda eigenvalues and eigenfunctions using techniques similar to those developed for generalized functions. Demonstration calculations have been performed to obtain these eigenfunctions

  11. Numerical Integration of a Class of Singularly Perturbed Delay Differential Equations with Small Shift

    Directory of Open Access Journals (Sweden)

    Gemechis File

    2012-01-01

    Full Text Available We have presented a numerical integration method to solve a class of singularly perturbed delay differential equations with small shift. First, we have replaced the second-order singularly perturbed delay differential equation by an asymptotically equivalent first-order delay differential equation. Then, Simpson’s rule and linear interpolation are employed to get the three-term recurrence relation which is solved easily by discrete invariant imbedding algorithm. The method is demonstrated by implementing it on several linear and nonlinear model examples by taking various values for the delay parameter and the perturbation parameter .

  12. Some applications of perturbation theory to numerical integration methods for the Schroedinger equation

    International Nuclear Information System (INIS)

    Killingbeck, J.

    1979-01-01

    By using the methods of perturbation theory it is possible to construct simple formulae for the numerical integration of the Schroedinger equation, and also to calculate expectation values solely by means of simple eigenvalue calculations. (Auth.)

  13. Numerical simulation of the regularized long wave equation by He's homotopy perturbation method

    International Nuclear Information System (INIS)

    Inc, Mustafa; Ugurlu, Yavuz

    2007-01-01

    In this Letter, we present the homotopy perturbation method (shortly HPM) for obtaining the numerical solution of the RLW equation. We obtain the exact and numerical solutions of the Regularized Long Wave (RLW) equation for certain initial condition. The initial approximation can be freely chosen with possible unknown constants which can be determined by imposing the boundary and initial conditions. Comparison of the results with those of other methods have led us to significant consequences. The numerical solutions are compared with the known analytical solutions

  14. Characteristics of equilibrium and perturbed transport coefficients in tokamaks

    International Nuclear Information System (INIS)

    Gentle, K.W.

    1995-01-01

    Although the evolution of a perturbation to a tokamak equilibrium can generally be described by local transport coefficients modestly enhanced above the equilibrium values, there are some significant cases for which this is inadequate. The density profile evolution in ASDEX-U occurs far more rapidly than is consistent with reasonable particle confinement times, and the evolution of cold pulses in TEXT requires nonlocal behavior in the core and some kind of anomaly near the periphery. The experiments are suggesting effects beyond standard local turbulent transport models. (orig.)

  15. An outline review of numerical transport methods

    International Nuclear Information System (INIS)

    Budd, C.

    1981-01-01

    A brief review is presented of numerical methods for solving the neutron transport equation in the context of reactor physics. First the various forms of transport equation are given. Second, the various ways of classifying numerical transport methods are discussed. Finally each method (or class of methods) is outlined in turn. (U.K.)

  16. GAPER-1D, 1-D Multigroup 1. Order Perturbation Transport Theory for Reactivity Coefficient

    International Nuclear Information System (INIS)

    Koch, P.K.

    1976-01-01

    1 - Description of problem or function: Reactivity coefficients are computed using first-order transport perturbation theory for one- dimensional multi-region reactor assemblies. The number of spatial mesh-points and energy groups is arbitrary. An elementary synthesis scheme is employed for treatment of two- and three-dimensional problems. The contributions to the change in inverse multiplication factor, delta(1/k), from perturbations in the individual capture, net fission, total scattering, (n,2n), inelastic scattering, and leakage cross sections are computed. A multi-dimensional prompt neutron lifetime calculation is also available. 2 - Method of solution: Broad group cross sections for the core and perturbing or sample materials are required as input. Scalar neutron fluxes and currents, as computed by SN transport calculations, are then utilized to solve the first-order transport perturbation theory equations. A synthesis scheme is used, along with independent SN calculations in two or three dimensions, to treat a multi- dimensional assembly. Spherical harmonics expansions of the angular fluxes and scattering source terms are used with leakage and anisotropic scattering treated in a P1 approximation. The angular integrations in the perturbation theory equations are performed analytically. Various reactivity coefficients and material worths are then easily computed at specified positions in the assembly. 3 - Restrictions on the complexity of the problem: The formulation of the synthesis scheme used for two- and three-dimensional problems assumes that the fluxes and currents were computed by the DTF4 code (NESC Abstract 209). Therefore, fluxes and currents from two- or three-dimensional transport or diffusion theory codes cannot be used

  17. Perturbative transport experiments in JET Advanced Tokamak plasmas

    Energy Technology Data Exchange (ETDEWEB)

    Mantica, P.; Gorini, G.; Sozzi, C. [Istituto di Fisica del Plasma, EURATOM-ENEA-CNR Association, Milan (Italy); Imbeaux, F.; Sarazin, Y.; Garbet, X. [Association Euratom-CEA, St. Paul-lez-Durance Cedex (France); Kinsey, J. [Lehigh Univ., Bethlehem, Pennsylvania (United States); Budny, R. [Princeton Plasma Physics Lab, New Jersey (United States); Coffey, I.; Parail, V.; Walden, A. [Euratom/UKAEA Fusion Association, Abingdon, Oxon (United Kingdom); Dux, R. [Max-Planck-Institut fuer Plasmaphysik, Garching (Germany); Garzotti, L. [Istituto Gas Ionizzati, Padova (Italy); Ingesson, C. [FOM-Instituut voor Plasmafysica, Nieuwegein (Netherlands); Kissick, M. [University of California, Los Angeles (United States)

    2003-07-01

    Perturbative transport experiments have been performed in JET Advanced Tokamak plasmas either in conditions of fully developed Internal Transport Barrier (ITB) or during a phase where an ITB was not observed. Transient peripheral cooling was induced by either Laser Ablation or Shallow Pellet Injection and the ensuing travelling cold pulse was used to probe the plasma transport in the electron and, for the first time, also in the ion channel. Cold pulses travelling through ITBs are observed to erode the ITB outer part, but, if the inner ITB portion survives, it strongly damps the propagating wave. The result is discussed in the context of proposed possible pictures for ITB formation. In the absence of an ITB, the cold pulse shows a fast propagation in the outer plasma half, which is consistent with a region of stiff transport, while in the inner half it slows down but shows the peculiar feature of amplitude growing while propagating. The data are powerful tests for the validation of theoretical transport models. (author)

  18. On Perturbation Components Correspondence between Diffusion and Transport

    Energy Technology Data Exchange (ETDEWEB)

    G. Palmiotti

    2012-11-01

    We have established a correspondence between perturbation components in diffusion and transport theory. In particular we have established the correspondence between the leakage perturbation component of the diffusion theory to that of the group self scattering in transport theory. This has been confirmed by practical applications on sodium void reactivity calculations of fast reactors. Why this is important for current investigations? Recently, there has been a renewed interest in designing fast reactors where the sodium void reactivity coefficient is minimized. In particular the ASTRID8,9 reactor concept has been optimized with this goal in mind. The correspondence on the leakage term that has been established here has a twofold implication for the design of this kind of reactors. First, this type of reactor has a radial reflector; therefore, as shown before, the sodium void reactivity coefficient calculation requires the use of transport theory. The minimization of the sodium reactivity coefficient is normally done by increasing the leakage component that has a negative sign. The correspondence established in this paper allows to directly look at this component in transport theory. The second implication is related to the uncertainty evaluation on sodium void reactivity. As it has shown before, the total sodium void reactivity effect is the result of a large compensation (opposite sign) between the scattering (called often spectral) component and the leakage one. Consequently, one has to evaluate separately the uncertainty on each separate component and then combine them statistically. If one wants to compute the cross section sensitivity coefficients of the two different components, the formulation established in this paper allows to achieve this goal by playing on the contribution to the sodium void reactivity coming from the group self scattering of the sodium cross section.

  19. Numerical perturbative methods in the quantum theory of physical systems

    International Nuclear Information System (INIS)

    Adam, G.

    1980-01-01

    During the last two decades, development of digital electronic computers has led to the deployment of new, distinct methods in theoretical physics. These methods, based on the advances of modern numerical analysis as well as on specific equations describing physical processes, enabled to perform precise calculations of high complexity which have completed and sometimes changed our image of many physical phenomena. Our efforts have concentrated on the development of numerical methods with such intrinsic performances as to allow a successful approach of some Key issues in present theoretical physics on smaller computation systems. The basic principle of such methods is to translate, in numerical analysis language, the theory of perturbations which is suited to numerical rather than to analytical computation. This idea has been illustrated by working out two problems which arise from the time independent Schroedinger equation in the non-relativistic approximation, within both quantum systems with a small number of particles and systems with a large number of particles, respectively. In the first case, we are led to the numerical solution of some quadratic ordinary differential equations (first section of the thesis) and in the second case, to the solution of some secular equations in the Brillouin area (second section). (author)

  20. Edge-Localized mode control and transport generated by externally applied magnetic perturbations

    International Nuclear Information System (INIS)

    Joseph, I.

    2012-01-01

    This article reviews the subject of edge localized mode (ELM) control using externally applied magnetic perturbations and proposes theoretical mechanisms that may be responsible for the induced transport changes. The first question that must be addressed is: what is the structure of magnetic field within the plasma? Although initial hypotheses focused on the possibility of the creation of a region of stochastic field lines at the tokamak edge, drift magnetohydrodynamics theory predicts that magnetic reconnection is strongly suppressed over the region of the pedestal with steep gradients and fast perpendicular rotation. Reconnection can only occur near the location where the perpendicular electron velocity vanishes, and hence the electron impedance nearly vanishes, or near the foot of the pedestal, where the plasma is sufficiently cold and resistive. The next question that must be addressed is: which processes are responsible for the observed transport changes, nonlinearity, turbulence, or stochasticity? Over the pedestal region where ions and electrons rotate in opposite directions relative to the perturbation, the quasilinear Lorentz force decelerates the electron fluid and accelerates the ion fluid. The quasilinear magnetic flutter flux is proportional to the force and produces an outward convective transport that can be significant. Over the pedestal region where the E x B flow and the electrons rotate in opposite directions relative to the perturbation, magnetic islands with a width on the order of the ion gyroradius can directly radiate drift waves. In addition, the combination of quasilinear electron transport and ion viscous transport can lead to a large net particle flux. Since there are many transport mechanisms that may be active simultaneously, it is important to determine which physical mechanisms are responsible for ELM control and to predict the scaling to future devices (copyright 2012 WILEY-VCH Verlag GmbH and Co. KGaA, Weinheim) (orig.)

  1. Transportation package design using numerical optimization

    International Nuclear Information System (INIS)

    Harding, D.C.; Witkowski, W.R.

    1992-01-01

    The design of structures and engineering systems has always been an iterative process whose complexity was dependent upon the boundary conditions, constraints and available analytical tools. Transportation packaging design is no exception with structural, thermal and radiation shielding constraints based on regulatory hypothetical accident conditions. Transportation packaging design is often accomplished by a group of specialists, each designing a single component based on one or more simple criteria, pooling results with the group, evaluating the open-quotes pooledclose quotes design, and then reiterating the entire process until a satisfactory design is reached. The manual iterative methods used by the designer/analyst can be summarized in the following steps: design the part, analyze the part, interpret the analysis results, modify the part, and re-analyze the part. The inefficiency of this design practice and the frequently conservative result suggests the need for a more structured design methodology, which can simultaneously consider all of the design constraints. Numerical optimization is a structured design methodology whose maturity in development has allowed it to become a primary design tool in many industries. The purpose of this overview is twofold: first, to outline the theory and basic elements of numerical optimization; and second, to show how numerical optimization can be applied to the transportation packaging industry and used to increase efficiency and safety of radioactive and hazardous material transportation packages. A more extensive review of numerical optimization and its applications to radioactive material transportation package design was performed previously by the authors (Witkowski and Harding 1992). A proof-of-concept Type B package design is also presented as a simplified example of potential improvements achievable using numerical optimization in the design process

  2. Born approximation to a perturbative numerical method for the solution of the Schroedinger equation

    International Nuclear Information System (INIS)

    Adam, Gh.

    1978-01-01

    A step function perturbative numerical method (SF-PN method) is developed for the solution of the Cauchy problem for the second order liniar differential equation in normal form. An important point stressed in the present paper, which seems to have been previously ignored in the literature devoted to the PN methods, is the close connection between the first order perturbation theory of the PN approach and the wellknown Born approximation, and, in general, the connection between the varjous orders of the PN corrections and the Neumann series. (author)

  3. Experimental evidence of off-diagonal transport term and the discrepancy between energy/particle balance and perturbation analyses

    International Nuclear Information System (INIS)

    Nagashima, Keisuke; Fukuda, Takeshi

    1991-12-01

    Evidence of temperature gradient driven particle flux was observed from the sawtooth induced density propagation phenomenon in JT-60. This off-diagonal particle flux was confirmed using the numerical calculation of measured chord integrated electron density. It was shown that the discrepancies between thermal and particle diffusivities estimated from the perturbation method and energy/particle balance analysis can be explained by considering the flux equations with off-diagonal transport terms. These flux equations were compared with the E x B convective fluxes in an electro-static drift wave instability and it was found that the E x B fluxes are consistent with several experimental observations. (author)

  4. Numerical simulation of the regularized long wave equation by He's homotopy perturbation method

    Energy Technology Data Exchange (ETDEWEB)

    Inc, Mustafa [Department of Mathematics, Firat University, 23119 Elazig (Turkey)], E-mail: minc@firat.edu.tr; Ugurlu, Yavuz [Department of Mathematics, Firat University, 23119 Elazig (Turkey)

    2007-09-17

    In this Letter, we present the homotopy perturbation method (shortly HPM) for obtaining the numerical solution of the RLW equation. We obtain the exact and numerical solutions of the Regularized Long Wave (RLW) equation for certain initial condition. The initial approximation can be freely chosen with possible unknown constants which can be determined by imposing the boundary and initial conditions. Comparison of the results with those of other methods have led us to significant consequences. The numerical solutions are compared with the known analytical solutions.

  5. Born approximation to a perturbative numerical method for the solution of the Schrodinger equation

    International Nuclear Information System (INIS)

    Adam, Gh.

    1978-05-01

    A perturbative numerical (PN) method is given for the solution of a regular one-dimensional Cauchy problem arising from the Schroedinger equation. The present method uses a step function approximation for the potential. Global, free of scaling difficulty, forward and backward PN algorithms are derived within first order perturbation theory (Born approximation). A rigorous analysis of the local truncation errors is performed. This shows that the order of accuracy of the method is equal to four. In between the mesh points, the global formula for the wavefunction is accurate within O(h 4 ), while that for the first order derivative is accurate within O(h 3 ). (author)

  6. Description of a neutron field perturbed by a probe using coupled Monte Carlo and discrete ordinates radiation transport calculations

    International Nuclear Information System (INIS)

    Zazula, J.M.

    1984-01-01

    This work concerns calculation of a neutron response, caused by a neutron field perturbed by materials surrounding the source or the detector. Solution of a problem is obtained using coupling of the Monte Carlo radiation transport computation for the perturbed region and the discrete ordinates transport computation for the unperturbed system. (author). 62 refs

  7. Diffusion in randomly perturbed dissipative dynamics

    Science.gov (United States)

    Rodrigues, Christian S.; Chechkin, Aleksei V.; de Moura, Alessandro P. S.; Grebogi, Celso; Klages, Rainer

    2014-11-01

    Dynamical systems having many coexisting attractors present interesting properties from both fundamental theoretical and modelling points of view. When such dynamics is under bounded random perturbations, the basins of attraction are no longer invariant and there is the possibility of transport among them. Here we introduce a basic theoretical setting which enables us to study this hopping process from the perspective of anomalous transport using the concept of a random dynamical system with holes. We apply it to a simple model by investigating the role of hyperbolicity for the transport among basins. We show numerically that our system exhibits non-Gaussian position distributions, power-law escape times, and subdiffusion. Our simulation results are reproduced consistently from stochastic continuous time random walk theory.

  8. Numerical simulation of CALIBAN reactivity perturbation experiments using neptunium-237 samples

    International Nuclear Information System (INIS)

    Humbert, Philippe; Mechitoua, Boukhmes

    2003-01-01

    In order to contribute to the validation of nuclear data used in critical mass computation, reactivity perturbation experiments using 237 Np samples have been performed at CEA-Valduc using the fast pulsed reactor CALIBAN operated in continuous mode. In this paper we report these experiments together with the numerical calculations. The calculations were carried out using PANDA, a S N code developed at CEA-Bruyeres-le-Chatel for classic criticality and stochastic neutronics applications and with MCNP4C which is a commonly used Monte Carlo code. A good agreement was found between experimental and deterministic results. (author)

  9. Numerical Modelling of Sediment Transport in Combined Sewer Systems

    DEFF Research Database (Denmark)

    Schlütter, Flemming

    A conceptual sediment transport model has been developed. Through a case study a comparison with other numerical models is performed.......A conceptual sediment transport model has been developed. Through a case study a comparison with other numerical models is performed....

  10. A stable high-order perturbation of surfaces method for numerical simulation of diffraction problems in triply layered media

    Energy Technology Data Exchange (ETDEWEB)

    Hong, Youngjoon, E-mail: hongy@uic.edu; Nicholls, David P., E-mail: davidn@uic.edu

    2017-02-01

    The accurate numerical simulation of linear waves interacting with periodic layered media is a crucial capability in engineering applications. In this contribution we study the stable and high-order accurate numerical simulation of the interaction of linear, time-harmonic waves with a periodic, triply layered medium with irregular interfaces. In contrast with volumetric approaches, High-Order Perturbation of Surfaces (HOPS) algorithms are inexpensive interfacial methods which rapidly and recursively estimate scattering returns by perturbation of the interface shape. In comparison with Boundary Integral/Element Methods, the stable HOPS algorithm we describe here does not require specialized quadrature rules, periodization strategies, or the solution of dense non-symmetric positive definite linear systems. In addition, the algorithm is provably stable as opposed to other classical HOPS approaches. With numerical experiments we show the remarkable efficiency, fidelity, and accuracy one can achieve with an implementation of this algorithm.

  11. Radiation transport in numerical astrophysics

    International Nuclear Information System (INIS)

    Lund, C.M.

    1983-02-01

    In this article, we discuss some of the numerical techniques developed by Jim Wilson and co-workers for the calculation of time-dependent radiation flow. Difference equations for multifrequency transport are given for both a discrete-angle representation of radiation transport and a Fick's law-like representation. These methods have the important property that they correctly describe both the streaming and diffusion limits of transport theory in problems where the mean free path divided by characteristic distances varies from much less than one to much greater than one. They are also stable for timesteps comparable to the changes in physical variables, rather than being limited by stability requirements

  12. New evidence and impact of electron transport non-linearities based on new perturbative inter-modulation analysis

    NARCIS (Netherlands)

    van Berkel, M.; Kobayashi, T.; Igami, H.; Vandersteen, Gerd; Hogeweij, G.M.D.; Tanaka, K.; Tamura, N.; Zwart, Hans; Kubo, S.; Ito, S.; Tsuchiya, H.; de Baar, M.R.

    2017-01-01

    A new methodology to analyze non-linear components in perturbative transport experiments is introduced. The methodology has been experimentally validated in the Large Helical Device for the electron heat transport channel. Electron cyclotron resonance heating with different modulation frequencies by

  13. Conceptual and Numerical Models for UZ Flow and Transport

    International Nuclear Information System (INIS)

    Liu, H.

    2000-01-01

    The purpose of this Analysis/Model Report (AMR) is to document the conceptual and numerical models used for modeling of unsaturated zone (UZ) fluid (water and air) flow and solute transport processes. This is in accordance with ''AMR Development Plan for U0030 Conceptual and Numerical Models for Unsaturated Zone (UZ) Flow and Transport Processes, Rev 00''. The conceptual and numerical modeling approaches described in this AMR are used for models of UZ flow and transport in fractured, unsaturated rock under ambient and thermal conditions, which are documented in separate AMRs. This AMR supports the UZ Flow and Transport Process Model Report (PMR), the Near Field Environment PMR, and the following models: Calibrated Properties Model; UZ Flow Models and Submodels; Mountain-Scale Coupled Processes Model; Thermal-Hydrologic-Chemical (THC) Seepage Model; Drift Scale Test (DST) THC Model; Seepage Model for Performance Assessment (PA); and UZ Radionuclide Transport Models

  14. Evaluation of toroidal torque by non-resonant magnetic perturbations in tokamaks for resonant transport regimes using a Hamiltonian approach

    Energy Technology Data Exchange (ETDEWEB)

    Albert, Christopher G.; Heyn, Martin F.; Kapper, Gernot; Kernbichler, Winfried; Martitsch, Andreas F. [Fusion@ÖAW, Institut für Theoretische Physik - Computational Physics, Technische Universität Graz, Petersgasse 16, 8010 Graz (Austria); Kasilov, Sergei V. [Fusion@ÖAW, Institut für Theoretische Physik - Computational Physics, Technische Universität Graz, Petersgasse 16, 8010 Graz (Austria); Institute of Plasma Physics, National Science Center “Kharkov Institute of Physics and Technology,” ul. Akademicheskaya 1, 61108 Kharkov (Ukraine)

    2016-08-15

    Toroidal torque generated by neoclassical viscosity caused by external non-resonant, non-axisymmetric perturbations has a significant influence on toroidal plasma rotation in tokamaks. In this article, a derivation for the expressions of toroidal torque and radial transport in resonant regimes is provided within quasilinear theory in canonical action-angle variables. The proposed approach treats all low-collisional quasilinear resonant neoclassical toroidal viscosity regimes including superbanana-plateau and drift-orbit resonances in a unified way and allows for magnetic drift in all regimes. It is valid for perturbations on toroidally symmetric flux surfaces of the unperturbed equilibrium without specific assumptions on geometry or aspect ratio. The resulting expressions are shown to match the existing analytical results in the large aspect ratio limit. Numerical results from the newly developed code NEO-RT are compared to calculations by the quasilinear version of the code NEO-2 at low collisionalities. The importance of the magnetic shear term in the magnetic drift frequency and a significant effect of the magnetic drift on drift-orbit resonances are demonstrated.

  15. The t-J model at small t/j: Numerical, perturbative, and supersymmetric results

    International Nuclear Information System (INIS)

    Barnes, T.; Tennessee Univ., Knoxville, TN

    1991-02-01

    We discuss some recent results for one- and two-hole states in the t-J model at small t/J. These include numerical results (bandwidth determinations and accurate t/J values for 4 x 4 lattice one-hole ground-state level crossings), hopping-parameter perturbation theory (which gives the small-t/J one-hole bandwidth in terms of the static-vacancy ground state), and results at the supersymmetric point t/J = 1/2 (exact results for energies and bandwidths.) The perturbative results leads us to a new conjecture regarding the staggered magnetization of higher-spin states in the two-dimensional Heisenberg model. We also discuss extrapolation of small-t/J results to high-T c parameter values; in the two-hole ground states we find (t/J) λ behavior in the rms hole-hole separation, and an extrapolation to t/J = 3 gives a bulk-limit rms hole-hole separation of ∼ 7 angstrom. 18 refs., 6 figs

  16. Developments in perturbation theory

    International Nuclear Information System (INIS)

    Greenspan, E.

    1976-01-01

    Included are sections dealing with perturbation expressions for reactivity, methods for the calculation of perturbed fluxes, integral transport theory formulations for reactivity, generalized perturbation theory, sensitivity and optimization studies, multigroup calculations of bilinear functionals, and solution of inhomogeneous Boltzmann equations with singular operators

  17. Electrokinetic Particle Transport in Micro-Nanofluidics Direct Numerical Simulation Analysis

    CERN Document Server

    Qian, Shizhi

    2012-01-01

    Numerous applications of micro-/nanofluidics are related to particle transport in micro-/nanoscale channels, and electrokinetics has proved to be one of the most promising tools to manipulate particles in micro/nanofluidics. Therefore, a comprehensive understanding of electrokinetic particle transport in micro-/nanoscale channels is crucial to the development of micro/nano-fluidic devices. Electrokinetic Particle Transport in Micro-/Nanofluidics: Direct Numerical Simulation Analysis provides a fundamental understanding of electrokinetic particle transport in micro-/nanofluidics involving elect

  18. Perturbative transport experiments in JET low or reverse magnetic shear plasmas

    Energy Technology Data Exchange (ETDEWEB)

    Mantica, P. [Istituto di Fisica del Plasma, EURATOM-ENEA-CNR Association, Milan (Italy); Gorini, G. [Istituto di Fisica del Plasma, EURATOM-ENEA-CNR Association, Milan (Italy); INFM, Department of Physics, University of Milano-Bicocca, Milan (Italy); Imbeaux, F. [Association Euratom-CEA, CEA Cadarache, St. Paul-lez-Durance (France)] (and others)

    2002-10-01

    Perturbative transport experiments have been performed in JET low or reverse magnetic shear plasmas either in conditions of fully developed internal transport barrier (ITB) or during a phase where an ITB was not observed. Transient peripheral cooling was induced either by laser ablation or by shallow pellet injection, and the ensuing travelling cold pulse was used to probe the plasma transport in the electron and, for the first time, also in the ion channel. Cold pulses travelling through ITBs are observed to erode the ITB outer part, but, if the inner ITB portion survives, it strongly damps the propagating wave. The result is discussed in the context of proposed possible pictures for ITB formation. In the absence of an ITB, the cold pulse shows a fast propagation in the outer plasma half, which is consistent with a region of stiff transport, while in the inner half it slows down but shows the peculiar feature of amplitude growing while propagating. The data are powerful tests for the validation of theoretical transport models. (author)

  19. Anisotropic Pressure, Transport, and Shielding of Magnetic Perturbations

    International Nuclear Information System (INIS)

    Mynick, H.E.; Boozer, A.H.

    2008-01-01

    We compute the effect on a tokamak of applying a nonaxisymmetric magnetic perturbation (delta)B. An equilibrium with scalar pressure p yields zero net radial current, and therefore zero torque. Thus, the usual approach, which assumes scalar pressure, is not self-consistent, and masks the close connection which exists between that radial current and the in-surface currents, which provide shielding or amplification of (delta)B. Here, we analytically compute the pressure anisotropy, anisotropy, p # parallel#, p # perpendicular# and ≠ p, and from this, both the radial and in-surface currents. The surface-average of the radial current recovers earlier expressions for ripple transport, while the in-surface currents provide an expression for the amount of self-consistent shielding the plasma provides.

  20. Improvement of numerical analysis method for FBR core characteristics. 3

    International Nuclear Information System (INIS)

    Takeda, Toshikazu; Yamamoto, Toshihisa; Kitada, Takanori; Katagi, Yousuke

    1998-03-01

    As the improvement of numerical analysis method for FBR core characteristics, studies on several topics have been conducted; multiband method, Monte Carlo perturbation and nodal transport method. This report is composed of the following three parts. Part 1: Improvement of Reaction Rate Calculation Method in the Blanket Region Based on the Multiband Method; A method was developed for precise evaluation of the reaction rate distribution in the blanket region using the multiband method. With the 3-band parameters obtained from the ordinary fitting method, major reaction rates such as U-238 capture, U-235 fission, Pu-239 fission and U-238 fission rate distributions were analyzed. Part 2: Improvement of Estimation Method for Reactivity Based on Monte-Carlo Perturbation Theory; Perturbation theory based on Monte-Carlo perturbation theory have been investigated and introduced into the calculational code. The Monte-Carlo perturbation code was applied to MONJU core and the calculational results were compared to the reference. Part 3: Improvement of Nodal Transport Calculation for Hexagonal Geometry; A method to evaluate the intra-subassembly power distribution from the nodal averaged neutron flux and surface fluxes at the node boundaries, was developed based on the transport theory. (J.P.N.)

  1. Numerical investigation of a perturbed swirling annular two-phase jet

    Energy Technology Data Exchange (ETDEWEB)

    Siamas, George A. [Mechanical Engineering, School of Engineering and Design, Brunel University, Uxbridge UB8 3PH (United Kingdom)], E-mail: siamas@spidernet.com.cy; Jiang, Xi; Wrobel, Luiz C. [Mechanical Engineering, School of Engineering and Design, Brunel University, Uxbridge UB8 3PH (United Kingdom)

    2009-06-15

    A swirling annular gas-liquid two-phase jet flow system has been investigated by solving the compressible, time-dependent, non-dimensional Navier-Stokes equations using highly accurate numerical methods. The mathematical formulation for the flow system is based on an Eulerian approach with mixed-fluid treatment while an adjusted volume of fluid method is utilised to account for the gas compressibility. Surface tension effects are captured by a continuum surface force model. Swirling motion is applied at the inlet while a small helical perturbation is also applied to initiate the instability. Three-dimensional spatial direct numerical simulation has been performed with parallelisation of the code based on domain decomposition. The results show that the flow is characterised by a geometrical recirculation zone adjacent to the nozzle exit and by a central recirculation zone further downstream. Swirl enhances the flow instability and vorticity and promotes liquid dispersion in the cross-streamwise directions. A dynamic precessing vortex core is developed demonstrating that the growth of such a vortex in annular configurations can be initiated even at low swirl numbers, in agreement with experimental findings. Analysis of the averaged results revealed the existence of a geometrical recirculation zone and a swirl induced central recirculation zone in the flow field.

  2. Perturbative studies of toroidal momentum transport using neutral beam injection modulation in the Joint European Torus: Experimental results, analysis methodology, and first principles modeling

    DEFF Research Database (Denmark)

    Mantica, P.; Tala, T.; Ferreira, J.S.

    2010-01-01

    Perturbative experiments have been carried out in the Joint European Torus [Fusion Sci. Technol. 53(4) (2008)] in order to identify the diffusive and convective components of toroidal momentum transport. The torque source was modulated either by modulating tangential neutral beam power...... or by modulating in antiphase tangential and normal beams to produce a torque perturbation in the absence of a power perturbation. The resulting periodic perturbation in the toroidal rotation velocity was modeled using time-dependent transport simulations in order to extract empirical profiles of momentum...

  3. Multi-scale modelling and numerical simulation of electronic kinetic transport

    International Nuclear Information System (INIS)

    Duclous, R.

    2009-11-01

    This research thesis which is at the interface between numerical analysis, plasma physics and applied mathematics, deals with the kinetic modelling and numerical simulations of the electron energy transport and deposition in laser-produced plasmas, having in view the processes of fuel assembly to temperature and density conditions necessary to ignite fusion reactions. After a brief review of the processes at play in the collisional kinetic theory of plasmas, with a focus on basic models and methods to implement, couple and validate them, the author focuses on the collective aspect related to the free-streaming electron transport equation in the non-relativistic limit as well as in the relativistic regime. He discusses the numerical development and analysis of the scheme for the Vlasov-Maxwell system, and the selection of a validation procedure and numerical tests. Then, he investigates more specific aspects of the collective transport: the multi-specie transport, submitted to phase-space discontinuities. Dealing with the multi-scale physics of electron transport with collision source terms, he validates the accuracy of a fast Monte Carlo multi-grid solver for the Fokker-Planck-Landau electron-electron collision operator. He reports realistic simulations for the kinetic electron transport in the frame of the shock ignition scheme, the development and validation of a reduced electron transport angular model. He finally explores the relative importance of the processes involving electron-electron collisions at high energy by means a multi-scale reduced model with relativistic Boltzmann terms

  4. Numerical simulation of increasing initial perturbations of a bubble in the bubble–shock interaction problem

    Energy Technology Data Exchange (ETDEWEB)

    Korneev, Boris [Moscow Institute of Physics and Technology, 9 Institutsky lane, Dolgoprudny 141700 (Russian Federation); Levchenko, Vadim, E-mail: boris.korneev@phystech.edu [Keldysh Institute of Applied Mathematics, 4 Miusskaya square, Moscow 125047 (Russian Federation)

    2016-12-15

    A set of numerical experiments on the interaction between a planar shock wave and a spherical bubble with a slightly perturbed surface is considered. Spectral analysis of the instability growth is carried out and three-dimensional Euler equations of fluid dynamics are chosen as the mathematical model for the process. The equations are solved via the Runge–Kutta discontinuous Galerkin method and the special DiamondTorre algorithm for multi-GPU implementation is used. (paper)

  5. A numerical scheme for singularly perturbed reaction-diffusion problems with a negative shift via numerov method

    Science.gov (United States)

    Dinesh Kumar, S.; Nageshwar Rao, R.; Pramod Chakravarthy, P.

    2017-11-01

    In this paper, we consider a boundary value problem for a singularly perturbed delay differential equation of reaction-diffusion type. We construct an exponentially fitted numerical method using Numerov finite difference scheme, which resolves not only the boundary layers but also the interior layers arising from the delay term. An extensive amount of computational work has been carried out to demonstrate the applicability of the proposed method.

  6. Analytic-Numerical Approach to Solving Singularly Perturbed Parabolic Equations with the Use of Dynamic Adapted Meshes

    Directory of Open Access Journals (Sweden)

    D. V. Lukyanenko

    2016-01-01

    Full Text Available The main objective of the paper is to present a new analytic-numerical approach to singularly perturbed reaction-diffusion-advection models with solutions containing moving interior layers (fronts. We describe some methods to generate the dynamic adapted meshes for an efficient numerical solution of such problems. It is based on a priori information about the moving front properties provided by the asymptotic analysis. In particular, for the mesh construction we take into account a priori asymptotic evaluation of the location and speed of the moving front, its width and structure. Our algorithms significantly reduce the CPU time and enhance the stability of the numerical process compared with classical approaches.The article is published in the authors’ wording.

  7. Numerical methods: Analytical benchmarking in transport theory

    International Nuclear Information System (INIS)

    Ganapol, B.D.

    1988-01-01

    Numerical methods applied to reactor technology have reached a high degree of maturity. Certainly one- and two-dimensional neutron transport calculations have become routine, with several programs available on personal computer and the most widely used programs adapted to workstation and minicomputer computational environments. With the introduction of massive parallelism and as experience with multitasking increases, even more improvement in the development of transport algorithms can be expected. Benchmarking an algorithm is usually not a very pleasant experience for the code developer. Proper algorithmic verification by benchmarking involves the following considerations: (1) conservation of particles, (2) confirmation of intuitive physical behavior, and (3) reproduction of analytical benchmark results. By using today's computational advantages, new basic numerical methods have been developed that allow a wider class of benchmark problems to be considered

  8. New methods in linear transport theory. Part of a coordinated programme on methods in neutron transport theory

    International Nuclear Information System (INIS)

    Mika, J.

    1975-09-01

    Originally the work was oriented towards two main topics: a) difference and integral methods in neutron transport theory. Two computers were used for numerical calculations GIER and CYBER-72. During the first year the main effort was shifted towards basic theoretical investigations. At the first step the ANIS code was adopted and later modified to check various finite difference approaches against each other. Then the general finite element method and the singular perturbation method were developed. The analysis of singularities of the one-dimensional neutron transport equation in spherical geometry has been done and presented. Later the same analysis for the case of cylindrical symmetry has been carried out. The second and the third year programme included the following topics: 1) finite difference methods in stationary neutron transport theory; 2)mathematical fundamentals of approximate methods for solving the transport equation; 3) singular perturbation method for the time-dependent transport equation; 4) investigation of various iterative procedures in reactor calculations. This investigation will help to better understanding of the mathematical basis for existing and developed numerical methods resulting in more effective algorithms for reactor computer codes

  9. Numerical approaches to model perturbation fire in turing pattern formations

    Science.gov (United States)

    Campagna, R.; Brancaccio, M.; Cuomo, S.; Mazzoleni, S.; Russo, L.; Siettos, K.; Giannino, F.

    2017-11-01

    Turing patterns were observed in chemical, physical and biological systems described by coupled reaction-diffusion equations. Several models have been formulated proposing the water as the causal mechanism of vegetation pattern formation, but this isn't an exhaustive hypothesis in some natural environments. An alternative explanation has been related to the plant-soil negative feedback. In Marasco et al. [1] the authors explored the hypothesis that both mechanisms contribute in the formation of regular and irregular vegetation patterns. The mathematical model consists in three partial differential equations (PDEs) that take into account for a dynamic balance between biomass, water and toxic compounds. A numerical approach is mandatory also to investigate on the predictions of this kind of models. In this paper we start from the mathematical model described in [1], set the model parameters such that the biomass reaches a stable spatial pattern (spots) and present preliminary studies about the occurrence of perturbing events, such as wildfire, that can affect the regularity of the biomass configuration.

  10. Assessing numerical methods used in nuclear aerosol transport models

    International Nuclear Information System (INIS)

    McDonald, B.H.

    1987-01-01

    Several computer codes are in use for predicting the behaviour of nuclear aerosols released into containment during postulated accidents in water-cooled reactors. Each of these codes uses numerical methods to discretize and integrate the equations that govern the aerosol transport process. Computers perform only algebraic operations and generate only numbers. It is in the numerical methods that sense can be made of these numbers and where they can be related to the actual solution of the equations. In this report, the numerical methods most commonly used in the aerosol transport codes are examined as special cases of a general solution procedure, the Method of Weighted Residuals. It would appear that the numerical methods used in the codes are all capable of producing reasonable answers to the mathematical problem when used with skill and care. 27 refs

  11. A numerical study for global atmospheric transport-chemistry problems

    NARCIS (Netherlands)

    E.J. Spee (Edwin); J.G. Verwer (Jan); P.M. de Zeeuw (Paul); J.G. Blom (Joke); W. Hundsdorfer (Willem)

    1998-01-01

    htmlabstractAtmospheric air quality modeling relies in part on numerical simulation. Required numerical simulations are often hampered by lack of computer capacity and computational speed. This problem is most severe in the field of global modeling where transport and exchange of trace constituents

  12. A numerical study for global atmospheric transport-chemistry problems

    NARCIS (Netherlands)

    E.J. Spee (Edwin); J.G. Verwer (Jan); P.M. de Zeeuw (Paul); J.G. Blom (Joke); W. Hundsdorfer (Willem)

    1997-01-01

    textabstractAtmospheric air quality modeling relies in part on numerical simulation. Required numerical simulations are often hampered by lack of computer capacity and computational speed. This problem is most severe in the field of global modeling where transport and exchange of trace constituents

  13. Variance analysis of the Monte Carlo perturbation source method in inhomogeneous linear particle transport problems. Derivation of formulae

    International Nuclear Information System (INIS)

    Noack, K.

    1981-01-01

    The perturbation source method is used in the Monte Carlo method in calculating small effects in a particle field. It offers primising possibilities for introducing positive correlation between subtracting estimates even in the cases where other methods fail, in the case of geometrical variations of a given arrangement. The perturbation source method is formulated on the basis of integral equations for the particle fields. The formulae for the second moment of the difference of events are derived. Explicity a certain class of transport games and different procedures for generating the so-called perturbation particles are considered [ru

  14. A synthetic ion transporter that disrupts autophagy and induces apoptosis by perturbing cellular chloride concentrations

    Science.gov (United States)

    Busschaert, Nathalie; Park, Seong-Hyun; Baek, Kyung-Hwa; Choi, Yoon Pyo; Park, Jinhong; Howe, Ethan N. W.; Hiscock, Jennifer R.; Karagiannidis, Louise E.; Marques, Igor; Félix, Vítor; Namkung, Wan; Sessler, Jonathan L.; Gale, Philip A.; Shin, Injae

    2017-07-01

    Perturbations in cellular chloride concentrations can affect cellular pH and autophagy and lead to the onset of apoptosis. With this in mind, synthetic ion transporters have been used to disturb cellular ion homeostasis and thereby induce cell death; however, it is not clear whether synthetic ion transporters can also be used to disrupt autophagy. Here, we show that squaramide-based ion transporters enhance the transport of chloride anions in liposomal models and promote sodium chloride influx into the cytosol. Liposomal and cellular transport activity of the squaramides is shown to correlate with cell death activity, which is attributed to caspase-dependent apoptosis. One ion transporter was also shown to cause additional changes in lysosomal pH, which leads to impairment of lysosomal enzyme activity and disruption of autophagic processes. This disruption is independent of the initiation of apoptosis by the ion transporter. This study provides the first experimental evidence that synthetic ion transporters can disrupt both autophagy and induce apoptosis.

  15. High-order accurate numerical algorithm for three-dimensional transport prediction

    Energy Technology Data Exchange (ETDEWEB)

    Pepper, D W [Savannah River Lab., Aiken, SC; Baker, A J

    1980-01-01

    The numerical solution of the three-dimensional pollutant transport equation is obtained with the method of fractional steps; advection is solved by the method of moments and diffusion by cubic splines. Topography and variable mesh spacing are accounted for with coordinate transformations. First estimate wind fields are obtained by interpolation to grid points surrounding specific data locations. Numerical results agree with results obtained from analytical Gaussian plume relations for ideal conditions. The numerical model is used to simulate the transport of tritium released from the Savannah River Plant on 2 May 1974. Predicted ground level air concentration 56 km from the release point is within 38% of the experimentally measured value.

  16. Transport, retention, and size perturbation of graphene oxide in saturated porous media: Effects of input concentration and grain size

    Science.gov (United States)

    Accurately predicting the fate and transport of graphene oxide (GO) in porous media is critical to assess its environmental impact. In this work, sand column experiments were conducted to determine the effect of input concentration and grain size on transport, retention, and size perturbation of GO ...

  17. Effect of perturbation of convective energy transport on the luminosity and radius of the sun

    International Nuclear Information System (INIS)

    Endal, A.S.; Twigg, L.W.

    1982-01-01

    The response of solar models to perturbations of the efficiency of convective energy transport is studied for a number of cases. Such perturbations primarily affect the shallow superadiabatic layer of the convective envelope (at depths 3 km below the photosphere). Independent of the details of the perturbation scheme, the resulting change in the solar radius (ΔR/R) is always very small compared to the change in luminosity (ΔL/L). This appears to be true for any physical mechanism of solar variability which operates in the outer layers of the convection zone. Changes of the solar radius have been inferred by Dunham et al. from historical observations of solar eclipses in 1715 and 1925. Considering the constraints on concurrent luminosity changes, this type of solar variability must be indicative of changes in the solar structure at substantial depths below the superadiabatic layer of the convective envelope

  18. Application of the numerical Laplace transform inversion to neutron transport theory

    International Nuclear Information System (INIS)

    Ganapol, B.D.

    1989-01-01

    A numerical Laplace transform inversion is developed using the Hurwitz-Zweifel method of evaluating the Fourier cosine integral coupled with an Euler-Knopp transformation. The numerical inversion is then applied to problems in linear transport theory concerning slowing down, time-dependence and featuring the determination of the interior scalar flux solution to the one-group stationary transport equation in half-space geometry

  19. Numerical solution of Euler's equation by perturbed functionals

    Science.gov (United States)

    Dey, S. K.

    1985-01-01

    A perturbed functional iteration has been developed to solve nonlinear systems. It adds at each iteration level, unique perturbation parameters to nonlinear Gauss-Seidel iterates which enhances its convergence properties. As convergence is approached these parameters are damped out. Local linearization along the diagonal has been used to compute these parameters. The method requires no computation of Jacobian or factorization of matrices. Analysis of convergence depends on properties of certain contraction-type mappings, known as D-mappings. In this article, application of this method to solve an implicit finite difference approximation of Euler's equation is studied. Some representative results for the well known shock tube problem and compressible flows in a nozzle are given.

  20. Synchronizing the noise-perturbed Lue chaotic system

    International Nuclear Information System (INIS)

    Zhang Yan; Chen Shihua; Zhou Hong

    2009-01-01

    In this paper, synchronization between unidirectionally coupled Lue chaotic systems with noise perturbation is investigated theoretically and numerically. Sufficient conditions of synchronization between these noise-perturbed systems are established by means of the so-called sliding mode control method. Some numerical simulations are also included to visualize the effectiveness and the feasibility of the developed approach.

  1. Quasi-Compact Perturbations of the Weyl Essential Spectrum and Application to Singular Transport Operators

    Directory of Open Access Journals (Sweden)

    Leila Mebarki

    2015-11-01

    Full Text Available This paper is devoted to the investigation of the stability of the Weyl essential spectrum of closed densely dened linear operator A subjected to additive perturbation K such that (lambda-A-K^{-1}K or K(lambda-A-K^{-1} is a quasi-compact operator. The obtained results are used to describe the Weyl essential spectrum of singular neutron transport operator.

  2. Modeling Small-Amplitude Perturbations in Inertial Confinement Fusion Pellets

    Science.gov (United States)

    Zalesak, Steven; Metzler, N.; Velikovich, A. L.; Gardner, J. H.; Manheimer, W.

    2005-10-01

    Recent advances in inertial confinement fusion (ICF) technology serve to ensure that imploding laser-driven ICF pellets will spend a significantly larger portion of their time in what is regarded as the ``linear'' portion of their perturbation evolution, i.e., in the presence of small-amplitude but nonetheless evolving perturbations. Since the evolution of these linear perturbations collectively form the initial conditions for the subsequent nonlinear evolution of the pellet, which in turn determines the energy yield of the pellet, the accurate numerical modeling of these small-amplitude perturbations has taken on an increased importance. This modeling is difficult despite the expected linear evolution of the perturbations themselves, because these perturbations are embedded in a highly nonlinear, strongly-shocked, and highly complex flow field which in and of itself stresses numerical computation capabilities, and whose simulation often employs numerical techniques which were not designed with the proper treatment of small-amplitude perturbations in mind. In this paper we will review some of the techniques that we have recently found to be of use toward this end.

  3. Development of numerical Grids for UZ Flow and Transport Modeling

    International Nuclear Information System (INIS)

    P. Dobson

    2004-01-01

    This report describes the methods used to develop numerical grids of the unsaturated hydrogeologic system beneath Yucca Mountain, Nevada. Numerical grid generation is an integral part of the development of the unsaturated zone (UZ) flow and transport model, a complex, three-dimensional (3-D) model of Yucca Mountain. This revision contains changes made to improve the clarity of the description of grid generation. The numerical grids, developed using current geologic, hydrogeologic, and mineralogic data, provide the necessary framework to: (1) develop calibrated hydrogeologic property sets and flow fields, (2) test conceptual hypotheses of flow and transport, and (3) predict flow and transport behavior under a variety of climatic and thermal-loading conditions. The technical scope, content, and management for the current revision of this report are described in the planning document ''Technical Work Plan for: Unsaturated Zone Flow Analysis and Model Report Integration'' (BSC 2004 [DIRS 169654], Section 2). Grids generated and documented in this report supersede those documented in Revision 00 of this report, ''Development of Numerical Grids for UZ Flow and Transport Modeling'' (BSC 2001 [DIRS 159356]). The grids presented in this report are the same as those developed in Revision 01 (BSC 2003 [DIRS 160109]); however, the documentation of the development of the grids in Revision 02 has been updated to address technical inconsistencies and achieve greater transparency, readability, and traceability. The constraints, assumptions, and limitations associated with this report are discussed in the appropriate sections that follow

  4. Numerical models of groundwater flow and transport

    International Nuclear Information System (INIS)

    Konikow, L.F.

    1996-01-01

    This chapter reviews the state-of-the-art in deterministic modeling of groundwater flow and transport processes, which can be used for interpretation of isotope data through groundwater flow analyses. Numerical models which are available for this purpose are described and their applications to complex field problems are discussed. The theoretical bases of deterministic modeling are summarized, and advantages and limitations of numerical models are described. The selection of models for specific applications and their calibration procedures are described, and results of a few illustrative case study type applications are provided. (author). 145 refs, 17 figs, 2 tabs

  5. Numerical models of groundwater flow and transport

    Energy Technology Data Exchange (ETDEWEB)

    Konikow, L F [Geological Survey, Reston, VA (United States)

    1996-10-01

    This chapter reviews the state-of-the-art in deterministic modeling of groundwater flow and transport processes, which can be used for interpretation of isotope data through groundwater flow analyses. Numerical models which are available for this purpose are described and their applications to complex field problems are discussed. The theoretical bases of deterministic modeling are summarized, and advantages and limitations of numerical models are described. The selection of models for specific applications and their calibration procedures are described, and results of a few illustrative case study type applications are provided. (author). 145 refs, 17 figs, 2 tabs.

  6. Development of Numerical Grids for UZ Flow and Transport Modeling

    International Nuclear Information System (INIS)

    Hinds, J.

    2001-01-01

    This Analysis/Model Report (AMR) describes the methods used to develop numerical grids of the unsaturated hydrogeologic system beneath Yucca Mountain. Numerical grid generation is an integral part of the development of a complex, three-dimensional (3-D) model, such as the Unsaturated-Zone Flow and Transport Model (UZ Model) of Yucca Mountain. The resulting numerical grids, developed using current geologic, hydrogeologic, and mineralogic data, provide the necessary framework to: (1) develop calibrated hydrogeologic property sets and flow fields, (2) test conceptual hypotheses of flow and transport, and (3) predict flow and transport behavior under a variety of climatic and thermal loading conditions. Revision 00 of the work described herein follows the planning and work direction outlined in the ''Development of Numerical Grids for UZ Flow and Transport Modeling'' (CRWMS M and O 1999c). The technical scope, content, and management of ICN 01 of this AMR is currently controlled by the planning document, ''Technical Work Plan for Unsaturated Zone (UZ) Flow and Transport Process Model Report'' (BSC 2001a). The scope for the TBV resolution actions in this ICN is described in the ''Technical Work Plan for: Integrated Management of Technical Product Input Department'' (BSC 2001 b, Addendum B, Section 4.1). The steps involved in numerical grid development include: (1) defining the location of important calibration features, (2) determining model grid layers and fault geometry based on the Geologic Framework Model (GFM), the Integrated Site Model (ISM), and definition of hydrogeologic units (HGUs), (3) analyzing and extracting GFM and ISM data pertaining to layer contacts and property distributions, (4) discretizing and refining the two-dimensional (2-D), plan-view numerical grid, (5) generating the 3-D grid with finer resolution at the repository horizon and within the Calico Hills nonwelded (CHn) hydrogeologic unit, and (6) formulating the dual-permeability mesh. The

  7. Numerical estimation of transport properties of cementitious materials using 3D digital images

    NARCIS (Netherlands)

    Ukrainczyk, N.; Koenders, E.A.B.; Van Breugel, K.

    2012-01-01

    A multi-scale characterisation of the transport process within cementitious microstructure possesses a great challenge in terms of modelling and schematization. In this paper a numerical method is proposed to mitigate the resolution problems in numerical methods for calculating effective transport

  8. Conceptual Model and Numerical Approaches for Unsaturated Zone Flow and Transport

    International Nuclear Information System (INIS)

    H.H. Liu

    2004-01-01

    The purpose of this model report is to document the conceptual and numerical models used for modeling unsaturated zone (UZ) fluid (water and air) flow and solute transport processes. This work was planned in ''Technical Work Plan for: Unsaturated Zone Flow Model and Analysis Report Integration'' (BSC 2004 [DIRS 169654], Sections 1.2.5, 2.1.1, 2.1.2 and 2.2.1). The conceptual and numerical modeling approaches described in this report are mainly used for models of UZ flow and transport in fractured, unsaturated rock under ambient conditions. Developments of these models are documented in the following model reports: (1) UZ Flow Model and Submodels; (2) Radionuclide Transport Models under Ambient Conditions. Conceptual models for flow and transport in unsaturated, fractured media are discussed in terms of their applicability to the UZ at Yucca Mountain. The rationale for selecting the conceptual models used for modeling of UZ flow and transport is documented. Numerical approaches for incorporating these conceptual models are evaluated in terms of their representation of the selected conceptual models and computational efficiency; and the rationales for selecting the numerical approaches used for modeling of UZ flow and transport are discussed. This report also documents activities to validate the active fracture model (AFM) based on experimental observations and theoretical developments. The AFM is a conceptual model that describes the fracture-matrix interaction in the UZ of Yucca Mountain. These validation activities are documented in Section 7 of this report regarding use of an independent line of evidence to provide additional confidence in the use of the AFM in the UZ models. The AFM has been used in UZ flow and transport models under both ambient and thermally disturbed conditions. Developments of these models are documented

  9. Variance analysis of the Monte-Carlo perturbation source method in inhomogeneous linear particle transport problems

    International Nuclear Information System (INIS)

    Noack, K.

    1982-01-01

    The perturbation source method may be a powerful Monte-Carlo means to calculate small effects in a particle field. In a preceding paper we have formulated this methos in inhomogeneous linear particle transport problems describing the particle fields by solutions of Fredholm integral equations and have derived formulae for the second moment of the difference event point estimator. In the present paper we analyse the general structure of its variance, point out the variance peculiarities, discuss the dependence on certain transport games and on generation procedures of the auxiliary particles and draw conclusions to improve this method

  10. Evaluation of the toroidal torque driven by external non-resonant non-axisymmetric magnetic field perturbations in a tokamak

    Energy Technology Data Exchange (ETDEWEB)

    Kasilov, Sergei V. [Fusion@ÖAW, Institut für Theoretische Physik—Computational Physics, Technische Universität Graz Petersgasse 16, A–8010 Graz (Austria); Institute of Plasma Physics National Science Center “Kharkov Institute of Physics and Technology” ul. Akademicheskaya 1, 61108 Kharkov (Ukraine); Kernbichler, Winfried; Martitsch, Andreas F.; Heyn, Martin F. [Fusion@ÖAW, Institut für Theoretische Physik—Computational Physics, Technische Universität Graz Petersgasse 16, A–8010 Graz (Austria); Maassberg, Henning [Max-Planck Institut für Plasmaphysik, D-17491 Greifswald (Germany)

    2014-09-15

    The toroidal torque driven by external non-resonant magnetic perturbations (neoclassical toroidal viscosity) is an important momentum source affecting the toroidal plasma rotation in tokamaks. The well-known force-flux relation directly links this torque to the non-ambipolar neoclassical particle fluxes arising due to the violation of the toroidal symmetry of the magnetic field. Here, a quasilinear approach for the numerical computation of these fluxes is described, which reduces the dimension of a standard neoclassical transport problem by one without model simplifications of the linearized drift kinetic equation. The only limiting condition is that the non-axisymmetric perturbation field is small enough such that the effect of the perturbation field on particle motion within the flux surface is negligible. Therefore, in addition to most of the transport regimes described by the banana (bounce averaged) kinetic equation also such regimes as, e.g., ripple-plateau and resonant diffusion regimes are naturally included in this approach. Based on this approach, a quasilinear version of the code NEO-2 [W. Kernbichler et al., Plasma Fusion Res. 3, S1061 (2008).] has been developed and benchmarked against a few analytical and numerical models. Results from NEO-2 stay in good agreement with results from these models in their pertinent range of validity.

  11. The effects of a perturbed source on contaminant transport near the Weldon Spring quarry

    International Nuclear Information System (INIS)

    Tomasko, D.

    1989-03-01

    The effects of a perturbed contamination source at the Weldon Spring quarry in St. Charles County, Missouri, on downstream solute concentrations were investigated using one-dimensional analytical solutions to an advection-dispersion equation developed for both constant-strength and multiple-stepped source functions. A sensitivity study using parameter base-case values and ranges consistent with the geologic conceptualization of the quarry area indicates that the parameters having the greatest effect on predicted concentrations are the distance from the quarry to the point of interest, the average linear groundwater velocity, the contaminant retardation coefficient, and the amplitude and duration of the source perturbation caused by response action activities. Use of base-case parameter value and realistic values for the amplitude and duration of the source perturbation produced a small effect on solute concentrations near the western extremity of the nearby municipal well field, as well as small uncertainties in the predicted results for the assumed model. The effect of simplifying assumptions made in deriving the analytic solution is unknown: use of a multidimensional flow and transport model and additional field work are needed to validate the model. 13 refs., 18 figs

  12. Dynamically Adapted Mesh Construction for the Efficient Numerical Solution of a Singular Perturbed Reaction-diffusion-advection Equation

    Directory of Open Access Journals (Sweden)

    Dmitry V. Lukyanenko

    2017-01-01

    Full Text Available This  work develops  a theory  of the  asymptotic-numerical investigation of the  moving fronts  in reaction-diffusion-advection models.  By considering  the  numerical  solution  of the  singularly perturbed Burgers’s  equation  we discuss a method  of dynamically  adapted mesh  construction that is able to significantly  improve  the  numerical  solution  of this  type of equations.  For  the  construction we use a priori information that is based  on the  asymptotic analysis  of the  problem.  In  particular, we take  into account the information about  the speed of the transition layer, its width  and structure. Our algorithms  are able to reduce significantly complexity and enhance stability of the numerical  calculations in comparison  with classical approaches for solving this class of problems.  The numerical  experiment is presented to demonstrate the effectiveness of the proposed  method.The article  is published  in the authors’  wording. 

  13. A New Numerical Scheme for Cosmic-Ray Transport

    Science.gov (United States)

    Jiang, Yan-Fei; Oh, S. Peng

    2018-02-01

    Numerical solutions of the cosmic-ray (CR) magnetohydrodynamic equations are dogged by a powerful numerical instability, which arises from the constraint that CRs can only stream down their gradient. The standard cure is to regularize by adding artificial diffusion. Besides introducing ad hoc smoothing, this has a significant negative impact on either computational cost or complexity and parallel scalings. We describe a new numerical algorithm for CR transport, with close parallels to two-moment methods for radiative transfer under the reduced speed of light approximation. It stably and robustly handles CR streaming without any artificial diffusion. It allows for both isotropic and field-aligned CR streaming and diffusion, with arbitrary streaming and diffusion coefficients. CR transport is handled explicitly, while source terms are handled implicitly. The overall time step scales linearly with resolution (even when computing CR diffusion) and has a perfect parallel scaling. It is given by the standard Courant condition with respect to a constant maximum velocity over the entire simulation domain. The computational cost is comparable to that of solving the ideal MHD equation. We demonstrate the accuracy and stability of this new scheme with a wide variety of tests, including anisotropic streaming and diffusion tests, CR-modified shocks, CR-driven blast waves, and CR transport in multiphase media. The new algorithm opens doors to much more ambitious and hitherto intractable calculations of CR physics in galaxies and galaxy clusters. It can also be applied to other physical processes with similar mathematical structure, such as saturated, anisotropic heat conduction.

  14. Novel Parallel Numerical Methods for Radiation and Neutron Transport

    International Nuclear Information System (INIS)

    Brown, P N

    2001-01-01

    In many of the multiphysics simulations performed at LLNL, transport calculations can take up 30 to 50% of the total run time. If Monte Carlo methods are used, the percentage can be as high as 80%. Thus, a significant core competence in the formulation, software implementation, and solution of the numerical problems arising in transport modeling is essential to Laboratory and DOE research. In this project, we worked on developing scalable solution methods for the equations that model the transport of photons and neutrons through materials. Our goal was to reduce the transport solve time in these simulations by means of more advanced numerical methods and their parallel implementations. These methods must be scalable, that is, the time to solution must remain constant as the problem size grows and additional computer resources are used. For iterative methods, scalability requires that (1) the number of iterations to reach convergence is independent of problem size, and (2) that the computational cost grows linearly with problem size. We focused on deterministic approaches to transport, building on our earlier work in which we performed a new, detailed analysis of some existing transport methods and developed new approaches. The Boltzmann equation (the underlying equation to be solved) and various solution methods have been developed over many years. Consequently, many laboratory codes are based on these methods, which are in some cases decades old. For the transport of x-rays through partially ionized plasmas in local thermodynamic equilibrium, the transport equation is coupled to nonlinear diffusion equations for the electron and ion temperatures via the highly nonlinear Planck function. We investigated the suitability of traditional-solution approaches to transport on terascale architectures and also designed new scalable algorithms; in some cases, we investigated hybrid approaches that combined both

  15. Sensitivity of the PEP beam transport line to perturbations

    International Nuclear Information System (INIS)

    Peterson, J.M.; Brown, K.L.

    1979-03-01

    The sensitivity of a beam-transport line to various perturbations determines the extent to which one can simplify component design and relax tolerances. For the PEP injection lines, effects of various fabrication errors, magnet misalignments, and residual gas scattering were studied. Using the TURTLE ray-tracing program, it is found that magnetic-field errors corresponding to a relative sextupole strength in the dipoles of 0.5% and/or a relative sextupole or octupole strength in the quadrupoles of 5% are permissible. This allows relatively loose tolerances in magnet fabrication. Transverse misalignment of a quadrupole by a distance x causes the beam centroid to be displaced downstream by as much as 5x. This requires a quadrupole alignment accuracy of +- 0.5 mm or better. No compensation for the earth's field is necessary because an integral number of optical wavelengths and a short wavelength were used for the design. Analysis shows that beam broadening from multiple coulomb scattering is insignificant for pressures of less than 1/10 torr

  16. Non-perturbative effects in supersymmetry

    International Nuclear Information System (INIS)

    Veneziano, G.

    1987-01-01

    Some non perturbative aspects of globally supersymmetric (SUSY) gauge theories are discussed. These share with their non-supersymmetric analogues interesting non perturbative features, such as the spontaneous breaking of chiral symmetries via condensates. What is peculiar about supersymmetric theories, however, is that one is able to say a lot about non-perturbative effects even without resorting to elaborate numerical calculations: general arguments, supersymmetric and chiral Ward identities and analytic, dynamical calculations will turn out to effectively determine most of the supersymmetric vacuum properties. 28 references, 5 figures

  17. Non-Perturbative Asymptotic Improvement of Perturbation Theory and Mellin-Barnes Representation

    Directory of Open Access Journals (Sweden)

    Samuel Friot

    2010-10-01

    Full Text Available Using a method mixing Mellin-Barnes representation and Borel resummation we show how to obtain hyperasymptotic expansions from the (divergent formal power series which follow from the perturbative evaluation of arbitrary ''N-point'' functions for the simple case of zero-dimensional φ4 field theory. This hyperasymptotic improvement appears from an iterative procedure, based on inverse factorial expansions, and gives birth to interwoven non-perturbative partial sums whose coefficients are related to the perturbative ones by an interesting resurgence phenomenon. It is a non-perturbative improvement in the sense that, for some optimal truncations of the partial sums, the remainder at a given hyperasymptotic level is exponentially suppressed compared to the remainder at the preceding hyperasymptotic level. The Mellin-Barnes representation allows our results to be automatically valid for a wide range of the phase of the complex coupling constant, including Stokes lines. A numerical analysis is performed to emphasize the improved accuracy that this method allows to reach compared to the usual perturbative approach, and the importance of hyperasymptotic optimal truncation schemes.

  18. Three points of view in transport theory

    International Nuclear Information System (INIS)

    Ruben, Panta Pazos; Tilio de Vilhena, M.

    2001-01-01

    A lot of efforts in Transport Theory is used to develop numerical methods or hybrid numerical-analytical techniques. We present in this work three points of view about transport problems. First the C0 semigroup approach, in which the free transport operator ψ → μ ∇ generates an strongly continuous semigroup. The operators operator ψ → σt and operator ψ → ∫ ∇ k(x,μ,μ' ψ(x,μ') dμ' are bounded operators, and by perturbation the transport operator ψ → μ ∇ ψ + σt ψ - K ψ also generates an strongly continuous semigroup. To prove the convergence of the approximations of a numerical methods to the exact solution we use the approximation theorem of C0 semi-groups in canonical form. In other way, the discrete schemes theory is employed in searching the rate of convergence of numerical techniques in transport theory. For 1D dependent of time transport problem and two-dimensional steady state problem we summarize some estimates, incorporating different boundary conditions. Finally we give a survey about the dynamical behavior of the SN approximations. In order to give a unified approach, some results illustrates the equivalence of the three points of views for the case of the steady-state transport problem for slab geometry. (author)

  19. Structural instability of atmospheric flows under perturbations of the mass balance and effect in transport calculations

    International Nuclear Information System (INIS)

    Núñez, M A; Mendoza, R

    2015-01-01

    Several methods to estimate the velocity field of atmospheric flows, have been proposed to the date for applications such as emergency response systems, transport calculations and for budget studies of all kinds. These applications require a wind field that satisfies the conservation of mass but, in general, estimated wind fields do not satisfy exactly the continuity equation. An approach to reduce the effect of using a divergent wind field as input in the transport-diffusion equations, was proposed in the literature. In this work, a linear local analysis of a wind field, is used to show analytically that the perturbation of a large-scale nondivergent flow can yield a divergent flow with a substantially different structure. The effects of these structural changes in transport calculations are illustrated by means of analytic solutions of the transport equation

  20. A possible origin of viscosity in Keplerian accretion disks due to secondary perturbation: Turbulent transport without magnetic fields

    International Nuclear Information System (INIS)

    Mukhopadhyay, Banibrata; Saha, Kanak

    2011-01-01

    The origin of hydrodynamic turbulence in rotating shear flow is a long standing puzzle. Resolving it is especially important in astrophysics when the flow's angular momentum profile is Keplerian which forms an accretion disk having negligible molecular viscosity. Hence, any viscosity in such systems must be due to turbulence, arguably governed by magnetorotational instability, especially when temperature T > or approx. 10 5 . However, such disks around quiescent cataclysmic variables, protoplanetary and star-forming disks, and the outer regions of disks in active galactic nuclei are practically neutral in charge because of their low temperature, and thus are not expected to be coupled with magnetic fields enough to generate any transport due to the magnetorotational instability. This flow is similar to plane Couette flow including the Coriolis force, at least locally. What drives their turbulence and then transport, when such flows do not exhibit any unstable mode under linear hydrodynamic perturbation? We demonstrate that the three-dimensional secondary disturbance to the primarily perturbed flow that triggers elliptical instability may generate significant turbulent viscosity in the range 0.0001 ∼ t ∼< 0.1, which can explain transport in accretion flows.

  1. Perturbative approach to non-Markovian stochastic Schroedinger equations

    International Nuclear Information System (INIS)

    Gambetta, Jay; Wiseman, H.M.

    2002-01-01

    In this paper we present a perturbative procedure that allows one to numerically solve diffusive non-Markovian stochastic Schroedinger equations, for a wide range of memory functions. To illustrate this procedure numerical results are presented for a classically driven two-level atom immersed in an environment with a simple memory function. It is observed that as the order of the perturbation is increased the numerical results for the ensemble average state ρ red (t) approach the exact reduced state found via Imamog-barlu ' s enlarged system method [Phys. Rev. A 50, 3650 (1994)

  2. Tsunami-induced boulder transport - combining physical experiments and numerical modelling

    Science.gov (United States)

    Oetjen, Jan; Engel, Max; May, Simon Matthias; Schüttrumpf, Holger; Brueckner, Helmut; Prasad Pudasaini, Shiva

    2016-04-01

    Coasts are crucial areas for living, economy, recreation, transportation, and various sectors of industry. Many of them are exposed to high-energy wave events. With regard to the ongoing population growth in low-elevation coastal areas, the urgent need for developing suitable management measures, especially for hazards like tsunamis, becomes obvious. These measures require supporting tools which allow an exact estimation of impact parameters like inundation height, inundation area, and wave energy. Focussing on tsunamis, geological archives can provide essential information on frequency and magnitude on a longer time scale in order to support coastal hazard management. While fine-grained deposits may quickly be altered after deposition, multi-ton coarse clasts (boulders) may represent an information source on past tsunami events with a much higher preservation potential. Applying numerical hydrodynamic coupled boulder transport models (BTM) is a commonly used approach to analyse characteristics (e.g. wave height, flow velocity) of the corresponding tsunami. Correct computations of tsunamis and the induced boulder transport can provide essential event-specific information, including wave heights, runup and direction. Although several valuable numerical models for tsunami-induced boulder transport exist (e. g. Goto et al., 2007; Imamura et al., 2008), some important basic aspects of both tsunami hydrodynamics and corresponding boulder transport have not yet been entirely understood. Therefore, our project aims at these questions in four crucial aspects of boulder transport by a tsunami: (i) influence of sediment load, (ii) influence of complex boulder shapes other than idealized rectangular shapes, (iii) momentum transfers between multiple boulders, and (iv) influence of non-uniform bathymetries and topographies both on tsunami and boulder. The investigation of these aspects in physical experiments and the correct implementation of an advanced model is an urgent need

  3. Mode coupling of Schwarzschild perturbations: Ringdown frequencies

    International Nuclear Information System (INIS)

    Pazos, Enrique; Brizuela, David; Martin-Garcia, Jose M.; Tiglio, Manuel

    2010-01-01

    Within linearized perturbation theory, black holes decay to their final stationary state through the well-known spectrum of quasinormal modes. Here we numerically study whether nonlinearities change this picture. For that purpose we study the ringdown frequencies of gauge-invariant second-order gravitational perturbations induced by self-coupling of linearized perturbations of Schwarzschild black holes. We do so through high-accuracy simulations in the time domain of first and second-order Regge-Wheeler-Zerilli type equations, for a variety of initial data sets. We consider first-order even-parity (l=2, m=±2) perturbations and odd-parity (l=2, m=0) ones, and all the multipoles that they generate through self-coupling. For all of them and all the initial data sets considered we find that--in contrast to previous predictions in the literature--the numerical decay frequencies of second-order perturbations are the same ones of linearized theory, and we explain the observed behavior. This would indicate, in particular, that when modeling or searching for ringdown gravitational waves, appropriately including the standard quasinormal modes already takes into account nonlinear effects.

  4. Numerical computation of discrete differential scattering cross sections for Monte Carlo charged particle transport

    International Nuclear Information System (INIS)

    Walsh, Jonathan A.; Palmer, Todd S.; Urbatsch, Todd J.

    2015-01-01

    Highlights: • Generation of discrete differential scattering angle and energy loss cross sections. • Gauss–Radau quadrature utilizing numerically computed cross section moments. • Development of a charged particle transport capability in the Milagro IMC code. • Integration of cross section generation and charged particle transport capabilities. - Abstract: We investigate a method for numerically generating discrete scattering cross sections for use in charged particle transport simulations. We describe the cross section generation procedure and compare it to existing methods used to obtain discrete cross sections. The numerical approach presented here is generalized to allow greater flexibility in choosing a cross section model from which to derive discrete values. Cross section data computed with this method compare favorably with discrete data generated with an existing method. Additionally, a charged particle transport capability is demonstrated in the time-dependent Implicit Monte Carlo radiative transfer code, Milagro. We verify the implementation of charged particle transport in Milagro with analytic test problems and we compare calculated electron depth–dose profiles with another particle transport code that has a validated electron transport capability. Finally, we investigate the integration of the new discrete cross section generation method with the charged particle transport capability in Milagro.

  5. Dynamics of a single ion in a perturbed Penning trap: Octupolar perturbation

    International Nuclear Information System (INIS)

    Lara, Martin; Salas, J. Pablo

    2004-01-01

    Imperfections in the design or implementation of Penning traps may give rise to electrostatic perturbations that introduce nonlinearities in the dynamics. In this paper we investigate, from the point of view of classical mechanics, the dynamics of a single ion trapped in a Penning trap perturbed by an octupolar perturbation. Because of the axial symmetry of the problem, the system has two degrees of freedom. Hence, this model is ideal to be managed by numerical techniques like continuation of families of periodic orbits and Poincare surfaces of section. We find that, through the variation of the two parameters controlling the dynamics, several periodic orbits emanate from two fundamental periodic orbits. This process produces important changes (bifurcations) in the phase space structure leading to chaotic behavior

  6. A numerical method for two-dimensional anisotropic transport problem in cylindrical geometry

    International Nuclear Information System (INIS)

    Du Mingsheng; Feng Tiekai; Fu Lianxiang; Cao Changshu; Liu Yulan

    1988-01-01

    The authors deal with the triangular mesh-discontinuous finite element method for solving the time-dependent anisotropic neutron transport problem in two-dimensional cylindrical geometry. A prior estimate of the numerical solution is given. Stability is proved. The authors have computed a two dimensional anisotropic neutron transport problem and a Tungsten-Carbide critical assembly problem by using the numerical method. In comparision with DSN method and the experimental results obtained by others both at home and abroad, the method is satisfactory

  7. Numerical modelling of flow and transport in rough fractures

    Directory of Open Access Journals (Sweden)

    Scott Briggs

    2014-12-01

    Full Text Available Simulation of flow and transport through rough walled rock fractures is investigated using the lattice Boltzmann method (LBM and random walk (RW, respectively. The numerical implementation is developed and validated on general purpose graphic processing units (GPGPUs. Both the LBM and RW method are well suited to parallel implementation on GPGPUs because they require only next-neighbour communication and thus can reduce expenses. The LBM model is an order of magnitude faster on GPGPUs than published results for LBM simulations run on modern CPUs. The fluid model is verified for parallel plate flow, backward facing step and single fracture flow; and the RW model is verified for point-source diffusion, Taylor-Aris dispersion and breakthrough behaviour in a single fracture. Both algorithms place limitations on the discrete displacement of fluid or particle transport per time step to minimise the numerical error that must be considered during implementation.

  8. Three points of view in transport theory

    Energy Technology Data Exchange (ETDEWEB)

    Ruben, Panta Pazos [Faculdade de Matematica, PUCRS, Porto Alegre, RS (Brazil); Tilio de Vilhena, M. [Instituto de Matematica, UFRGS, Porto Alegre, RS (Brazil)

    2001-07-01

    A lot of efforts in Transport Theory is used to develop numerical methods or hybrid numerical-analytical techniques. We present in this work three points of view about transport problems. First the C0 semigroup approach, in which the free transport operator {psi} {yields} {mu} {nabla} generates an strongly continuous semigroup. The operators operator {psi} {yields} {sigma}t and operator {psi} {yields} {integral} {nabla} k(x,{mu},{mu}') {psi}(x,{mu}') d{mu}' are bounded operators, and by perturbation the transport operator {psi} {yields} {mu} {nabla} {psi} + {sigma}t {psi} - K {psi} also generates an strongly continuous semigroup. To prove the convergence of the approximations of a numerical methods to the exact solution we use the approximation theorem of C0 semi-groups in canonical form. In other way, the discrete schemes theory is employed in searching the rate of convergence of numerical techniques in transport theory. For 1D dependent of time transport problem and two-dimensional steady state problem we summarize some estimates, incorporating different boundary conditions. Finally we give a survey about the dynamical behavior of the SN approximations. In order to give a unified approach, some results illustrates the equivalence of the three points of views for the case of the steady-state transport problem for slab geometry. (author)

  9. Ignition condition and gain prediction for perturbed inertial confinement fusion targets

    International Nuclear Information System (INIS)

    Kishony, Roy; Shvarts, Dov

    2001-01-01

    The effect of perturbations on hot spot ignition is studied using full two-dimensional (2D) numerical simulations of the National Ignition Facility [J. D. Lindl, Phys. Plasmas 2, 3933 (1995)] direct drive Laboratory for Laser Energetics target design and newly derived 2D self-similar solutions for a perturbed burn wave propagation. It is shown that the required implosion velocity needed for ignition increases with the perturbation mode number and final amplitude, reaching an asymptotic value for high enough perturbation mode numbers, when the entire mixing zone no longer contributes to the ignition of the hot spot. Using the new self-similar solutions, ignition conditions for various perturbation mode numbers and amplitudes are obtained. These ignition conditions, which correspond to areal densities higher than needed for ignition in the symmetric case, are translated to a required increase in the implosion velocity needed for ignition, using the 1D Levendahl-Lindl scaling, in good agreement with the full 2D numerical simulation results. Finally, using the above results, a model for predicting the gain of a perturbed targets as a function of the perturbation spectra (single-mode and multi-mode) is presented, in good agreement with full numerical simulations

  10. Perturbative spacetimes from Yang-Mills theory

    Energy Technology Data Exchange (ETDEWEB)

    Luna, Andrés [School of Physics and Astronomy, University of Glasgow,Glasgow G12 8QQ, Scotland (United Kingdom); Monteiro, Ricardo [Theoretical Physics Department, CERN,Geneva (Switzerland); Nicholson, Isobel; Ochirov, Alexander; O’Connell, Donal [Higgs Centre for Theoretical Physics,School of Physics and Astronomy, The University of Edinburgh,Edinburgh EH9 3JZ, Scotland (United Kingdom); Westerberg, Niclas [Institute of Photonics and Quantum Sciences,School of Engineering and Physical Sciences, Heriot-Watt University,Edinburgh (United Kingdom); Higgs Centre for Theoretical Physics,School of Physics and Astronomy, The University of Edinburgh,Edinburgh EH9 3JZ, Scotland (United Kingdom); White, Chris D. [Centre for Research in String Theory,School of Physics and Astronomy, Queen Mary University of London,327 Mile End Road, London E1 4NS (United Kingdom)

    2017-04-12

    The double copy relates scattering amplitudes in gauge and gravity theories. In this paper, we expand the scope of the double copy to construct spacetime metrics through a systematic perturbative expansion. The perturbative procedure is based on direct calculation in Yang-Mills theory, followed by squaring the numerator of certain perturbative diagrams as specified by the double-copy algorithm. The simplest spherically symmetric, stationary spacetime from the point of view of this procedure is a particular member of the Janis-Newman-Winicour family of naked singularities. Our work paves the way for applications of the double copy to physically interesting problems such as perturbative black-hole scattering.

  11. Numerical analysis of gas puff modulation experiment on JT-60U

    International Nuclear Information System (INIS)

    Nagashima, Keisuke; Sakasai, Akira

    1992-03-01

    In tokamak transport physics, source modulation experiments are one of the most effective methods. For an analysis of these modulation experiments, a simple numerical method was developed to solve the general transport equations. This method was applied to gas puff modulation experiments on JT-60U. From the comparison between the measured and calculated density perturbations, it was found that the particle diffusion coefficient is about 0.8 m 2 /sec in the edge region and 0.1-0.2 m 2 /sec in the central region. (author)

  12. Perturbative approach to Markovian open quantum systems.

    Science.gov (United States)

    Li, Andy C Y; Petruccione, F; Koch, Jens

    2014-05-08

    The exact treatment of Markovian open quantum systems, when based on numerical diagonalization of the Liouville super-operator or averaging over quantum trajectories, is severely limited by Hilbert space size. Perturbation theory, standard in the investigation of closed quantum systems, has remained much less developed for open quantum systems where a direct application to the Lindblad master equation is desirable. We present such a perturbative treatment which will be useful for an analytical understanding of open quantum systems and for numerical calculation of system observables which would otherwise be impractical.

  13. Difference scheme for a singularly perturbed parabolic convection-diffusion equation in the presence of perturbations

    Science.gov (United States)

    Shishkin, G. I.

    2015-11-01

    An initial-boundary value problem is considered for a singularly perturbed parabolic convection-diffusion equation with a perturbation parameter ɛ (ɛ ∈ (0, 1]) multiplying the highest order derivative. The stability of a standard difference scheme based on monotone approximations of the problem on a uniform mesh is analyzed, and the behavior of discrete solutions in the presence of perturbations is examined. The scheme does not converge ɛ-uniformly in the maximum norm as the number of its grid nodes is increased. When the solution of the difference scheme converges, which occurs if N -1 ≪ ɛ and N -1 0 ≪ 1, where N and N 0 are the numbers of grid intervals in x and t, respectively, the scheme is not ɛ-uniformly well conditioned or stable to data perturbations in the grid problem and to computer perturbations. For the standard difference scheme in the presence of data perturbations in the grid problem and/or computer perturbations, conditions on the "parameters" of the difference scheme and of the computer (namely, on ɛ, N, N 0, admissible data perturbations in the grid problem, and admissible computer perturbations) are obtained that ensure the convergence of the perturbed solutions. Additionally, the conditions are obtained under which the perturbed numerical solution has the same order of convergence as the solution of the unperturbed standard difference scheme.

  14. The simulation of solute transport: An approach free of numerical dispersion

    International Nuclear Information System (INIS)

    Carrera, J.; Melloni, G.

    1987-01-01

    The applicability of most algorithms for simulation of solute transport is limited either by instability or by numerical dispersion, as seen by a review of existing methods. A new approach is proposed that is free of these two problems. The method is based on the mixed Eulerian-Lagrangian formulation of the mass-transport problem, thus ensuring stability. Advection is simulated by a variation of reverse-particle tracking that avoids the accumulation of interpolation errors, thus preventing numerical dispersion. The algorithm has been implemented in a one-dimensional code. Excellent results are obtained, in comparison with an analytical solution. 36 refs., 14 figs., 1 tab

  15. Numerical solution of neutron transport equations in discrete ordinates and slab geometry

    International Nuclear Information System (INIS)

    Serrano Pedraza, F.

    1985-01-01

    An unified formalism to solve numerically, between other equation, the neutron transport in discrete ordinates, slab geometry, several energy groups and independents of time, has been developed recently. Such a formalism cover some of the conventional schemes as diamond difference, (WDD) characteristic step (SC) lineal characteristic (LC), quadratic characteristic (QC) and lineal discontinuous. Unified formation gives before hand the convergence order of the previously selected scheme. In fact it allows besides to generate a big amount of numerical schemes, with which is also possible to solve numerical equations as soon as neutron transport. The essential purpose of this work was to solve the neutron transport equations in slab geometry and discrete ordinates considering several energy groups without to take under advisement time dependence based in the above mentioned unified formalism. To reach this purpose it was necesary to design a computer code with the name TNOD1 (Neutron transport in discrete ordinates and 1 dimension) which includes each one of the schemes already pointed out. there exist two numerical schemes, also recently developed, quadratic continuous (QC) and cubic continuous (CN), although covered by unified formalism, it has been possible to include them inside this computer code without make substantial changes in its structure. In chapter I, derivative of neutron transport equation independent of time is taken, for angular flux, including boundary conditions and discontinuity. In chapter II the neutron transport equations are obtained in multigroups, independents of time, for approximation of discrete ordinates. Description of theory related with unified formalism and its relationship with mentioned discretization schemes is presented in chapter III. Chapter IV describes the computer code developed and finally, in chapter V different numerical results obtained with TNOD1 program are shown. In Appendix A theorems and mathematical arguments used

  16. Importance of Plasma Response to Non-axisymmetric Perturbations in Tokamaks

    International Nuclear Information System (INIS)

    Park, Jong-kyu; Boozer, Allen H.; Menard, Jonathan E.; Garofalo, Andrea M.; Schaffer, Michael J.; Hawryluk, Richard J.; Kaye, Stanley M.; Gerhardt, Stefan P.; Sabbagh, Steve A. and the NSTX Team

    2009-01-01

    Tokamaks are sensitive to deviations from axisymmetry as small as (delta)B/B 0 ∼ 10 -4 . These non-axisymmetric perturbations greatly modify plasma confinement and performance by either destroying magnetic surfaces with subsequent locking or deforming magnetic surfaces with associated non-ambipolar transport. The Ideal Perturbed Equilibrium Code (IPEC) calculates ideal perturbed equilibria and provides important basis for understanding the sensitivity of tokamak plasmas to perturbations. IPEC calculations indicate that the ideal plasma response, or equivalently the effect by ideally perturbed plasma currents, is essential to explain locking experiments on National Spherical Torus eXperiment (NSTX) and DIII-D. The ideal plasma response is also important for Neoclassical Toroidal Viscosity (NTV) in non-ambipolar transport. The consistency between NTV theory and magnetic braking experiments on NSTX and DIII-D can be improved when the variation in the field strength in IPEC is coupled with generalized NTV theory. These plasma response effects will be compared with the previous vacuum superpositions to illustrate the importance. However, plasma response based on ideal perturbed equilibria is still not sufficiently accurate to predict the details of NTV transport, and can be inconsistent when currents associated with a toroidal torque become comparable to ideal perturbed currents

  17. Numerical transport of an arbitrary number of components

    International Nuclear Information System (INIS)

    Jaouen, S.; Lagoutiere, F.

    2007-01-01

    This paper deals with the numerical transport of an arbitrary number of materials having the same velocity. One difficulty is to derive numerical algorithms that are conservative for the mass of each component and that satisfy some inequality and equality constraints: each mass fraction has to stay in [0, 1] and the sum of all mass fractions should be 1. These constraints are satisfied by the classical upwind scheme (which is very dissipative) but not for most of nonlinear (high-order or anti-dissipative) schemes. Here we propose local conditions of inequality type for the finite volume fluxes of mass fractions to ensure the aforementioned constraints. More precisely, we give explicit stability intervals for each flux. This is done in the manner of Despres and Lagoutiere for hyperbolic systems, for the transport of two components, for the same type of inequality constraints for nonlinear conservation laws. Comparisons on two dimensional test-cases with the Youngs' interface reconstruction algorithm show that results are qualitatively comparable. The advantages of this approach are its simplicity, its low computational cost, and its flexibility since it can deal with interfaces as well as mixing zones. (authors)

  18. TP1 - A computer program for the calculation of reactivity and kinetic parameters by one-dimensional neutron transport perturbation theory

    International Nuclear Information System (INIS)

    Kobayashi, K.

    1979-03-01

    TP1, a FORTRAN-IV program based on transport theory, has been developed to determine reactivity effects and kinetic parameters such as effective delayed neutron fractions and mean generation time by applying the usual perturbation formalism for one-dimensional geometry. Direct and adjoint angular dependent neutron fluxes are read from an interface file prepared by using the one-dimensional Ssub(n)-code DTK which provides options for slab, cylindrical and spherical geometry. Multigroup cross sections which are equivalent to those of the DTK-calculations are supplied in the SIGM-block which is also read from an interface file. This block which is usually produced by the code GRUCAL should contain the necessary delayed neutron data, which can be added to the original SIGMN-block by using the code SIGMUT. Two perturbation options are included in TP1: a) the usual first oder perturbation theory can be applied to determine probe reactivities, b) assuming that there are available direct fluxes for the unperturbed reactor system and adjoint fluxes for the perturbed system, the exact reactivity effect induced by the perturbation can be determined by an exact perturbation calculation. According to the input specifications, the output lists the reactivity contributions for each neutron reaction process in the desired detailed spatial and energy group resolution. (orig./RW) [de

  19. Numerical investigation of nanoparticles transport in anisotropic porous media

    KAUST Repository

    Salama, Amgad

    2015-07-13

    In this work the problem related to the transport of nanoparticles in anisotropic porous media is investigated numerically using the multipoint flux approximation. Anisotropy of porous media properties are an essential feature that exist almost everywhere in subsurface formations. In anisotropic media, the flux and the pressure gradient vectors are no longer collinear and therefore interesting patterns emerge. The transport of nanoparticles in subsurface formations is affected by several complex processes including surface charges, heterogeneity of nanoparticles and soil grain collectors, interfacial dynamics of double-layer and many others. We use the framework of the theory of filtration in this investigation. Processes like particles deposition, entrapment, as well as detachment are accounted for. From the numerical methods point of view, traditional two-point flux finite difference approximation cannot handle anisotropy of media properties. Therefore, in this work we use the multipoint flux approximation (MPFA). In this technique, the flux components are affected by more neighboring points as opposed to the mere two points that are usually used in traditional finite volume methods. We also use the experimenting pressure field approach which automatically constructs the global system of equations by solving multitude of local problems. This approach facilitates to a large extent the construction of the global system. A set of numerical examples is considered involving two-dimensional rectangular domain. A source of nanoparticles is inserted in the middle of the anisotropic layer. We investigate the effects of both anisotropy angle and anisotropy ratio on the transport of nanoparticles in saturated porous media. It is found that the concentration plume and porosity contours follow closely the principal direction of anisotropy of permeability of the central domain.

  20. Numerical investigation of nanoparticles transport in anisotropic porous media

    KAUST Repository

    Salama, Amgad; Negara, Ardiansyah; El Amin, Mohamed; Sun, Shuyu

    2015-01-01

    In this work the problem related to the transport of nanoparticles in anisotropic porous media is investigated numerically using the multipoint flux approximation. Anisotropy of porous media properties are an essential feature that exist almost everywhere in subsurface formations. In anisotropic media, the flux and the pressure gradient vectors are no longer collinear and therefore interesting patterns emerge. The transport of nanoparticles in subsurface formations is affected by several complex processes including surface charges, heterogeneity of nanoparticles and soil grain collectors, interfacial dynamics of double-layer and many others. We use the framework of the theory of filtration in this investigation. Processes like particles deposition, entrapment, as well as detachment are accounted for. From the numerical methods point of view, traditional two-point flux finite difference approximation cannot handle anisotropy of media properties. Therefore, in this work we use the multipoint flux approximation (MPFA). In this technique, the flux components are affected by more neighboring points as opposed to the mere two points that are usually used in traditional finite volume methods. We also use the experimenting pressure field approach which automatically constructs the global system of equations by solving multitude of local problems. This approach facilitates to a large extent the construction of the global system. A set of numerical examples is considered involving two-dimensional rectangular domain. A source of nanoparticles is inserted in the middle of the anisotropic layer. We investigate the effects of both anisotropy angle and anisotropy ratio on the transport of nanoparticles in saturated porous media. It is found that the concentration plume and porosity contours follow closely the principal direction of anisotropy of permeability of the central domain.

  1. Conductance maps of quantum rings due to a local potential perturbation.

    Science.gov (United States)

    Petrović, M D; Peeters, F M; Chaves, A; Farias, G A

    2013-12-11

    We performed a numerical simulation of the dynamics of a Gaussian shaped wavepacket inside a small sized quantum ring, smoothly connected to two leads and exposed to a perturbing potential of a biased atomic force microscope tip. Using the Landauer formalism, we calculated conductance maps of this system in the case of single and two subband transport. We explain the main features in the conductance maps as due to the AFM tip influence on the wavepacket phase and amplitude. In the presence of an external magnetic field, the tip modifies the ϕ0 periodic Aharonov-Bohm oscillation pattern into a ϕ0/2 periodic Al'tshuler-Aronov-Spivak oscillation pattern. Our results in the case of multiband transport suggest tip selectivity to higher subbands, making them more observable in the total conductance map.

  2. A Parameter Robust Method for Singularly Perturbed Delay Differential Equations

    Directory of Open Access Journals (Sweden)

    Erdogan Fevzi

    2010-01-01

    Full Text Available Uniform finite difference methods are constructed via nonstandard finite difference methods for the numerical solution of singularly perturbed quasilinear initial value problem for delay differential equations. A numerical method is constructed for this problem which involves the appropriate Bakhvalov meshes on each time subinterval. The method is shown to be uniformly convergent with respect to the perturbation parameter. A numerical example is solved using the presented method, and the computed result is compared with exact solution of the problem.

  3. On dark energy isocurvature perturbation

    International Nuclear Information System (INIS)

    Liu, Jie; Zhang, Xinmin; Li, Mingzhe

    2011-01-01

    Determining the equation of state of dark energy with astronomical observations is crucially important to understand the nature of dark energy. In performing a likelihood analysis of the data, especially of the cosmic microwave background and large scale structure data the dark energy perturbations have to be taken into account both for theoretical consistency and for numerical accuracy. Usually, one assumes in the global fitting analysis that the dark energy perturbations are adiabatic. In this paper, we study the dark energy isocurvature perturbation analytically and discuss its implications for the cosmic microwave background radiation and large scale structure. Furthermore, with the current astronomical observational data and by employing Markov Chain Monte Carlo method, we perform a global analysis of cosmological parameters assuming general initial conditions for the dark energy perturbations. The results show that the dark energy isocurvature perturbations are very weakly constrained and that purely adiabatic initial conditions are consistent with the data

  4. Numerical simulations of local circulations and pollution transport over Reunion Island

    Directory of Open Access Journals (Sweden)

    D. Lesouëf

    2011-01-01

    Full Text Available A series of high-resolution (1 km numerical simulations with a limited-area numerical model has been performed over Reunion Island. In the dynamical context of a regular maritime flow perturbed by a major topographic obstacle such as Reunion Island, the objectives are to identify the main atmospheric circulations at local-scale over the island and to improve the understanding of local-scale transport and dispersion of pollutants emitted from local sources. To investigate the effects of topography and land surface heating on low-level flows over the island, simulations representative of austral winter were performed in idealized conditions keeping the radiative forcing plus a background east-south-easterly synoptic flux of varying strengths, typical of the prevailing trade-wind conditions. The numerical experiments show mainly that flow splitting of the trade-wind occurs around the island, with enhanced winds blowing along the coast lines parallel to the synoptic flux, due to the lateral constriction of the flow by the island and resulting Venturi effect. Blocking occurs on the island side facing the trade-wind. The north-western area on the leeside is screened from the trade-wind by high mountains, and this enables the development of diurnal thermally-induced circulations, combining downslope and land-breeze at night, and upslope and sea breeze at daytime. Flow splitting is modulated by radiative convergence toward the island at daytime, and divergence from the island at night. Stronger winds than the large-scale trade-wind occur along the coast at daytime (Venturi effect, whereas at night, the trade-wind flow is pushed few kilometres offshore by divergence of cooled air from the land. At night, the trade-wind flow is pushed few kilometres offshore by divergence of cooled air from the land. Consequently, a number of processes of pollution transport and dispersion have been identified. Vortices in the wake of the island were found to cause

  5. Numerical simulations of local circulations and pollution transport over Reunion Island

    Energy Technology Data Exchange (ETDEWEB)

    Lesouef, D.; Delmas, R. [La Reunion Univ., CNRS/INSU UMR8105 (France). Lab. de l' Atmosphere et des Cyclones; Gheusi, F.; Escobar, J. [Toulouse III Univ., CNRS/INSU UMR5560 (France). Lab. d' Aerologie

    2011-07-01

    A series of high-resolution (1 km) numerical simulations with a limited-area numerical model has been performed over Reunion Island. In the dynamical context of a regular maritime flow perturbed by a major topographic obstacle such as Reunion Island, the objectives are to identify the main atmospheric circulations at local-scale over the island and to improve the understanding of local-scale transport and dispersion of pollutants emitted from local sources. To investigate the effects of topography and land surface heating on low-level flows over the island, simulations representative of austral winter were performed in idealized conditions keeping the radiative forcing plus a background east-south-easterly synoptic flux of varying strengths, typical of the prevailing trade-wind conditions. The numerical experiments show mainly that flow splitting of the trade-wind occurs around the island, with enhanced winds blowing along the coast lines parallel to the synoptic flux, due to the lateral constriction of the flow by the island and resulting Venturi effect. Blocking occurs on the island side facing the trade-wind. The north-western area on the leeside is screened from the trade-wind by high mountains, and this enables the development of diurnal thermally-induced circulations, combining downslope and land-breeze at night, and upslope and sea breeze at daytime. Flow splitting is modulated by radiative convergence toward the island at daytime, and divergence from the island at night. Stronger winds than the large-scale trade-wind occur along the coast at daytime (Venturi effect), whereas at night, the trade-wind flow is pushed few kilometres offshore by divergence of cooled air from the land. At night, the trade-wind flow is pushed few kilometres offshore by divergence of cooled air from the land. Consequently, a number of processes of pollution transport and dispersion have been identified. Vortices in the wake of the island were found to cause counterflow circulation

  6. Mathematical and numerical analysis of PN models for photons transport problems

    International Nuclear Information System (INIS)

    Valentin, Xavier

    2015-01-01

    Computational costs for direct numerical simulations of photon transport problems are very high in terms of CPU time and memory. One way to tackle this issue is to develop reduced models that a cheaper to solve numerically. There exists number of these models: moments models, discrete ordinates models (S N ), diffusion-like models... In this thesis, we focus on P N models in which the transport operator is approached by mean of a truncated development on the spherical harmonics basis. These models are arbitrary accurate in the angular dimension and are rotationally invariants (in multiple space dimensions). The latter point is fundamental when one wants to simulate inertial confinement fusion (ICF) experiments where the spherical symmetry plays an important part in the accuracy of the numerical solutions. We study the mathematical structure of the PN models and construct a new numerical method in the special case of a one dimensional space dimension with spherical symmetry photon transport problems. We first focus on a linear transport problem in the vacuum. Even in this simple case, it appears in the P N equations geometrical source terms that are stiff in the neighborhood of r = 0 and thus hard to discretize. Existing numerical methods are not satisfactory for multiple reasons: (1) inaccuracy in the neighborhood of r = 0 ('flux-dip'), (2) do not capture steady states (well-balanced scheme), (3) no stability proof. Following recent works, we develop a new well-balanced scheme for which we show the L 2 stability. We then extend the scheme for photon transport problems within a no moving media, the linear Boltzmann equation, and interest ourselves on its behavior in the diffusion limit (asymptotic-preserving property). In a second part, we consider radiation hydrodynamics problems. Since modelization of these problems is still under discussion in the literature, we compare a set of existing models by mean of mathematical analysis and establish a hierarchy

  7. Numerical model for two-dimensional hydrodynamics and energy transport. [VECTRA code

    Energy Technology Data Exchange (ETDEWEB)

    Trent, D.S.

    1973-06-01

    The theoretical basis and computational procedure of the VECTRA computer program are presented. VECTRA (Vorticity-Energy Code for TRansport Analysis) is designed for applying numerical simulation to a broad range of intake/discharge flows in conjunction with power plant hydrological evaluation. The code computational procedure is based on finite-difference approximation of the vorticity-stream function partial differential equations which govern steady flow momentum transport of two-dimensional, incompressible, viscous fluids in conjunction with the transport of heat and other constituents.

  8. A numerical spectral approach to solve the dislocation density transport equation

    International Nuclear Information System (INIS)

    Djaka, K S; Taupin, V; Berbenni, S; Fressengeas, C

    2015-01-01

    A numerical spectral approach is developed to solve in a fast, stable and accurate fashion, the quasi-linear hyperbolic transport equation governing the spatio-temporal evolution of the dislocation density tensor in the mechanics of dislocation fields. The approach relies on using the Fast Fourier Transform algorithm. Low-pass spectral filters are employed to control both the high frequency Gibbs oscillations inherent to the Fourier method and the fast-growing numerical instabilities resulting from the hyperbolic nature of the transport equation. The numerical scheme is validated by comparison with an exact solution in the 1D case corresponding to dislocation dipole annihilation. The expansion and annihilation of dislocation loops in 2D and 3D settings are also produced and compared with finite element approximations. The spectral solutions are shown to be stable, more accurate for low Courant numbers and much less computation time-consuming than the finite element technique based on an explicit Galerkin-least squares scheme. (paper)

  9. Application of a numerical transport correction in diffusion calculations

    International Nuclear Information System (INIS)

    Tomatis, Daniele; Dall'Osso, Aldo

    2011-01-01

    Full core calculations by ordinary transport methods can demand considerable computational time, hardly acceptable in the industrial work frame. However, the trend of next generation nuclear cores goes toward more heterogeneous systems, where transport phenomena of neutrons become very important. On the other hand, using diffusion solvers is more practical allowing faster calculations, but a specific formulation of the diffusion coefficient is requested to reproduce the scalar flux with reliable physical accuracy. In this paper, the Ronen method is used to evaluate numerically the diffusion coefficient in the slab reactor. The new diffusion solution is driven toward the solution of the integral neutron transport equation by non linear iterations. Better estimates of currents are computed and diffusion coefficients are corrected at node interfaces, still assuming Fick's law. This method enables obtaining closer results to the transport solution by a common solver in multigroup diffusion. (author)

  10. Integration of numerical analysis tools for automated numerical optimization of a transportation package design

    International Nuclear Information System (INIS)

    Witkowski, W.R.; Eldred, M.S.; Harding, D.C.

    1994-01-01

    The use of state-of-the-art numerical analysis tools to determine the optimal design of a radioactive material (RAM) transportation container is investigated. The design of a RAM package's components involves a complex coupling of structural, thermal, and radioactive shielding analyses. The final design must adhere to very strict design constraints. The current technique used by cask designers is uncoupled and involves designing each component separately with respect to its driving constraint. With the use of numerical optimization schemes, the complex couplings can be considered directly, and the performance of the integrated package can be maximized with respect to the analysis conditions. This can lead to more efficient package designs. Thermal and structural accident conditions are analyzed in the shape optimization of a simplified cask design. In this paper, details of the integration of numerical analysis tools, development of a process model, nonsmoothness difficulties with the optimization of the cask, and preliminary results are discussed

  11. A numerical study of atmospheric perturbations induced by heat from a wildland fire: sensitivity to vertical canopy structure and heat source strength

    Science.gov (United States)

    Michael T. Kiefer; Shiyuan Zhong; Warren E. Heilman; Joseph J. Charney; Xindi. Bian

    2018-01-01

    An improved understanding of atmospheric perturbations within and above a forest during a wildland fire has relevance to many aspects of wildland fires including fire spread, smoke transport and dispersion, and tree mortality. In this study, the ARPS-CANOPY model, a version of the Advanced Regional Prediction System (ARPS) model with a canopy parameterization, is...

  12. Sensitivity of the solution of the Elder problem to density, velocity and numerical perturbations

    Science.gov (United States)

    Park, Chan-Hee; Aral, Mustafa M.

    2007-06-01

    In this paper the Elder problem is studied with the purpose of evaluating the inherent instabilities associated with the numerical solution of this problem. Our focus is first on the question of the existence of a unique numerical solution for this problem, and second on the grid density and fluid density requirements necessary for a unique numerical solution. In particular we have investigated the instability issues associated with the numerical solution of the Elder problem from the following perspectives: (i) physical instability issues associated with density differences; (ii) sensitivity of the numerical solution to idealization irregularities; and, (iii) the importance of a precise velocity field calculation and the association of this process with the grid density levels that is necessary to solve the Elder problem accurately. In the study discussed here we have used a finite element Galerkin model we have developed for solving density-dependent flow and transport problems, which will be identified as TechFlow. In our study, the numerical results of Frolkovič and de Schepper [Frolkovič, P. and H. de Schepper, 2001. Numerical modeling of convection dominated transport coupled with density-driven flow in porous media, Adv. Water Resour., 24, 63-72.] were replicated using the grid density employed in their work. We were also successful in duplicating the same result with a less dense grid but with more computational effort based on a global velocity estimation process we have adopted. Our results indicate that the global velocity estimation approach recommended by Yeh [Yeh, G.-T., 1981. On the computation of Darcian velocity and mass balance in finite element modelling of groundwater flow, Water Resour. Res., 17(5), 1529-1534.] allows the use of less dense grids while obtaining the same accuracy that can be achieved with denser grids. We have also observed that the regularity of the elements in the discretization of the solution domain does make a difference

  13. Plasmator. A numerical code for simulation of plasma transport in Tokamaks

    International Nuclear Information System (INIS)

    Guasp, J.

    1979-01-01

    Plasmator is a flexible monodimensional numerical code for plasma transport in Tokamaks of circular cross-section, it allows neutral particle transport and impurity effects. The code leaves a total freedom in the analytical form of transport coefficients. It has been writen in Fortran-V for the UNIVAC-1100/80 from JEN and allows for the possibility of graphics for radial profiles and temporal evolution of the main plasma magnitudes, as well in three-dimensional as in two-dimensional representation either on a Calcomp plotter or in the printer. (author)

  14. On perturbations of a quintom bounce

    International Nuclear Information System (INIS)

    Cai Yifu; Qiu Taotao; Zhang Xinmin; Brandenberger, Robert; Piao Yunsong

    2008-01-01

    A quintom universe with an equation of state crossing the cosmological constant boundary can provide a bouncing solution dubbed the quintom bounce and thus resolve the big bang singularity. In this paper, we investigate the cosmological perturbations of the quintom bounce both analytically and numerically. We find that the fluctuations in the dominant mode in the post-bounce expanding phase couple to the growing mode of the perturbations in the pre-bounce contracting phase

  15. Plasma transport in stochastic magnetic field caused by vacuum resonant magnetic perturbations at diverted tokamak edge

    International Nuclear Information System (INIS)

    Park, G.; Chang, C. S.; Joseph, I.; Moyer, R. A.

    2010-01-01

    A kinetic transport simulation for the first 4 ms of the vacuum resonant magnetic perturbations (RMPs) application has been performed for the first time in realistic diverted DIII-D tokamak geometry [J. Luxon, Nucl. Fusion 42, 614 (2002)], with the self-consistent evaluation of the radial electric field and the plasma rotation. It is found that, due to the kinetic effects, the stochastic parallel thermal transport is significantly reduced when compared to the standard analytic model [A. B. Rechester and M. N. Rosenbluth, Phys. Rev. Lett. 40, 38 (1978)] and the nonaxisymmetric perpendicular radial particle transport is significantly enhanced from the axisymmetric level. These trends agree with recent experimental result trends [T. E. Evans, R. A. Moyer, K. H. Burrell et al., Nat. Phys. 2, 419 (2006)]. It is also found, as a side product, that an artificial local reduction of the vacuum RMP fields in the vicinity of the magnetic separatrix can bring the kinetic simulation results to a more detailed agreement with experimental plasma profiles.

  16. Numerical Diffusion Effect in Dynamic Simulation of Thermohydraulic Systems

    International Nuclear Information System (INIS)

    Zanocco, Pablo; Gimenez, Marcelo; Delmastro, Dario

    2003-01-01

    In this work, the behavior of the explicit - up-wind method is studied in two phase natural convection circuit, near the instabilities boundaries.The effect of the numerical diffusion of the scheme upon the system stability is evaluated by means of linearization by small perturbations.The results are compared with a non-diffusive method, in the frequency domain, that solves analytically the linearized equations around a steady state condition.Moreover, a conservation equation transport model using the method of characteristics is implemented and studied.This method is compared with the explicit - up-wind scheme and it is found that it significantly reduces numerical diffusion in the equations solution. Several advantages are visualized for particular cases

  17. Numerical shoves and countershoves in electron transport calculations

    International Nuclear Information System (INIS)

    Filippone, W.L.

    1986-01-01

    The justification for applying the relatively complex (compared to S/sub n/) streaming ray (SR) algorithm to electron transport problems is its potential for doing rapid and accurate calculations. Because of the Lagrangian treatment of the cell-uncollided electrons, the only significant sources of error are the numerical treatment of the scattering kernel and the spatial differencing scheme used for the cell-collided electrons. Considerable progress has been made in reducing the former source of error. If one is willing to pay the price, the latter source of error can be reduced to any desired level by refining the mesh size or by using high-order differencing schemes. Here the method of numerical shoves and countershoves is introduced, which reduces spatial differencing errors using relatively little additional computational effort

  18. Variational Perturbation Treatment of the Confined Hydrogen Atom

    Science.gov (United States)

    Montgomery, H. E., Jr.

    2011-01-01

    The Schrodinger equation for the ground state of a hydrogen atom confined at the centre of an impenetrable cavity is treated using variational perturbation theory. Energies calculated from variational perturbation theory are comparable in accuracy to the results from a direct numerical solution. The goal of this exercise is to introduce the…

  19. Investigation of bacterial transport in the large-block test, a thermally perturbed block of Topopah Spring tuff

    Energy Technology Data Exchange (ETDEWEB)

    Chen, C.I.; Meike, A.; Chuu, Y.J.; Sawvel, A.; Lin, W.

    1999-07-01

    Transport of bacteria is investigated as part of the Large-Block Test (LBT), a thermally perturbed block of Topopah Spring tuff. Two bacterial species, Bacillus subtilis and Arthrobacter oxydans, were isolated from the Yucca Mountain Tuff. Natural mutants that can grow under the simultaneous presence of the two antibiotics, streptomycin and rifampicin, were selected from these species by laboratory procedures, cultured, and injected into the five heater boreholes of the large block hours before heating was initiated. The temperature, as measured 5 cm above one of the heater boreholes, rose slowly over a matter of months to a maximum of 142 C and to 60 C at the top and bottom of the block. Samples were collected from boreholes located approximately 5 ft below the injection points. Double-drug-resistant microbes also appeared in the heater boreholes where the temperature had been sustainably high throughout the test. The number of double-drug-resistant bacteria that were identified in the collection boreholes increased with time until the heater was deactivated. Negative indications in the collection holes after the heater was deactivated support the supposition that these bacteria were the species that were injected. An apparent homogeneous distribution among the collection boreholes suggests no pattern to the migration of bacteria through the block. The relationship between bacterial migration and the movement of water is not yet understood. These observations indicate the possibility of rapid bacterial transport in a thermally perturbed geologic setting. The implications for colloid transport need to be reviewed.

  20. Investigation of bacterial transport in the large-block test, a thermally perturbed block of Topopah Spring tuff

    International Nuclear Information System (INIS)

    Chen, C.I.; Meike, A.; Chuu, Y.J.; Sawvel, A.; Lin, W.

    1999-01-01

    Transport of bacteria is investigated as part of the Large-Block Test (LBT), a thermally perturbed block of Topopah Spring tuff. Two bacterial species, Bacillus subtilis and Arthrobacter oxydans, were isolated from the Yucca Mountain Tuff. Natural mutants that can grow under the simultaneous presence of the two antibiotics, streptomycin and rifampicin, were selected from these species by laboratory procedures, cultured, and injected into the five heater boreholes of the large block hours before heating was initiated. The temperature, as measured 5 cm above one of the heater boreholes, rose slowly over a matter of months to a maximum of 142 C and to 60 C at the top and bottom of the block. Samples were collected from boreholes located approximately 5 ft below the injection points. Double-drug-resistant microbes also appeared in the heater boreholes where the temperature had been sustainably high throughout the test. The number of double-drug-resistant bacteria that were identified in the collection boreholes increased with time until the heater was deactivated. Negative indications in the collection holes after the heater was deactivated support the supposition that these bacteria were the species that were injected. An apparent homogeneous distribution among the collection boreholes suggests no pattern to the migration of bacteria through the block. The relationship between bacterial migration and the movement of water is not yet understood. These observations indicate the possibility of rapid bacterial transport in a thermally perturbed geologic setting. The implications for colloid transport need to be reviewed

  1. Uncertainty analysis of neutron transport calculation

    International Nuclear Information System (INIS)

    Oka, Y.; Furuta, K.; Kondo, S.

    1987-01-01

    A cross section sensitivity-uncertainty analysis code, SUSD was developed. The code calculates sensitivity coefficients for one and two-dimensional transport problems based on the first order perturbation theory. Variance and standard deviation of detector responses or design parameters can be obtained using cross section covariance matrix. The code is able to perform sensitivity-uncertainty analysis for secondary neutron angular distribution(SAD) and secondary neutron energy distribution(SED). Covariances of 6 Li and 7 Li neutron cross sections in JENDL-3PR1 were evaluated including SAD and SED. Covariances of Fe and Be were also evaluated. The uncertainty of tritium breeding ratio, fast neutron leakage flux and neutron heating was analysed on four types of blanket concepts for a commercial tokamak fusion reactor. The uncertainty of tritium breeding ratio was less than 6 percent. Contribution from SAD/SED uncertainties are significant for some parameters. Formulas to estimate the errors of numerical solution of the transport equation were derived based on the perturbation theory. This method enables us to deterministically estimate the numerical errors due to iterative solution, spacial discretization and Legendre polynomial expansion of transfer cross-sections. The calculational errors of the tritium breeding ratio and the fast neutron leakage flux of the fusion blankets were analysed. (author)

  2. Numerical simulation of ion transport membrane reactors: Oxygen permeation and transport and fuel conversion

    KAUST Repository

    Hong, Jongsup

    2012-07-01

    Ion transport membrane (ITM) based reactors have been suggested as a novel technology for several applications including fuel reforming and oxy-fuel combustion, which integrates air separation and fuel conversion while reducing complexity and the associated energy penalty. To utilize this technology more effectively, it is necessary to develop a better understanding of the fundamental processes of oxygen transport and fuel conversion in the immediate vicinity of the membrane. In this paper, a numerical model that spatially resolves the gas flow, transport and reactions is presented. The model incorporates detailed gas phase chemistry and transport. The model is used to express the oxygen permeation flux in terms of the oxygen concentrations at the membrane surface given data on the bulk concentration, which is necessary for cases when mass transfer limitations on the permeate side are important and for reactive flow modeling. The simulation results show the dependence of oxygen transport and fuel conversion on the geometry and flow parameters including the membrane temperature, feed and sweep gas flow, oxygen concentration in the feed and fuel concentration in the sweep gas. © 2012 Elsevier B.V.

  3. Adaptation of reach-to-grasp movement in response to force perturbations.

    Science.gov (United States)

    Rand, M K; Shimansky, Y; Stelmach, G E; Bloedel, J R

    2004-01-01

    This study examined how reach-to-grasp movements are modified during adaptation to external force perturbations applied on the arm during reach. Specifically, we examined whether the organization of these movements was dependent upon the condition under which the perturbation was applied. In response to an auditory signal, all subjects were asked to reach for a vertical dowel, grasp it between the index finger and thumb, and lift it a short distance off the table. The subjects were instructed to do the task as fast as possible. The perturbation was an elastic load acting on the wrist at an angle of 105 deg lateral to the reaching direction. The condition was modified by changing the predictability with which the perturbation was applied in a given trial. After recording unperturbed control trials, perturbations were applied first on successive trials (predictable perturbations) and then were applied randomly (unpredictable perturbations). In the early predictable perturbation trials, reach path length became longer and reaching duration increased. As more predictable perturbations were applied, the reach path length gradually decreased and became similar to that of control trials. Reaching duration also decreased gradually as the subjects adapted by exerting force against the perturbation. In addition, the amplitude of peak grip aperture during arm transport initially increased in response to repeated perturbations. During the course of learning, it reached its maximum and thereafter slightly decreased. However, it did not return to the normal level. The subjects also adapted to the unpredictable perturbations through changes in both arm transport and grasping components, indicating that they can compensate even when the occurrence of the perturbation cannot be predicted during the inter-trial interval. Throughout random perturbation trials, large grip aperture values were observed, suggesting that a conservative aperture level is set regardless of whether the

  4. Generalized perturbation theory in DRAGON: application to CANDU cell calculations

    International Nuclear Information System (INIS)

    Courau, T.; Marleau, G.

    2001-01-01

    Generalized perturbation theory (GPT) in neutron transport is a means to evaluate eigenvalue and reaction rate variations due to small changes in the reactor properties (macroscopic cross sections). These variations can be decomposed in two terms: a direct term corresponding to the changes in the cross section themselves and an indirect term that takes into account the perturbations in the neutron flux. As we will show, taking into account the indirect term using a GPT method is generally straight forward since this term is the scalar product of the unperturbed generalized adjoint with the product of the variation of the transport operator and the unperturbed flux. In the case where the collision probability (CP) method is used to solve the transport equation, evaluating the perturbed transport operator involves calculating the variations in the CP matrix for each change in the reactor properties. Because most of the computational effort is dedicated to the CP matrix calculation the gains expected form the GPT method would therefore be annihilated. Here we will present a technique to approximate the variations in the CP matrices thereby replacing the variations in the transport operator with source term variations. We will show that this approximation yields errors fully compatible with the standard generalized perturbation theory errors. Results for 2D CANDU cell calculations will be presented. (author)

  5. Edge momentum transport by neutrals: an interpretive numerical framework

    Science.gov (United States)

    Omotani, J. T.; Newton, S. L.; Pusztai, I.; Viezzer, E.; Fülöp, T.; The ASDEX Upgrade Team

    2017-06-01

    Due to their high cross-field mobility, neutrals can contribute to momentum transport even at the low relative densities found inside the separatrix and they can generate intrinsic rotation. We use a charge-exchange dominated solution to the neutral kinetic equation, coupled to neoclassical ions, to evaluate the momentum transport due to neutrals. Numerical solutions to the drift-kinetic equation allow us to cover the full range of collisionality, including the intermediate levels typical of the tokamak edge. In the edge there are several processes likely to contribute to momentum transport in addition to neutrals. Therefore, we present here an interpretive framework that can evaluate the momentum transport through neutrals based on radial plasma profiles. We demonstrate its application by analysing the neutral angular momentum flux for an L-mode discharge in the ASDEX Upgrade tokamak. The magnitudes of the angular momentum fluxes we find here due to neutrals of 0.6-2 \\text{N} \\text{m} are comparable to the net torque on the plasma from neutral beam injection, indicating the importance of neutrals for rotation in the edge.

  6. Very high order lattice perturbation theory for Wilson loops

    International Nuclear Information System (INIS)

    Horsley, R.

    2010-10-01

    We calculate perturbativeWilson loops of various sizes up to loop order n=20 at different lattice sizes for pure plaquette and tree-level improved Symanzik gauge theories using the technique of Numerical Stochastic Perturbation Theory. This allows us to investigate the behavior of the perturbative series at high orders. We observe differences in the behavior of perturbative coefficients as a function of the loop order. Up to n=20 we do not see evidence for the often assumed factorial growth of the coefficients. Based on the observed behavior we sum this series in a model with hypergeometric functions. Alternatively we estimate the series in boosted perturbation theory. Subtracting the estimated perturbative series for the average plaquette from the non-perturbative Monte Carlo result we estimate the gluon condensate. (orig.)

  7. Numerical study of thermal test of a cask of transportation for radioactive material

    International Nuclear Information System (INIS)

    Vieira, Tiago A.S.; Santos, André A.C. dos; Vidal, Guilherme A.M.; Silva Junior, Geraldo E.

    2017-01-01

    In this study numerical simulations of a transport cask for radioactive material were made and the numerical results were compared with experimental results of tests carried out in two different opportunities. A mesh study was also made regarding the previously designed geometry of the same cask, in order to evaluate its impact in relation to the stability of numerical results for this type of problem. The comparison of the numerical and experimental results allowed to evaluate the need to plan and carry out a new test in order to validate the CFD codes used in the numerical simulations

  8. Transportation package design using numerical optimization

    International Nuclear Information System (INIS)

    Harding, D.C.; Witkowski, W.R.

    1993-01-01

    Since the design of transportation packages involves a complex coupling of structural, thermal and radiation shielding analyses and must follow very strict design constraints, numerical optimization provides the potential for more efficient container designs. In numerical optimization, the requirements of the design problem are mathematically formulated through the use of an objective function and constraints. The objective function(s), e.g., package weight, cost, volume, or combination thereof, is the function to be minimized or maximized by altering a set of design variables that define the package's shape and dimensions. Constraints are limitations on the performance of the system, such as resisting structural and thermal accident environments. Two constraints defined for an example wire mesh composite Type B package are: 1) deformation in the containment vessel seal region remains small enough throughout the 10 CFR-71 accident conditions to meet containment criteria, and 2) the elastomeric seal region remains below its operational temperature limit to guarantee seal integrity in the fire environment. The first constraint of a minimum energy absorbing layer thickness is evaluated with finite element analyses of the proposed dynamic crush accident criteria. The second constraint is evaluated with a 1-D transient thermal finite difference code parametrized for variable composite layer thicknesses, and is integrated with the optimization process. (J.P.N.)

  9. Perturbation theory and collision probability formalism. Vol. 2

    Energy Technology Data Exchange (ETDEWEB)

    Nasr, M [National Center for Nuclear Safety and Radiation Control, Atomic Energy Authority, Cairo (Egypt)

    1996-03-01

    Perturbation theory is commonly used in evaluating the activity effects, particularly those resulting from small and localized perturbation in multiplying media., e.g. in small sample reactivity measurements. The Boltzmann integral transport equation is generally used for evaluating the direct and adjoint fluxes in the heterogenous lattice cells to be used in the perturbation equations. When applying perturbation theory in this formalism, a term involving the perturbation effects on the special transfer kernel arises. This term is difficult to evaluate correctly, since it involves an integration all over the entire system. The main advantage of the perturbation theory which is the limitation of the integration procedure on the perturbation region is found to be of no practical use in such cases. In the present work, the perturbation equation in the collision probability formalism is analyzed. A mathematical treatment of the term in question is performed. A new mathematical expression for this term is derived. The new expression which can be estimated easily is derived.

  10. Fractional diffusion models of nonlocal transport

    International Nuclear Information System (INIS)

    Castillo-Negrete, D. del

    2006-01-01

    A class of nonlocal models based on the use of fractional derivatives (FDs) is proposed to describe nondiffusive transport in magnetically confined plasmas. FDs are integro-differential operators that incorporate in a unified framework asymmetric non-Fickian transport, non-Markovian ('memory') effects, and nondiffusive scaling. To overcome the limitations of fractional models in unbounded domains, we use regularized FDs that allow the incorporation of finite-size domain effects, boundary conditions, and variable diffusivities. We present an α-weighted explicit/implicit numerical integration scheme based on the Grunwald-Letnikov representation of the regularized fractional diffusion operator in flux conserving form. In sharp contrast with the standard diffusive model, the strong nonlocality of fractional diffusion leads to a linear in time response for a decaying pulse at short times. In addition, an anomalous fractional pinch is observed, accompanied by the development of an uphill transport region where the 'effective' diffusivity becomes negative. The fractional flux is in general asymmetric and, for steady states, it has a negative (toward the core) component that enhances confinement and a positive component that increases toward the edge and leads to poor confinement. The model exhibits the characteristic anomalous scaling of the confinement time, τ, with the system's size, L, τ∼L α , of low-confinement mode plasma where 1<α<2 is the order of the FD operator. Numerical solutions of the model with an off-axis source show that the fractional inward transport gives rise to profile peaking reminiscent of what is observed in tokamak discharges with auxiliary off-axis heating. Also, cold-pulse perturbations to steady sates in the model exhibit fast, nondiffusive propagation phenomena that resemble perturbative experiments

  11. Perturbation Solutions of the Quintic Duffing Equation with Strong Nonlinearities

    Directory of Open Access Journals (Sweden)

    Mehmet Pakdemirli

    Full Text Available The quintic Duffing equation with strong nonlinearities is considered. Perturbation solutions are constructed using two different techniques: The classical multiple scales method (MS and the newly developed multiple scales Lindstedt Poincare method (MSLP. The validity criteria for admissible solutions are derived. Both approximate solutions are contrasted with the numerical solutions. It is found that MSLP provides compatible solution with the numerical solution for strong nonlinearities whereas MS solution fail to produce physically acceptable solution for large perturbation parameters.

  12. A perturbed martingale approach to global optimization

    Energy Technology Data Exchange (ETDEWEB)

    Sarkar, Saikat [Computational Mechanics Lab, Department of Civil Engineering, Indian Institute of Science, Bangalore 560012 (India); Roy, Debasish, E-mail: royd@civil.iisc.ernet.in [Computational Mechanics Lab, Department of Civil Engineering, Indian Institute of Science, Bangalore 560012 (India); Vasu, Ram Mohan [Department of Instrumentation and Applied Physics, Indian Institute of Science, Bangalore 560012 (India)

    2014-08-01

    A new global stochastic search, guided mainly through derivative-free directional information computable from the sample statistical moments of the design variables within a Monte Carlo setup, is proposed. The search is aided by imparting to the directional update term additional layers of random perturbations referred to as ‘coalescence’ and ‘scrambling’. A selection step, constituting yet another avenue for random perturbation, completes the global search. The direction-driven nature of the search is manifest in the local extremization and coalescence components, which are posed as martingale problems that yield gain-like update terms upon discretization. As anticipated and numerically demonstrated, to a limited extent, against the problem of parameter recovery given the chaotic response histories of a couple of nonlinear oscillators, the proposed method appears to offer a more rational, more accurate and faster alternative to most available evolutionary schemes, prominently the particle swarm optimization. - Highlights: • Evolutionary global optimization is posed as a perturbed martingale problem. • Resulting search via additive updates is a generalization over Gateaux derivatives. • Additional layers of random perturbation help avoid trapping at local extrema. • The approach ensures efficient design space exploration and high accuracy. • The method is numerically assessed via parameter recovery of chaotic oscillators.

  13. Numerical Modelling of Suspended Transport and Deposition of Highway Deposited Sediments

    DEFF Research Database (Denmark)

    Bentzen, Thomas Ruby; Larsen, Torben; Bach, Christine

    Good data for calibration and validation of numerical models are of high importance. In the natural environment data can be hard to archive and the stochastic nature have governing influence on the data archived. Hence for modelling of suspended transport and deposition of particles, originating ...... from the highway surfaces, in highway detention ponds, four experiments are carried out. To simplify the complexity of a real pond and for easy control and measurement the sediment transports where carried out in two rectangular channels....

  14. New numerical method for solving the solute transport equation

    International Nuclear Information System (INIS)

    Ross, B.; Koplik, C.M.

    1978-01-01

    The solute transport equation can be solved numerically by approximating the water flow field by a network of stream tubes and using a Green's function solution within each stream tube. Compared to previous methods, this approach permits greater computational efficiency and easier representation of small discontinuities, and the results are easier to interpret physically. The method has been used to study hypothetical sites for disposal of high-level radioactive waste

  15. Evolution of nonlinear perturbations inside Einstein-Yang-Mills black holes

    International Nuclear Information System (INIS)

    Donets, E.E.; Tentyukov, M.N.; Tsulaya, M.M.

    1998-01-01

    We present our results on numerical study of evolution of nonlinear perturbations inside spherically symmetric black holes in the SU(2) Einstein-Yang-Mills (EYM) theory. Recent developments demonstrate a new type of the behaviour of the metric for EYM black hole interiors; the generic metric exhibits an infinitely oscillating approach to the singularity, which is a spacelike but not of the mixmaster type. The evolution of various types of spherically symmetric perturbations, propagating from the internal vicinity of the external horizon towards the singularity is investigated in a self-consistent way using an adaptive numerical algorithm. The obtained results give strong numerical evidence in favor of nonlinear stability of the generic EYM black hole interiors. Alternatively, the EYM black hole interiors of S (schwarzschild)-type, which form only a zero measure subset in the space of all internal solutions are found to be unstable and transform to the generic type as perturbations are developed

  16. Wilson loops in very high order lattice perturbation theory

    International Nuclear Information System (INIS)

    Ilgenfritz, E.M.; Nakamura, Y.; Perlt, H.; Schiller, A.; Rakow, P.E.L.; Schierholz, G.; Regensburg Univ.

    2009-10-01

    We calculate Wilson loops of various sizes up to loop order n=20 for lattice sizes of L 4 (L=4,6,8,12) using the technique of Numerical Stochastic Perturbation Theory in quenched QCD. This allows to investigate the behaviour of the perturbative series at high orders. We discuss three models to estimate the perturbative series: a renormalon inspired fit, a heuristic fit based on an assumed power-law singularity and boosted perturbation theory. We have found differences in the behavior of the perturbative series for smaller and larger Wilson loops at moderate n. A factorial growth of the coefficients could not be confirmed up to n=20. From Monte Carlo measured plaquette data and our perturbative result we estimate a value of the gluon condensate left angle (α)/(π)GG right angle. (orig.)

  17. Travelling wave solutions for a singularly perturbed Burgers–KdV ...

    Indian Academy of Sciences (India)

    This paper concerns with the existence problem of travelling wave solutions to a singularly perturbed Burgers–KdV equation. For this, we use the dynamical systems approach, specifically, the geometric singular perturbation theory and centre manifold theory. We also numerically show approximations, in particular, for ...

  18. Transversal magnetotransport in Weyl semimetals: Exact numerical approach

    Science.gov (United States)

    Behrends, Jan; Kunst, Flore K.; Sbierski, Björn

    2018-02-01

    Magnetotransport experiments on Weyl semimetals are essential for investigating the intriguing topological and low-energy properties of Weyl nodes. If the transport direction is perpendicular to the applied magnetic field, experiments have shown a large positive magnetoresistance. In this work we present a theoretical scattering matrix approach to transversal magnetotransport in a Weyl node. Our numerical method confirms and goes beyond the existing perturbative analytical approach by treating disorder exactly. It is formulated in real space and is applicable to mesoscopic samples as well as in the bulk limit. In particular, we study the case of clean and strongly disordered samples.

  19. Plasmodium falciparum chloroquine resistance transporter (PfCRT) isoforms PH1 and PH2 perturb vacuolar physiology.

    Science.gov (United States)

    Callaghan, Paul S; Siriwardana, Amila; Hassett, Matthew R; Roepe, Paul D

    2016-03-31

    Recent work has perfected yeast-based methods for measuring drug transport by the Plasmodium falciparum chloroquine (CQ) resistance transporter (PfCRT). The approach relies on inducible heterologous expression of PfCRT in Saccharomyces cerevisiae yeast. In these experiments selecting drug concentrations are not toxic to the yeast, nor is expression of PfCRT alone toxic. Only when PfCRT is expressed in the presence of CQ is the growth of yeast impaired, due to inward transport of chloroquine (CQ) via the transporter. During analysis of all 53 known naturally occurring PfCRT isoforms, two isoforms (PH1 and PH2 PfCRT) were found to be intrinsically toxic to yeast, even in the absence of CQ. Additional analysis of six very recently identified PfCRT isoforms from Malaysia also showed some toxicity. In this paper the nature of this yeast toxicity is examined. Data also show that PH1 and PH2 isoforms of PfCRT transport CQ with an efficiency intermediate to that catalyzed by previously studied CQR conferring isoforms. Mutation of PfCRT at position 160 is found to perturb vacuolar physiology, suggesting a fitness cost to position 160 amino acid substitutions. These data further define the wide range of activities that exist for PfCRT isoforms found in P. falciparum isolates from around the globe.

  20. Numerical modelling of ion transport in flames

    KAUST Repository

    Han, Jie

    2015-10-20

    This paper presents a modelling framework to compute the diffusivity and mobility of ions in flames. The (n, 6, 4) interaction potential is adopted to model collisions between neutral and charged species. All required parameters in the potential are related to the polarizability of the species pair via semi-empirical formulas, which are derived using the most recently published data or best estimates. The resulting framework permits computation of the transport coefficients of any ion found in a hydrocarbon flame. The accuracy of the proposed method is evaluated by comparing its predictions with experimental data on the mobility of selected ions in single-component neutral gases. Based on this analysis, the value of a model constant available in the literature is modified in order to improve the model\\'s predictions. The newly determined ion transport coefficients are used as part of a previously developed numerical approach to compute the distribution of charged species in a freely propagating premixed lean CH4/O2 flame. Since a significant scatter of polarizability data exists in the literature, the effects of changes in polarizability on ion transport properties and the spatial distribution of ions in flames are explored. Our analysis shows that changes in polarizability propagate with decreasing effect from binary transport coefficients to species number densities. We conclude that the chosen polarizability value has a limited effect on the ion distribution in freely propagating flames. We expect that the modelling framework proposed here will benefit future efforts in modelling the effect of external voltages on flames. Supplemental data for this article can be accessed at http://dx.doi.org/10.1080/13647830.2015.1090018. © 2015 Taylor & Francis.

  1. Inhibition of serotonin but not norepinephrine transport during development produces delayed, persistent perturbations of emotional behaviors in mice.

    Science.gov (United States)

    Ansorge, Mark S; Morelli, Emanuela; Gingrich, Jay A

    2008-01-02

    Serotonin (5-HT) acts as a neurotransmitter, but also modulates brain maturation during early development. The demonstrated influence of genetic variants on brain function, personality traits, and susceptibility to neuropsychiatric disorders suggests a critical importance of developmental mechanisms. However, little is known about how and when developmentally perturbed 5-HT signaling affects circuitry and resulting behavior. The 5-HT transporter (5-HTT) is a key regulator of extracellular 5-HT levels and we used pharmacologic strategies to manipulate 5-HTT function during development and determine behavioral consequences. Transient exposure to the 5-HTT inhibitors fluoxetine, clomipramine, and citalopram from postnatal day 4 (P4) to P21 produced abnormal emotional behaviors in adult mice. Similar treatment with the norepinephrine transporter (NET) inhibitor, desipramine, did not adversely affect adult behavior, suggesting that 5-HT and norepinephrine (NE) do not share the same effects on brain development. Shifting our period of treatment/testing to P90/P185 failed to mimic the effect of earlier exposure, demonstrating that 5-HT effects on adult behavior are developmentally specific. We have hypothesized that early-life perturbations of 5-HT signaling affect corticolimbic circuits that do not reach maturity until the peri-adolescent period. In support of this idea, we found that abnormal behaviors resulting from postnatal fluoxetine exposure have a post-pubescent onset and persist long after reaching adult age. A better understanding of the underlying 5-HT sensitive circuits and how they are perturbed should lead to new insights into how various genetic polymorphisms confer their risk to carriers. Furthermore, these studies should help determine whether in utero exposure to 5-HTT blocking drugs poses a risk for behavioral abnormalities in later life.

  2. Extended numerical modeling of impurity neoclassical transport in tokamak edge plasmas

    International Nuclear Information System (INIS)

    Inoue, H.; Yamoto, S.; Hatayama, A.; Homma, Y.

    2016-01-01

    Understanding of impurity transport in tokamaks is an important issue in order to reduce the impurity contamination in fusion core plasmas. Recently, a new kinetic numerical scheme of impurity classical/neoclassical transport has been developed. This numerical scheme makes it possible to include classical self-diffusion (CL SD), classical inward pinch (CL IWP), and classical temperature screening effect (CL TSE) of impurity ions. However, impurity neoclassical transport has been modeled only in the case where background plasmas are in the Pfirsch-Schluter (PS) regime. The purpose of this study is to extend our previous model to wider range of collisionality regimes, i.e., not only the PS regime, but also the plateau regime. As in the previous study, a kinetic model with Binary Collision Monte-Carlo Model (BMC) has been adopted. We focus on the modeling of the neoclassical self-diffusion (NC SD) and the neoclassical inward pinch (NC IWP). In order to simulate the neoclassical transport with the BCM, velocity distribution of background plasma ions has been modeled as a deformed Maxwell distribution which includes plasma density gradient. Some test simulations have been done. As for NC SD of impurity ions, our scheme reproduces the dependence on the collisionality parameter in wide range of collisionality regime. As for NC IWP, in cases where test impurity ions and background ions are in the PS and plateau regimes, parameter dependences have been reproduced. (copyright 2016 WILEY-VCH Verlag GmbH and Co. KGaA, Weinheim)

  3. Extended numerical modeling of impurity neoclassical transport in tokamak edge plasmas

    Energy Technology Data Exchange (ETDEWEB)

    Inoue, H.; Yamoto, S.; Hatayama, A. [Graduate School of Science and Technology, Keio University, Hiyoshi, Yokohama (Japan); Homma, Y. [Graduate School of Science and Technology, Keio University, Hiyoshi, Yokohama (Japan); Research Fellow of Japan Society for the Promotion of Science, Tokyo (Japan)

    2016-08-15

    Understanding of impurity transport in tokamaks is an important issue in order to reduce the impurity contamination in fusion core plasmas. Recently, a new kinetic numerical scheme of impurity classical/neoclassical transport has been developed. This numerical scheme makes it possible to include classical self-diffusion (CL SD), classical inward pinch (CL IWP), and classical temperature screening effect (CL TSE) of impurity ions. However, impurity neoclassical transport has been modeled only in the case where background plasmas are in the Pfirsch-Schluter (PS) regime. The purpose of this study is to extend our previous model to wider range of collisionality regimes, i.e., not only the PS regime, but also the plateau regime. As in the previous study, a kinetic model with Binary Collision Monte-Carlo Model (BMC) has been adopted. We focus on the modeling of the neoclassical self-diffusion (NC SD) and the neoclassical inward pinch (NC IWP). In order to simulate the neoclassical transport with the BCM, velocity distribution of background plasma ions has been modeled as a deformed Maxwell distribution which includes plasma density gradient. Some test simulations have been done. As for NC SD of impurity ions, our scheme reproduces the dependence on the collisionality parameter in wide range of collisionality regime. As for NC IWP, in cases where test impurity ions and background ions are in the PS and plateau regimes, parameter dependences have been reproduced. (copyright 2016 WILEY-VCH Verlag GmbH and Co. KGaA, Weinheim)

  4. Effects of 3D Magnetic Perturbations on Toroidal Plasmas

    International Nuclear Information System (INIS)

    Callen, J.D.

    2010-01-01

    Full text: To lowest order tokamaks are two-dimensional (2D) axisymmetric magnetic systems. But small 3D magnetic perturbations (both externally applied and from plasma instabilities) have many interesting and useful effects on tokamak (and quasi-symmetric stellarator) plasmas. Plasma transport equations that include these effects, especially on diamagnetic-level toroidal plasma rotation, have recently been developed. The 3D magnetic perturbations and their plasma effects can be classified according to their toroidal mode number n: low n (1 to 5) resonant (q = m/n in plasma) and non-resonant fields, medium n (due to toroidal field ripple), and high n (due to microturbulence). This paper concentrates on low and medium n perturbations. Low n non-resonant magnetic fields induce a neoclassical toroidal viscosity (NTV) that damps toroidal plasma rotation throughout the plasma toward an offset flow in the counter-I p direction; recent tokamak experiments have confirmed and exploited these predictions by applying external low n non-resonant magnetic perturbations. Medium n perturbations have similar effects plus possible ripple trapping and resultant edge ion losses. A low n resonant magnetic field induces a toroidal plasma torque in the vicinity of the rational surface; when large enough it can stop plasma rotation there and lead to a locked mode, which often causes a plasma disruption. Externally applied 3D magnetic perturbations usually have many components; in the plasma their lowest n components are amplified by plasma responses, particularly at high beta. Low n plasma instabilities (e.g., NTMs, RWMs) cause additional 3D magnetic perturbations in tokamak plasmas; tearing modes can bifurcate the topology and form magnetic islands. Finally, multiple resonant magnetic perturbations (RMPs) can cause local magnetic stochasticity and influence H-mode edge pedestal transport. These various effects of 3D magnetic perturbations can be used to control the toroidal plasma

  5. New evidence and impact of electron transport non-linearities based on new perturbative inter-modulation analysis

    Science.gov (United States)

    van Berkel, M.; Kobayashi, T.; Igami, H.; Vandersteen, G.; Hogeweij, G. M. D.; Tanaka, K.; Tamura, N.; Zwart, H. J.; Kubo, S.; Ito, S.; Tsuchiya, H.; de Baar, M. R.; LHD Experiment Group

    2017-12-01

    A new methodology to analyze non-linear components in perturbative transport experiments is introduced. The methodology has been experimentally validated in the Large Helical Device for the electron heat transport channel. Electron cyclotron resonance heating with different modulation frequencies by two gyrotrons has been used to directly quantify the amplitude of the non-linear component at the inter-modulation frequencies. The measurements show significant quadratic non-linear contributions and also the absence of cubic and higher order components. The non-linear component is analyzed using the Volterra series, which is the non-linear generalization of transfer functions. This allows us to study the radial distribution of the non-linearity of the plasma and to reconstruct linear profiles where the measurements were not distorted by non-linearities. The reconstructed linear profiles are significantly different from the measured profiles, demonstrating the significant impact that non-linearity can have.

  6. Numerical solution of the radionuclide transport equation

    International Nuclear Information System (INIS)

    Hadermann, J.; Roesel, F.

    1983-11-01

    A numerical solution of the one-dimensional geospheric radionuclide chain transport equation based on the pseudospectral method is developed. The advantages of this approach are flexibility in incorporating space and time dependent migration parameters, arbitrary boundary conditions and solute rock interactions as well as efficiency and reliability. As an application the authors investigate the impact of non-linear sorption isotherms on migration in crystalline rock. It is shown that non-linear sorption, in the present case a Freundlich isotherm, may reduce concentration at the geosphere outlet by orders of magnitude provided the migration time is comparable or larger than the half-life of the nuclide in question. The importance of fixing dispersivity within the continuum approach is stressed. (Auth.)

  7. A numerical solution of the coupled proton-H atom transport equations for the proton aurora

    International Nuclear Information System (INIS)

    Basu, B.; Jasperse, J.R.; Grossbard, N.J.

    1990-01-01

    A numerical code has been developed to solve the coupled proton-H atom linear transport equations for the proton aurora. The transport equations have been simplified by using plane-parallel geometry and the forward-scattering approximations only. Otherwise, the equations and their numerical solutions are exact. Results are presented for the particle fluxes and the energy deposition rates, and they are compared with the previous analytical results that were obtained by using additional simplifying approximations. It is found that although the analytical solutions for the particle fluxes differ somewhat from the numerical solutions, the energy deposition rates calculated by the two methods agree to within a few percent. The accurate particle fluxes given by the numerical code are useful for accurate calculation of the characteristic quantities of the proton aurora, such as the ionization rates and the emission rates

  8. An analytically-based method for rapid evaluation of MeV ion loss in tokamaks with low-n perturbations

    International Nuclear Information System (INIS)

    Mynick, H.E.

    1993-01-01

    Recent work has developed an analytic theory for the stochastic transport of passing MeV ions due to low-n magnetic perturbations, valid for frequencies from ω = 0 to ω ∼ ω TAE ∼ 100 kHz, and for modes with multiple harmonics and nontrivial radial structure, which predicts stochastic thresholds in agreement with guiding-center (GC) results. Obtaining GC results is time consuming, typically requiring hours of computer time to obtain loss results for a single point in parameter space. Along with earlier theory developed for the stochastic transport of trapped particles in such perturbations, this theory gives the basis for a far more rapid means of numerically assessing energetic ion loss in a given configuration, somewhat akin to the RIPLOS code for rapid evaluation of loss due to TF ripple. The authors present the details of implementing such a code, now being developed. The implementation also raises some further theoretical issues. The currently available stochastic thresholds for passing and trapped particles are not the same, and an analytic understanding of the transition between them awaits development

  9. Multicomponent mass transport model: theory and numerical implementation (discrete-parcel-random-walk version)

    International Nuclear Information System (INIS)

    Ahlstrom, S.W.; Foote, H.P.; Arnett, R.C.; Cole, C.R.; Serne, R.J.

    1977-05-01

    The Multicomponent Mass Transfer (MMT) Model is a generic computer code, currently in its third generation, that was developed to predict the movement of radiocontaminants in the saturated and unsaturated sediments of the Hanford Site. This model was designed to use the water movement patterns produced by the unsaturated and saturated flow models coupled with dispersion and soil-waste reaction submodels to predict contaminant transport. This report documents the theorical foundation and the numerical solution procedure of the current (third) generation of the MMT Model. The present model simulates mass transport processes using an analog referred to as the Discrete-Parcel-Random-Walk (DPRW) algorithm. The basic concepts of this solution technique are described and the advantages and disadvantages of the DPRW scheme are discussed in relation to more conventional numerical techniques such as the finite-difference and finite-element methods. Verification of the numerical algorithm is demonstrated by comparing model results with known closed-form solutions. A brief error and sensitivity analysis of the algorithm with respect to numerical parameters is also presented. A simulation of the tritium plume beneath the Hanford Site is included to illustrate the use of the model in a typical application. 32 figs

  10. Prospects of inflation with perturbed throat geometry

    International Nuclear Information System (INIS)

    Ali, Amna; Chingangbam, R.; Panda, Sudhakar; Sami, M.

    2009-01-01

    We study brane inflation in a warped deformed conifold background that includes general possible corrections to the throat geometry sourced by coupling to the bulk of a compact Calabi-Yau space. We focus specifically, on the perturbation by chiral operator of dimension 3/2 in the CFT. We find that the effective potential in this case can give rise to required number of e-foldings and the spectral index n S consistent with observation. The tensor to scalar ratio of perturbations is generally very low in this scenario. The COBE normalization, however, poses certain difficulties which can be circumvented provided model parameters are properly fine tuned. We find the numerical values of parameters which can give rise to enough inflation, observationally consistent values of density perturbations, scalar to tensor ratio of perturbations and the spectral index n S .

  11. On modelling adiabatic N-soliton interactions and perturbations. Effects of external potentials

    International Nuclear Information System (INIS)

    Gerdjikov, V.; Baizakov, B.

    2005-01-01

    We analyze several perturbed versions of the complex Toda chain (CTC) in an attempt to describe the adiabatic N-soliton train interactions of the perturbed nonlinear Schrodinger equation (NLS). Particular types of perturbations, including quadratic and periodic external potentials are treated by both analytical and numerical means. We show that the perturbed CTC model provides a good description for the N-soliton interactions in the presence of a weak external potential. (authors)

  12. Theoretical and Numerical Modeling of Transport of Land Use-Specific Fecal Source Identifiers

    Science.gov (United States)

    Bombardelli, F. A.; Sirikanchana, K. J.; Bae, S.; Wuertz, S.

    2008-12-01

    Microbial contamination in coastal and estuarine waters is of particular concern to public health officials. In this work, we advocate that well-formulated and developed mathematical and numerical transport models can be combined with modern molecular techniques in order to predict continuous concentrations of microbial indicators under diverse scenarios of interest, and that they can help in source identification of fecal pollution. As a proof of concept, we present initially the theory, numerical implementation and validation of one- and two-dimensional numerical models aimed at computing the distribution of fecal source identifiers in water bodies (based on Bacteroidales marker DNA sequences) coming from different land uses such as wildlife, livestock, humans, dogs or cats. These models have been developed to allow for source identification of fecal contamination in large bodies of water. We test the model predictions using diverse velocity fields and boundary conditions. Then, we present some preliminary results of an application of a three-dimensional water quality model to address the source of fecal contamination in the San Pablo Bay (SPB), United States, which constitutes an important sub-embayment of the San Francisco Bay. The transport equations for Bacteroidales include the processes of advection, diffusion, and decay of Bacteroidales. We discuss the validation of the developed models through comparisons of numerical results with field campaigns developed in the SPB. We determine the extent and importance of the contamination in the bay for two decay rates obtained from field observations, corresponding to total host-specific Bacteroidales DNA and host-specific viable Bacteroidales cells, respectively. Finally, we infer transport conditions in the SPB based on the numerical results, characterizing the fate of outflows coming from the Napa, Petaluma and Sonoma rivers.

  13. MCNP perturbation technique for criticality analysis

    International Nuclear Information System (INIS)

    McKinney, G.W.; Iverson, J.L.

    1995-01-01

    The differential operator perturbation technique has been incorporated into the Monte Carlo N-Particle transport code MCNP and will become a standard feature of future releases. This feature includes first and/or second order terms of the Taylor Series expansion for response perturbations related to cross-section data (i.e., density, composition, etc.). Criticality analyses can benefit from this technique in that predicted changes in the track-length tally estimator of K eff may be obtained for multiple perturbations in a single run. A key advantage of this method is that a precise estimate of a small change in response (i.e., < 1%) is easily obtained. This technique can also offer acceptable accuracy, to within a few percent, for up to 20-30% changes in a response

  14. Approximate damped oscillatory solutions and error estimates for the perturbed Klein–Gordon equation

    International Nuclear Information System (INIS)

    Ye, Caier; Zhang, Weiguo

    2015-01-01

    Highlights: • Analyze the dynamical behavior of the planar dynamical system corresponding to the perturbed Klein–Gordon equation. • Present the relations between the properties of traveling wave solutions and the perturbation coefficient. • Obtain all explicit expressions of approximate damped oscillatory solutions. • Investigate error estimates between exact damped oscillatory solutions and the approximate solutions and give some numerical simulations. - Abstract: The influence of perturbation on traveling wave solutions of the perturbed Klein–Gordon equation is studied by applying the bifurcation method and qualitative theory of dynamical systems. All possible approximate damped oscillatory solutions for this equation are obtained by using undetermined coefficient method. Error estimates indicate that the approximate solutions are meaningful. The results of numerical simulations also establish our analysis

  15. Steady-state transport equation resolution by particle methods, and numerical results

    International Nuclear Information System (INIS)

    Mercier, B.

    1985-10-01

    A method to solve steady-state transport equation has been given. Principles of the method are given. The method is studied in two different cases; estimations given by the theory are compared to numerical results. Results got in 1-D (spherical geometry) and in 2-D (axisymmetric geometry) are given [fr

  16. Vectorization and parallelization of a numerical scheme for 3D global atmospheric transport-chemistry problems

    NARCIS (Netherlands)

    E.J. Spee (Edwin); P.M. de Zeeuw (Paul); J.G. Verwer (Jan); J.G. Blom (Joke); W. Hundsdorfer (Willem)

    1996-01-01

    textabstractAtmospheric air quality modeling relies in part on numerical simulation. Required numerical simulations are often hampered by lack of computer capacity and computational speed. This problem is most severe in the field of global modeling where transport and exchange of trace constituents

  17. Numerical simulation of the anomalous transport at the plasma-edge

    International Nuclear Information System (INIS)

    Pohn, E.

    2001-03-01

    In addition to the classical transport which is caused by Coloumb-collisions two further transport mechanisms take place in an inhomogeneous magnetically confined thermonuclear fusion-plasma, the neoclassical and the anomalous transport. The anomalous transport is caused by collective motion of the plasma-particles respectively turbulence and essentially affects the energy-confinement-time of the plasma. The energy-confinement-time in turn constitutes an important criterion with respect to the feasibility of using nuclear fusion for energy production. The anomalous transport is theoretically not yet well understood. By means of numerical simulations of the anomalous transport in the plasma edge, it is the intention of this work to contribute to the understanding of this transport mechanism. The Vlasov-Poisson-system constitutes the starting point for all performed simulations. This system consists of kinetic equations, which model for each particle-species the motion of the particles composing the plasma in six-dimensional phase-space. A coupling of these kinetic equations occurs due to the Poisson-equation, resulting in a nonlinear system of differential equations. The time evolution of this system was calculated numerically. On the one hand, simulations were performed where the whole velocity-space was retained. This fully-kinetic model was applied for the spatially one- as well as two-dimensional case. In the one-dimensional case only the radial direction of the plasma-edge was modeled, i.e. the direction along which the plasma joins to the vacuum. When performing the spatially two-dimensional simulations, in addition the poloidal direction has been regarded. A second set of simulations was performed using a gyro-kinetic model. In this model only the velocity-component parallel to the magnetic field vector is retained. The components perpendicular to the magnetic field vector, which are responsible for the gyration of particles, are omitted from phase-space but

  18. Numerical Solution of the Electron Transport Equation in the Upper Atmosphere

    Energy Technology Data Exchange (ETDEWEB)

    Woods, Mark Christopher [Sandia National Lab. (SNL-NM), Albuquerque, NM (United States); Holmes, Mark [Rensselaer Polytechnic Inst., Troy, NY (United States); Sailor, William C [Sandia National Lab. (SNL-NM), Albuquerque, NM (United States)

    2017-07-01

    A new approach for solving the electron transport equation in the upper atmosphere is derived. The problem is a very stiff boundary value problem, and to obtain an accurate numerical solution, matrix factorizations are used to decouple the fast and slow modes. A stable finite difference method is applied to each mode. This solver is applied to a simplifieed problem for which an exact solution exists using various versions of the boundary conditions that might arise in a natural auroral display. The numerical and exact solutions are found to agree with each other to at least two significant digits.

  19. Asymptotic solutions of numerical transport problems in optically thick, diffusive regimes II

    International Nuclear Information System (INIS)

    Larsen, E.W.; Morel, J.E.

    1989-01-01

    In a recent article (Larsen, Morel, and Miller, J. Comput. Phys. 69, 283 (1987)), a theoretical method is described for assessing the accuracy of transport differencing schemes in highly scattering media with optically thick spatial meshes. In the present article, this method is extended to enable one to determine the accuracy of such schemes in the presence of numerically unresolved boundary layers. Numerical results are presented that demonstrate the validity and accuracy of our analysis. copyright 1989 Academic Press, Inc

  20. Controlling chaos in low and high dimensional systems with periodic parametric perturbations

    International Nuclear Information System (INIS)

    Mirus, K.A.; Sprott, J.C.

    1998-06-01

    The effect of applying a periodic perturbation to an accessible parameter of various chaotic systems is examined. Numerical results indicate that perturbation frequencies near the natural frequencies of the unstable periodic orbits of the chaotic systems can result in limit cycles for relatively small perturbations. Such perturbations can also control or significantly reduce the dimension of high-dimensional systems. Initial application to the control of fluctuations in a prototypical magnetic fusion plasma device will be reviewed

  1. Theory of Perturbed Equilibria for Solving the Grad-Shafranov Equation

    International Nuclear Information System (INIS)

    Pletzer, A.; Zakharov, L.E.

    1999-01-01

    The theory of perturbed magnetohydrodynamic equilibria is presented for different formulations of the tokamak equilibrium problem. For numerical codes, it gives an explicit Newton scheme for solving the Grad-Shafranov equation subject to different constraints. The problem of stability of axisymmetric modes is shown to be a particular case of the equilibrium perturbation theory

  2. Non-perturbative calculation of equilibrium polarization of stored electron beams

    International Nuclear Information System (INIS)

    Yokoya, Kaoru.

    1992-05-01

    Stored electron/positron beams polarize spontaneously owing to the spin-flip synchrotron radiation. In the existing computer codes, the degree of the equilibrium polarization has been calculated using perturbation expansions in terms of the orbital oscillation amplitudes. In this paper a new numerical method is presented which does not employ the perturbation expansion. (author)

  3. In what sense the canonical perturbation theory is gauge-invariant

    International Nuclear Information System (INIS)

    Chen, C.Y.

    1992-07-01

    It is shown that the time-dependent canonical perturbation theory in classical mechanics has unsatisfactory features when dealing with electromagnetic perturbed fields (the perturbed vector potential A-tilde ≠ 0). As a numerical apparatus, the theory relates to gauge-dependent vectors larger than expected. As an analytic apparatus, the theory is involved in unphysical concepts and yields inherently non-gauge-invariant formalisms. By defining the root cause of the problem, an alternative approach is accordingly introduced. (author). 8 refs, 2 figs

  4. Development of Numerical Grids for UZ Flow and Transport Modeling

    International Nuclear Information System (INIS)

    P. Dobson

    2003-01-01

    This Scientific Analysis report describes the methods used to develop numerical grids of the unsaturated hydrogeologic system beneath Yucca Mountain. Numerical grid generation is an integral part of the development of the Unsaturated Zone Flow and Transport Model (UZ Model), a complex, three-dimensional (3-D) model of Yucca Mountain. This revision incorporates changes made to both the geologic framework model and the proposed repository layout. The resulting numerical grids, developed using current geologic, hydrogeologic, and mineralogic data, provide the necessary framework to: (1) develop calibrated hydrogeologic property sets and flow fields, (2) test conceptual hypotheses of flow and transport, and (3) predict flow and transport behavior under a variety of climatic and thermal-loading conditions. The technical scope, content, and management of this Scientific Analysis report was initially controlled by the planning document, ''Technical Work Plan (TWP) for: Unsaturated Zone Sections of License Application Chapters 8 and 12'' (BSC 2002 [159051], Section 1.6.4). This TWP was later superseded by ''Technical Work Plan for: Performance Assessment Unsaturated Zone'' (BSC 2002 [160819]), which contains the Data Qualification Plan used to qualify the DTN: MO0212GWLSSPAX.000 [161271] (See Attachment IV). Grids generated and documented in this report supersede those documented in previous versions of this report (BSC 2001 [159356]). The constraints, assumptions, and limitations associated with this report are discussed in the appropriate sections that follow. There were no deviations from the TWP scope of work in this report. Two software packages not listed in Table IV-2 of the TWP (BSC 2002 [159051]), ARCINFO V7.2.1 (CRWMS M and O 2000 [157019]; USGS 2000 [148304]) and 2kgrid8.for V1.0 (LBNL 2002 [154787]), were utilized in the development of the numerical grids; the use of additional software is accounted for in the TWP (BSC 2002 [159051], Section 13). The use of

  5. Non-Perturbative Quantum Geometry III

    CERN Document Server

    Krefl, Daniel

    2016-08-02

    The Nekrasov-Shatashvili limit of the refined topological string on toric Calabi-Yau manifolds and the resulting quantum geometry is studied from a non-perturbative perspective. The quantum differential and thus the quantum periods exhibit Stockes phenomena over the combined string coupling and quantized Kaehler moduli space. We outline that the underlying formalism of exact quantization is generally applicable to points in moduli space featuring massless hypermultiplets, leading to non-perturbative band splitting. Our prime example is local P1xP1 near a conifold point in moduli space. In particular, we will present numerical evidence that in a Stockes chamber of interest the string based quantum geometry reproduces the non-perturbative corrections for the Nekrasov-Shatashvili limit of 4d supersymmetric SU(2) gauge theory at strong coupling found in the previous part of this series. A preliminary discussion of local P2 near the conifold point in moduli space is also provided.

  6. Effects of 3D magnetic perturbations on toroidal plasmas

    International Nuclear Information System (INIS)

    Callen, J.D.

    2011-01-01

    Small three-dimensional (3D) magnetic field perturbations have many interesting and possibly useful effects on tokamak and quasi-symmetric stellarator plasmas. Plasma transport equations that include these effects, most notably on diamagnetic-level toroidal plasma flows, have recently been developed. The 3D field perturbations and their plasma effects can be classified according to their toroidal mode number n: low n (say 1-5) resonant (with field line pitch, q = m/n) and non-resonant fields, medium n (∼20, due to toroidal field ripple) and high n (due to microturbulence). Low n non-resonant fields induce a neoclassical toroidal viscosity (NTV) that damps toroidal rotation throughout the plasma towards an offset rotation in the counter-current direction. Recent tokamak experiments have generally confirmed and exploited these predictions by applying external low n non-resonant magnetic perturbations. Medium n toroidal field ripple produces similar effects plus possible ripple-trapping NTV effects and ion direct losses in the edge. A low n (e.g. n = 1) resonant field is mostly shielded by the toroidally rotating plasma at and inside the resonant (rational) surface. If it is large enough it can stop plasma rotation at the rational surface, facilitate magnetic reconnection there and lead to a growing stationary magnetic island (locked mode), which often causes a plasma disruption. Externally applied 3D magnetic perturbations usually have many components. In the plasma their lowest n (e.g. n = 1) externally resonant components can be amplified by kink-type plasma responses, particularly at high β. Low n plasma instabilities (e.g. resistive wall modes, neoclassical tearing modes) cause additional 3D magnetic perturbations in tokamak plasmas. Tearing modes in their nonlinear (Rutherford) regime bifurcate the topology and form magnetic islands. Finally, multiple resonant magnetic perturbations (RMPs) can, if not shielded by plasma rotation effects, cause local magnetic

  7. Research on numerical simulation and protection of transient process in long-distance slurry transportation pipelines

    International Nuclear Information System (INIS)

    Lan, G; Jiang, J; Li, D D; Yi, W S; Zhao, Z; Nie, L N

    2013-01-01

    The calculation of water-hammer pressure phenomenon of single-phase liquid is already more mature for a pipeline of uniform characteristics, but less research has addressed the calculation of slurry water hammer pressure in complex pipelines with slurry flows carrying solid particles. In this paper, based on the developments of slurry pipelines at home and abroad, the fundamental principle and method of numerical simulation of transient processes are presented, and several boundary conditions are given. Through the numerical simulation and analysis of transient processes of a practical engineering of long-distance slurry transportation pipeline system, effective protection measures and operating suggestions are presented. A model for calculating the water impact of solid and fluid phases is established based on a practical engineering of long-distance slurry pipeline transportation system. After performing a numerical simulation of the transient process, analyzing and comparing the results, effective protection measures and operating advice are recommended, which has guiding significance to the design and operating management of practical engineering of longdistance slurry pipeline transportation system

  8. Research on numerical simulation and protection of transient process in long-distance slurry transportation pipelines

    Science.gov (United States)

    Lan, G.; Jiang, J.; Li, D. D.; Yi, W. S.; Zhao, Z.; Nie, L. N.

    2013-12-01

    The calculation of water-hammer pressure phenomenon of single-phase liquid is already more mature for a pipeline of uniform characteristics, but less research has addressed the calculation of slurry water hammer pressure in complex pipelines with slurry flows carrying solid particles. In this paper, based on the developments of slurry pipelines at home and abroad, the fundamental principle and method of numerical simulation of transient processes are presented, and several boundary conditions are given. Through the numerical simulation and analysis of transient processes of a practical engineering of long-distance slurry transportation pipeline system, effective protection measures and operating suggestions are presented. A model for calculating the water impact of solid and fluid phases is established based on a practical engineering of long-distance slurry pipeline transportation system. After performing a numerical simulation of the transient process, analyzing and comparing the results, effective protection measures and operating advice are recommended, which has guiding significance to the design and operating management of practical engineering of longdistance slurry pipeline transportation system.

  9. Numerical Integration of the Transport Equation For Infinite Homogeneous Media

    Energy Technology Data Exchange (ETDEWEB)

    Haakansson, Rune

    1962-01-15

    The transport equation for neutrons in infinite homogeneous media is solved by direct numerical integration. Accounts are taken to the anisotropy and the inelastic scattering. The integration has been performed by means of the trapezoidal rule and the length of the energy intervals are constant in lethargy scale. The machine used is a Ferranti Mercury computer. Results are given for water, heavy water, aluminium water mixture and iron-aluminium-water mixture.

  10. Numerical assessment of the ion turbulent thermal transport scaling laws

    International Nuclear Information System (INIS)

    Ottaviani, M.; Manfredi, G.

    2001-01-01

    Numerical simulations of ion temperature gradient (ITG) driven turbulence were carried out to investigate the parametric dependence of the ion thermal transport on the reduced gyroradius and on the local safety factor. Whereas the simulations show a clear proportionality of the conductivity to the gyroradius, the dependence on the safety factor cannot be represented as a simple power law like the one exhibited by the empirical scaling laws. (author)

  11. Numerical simulations of time-resolved quantum electronics

    International Nuclear Information System (INIS)

    Gaury, Benoit; Weston, Joseph; Santin, Matthieu; Houzet, Manuel; Groth, Christoph; Waintal, Xavier

    2014-01-01

    Numerical simulation has become a major tool in quantum electronics both for fundamental and applied purposes. While for a long time those simulations focused on stationary properties (e.g. DC currents), the recent experimental trend toward GHz frequencies and beyond has triggered a new interest for handling time-dependent perturbations. As the experimental frequencies get higher, it becomes possible to conceive experiments which are both time-resolved and fast enough to probe the internal quantum dynamics of the system. This paper discusses the technical aspects–mathematical and numerical–associated with the numerical simulations of such a setup in the time domain (i.e. beyond the single-frequency AC limit). After a short review of the state of the art, we develop a theoretical framework for the calculation of time-resolved observables in a general multiterminal system subject to an arbitrary time-dependent perturbation (oscillating electrostatic gates, voltage pulses, time-varying magnetic fields, etc.) The approach is mathematically equivalent to (i) the time-dependent scattering formalism, (ii) the time-resolved non-equilibrium Green’s function (NEGF) formalism and (iii) the partition-free approach. The central object of our theory is a wave function that obeys a simple Schrödinger equation with an additional source term that accounts for the electrons injected from the electrodes. The time-resolved observables (current, density, etc.) and the (inelastic) scattering matrix are simply expressed in terms of this wave function. We use our approach to develop a numerical technique for simulating time-resolved quantum transport. We find that the use of this wave function is advantageous for numerical simulations resulting in a speed up of many orders of magnitude with respect to the direct integration of NEGF equations. Our technique allows one to simulate realistic situations beyond simple models, a subject that was until now beyond the simulation

  12. Application of generalized perturbation theory to flux disadvantage factor calculations

    International Nuclear Information System (INIS)

    Sallam, O.H.; Akimov, I.S.; Naguib, K.; Hamouda, I.

    1979-01-01

    The possibility of using the generalized perturbation theory to calculate the perturbation of the flux disadvantage factors of reactor cell, resulting from the variation of the cell parameters, is studied. For simplicity the one-group diffusion approximation is considered. All necessary equations are derived for variations both of the cell dimensions. Numerical results are presented in the paper

  13. A finite element formulation for perturbation theory calculations

    International Nuclear Information System (INIS)

    Ozgener, B.; Kaluc, S.

    2004-01-01

    Full text: When the introduced change in the configuration of a nuclear system is neutronically not too significant, the use of the perturbation theory approximation ('the perturbation theory method' or PTM) is usually considered as an alternative to the recalculation of the effective multiplication factor (K eff ) of the modified system ('the diffusion theory method' or DTM) for the determination of the ensuing change in reactivity. In the DTM, the change in reactivity due to the introduced change can be calculated by the multigroup diffusion theory by performing two K eff determinations, one for the original and one for the modified system. The accuracy of this method is only limited by the approximations inherent in the multigroup diffusion theory and the numerical method employed for its solution. The error stemming from the numerical approximation can be nearly eliminated by utilizing a fine enough spatial mesh ad an 'exact' solution is nearly possible. Its basic disadvantage relative to the PTM is the necessity of a new K eff calculation for every change in the configuration no matter how small. On the other hand, if we use PTM, with an only one-time calculation of the flux and the adjoint flux of the original system, the change in reactivity due to any kind of perturbation can be approximately calculated using the changes in the cross section data in the perturbation theory reactivity formula. The accuracy of the PTM is restricted by the size and location of the induced change. In this work, our aim is to assess the accuracy of PTM relative to the DTM and determine criteria for the justification of its use. For all required solutions of the normal and adjoint multigroup diffusion equations, we choose the finite element method (FEM) as our numerical method and a 1-D cylindrical geometry model. The underlying theory is implemented in our FORTRAN program PERTURB. The validation of PERTURB is carried out via comparisons with analytical solutions for bare and

  14. To the development of numerical methods in problems of radiation transport

    International Nuclear Information System (INIS)

    Germogenova, T.A.

    1990-01-01

    Review of studies on the development of numerical methods and the discrete ordinate method in particular, used for solution of radiation protection physics problems is given. Consideration is given to the problems, which arise when calculating fields of penetrating radiation and when studying processes of charged-particle transport and cascade processes, generated by high-energy primary radiation

  15. Thermal transport in phosphorene and phosphorene-based materials: A review on numerical studies

    Science.gov (United States)

    Hong, Yang; Zhang, Jingchao; Zeng, Xiao Cheng

    2018-03-01

    The recently discovered two-dimensional (2D) layered material phosphorene has attracted considerable interest as a promising p-type semiconducting material. In this article, we review the recent advances in numerical studies of the thermal properties of monolayer phosphorene and phosphorene-based heterostructures. We first briefly review the commonly used first-principles and molecular dynamics (MD) approaches to evaluate the thermal conductivity and interfacial thermal resistance of 2D phosphorene. Principles of different steady-state and transient MD techniques have been elaborated on in detail. Next, we discuss the anisotropic thermal transport of phosphorene in zigzag and armchair chiral directions. Subsequently, the in-plane and cross-plane thermal transport in phosphorene-based heterostructures such as phosphorene/silicon and phosphorene/graphene is summarized. Finally, the numerical research in the field of thermal transport in 2D phosphorene is highlighted along with our perspective of potentials and opportunities of 2D phosphorenes in electronic applications such as photodetectors, field-effect transistors, lithium ion batteries, sodium ion batteries, and thermoelectric devices.

  16. Nonperturbative perturbation theory

    International Nuclear Information System (INIS)

    Bender, C.M.

    1989-01-01

    In this talk we describe a recently proposed graphical perturbative calculational scheme for quantum field theory. The basic idea is to expand in the power of the interaction term. For example, to solve a λφ 4 theory in d-dimensional space-time, we introduce a small parameter δ and consider a λ(φ 2 ) 1+δ field theory. We show how to expand such a theory as a series in powers of δ. The resulting perturbation series appears to have a finite radius of convergence and numerical results for low-dimensional models are good. We have computed the two-point and four-point Green's functions to second order in powers of δ and the 2n-point Green's functions (n>2) to order δ. We explain how to renormalize the theory and show that, to first order in powers of δ, when δ>0 and d≥4 the theory is free. This conclusion remains valid to second order in powers of δ, and we believe that it remains valid to all orders in powers of δ. The new perturbative scheme is consistent with global supersymmetry invariance. We examine a two-dimensional supersymmetric quantum field theory in which we do not know of any other means for doing analytical calculations. We illustrate the power of this new technique by computing the ground-state energy density E to second order in this new perturbation theory. We show that there is a beautiful and delicate cancellation between infinite classes of graphs which leads to the result that E=0. (orig.)

  17. Numerical modelling of coupled fluid, heat, and solute transport in deformable fractured rock

    International Nuclear Information System (INIS)

    Chan, T.; Reid, J.A.K.

    1987-01-01

    This paper reports on a three-dimensional (3D) finite-element code, MOTIF (model of transport in fractured/porous media), developed to model the coupled processes of groundwater flow, heat transport, brine transport, and one-species radionuclide transport in geological media. Three types of elements are available: a 3D continuum element, a planar fracture element that can be oriented in any arbitrary direction in 3D space or pipe flow in 3D space, and a line element for simulating fracture flow in 2D space or pipe flow in 3D space. As a quality-assurance measure, the MOTIF code was verified by comparison of its results with analytical solutions and other published numerical solutions

  18. A generalized perturbation program for CANDU reactor

    Energy Technology Data Exchange (ETDEWEB)

    Kim, Do Heon; Kim, Jong Kyung [Hanyang University, Seoul (Korea, Republic of); Choi, Hang Bok; Roh, Gyu Hong [Korea Atomic Energy Research Institute, Taejon (Korea, Republic of); Yang, Won Sik [Chosun University, Kwangju (Korea, Republic of)

    1999-12-31

    A generalized perturbation program has been developed for the purpose of estimating zonal power variation of a CANDU reactor upon refueling operation. The forward and adjoint calculation modules of RFSP code were used to construct the generalized perturbation program. The numerical algorithm for the generalized adjoint flux calculation was verified by comparing the zone power estimates upon refueling with those of forward calculation. It was, however, noticed that the truncation error from the iteration process of the generalized adjoint flux is not negligible. 2 refs., 1 figs., 1 tab. (Author)

  19. A generalized perturbation program for CANDU reactor

    Energy Technology Data Exchange (ETDEWEB)

    Kim, Do Heon; Kim, Jong Kyung [Hanyang University, Seoul (Korea, Republic of); Choi, Hang Bok; Roh, Gyu Hong [Korea Atomic Energy Research Institute, Taejon (Korea, Republic of); Yang, Won Sik [Chosun University, Kwangju (Korea, Republic of)

    1998-12-31

    A generalized perturbation program has been developed for the purpose of estimating zonal power variation of a CANDU reactor upon refueling operation. The forward and adjoint calculation modules of RFSP code were used to construct the generalized perturbation program. The numerical algorithm for the generalized adjoint flux calculation was verified by comparing the zone power estimates upon refueling with those of forward calculation. It was, however, noticed that the truncation error from the iteration process of the generalized adjoint flux is not negligible. 2 refs., 1 figs., 1 tab. (Author)

  20. A numerical study on the charge transport in TPD/Alq3-based organic light emitting diodes.

    Science.gov (United States)

    Kim, K S; Hwang, Y W; Lee, H G; Won, T Y

    2014-08-01

    We report our simulation study on the charge transport characteristic of the multi-layer structure for organic light emitting diodes (OLEDs). We performed a numerical simulation on a multilayer structure comprising a hole transport layer (HTL), an emission layer (EML), and an electron transport layer (ETL) between both electrodes. The material of the HTL is TPD (N,N'-Bis (3-methylphenyl)-N,N'-bis(phenyl) benzidine), and the ETL includes Alq3 (Tris (8-hyroxyquinolinato) aluminium). Here, we investigated the parameters such as recombination rates which influence the efficiency of the charge transport between layers in bilayer OLEDs. We also analyzed a transient response during the turn on/off period and the carrier transport in accordance with the variation of the injection barrier and applied voltage. In addition, our numerical simulation revealed that the insertion of the EML affects the photonic characteristics in bilayer structure and also the efficiency due to the difference in the internal barrier height.

  1. Radial transport with perturbed magnetic field

    Energy Technology Data Exchange (ETDEWEB)

    Hazeltine, R. D. [Institute for Fusion Studies, University of Texas at Austin, Austin, Texas 78712 (United States)

    2015-05-15

    It is pointed out that the viscosity coefficient describing radial transport of toroidal angular momentum is proportional to the second power of the gyro-radius—like the corresponding coefficients for particle and heat transport—regardless of any geometrical symmetry. The observation is widely appreciated, but worth emphasizing because some literature gives the misleading impression that asymmetry can allow radial moment transport in first-order.

  2. Radial transport with perturbed magnetic field

    International Nuclear Information System (INIS)

    Hazeltine, R. D.

    2015-01-01

    It is pointed out that the viscosity coefficient describing radial transport of toroidal angular momentum is proportional to the second power of the gyro-radius—like the corresponding coefficients for particle and heat transport—regardless of any geometrical symmetry. The observation is widely appreciated, but worth emphasizing because some literature gives the misleading impression that asymmetry can allow radial moment transport in first-order

  3. Non-perturbative QCD Effect on K-Factor of Drell-Yan Process

    International Nuclear Information System (INIS)

    Hou Zhaoyu; Zhi Haisu; Chen Junxiao

    2006-01-01

    By using a non-perturbative quark propagator with the lowest-dimensional condensate contributions from the QCD vacuum, the non-perturbative effect to K-factor of the Drell-Yan process is numerically investigated for 12 6 C- 12 6 C collision at the center-of-mass energy (s) 1/2 = 200 GeV, 630 GeV respectively. Calculated results show that the non-perturbative QCD effect has just a weak influence on K-factor in the two cases.

  4. Numerical simulation for fractional order stationary neutron transport equation using Haar wavelet collocation method

    Energy Technology Data Exchange (ETDEWEB)

    Saha Ray, S., E-mail: santanusaharay@yahoo.com; Patra, A.

    2014-10-15

    Highlights: • A stationary transport equation has been solved using the technique of Haar wavelet collocation method. • This paper intends to provide the great utility of Haar wavelets to nuclear science problem. • In the present paper, two-dimensional Haar wavelets are applied. • The proposed method is mathematically very simple, easy and fast. - Abstract: In this paper the numerical solution for the fractional order stationary neutron transport equation is presented using Haar wavelet Collocation Method (HWCM). Haar wavelet collocation method is efficient and powerful in solving wide class of linear and nonlinear differential equations. This paper intends to provide an application of Haar wavelets to nuclear science problems. This paper describes the application of Haar wavelets for the numerical solution of fractional order stationary neutron transport equation in homogeneous medium with isotropic scattering. The proposed method is mathematically very simple, easy and fast. To demonstrate about the efficiency and applicability of the method, two test problems are discussed.

  5. On the C(R) stability of uncertain singularly perturbed systems

    International Nuclear Information System (INIS)

    Sun, Y.-J.

    2009-01-01

    In this paper, a simple criterion for the C(R) stability of uncertain singularly perturbed systems is proposed. Such a criterion can be easily checked by some algebraic inequality. The upper bound of the singular perturbation parameter ε is also given by estimating the unique positive zero of specific function. Finally, a numerical example is provided to illustrate the main result

  6. Development of numerical methods for reactive transport

    International Nuclear Information System (INIS)

    Bouillard, N.

    2006-12-01

    When a radioactive waste is stored in deep geological disposals, it is expected that the waste package will be damaged under water action (concrete leaching, iron corrosion). Then, to understand these damaging processes, chemical reactions and solutes transport are modelled. Numerical simulations of reactive transport can be done sequentially by the coupling of several codes. This is the case of the software platform ALLIANCES which is developed jointly with CEA, ANDRA and EDF. Stiff reactions like precipitation-dissolution are crucial for the radioactive waste storage applications, but standard sequential iterative approaches like Picard's fail in solving rapidly reactive transport simulations with such stiff reactions. In the first part of this work, we focus on a simplified precipitation and dissolution process: a system made up with one solid species and two aqueous species moving by diffusion is studied mathematically. It is assumed that a precipitation dissolution reaction occurs in between them, and it is modelled by a discontinuous kinetics law of unknown sign. By using monotonicity properties, the convergence of a finite volume scheme on admissible mesh is proved. Existence of a weak solution is obtained as a by-product of the convergence of the scheme. The second part is dedicated to coupling algorithms which improve Picard's method and can be easily used in an existing coupling code. By extending previous works, we propose a general and adaptable framework to solve nonlinear systems. Indeed by selecting special options, we can either recover well known methods, like nonlinear conjugate gradient methods, or design specific method. This algorithm has two main steps, a preconditioning one and an acceleration one. This algorithm is tested on several examples, some of them being rather academical and others being more realistic. We test it on the 'three species model'' example. Other reactive transport simulations use an external chemical code CHESS. For a

  7. Numerical and experimental approaches to study soil transport and clogging in granular filters

    Science.gov (United States)

    Kanarska, Y.; Smith, J. J.; Ezzedine, S. M.; Lomov, I.; Glascoe, L. G.

    2012-12-01

    Failure of a dam by erosion ranks among the most serious accidents in civil engineering. The best way to prevent internal erosion is using adequate granular filters in the transition areas where important hydraulic gradients can appear. In case of cracking and erosion, if the filter is capable of retaining the eroded particles, the crack will seal and the dam safety will be ensured. Numerical modeling has proved to be a cost-effective tool for improving our understanding of physical processes. Traditionally, the consideration of flow and particle transport in porous media has focused on treating the media as continuum. Practical models typically address flow and transport based on the Darcy's law as a function of a pressure gradient and a medium-dependent permeability parameter. Additional macroscopic constitutes describe porosity, and permeability changes during the migration of a suspension through porous media. However, most of them rely on empirical correlations, which often need to be recalibrated for each application. Grain-scale modeling can be used to gain insight into scale dependence of continuum macroscale parameters. A finite element numerical solution of the Navier-Stokes equations for fluid flow together with Lagrange multiplier technique for solid particles was applied to the simulation of soil filtration in the filter layers of gravity dam. The numerical approach was validated through comparison of numerical simulations with the experimental results of base soil particle clogging in the filter layers performed at ERDC. The numerical simulation correctly predicted flow and pressure decay due to particle clogging. The base soil particle distribution was almost identical to those measured in the laboratory experiment. It is believed that the agreement between simulations and experimental data demonstrates the applicability of the proposed approach for prediction of the soil transport and clogging in embankment dams. To get more precise understanding of

  8. Studying the perturbative Reggeon

    International Nuclear Information System (INIS)

    Griffiths, S.; Ross, D.A.

    2000-01-01

    We consider the flavour non-singlet Reggeon within the context of perturbative QCD. This consists of ladders built out of ''reggeized'' quarks. We propose a method for the numerical solution of the integro-differential equation for the amplitude describing the exchange of such a Reggeon. The solution is known to have a sharp rise at low values of Bjorken-x when applied to non-singlet quantities in deep-inelastic scattering. We show that when the running of the coupling is taken into account this sharp rise is further enhanced, although the Q 2 dependence is suppressed by the introduction of the running coupling. We also investigate the effects of simulating non-perturbative physics by introducing a constituent mass for the soft quarks and an effective mass for the soft gluons exchanged in the t-channel. (orig.)

  9. Introduction and overview to some topics in perturbative QCD and their relationship to non perturbative effects

    International Nuclear Information System (INIS)

    West, G.

    1990-01-01

    The main thrust of this talk is to review and discuss various topics in both perturbative and non-perturbative QCD that are, by and large, model independent. This inevitably means that we shall rely heavily on the renormalization group and asymptotic freedom. Although this usually means that one has to concentrate on high energy phenomena, there are some physical processes even involving bound states which are certainly highly non-perturbative, where one can make some progress without becoming overly model independent. Experience with the EMC effect, where there are about as many ''explanations'' as authors, has surely taught us that it may well be worth returning to ''basics'' and thinking about general properties of QCD rather than guessing, essentially arbitrarily, what we think is its low energy structure. No doubt we shall have to await further numerical progress or for some inspired theoretical insight before we can, with confidence, attack these extremely difficult problems. So, with this in mine, I shall review a smattering of problems which do have a non-perturbative component and where some rather modest progress can actually be made; I emphasize the adjective ''modest''exclamation point

  10. Application of an efficient materials perturbation technique to Monte Carlo photon transport calculations in borehole logging

    International Nuclear Information System (INIS)

    Picton, D.J.; Harris, R.G.; Randle, K.; Weaver, D.R.

    1995-01-01

    This paper describes a simple, accurate and efficient technique for the calculation of materials perturbation effects in Monte Carlo photon transport calculations. It is particularly suited to the application for which it was developed, namely the modelling of a dual detector density tool as used in borehole logging. However, the method would be appropriate to any photon transport calculation in the energy range 0.1 to 2 MeV, in which the predominant processes are Compton scattering and photoelectric absorption. The method enables a single set of particle histories to provide results for an array of configurations in which material densities or compositions vary. It can calculate the effects of small perturbations very accurately, but is by no means restricted to such cases. For the borehole logging application described here the method has been found to be efficient for a moderate range of variation in the bulk density (of the order of ±30% from a reference value) or even larger changes to a limited portion of the system (e.g. a low density mudcake of the order of a few tens of mm in thickness). The effective speed enhancement over an equivalent set of individual calculations is in the region of an order of magnitude or more. Examples of calculations on a dual detector density tool are given. It is demonstrated that the method predicts, to a high degree of accuracy, the variation of detector count rates with formation density, and that good results are also obtained for the effects of mudcake layers. An interesting feature of the results is that relative count rates (the ratios of count rates obtained with different configurations) can usually be determined more accurately than the absolute values of the count rates. (orig.)

  11. Seeded perturbations in wire array z-pinches

    International Nuclear Information System (INIS)

    Robinson, Allen Conrad; Kantsyrev, Victor Leonidovich; Wunsch, Scott Edward; Oliver, Bryan Velten; Lebedev, Sergey V.; Safronova, Alla S.; Maxwell, J.; McKenney, John Lee; Ampleford, David J.; Rapley, J.; Bott, S.C.; Palmer, J.B.A.; Bland, Simon Nicholas; Jones, Brent Manley; Chittenden, Jeremy Paul; Garasi, Christopher Joseph; Hall, Gareth Neville; Mehlhorn, Thomas Alan; Deeney, Christopher

    2004-01-01

    The impact of 3D structure on wire array z-pinch dynamics is a topic of current interest, and has been studied by the controlled seeding of wire perturbations. First, Al wires were etched at Sandia, creating 20% radial perturbations with variable axial wavelength. Observations of magnetic bubble formation in the etched regions during experiments on the MAGPIE accelerator are discussed and compared to 3D MHD modeling. Second, thin NaF coatings of 1 mm axial extent were deposited on Al wires and fielded on the Zebra accelerator. Little or no axial transport of the NaF spectroscopic dopant was observed in spatially resolved K-shell spectra, which places constraints on particle diffusivity in dense z-pinch plasmas. Finally, technology development for seeding perturbations is discussed

  12. Toroidal rotation braking with n = 1 magnetic perturbation field on JET

    DEFF Research Database (Denmark)

    Sun, Y; Liang, Y; Koslowski, H R

    2010-01-01

    A strong toroidal rotation braking has been observed in plasmas with application of an n = 1 magnetic perturbation field on the JET tokamak. Calculation results from the momentum transport analysis show that the torque induced by the n = 1 perturbation field has a global profile. The maximal value...

  13. THC-MP: High performance numerical simulation of reactive transport and multiphase flow in porous media

    Science.gov (United States)

    Wei, Xiaohui; Li, Weishan; Tian, Hailong; Li, Hongliang; Xu, Haixiao; Xu, Tianfu

    2015-07-01

    The numerical simulation of multiphase flow and reactive transport in the porous media on complex subsurface problem is a computationally intensive application. To meet the increasingly computational requirements, this paper presents a parallel computing method and architecture. Derived from TOUGHREACT that is a well-established code for simulating subsurface multi-phase flow and reactive transport problems, we developed a high performance computing THC-MP based on massive parallel computer, which extends greatly on the computational capability for the original code. The domain decomposition method was applied to the coupled numerical computing procedure in the THC-MP. We designed the distributed data structure, implemented the data initialization and exchange between the computing nodes and the core solving module using the hybrid parallel iterative and direct solver. Numerical accuracy of the THC-MP was verified through a CO2 injection-induced reactive transport problem by comparing the results obtained from the parallel computing and sequential computing (original code). Execution efficiency and code scalability were examined through field scale carbon sequestration applications on the multicore cluster. The results demonstrate successfully the enhanced performance using the THC-MP on parallel computing facilities.

  14. Short-term memories with a stochastic perturbation

    International Nuclear Information System (INIS)

    Pontes, Jose C.A. de; Batista, Antonio M.; Viana, Ricardo L.; Lopes, Sergio R.

    2005-01-01

    We investigate short-term memories in linear and weakly nonlinear coupled map lattices with a periodic external input. We use locally coupled maps to present numerical results about short-term memory formation adding a stochastic perturbation in the maps and in the external input

  15. NUMERICALLY DETERMINED TRANSPORT LAWS FOR FINGERING ('THERMOHALINE') CONVECTION IN ASTROPHYSICS

    International Nuclear Information System (INIS)

    Traxler, A.; Garaud, P.; Stellmach, S.

    2011-01-01

    We present the first three-dimensional simulations of fingering convection performed at parameter values approaching those relevant for astrophysics. Our simulations reveal the existence of simple asymptotic scaling laws for turbulent heat and compositional transport, which can be straightforwardly extrapolated from our numerically tractable values to the true astrophysical regime. Our investigation also indicates that thermo-compositional 'staircases', a key consequence of fingering convection in the ocean, cannot form spontaneously in the fingering regime in stellar interiors. Our proposed empirically determined transport laws thus provide simple prescriptions for mixing by fingering convection in a variety of astrophysical situations, and should, from here on, be used preferentially over older and less accurate parameterizations. They also establish that fingering convection does not provide sufficient extra-mixing to explain observed chemical abundances in red giant branch stars.

  16. Instantons and Borel resummability for the perturbed supersymmetric anharmonic oscillator

    International Nuclear Information System (INIS)

    Verbaarschot, J.J.M.; West, P.

    1991-01-01

    In this paper we give an analytical derivation of the large-order behavior of the perturbation series for both the ground state and the excited states of the supersymmetric anharmonic oscillator and of the anharmonic oscillator obtained from the supersymmetric case by varying the strength of the fermion coupling. The results which are obtained with the help of instanton calculus coincide with those obtained numerically in previous work. The large-order perturbation series of the ground state vanishes in the supersymmetric case, whereas away from the supersymmetric point the perturbation series diverges factorially. The perturbation series of the excited states diverges factorially both at the supersymmetric point and away from this point

  17. Anharmonic, dimensionality and size effects in phonon transport

    Science.gov (United States)

    Thomas, Iorwerth O.; Srivastava, G. P.

    2017-12-01

    We have developed and employed a numerically efficient semi- ab initio theory, based on density-functional and relaxation-time schemes, to examine anharmonic, dimensionality and size effects in phonon transport in three- and two-dimensional solids of different crystal symmetries. Our method uses third- and fourth-order terms in crystal Hamiltonian expressed in terms of a temperature-dependent Grüneisen’s constant. All input to numerical calculations are generated from phonon calculations based on the density-functional perturbation theory. It is found that four-phonon processes make important and measurable contribution to lattice thermal resistivity above the Debye temperature. From our numerical results for bulk Si, bulk Ge, bulk MoS2 and monolayer MoS2 we find that the sample length dependence of phonon conductivity is significantly stronger in low-dimensional solids.

  18. An advanced three-phase physical, experimental and numerical method for tsunami induced boulder transport

    Science.gov (United States)

    Oetjen, Jan; Engel, Max; Prasad Pudasaini, Shiva; Schüttrumpf, Holger; Brückner, Helmut

    2017-04-01

    Coasts around the world are affected by high-energy wave events like storm surges or tsunamis depending on their regional climatological and geological settings. By focusing on tsunami impacts, we combine the abilities and experiences of different scientific fields aiming at improved insights of near- and onshore tsunami hydrodynamics. We investigate the transport of coarse clasts - so called boulders - due to tsunami impacts by a multi-methodology approach of numerical modelling, laboratory experiments, and sedimentary field records. Coupled numerical hydrodynamic and boulder transport models (BTM) are widely applied for analysing the impact characteristics of the transport by tsunami, such as wave height and flow velocity. Numerical models able to simulate past tsunami events and the corresponding boulder transport patterns with high accuracy and acceptable computational effort can be utilized as powerful forecasting models predicting the impact of a coast approaching tsunami. We have conducted small-scale physical experiments in the tilting flume with real shaped boulder models. Utilizing the structure from motion technique (Westoby et al., 2012) we reconstructed real boulders from a field study on the Island of Bonaire (Lesser Antilles, Caribbean Sea, Engel & May, 2012). The obtained three-dimensional boulder meshes are utilized for creating downscaled replica of the real boulder for physical experiments. The results of the irregular shaped boulder are compared to experiments with regular shaped boulder models to achieve a better insight about the shape related influence on transport patterns. The numerical model is based on the general two-phase mass flow model by Pudasaini (2012) enhanced for boulder transport simulations. The boulder is implemented using the immersed boundary technique (Peskin, 2002) and the direct forcing approach. In this method Cartesian grids (fluid and particle phase) and Lagrangian meshes (boulder) are combined. By applying the

  19. Peristaltic transport of Bingham plastic fluid considering magnetic field, Soret and Dufour effects

    Science.gov (United States)

    Hayat, T.; Farooq, S.; Mustafa, M.; Ahmad, B.

    Current attempt addresses the peristaltic transport of Bingham plastic fluid under the influence of magnetic force. Space dependent viscosity is considered. Novel Soret and Dufour effects are retained in the mathematical model. Problem formulation is presented through the conventional lubrication approach. Series solutions of the arising non-linear problem are developed via regular perturbation approach. Special attention is given to the role of embedded parameters on the axial velocity, temperature, concentration and pressure distributions. Furthermore the numerical solution of pressure rise per wavelength is obtained through numerical integration because its analytical solution seems impossible.

  20. An analytical and numerical study of peristaltic transport of a Johnson—Segalman fluid in an endoscope

    International Nuclear Information System (INIS)

    Akbar, Noreen Sher; Nadeem, S.

    2013-01-01

    In the present study, we discuss the peristaltic flow of a Johnson—Segalman fluid in an endoscope. Perturbation, homotopy, and numerical solutions are found for the non-linear differential equation. The comparative study is also made to check the validity of the solutions. The expressions for pressure rise frictional forces, pressure gradient, and stream lines are presented to interpret the behavior of various physical quantities of the Johnson—Segalman fluid. (electromagnetism, optics, acoustics, heat transfer, classical mechanics, and fluid dynamics)

  1. Application of linear and higher perturbation theory in reactor physics

    International Nuclear Information System (INIS)

    Woerner, D.

    1978-01-01

    For small perturbations in the material composition of a reactor according to the first approximation of perturbation theory the eigenvalue perturbation is proportional to the perturbation of the system. This assumption is true for the neutron flux not influenced by the perturbance. The two-dimensional code LINESTO developed for such problems in this paper on the basis of diffusion theory determines the relative change of the multiplication constant. For perturbations varying the neutron flux in the space of energy and position the eigenvalue perturbation is also influenced by this changed neutron flux. In such cases linear perturbation theory yields larger errors. Starting from the methods of calculus of variations there is additionally developed in this paper a perturbation method of calculation permitting in a quick and simple manner to assess the influence of flux perturbation on the eigenvalue perturbation. While the source of perturbations is evaluated in isotropic approximation of diffusion theory the associated inhomogeneous equation may be used to determine the flux perturbation by means of diffusion or transport theory. Possibilities of application and limitations of this method are studied in further systematic investigations on local perturbations. It is shown that with the integrated code system developed in this paper a number of local perturbations may be checked requiring little computing time. With it flux perturbations in first approximation and perturbations of the multiplication constant in second approximation can be evaluated. (orig./RW) [de

  2. Numerical solution of the time dependent neutron transport equation by the method of the characteristics

    International Nuclear Information System (INIS)

    Talamo, Alberto

    2013-01-01

    This study presents three numerical algorithms to solve the time dependent neutron transport equation by the method of the characteristics. The algorithms have been developed taking into account delayed neutrons and they have been implemented into the novel MCART code, which solves the neutron transport equation for two-dimensional geometry and an arbitrary number of energy groups. The MCART code uses regular mesh for the representation of the spatial domain, it models up-scattering, and takes advantage of OPENMP and OPENGL algorithms for parallel computing and plotting, respectively. The code has been benchmarked with the multiplication factor results of a Boiling Water Reactor, with the analytical results for a prompt jump transient in an infinite medium, and with PARTISN and TDTORT results for cross section and source transients. The numerical simulations have shown that only two numerical algorithms are stable for small time steps

  3. Numerical solution of the time dependent neutron transport equation by the method of the characteristics

    Energy Technology Data Exchange (ETDEWEB)

    Talamo, Alberto, E-mail: alby@anl.gov [Nuclear Engineering Division, Argonne National Laboratory, 9700 South Cass Avenue, Lemont, IL 60439 (United States)

    2013-05-01

    This study presents three numerical algorithms to solve the time dependent neutron transport equation by the method of the characteristics. The algorithms have been developed taking into account delayed neutrons and they have been implemented into the novel MCART code, which solves the neutron transport equation for two-dimensional geometry and an arbitrary number of energy groups. The MCART code uses regular mesh for the representation of the spatial domain, it models up-scattering, and takes advantage of OPENMP and OPENGL algorithms for parallel computing and plotting, respectively. The code has been benchmarked with the multiplication factor results of a Boiling Water Reactor, with the analytical results for a prompt jump transient in an infinite medium, and with PARTISN and TDTORT results for cross section and source transients. The numerical simulations have shown that only two numerical algorithms are stable for small time steps.

  4. Perturbation expansions generated by an approximate propagator

    International Nuclear Information System (INIS)

    Znojil, M.

    1987-01-01

    Starting from a knowledge of an approximate propagator R at some trial energy guess E 0 , a new perturbative prescription for p-plet of bound states and of their energies is proposed. It generalizes the Rayleigh-Schroedinger (RS) degenerate perturbation theory to the nondiagonal operators R (eliminates a RS need of their diagnolisation) and defines an approximate Hamiltonian T by mere inversion. The deviation V of T from the exact Hamiltonian H is assumed small only after a substraction of a further auxiliary Hartree-Fock-like separable ''selfconsistent'' potential U of rank p. The convergence is illustrated numerically on the anharmonic oscillator example

  5. TLC scheme for numerical solution of the transport equation on equilateral triangular meshes

    International Nuclear Information System (INIS)

    Walters, W.F.

    1983-01-01

    A new triangular linear characteristic TLC scheme for numerically solving the transport equation on equilateral triangular meshes has been developed. This scheme uses the analytic solution of the transport equation in the triangle as its basis. The data on edges of the triangle are assumed linear as is the source representation. A characteristic approach or nodal approach is used to obtain the analytic solution. Test problems indicate that the new TLC is superior to the widely used DITRI scheme for accuracy

  6. Numerical and theoretical investigations of resistive drift wave turbulence

    International Nuclear Information System (INIS)

    Sunn Pedersen, T.

    1995-07-01

    With regard to the development of thermonuclear fusion utilizing a plasma confined in a magnetic field, anomalous transport is a major problem and is considered to be caused by electrostatic drift wave turbulence. A simplified quasi-two-dimensional slab model of resistive drift wave turbulence is investigated numerically and theoretically. The model (Hasegawa and Wakatani), consists of two nonlinear partial differential equations for the density perturbation n and the electrostatic potential perturbation φ. It includes the effect of a background density gradient perpendicular to the magnetic field and a generalized Ohm's law for the electrons in the direction parallel to the magnetic field. It may be used to model the basic features of electrostatic turbulence and the associated transport in an edge plasma. Model equations are derived and some important properties of the system are discussed. It is described how the Fourier spectral method is applied to the Hasegawa-Wakatani equations, how the time integration is developed to ensure accurate and fast simulations in a large parameter regime, and how the accuracy of the code is checked. Numerical diagnostics are developed to verify and extend the results in publications concerning quasi-stationary turbulent states and to give an overview of the properties of the quasi-stationary turbulent state. The use of analysis tools, not previously applied to the Hasegawa-Wakatani system, and the results obtained are described. Fluid particles are tracked to obtain Lagrangian statistics for the turbulence. A new theoretical analysis of relative dispersion leads to a decomposition criterion for the particles. The significance of this is investigated numerically and characteristic time scales for particles are determined for a range of parameter values. It is indicated that the turbulent state can be characterized in the context of nonlinear dynamics and chaos theory as an attractor with a large basin of attraction. The basic

  7. Acoustic anisotropic wavefields through perturbation theory

    KAUST Repository

    Alkhalifah, Tariq Ali

    2013-09-01

    Solving the anisotropic acoustic wave equation numerically using finite-difference methods introduces many problems and media restriction requirements, and it rarely contributes to the ability to resolve the anisotropy parameters. Among these restrictions are the inability to handle media with η<0 and the presence of shear-wave artifacts in the solution. Both limitations do not exist in the solution of the elliptical anisotropic acoustic wave equation. Using perturbation theory in developing the solution of the anisotropic acoustic wave equation allows direct access to the desired limitation-free solutions, that is, solutions perturbed from the elliptical anisotropic background medium. It also provides a platform for parameter estimation because of the ability to isolate the wavefield dependency on the perturbed anisotropy parameters. As a result, I derive partial differential equations that relate changes in the wavefield to perturbations in the anisotropy parameters. The solutions of the perturbation equations represented the coefficients of a Taylor-series-type expansion of the wavefield as a function of the perturbed parameter, which is in this case η or the tilt of the symmetry axis. The expansion with respect to the symmetry axis allows use of an acoustic transversely isotropic media with a vertical symmetry axis (VTI) kernel to estimate the background wavefield and the corresponding perturbation coefficients. The VTI extrapolation kernel is about one-fourth the cost of the transversely isotropic model with a tilt in the symmetry axis kernel. Thus, for a small symmetry axis tilt, the cost of migration using a first-order expansion can be reduced. The effectiveness of the approach was demonstrated on the Marmousi model.

  8. Reduction of the turbulent blob transport in the scrape-off layer by a resonant magnetic perturbation in TEXTOR

    International Nuclear Information System (INIS)

    Xu, Y.; Weynants, R.R.; Van Schoor, M.; Vergote, M.; Jachmich, S.; Jakubowski, M.W.; Mitri, M.; Schmitz, O.; Unterberg, B.; Reiser, D.; Finken, K.H.; Lehnen, M.; Beyer, P.

    2009-01-01

    During the static 6/2 Dynamic Ergodic Divertor experiments in TEXTOR, a significant influence of the edge resonant magnetic perturbation (RMP) on the turbulent blob transport in the scrape-off layer (SOL) has been observed. In ohmic discharges without the RMP, the blobs extend 4-5 cm deep into the SOL with a radially outward moving speed of about 1 km s -1 and hence constitute a strong outflow of mass. With the application of the RMP, the blob amplitudes and their radially moving velocity are both reduced, resulting in a significant reduction of the blob transport in the SOL. The reduction effect of the RMP on blobs is found to be robust to changes in the operational regime and to phasing variations of the RMP as well. The blob dynamics appears to be consistent with the paradigm of the radial motions of the blob structures driven by the interchange instability.

  9. A food chain model with impulsive perturbations and Holling IV functional response

    International Nuclear Information System (INIS)

    Zhang Shuwen; Wang Fengyan; Chen Lansun

    2005-01-01

    In this paper, we investigate a three trophic level food chain system with Holling IV functional responses and periodic constant impulsive perturbations of top predator. Conditions for extinction of predator are given. By using the Floquet theory of impulsive equation and small amplitude perturbation skills, we consider the local stability of predator eradication periodic solution. Further, influences of the impulsive perturbation on the inherent oscillation are studied numerically, which shows the rich dynamics in the positive octant

  10. Numerical Solutions of Singularly Perturbed Reaction Diffusion Equation with Sobolev Gradients

    Directory of Open Access Journals (Sweden)

    Nauman Raza

    2013-01-01

    Full Text Available Critical points related to the singular perturbed reaction diffusion models are calculated using weighted Sobolev gradient method in finite element setting. Performance of different Sobolev gradients has been discussed for varying diffusion coefficient values. A comparison is shown between the weighted and unweighted Sobolev gradients in two and three dimensions. The superiority of the method is also demonstrated by showing comparison with Newton's method.

  11. Perturbation approach for nuclear magnetic resonance solid-state quantum computation

    Directory of Open Access Journals (Sweden)

    G. P. Berman

    2003-01-01

    Full Text Available A dynamics of a nuclear-spin quantum computer with a large number (L=1000 of qubits is considered using a perturbation approach. Small parameters are introduced and used to compute the error in an implementation of an entanglement between remote qubits, using a sequence of radio-frequency pulses. The error is computed up to the different orders of the perturbation theory and tested using exact numerical solution.

  12. Peristaltic transport of Johnson-Segalman fluid under effect of a magnetic field

    Directory of Open Access Journals (Sweden)

    Moustafa Elshahed

    2005-01-01

    Full Text Available The peristaltic transport of Johnson-Segalman fluid by means of an infinite train of sinusoidal waves traveling along the walls of a two-dimensional flexible channel is investigated. The fluid is electrically conducted by a transverse magnetic field. A perturbation solution is obtained for the case in which amplitude ratio is small. Numerical results are reported for various values of the physical parameters of interest.

  13. Finding a nonlinear lattice with improved integrability using Lie transform perturbation theory

    International Nuclear Information System (INIS)

    Sonnad, Kiran G.; Cary, John R.

    2004-01-01

    A condition for improved dynamic aperture for nonlinear, alternating gradient transport systems is derived using Lie transform perturbation theory. The Lie transform perturbation method is used here to perform averaging over fast oscillations by canonically transforming to slowly oscillating variables. This is first demonstrated for a linear sinusoidal focusing system. This method is then employed to average the dynamics over a lattice period for a nonlinear focusing system, provided by the use of higher order poles such as sextupoles and octupoles along with alternate gradient quadrupoles. Unlike the traditional approach, the higher order focusing is not treated as a perturbation. The Lie transform method is particularly advantageous for such a system where the form of the Hamiltonian is complex. This is because the method exploits the property of canonical invariance of Poisson brackets so that the change of variables is accomplished by just replacing the old ones with the new. The analysis shows the existence of a condition in which the system is azimuthally symmetric in the transformed, slowly oscillating frame. Such a symmetry in the time averaged frame renders the system nearly integrable in the laboratory frame. This condition leads to reduced chaos and improved confinement when compared to a system that is not close to integrability. Numerical calculations of single-particle trajectories and phase space projections of the dynamic aperture performed for a lattice with quadrupoles and sextupoles confirm that this is indeed the case

  14. Application of perturbation methods for sensitivity analysis for nuclear power plant steam generators

    International Nuclear Information System (INIS)

    Gurjao, Emir Candeia

    1996-02-01

    The differential and GPT (Generalized Perturbation Theory) formalisms of the Perturbation Theory were applied in this work to a simplified U-tubes steam generator model to perform sensitivity analysis. The adjoint and importance equations, with the corresponding expressions for the sensitivity coefficients, were derived for this steam generator model. The system was numerically was numerically solved in a Fortran program, called GEVADJ, in order to calculate the sensitivity coefficients. A transient loss of forced primary coolant in the nuclear power plant Angra-1 was used as example case. The average and final values of functionals: secondary pressure and enthalpy were studied in relation to changes in the secondary feedwater flow, enthalpy and total volume in secondary circuit. Absolute variations in the above functionals were calculated using the perturbative methods, considering the variations in the feedwater flow and total secondary volume. Comparison with the same variations obtained via direct model showed in general good agreement, demonstrating the potentiality of perturbative methods for sensitivity analysis of nuclear systems. (author)

  15. Direct numerical simulation of the Rayleigh-Taylor instability with the spectral element method

    International Nuclear Information System (INIS)

    Zhang Xu; Tan Duowang

    2009-01-01

    A novel method is proposed to simulate Rayleigh-Taylor instabilities using a specially-developed unsteady three-dimensional high-order spectral element method code. The numerical model used consists of Navier-Stokes equations and a transport-diffusive equation. The code is first validated with the results of linear stability perturbation theory. Then several characteristics of the Rayleigh-Taylor instabilities are studied using this three-dimensional unsteady code, including instantaneous turbulent structures and statistical turbulent mixing heights under different initial wave numbers. These results indicate that turbulent structures of Rayleigh-Taylor instabilities are strongly dependent on the initial conditions. The results also suggest that a high-order numerical method should provide the capability of simulating small scale fluctuations of Rayleigh-Taylor instabilities of turbulent flows. (authors)

  16. COMSOL-PHREEQC: a tool for high performance numerical simulation of reactive transport phenomena

    International Nuclear Information System (INIS)

    Nardi, Albert; Vries, Luis Manuel de; Trinchero, Paolo; Idiart, Andres; Molinero, Jorge

    2012-01-01

    Document available in extended abstract form only. Comsol Multiphysics (COMSOL, from now on) is a powerful Finite Element software environment for the modelling and simulation of a large number of physics-based systems. The user can apply variables, expressions or numbers directly to solid and fluid domains, boundaries, edges and points, independently of the computational mesh. COMSOL then internally compiles a set of equations representing the entire model. The availability of extremely powerful pre and post processors makes COMSOL a numerical platform well known and extensively used in many branches of sciences and engineering. On the other hand, PHREEQC is a freely available computer program for simulating chemical reactions and transport processes in aqueous systems. It is perhaps the most widely used geochemical code in the scientific community and is openly distributed. The program is based on equilibrium chemistry of aqueous solutions interacting with minerals, gases, solid solutions, exchangers, and sorption surfaces, but also includes the capability to model kinetic reactions with rate equations that are user-specified in a very flexible way by means of Basic statements directly written in the input file. Here we present COMSOL-PHREEQC, a software interface able to communicate and couple these two powerful simulators by means of a Java interface. The methodology is based on Sequential Non Iterative Approach (SNIA), where PHREEQC is compiled as a dynamic subroutine (iPhreeqc) that is called by the interface to solve the geochemical system at every element of the finite element mesh of COMSOL. The numerical tool has been extensively verified by comparison with computed results of 1D, 2D and 3D benchmark examples solved with other reactive transport simulators. COMSOL-PHREEQC is parallelized so that CPU time can be highly optimized in multi-core processors or clusters. Then, fully 3D detailed reactive transport problems can be readily simulated by means of

  17. Calculations of reactivity based in the solution of the Neutron transport equation in X Y geometry and Lineal perturbation theory

    International Nuclear Information System (INIS)

    Valle G, E. del; Mugica R, C.A.

    2005-01-01

    In our country, in last congresses, Gomez et al carried out reactivity calculations based on the solution of the diffusion equation for an energy group using nodal methods in one dimension and the TPL approach (Lineal Perturbation Theory). Later on, Mugica extended the application to the case of multigroup so much so much in one as in two dimensions (X Y geometry) with excellent results. Presently work is carried out similar calculations but this time based on the solution of the neutron transport equation in X Y geometry using nodal methods and again the TPL approximation. The idea is to provide a calculation method that allows to obtain in quick form the reactivity solving the direct problem as well as the enclosed problem of the not perturbed problem. A test problem for the one that results are provided for the effective multiplication factor is described and its are offered some conclusions. (Author)

  18. Investigation of bacterial transport in the large-block test, a thermally perturbed block of Topopah Spring Tuff

    International Nuclear Information System (INIS)

    Chen, C. I.; Chuu, Y. J.; Lin, W.; Meike, A.; Sawvel, A.

    1998-01-01

    This study investigates the transport of bacteria in a large, thermally perturbed block of Topopah Spring tuff. The study was part of the Large-Block Test (LBT), thermochemical and physical studies conducted on a 10 ft x 10 ft x 14 ft block of volcanic tuff excavated on 5 of 6 sides out of Fran Ridge, Nevada. Two bacterial species, Bacillus subtilis and Arthrobacter oxydans, were isolated from the Yucca Mountain tuff. Natural mutants that can grow under the simultaneous presence of the two antibiotics, streptomycin and rifampicin, were selected from these species by laboratory procedures. The double-drug-resistant mutants, which could be thus distinguished from the indigenous species, were injected into the five heater boreholes of the large block hours before heating was initiated. The temperature, as measured 5 cm above one of the heater boreholes, rose slowly and steadily over a matter of months to a maximum of 142 C. Samples (cotton cloths inserted the length of the hole, glass fiber swabs, and filter papers) were collected from the boreholes that were approximately 5 ft below the injection points. Double-drug-resistant bacteria were found in the collection boreholes nine months after injection. Surprisingly, they also appeared in the heater boreholes where the temperature had been sustainably high throughout the test. These bacteria appear to be the species that were injected. The number of double-drug-resistant bacteria that were identified in the collection boreholes increased with time. An apparent homogeneous distribution among the observation boreholes and heater boreholes suggests that a random motion could be the pattern that the bacteria migrated in the block. These observations indicated the possibility of rapid bacterial transport in a thermally perturbed geologic setting

  19. Numerically evaluating the bispectrum in curved field-space— with PyTransport 2.0

    Science.gov (United States)

    Ronayne, John W.; Mulryne, David J.

    2018-01-01

    We extend the transport framework for numerically evaluating the power spectrum and bispectrum in multi-field inflation to the case of a curved field-space metric. This method naturally accounts for all sub- and super-horizon tree level effects, including those induced by the curvature of the field-space. We present an open source implementation of our equations in an extension of the publicly available PyTransport code. Finally we illustrate how our technique is applied to examples of inflationary models with a non-trivial field-space metric.

  20. Longitudinal dispersion coefficients for numerical modeling of groundwater solute transport in heterogeneous formations.

    Science.gov (United States)

    Lee, Jonghyun; Rolle, Massimo; Kitanidis, Peter K

    2017-09-15

    Most recent research on hydrodynamic dispersion in porous media has focused on whole-domain dispersion while other research is largely on laboratory-scale dispersion. This work focuses on the contribution of a single block in a numerical model to dispersion. Variability of fluid velocity and concentration within a block is not resolved and the combined spreading effect is approximated using resolved quantities and macroscopic parameters. This applies whether the formation is modeled as homogeneous or discretized into homogeneous blocks but the emphasis here being on the latter. The process of dispersion is typically described through the Fickian model, i.e., the dispersive flux is proportional to the gradient of the resolved concentration, commonly with the Scheidegger parameterization, which is a particular way to compute the dispersion coefficients utilizing dispersivity coefficients. Although such parameterization is by far the most commonly used in solute transport applications, its validity has been questioned. Here, our goal is to investigate the effects of heterogeneity and mass transfer limitations on block-scale longitudinal dispersion and to evaluate under which conditions the Scheidegger parameterization is valid. We compute the relaxation time or memory of the system; changes in time with periods larger than the relaxation time are gradually leading to a condition of local equilibrium under which dispersion is Fickian. The method we use requires the solution of a steady-state advection-dispersion equation, and thus is computationally efficient, and applicable to any heterogeneous hydraulic conductivity K field without requiring statistical or structural assumptions. The method was validated by comparing with other approaches such as the moment analysis and the first order perturbation method. We investigate the impact of heterogeneity, both in degree and structure, on the longitudinal dispersion coefficient and then discuss the role of local dispersion

  1. Fate and Transport of Nanoparticles in Porous Media: A Numerical Study

    Science.gov (United States)

    Taghavy, Amir

    Understanding the transport characteristics of NPs in natural soil systems is essential to revealing their potential impact on the food chain and groundwater. In addition, many nanotechnology-based remedial measures require effective transport of NPs through soil, which necessitates accurate understanding of their transport and retention behavior. Based upon the conceptual knowledge of environmental behavior of NPs, mathematical models can be developed to represent the coupling of processes that govern the fate of NPs in subsurface, serving as effective tools for risk assessment and/or design of remedial strategies. This work presents an innovative hybrid Eulerian-Lagrangian modeling technique for simulating the simultaneous reactive transport of nanoparticles (NPs) and dissolved constituents in porous media. Governing mechanisms considered in the conceptual model include particle-soil grain, particle-particle, particle-dissolved constituents, and particle- oil/water interface interactions. The main advantage of this technique, compared to conventional Eulerian models, lies in its ability to address non-uniformity in physicochemical particle characteristics. The developed numerical simulator was applied to investigate the fate and transport of NPs in a number of practical problems relevant to the subsurface environment. These problems included: (1) reductive dechlorination of chlorinated solvents by zero-valent iron nanoparticles (nZVI) in dense non-aqueous phase liquid (DNAPL) source zones; (2) reactive transport of dissolving silver nanoparticles (nAg) and the dissolved silver ions; (3) particle-particle interactions and their effects on the particle-soil grain interactions; and (4) influence of particle-oil/water interface interactions on NP transport in porous media.

  2. Concatenating algorithms for parallel numerical simulations coupling radiation hydrodynamics with neutron transport

    International Nuclear Information System (INIS)

    Mo Zeyao

    2004-11-01

    Multiphysics parallel numerical simulations are usually essential to simplify researches on complex physical phenomena in which several physics are tightly coupled. It is very important on how to concatenate those coupled physics for fully scalable parallel simulation. Meanwhile, three objectives should be balanced, the first is efficient data transfer among simulations, the second and the third are efficient parallel executions and simultaneously developments of those simulation codes. Two concatenating algorithms for multiphysics parallel numerical simulations coupling radiation hydrodynamics with neutron transport on unstructured grid are presented. The first algorithm, Fully Loosely Concatenation (FLC), focuses on the independence of code development and the independence running with optimal performance of code. The second algorithm. Two Level Tightly Concatenation (TLTC), focuses on the optimal tradeoffs among above three objectives. Theoretical analyses for communicational complexity and parallel numerical experiments on hundreds of processors on two parallel machines have showed that these two algorithms are efficient and can be generalized to other multiphysics parallel numerical simulations. In especial, algorithm TLTC is linearly scalable and has achieved the optimal parallel performance. (authors)

  3. A hybrid perturbation-Galerkin technique for partial differential equations

    Science.gov (United States)

    Geer, James F.; Anderson, Carl M.

    1990-01-01

    A two-step hybrid perturbation-Galerkin technique for improving the usefulness of perturbation solutions to partial differential equations which contain a parameter is presented and discussed. In the first step of the method, the leading terms in the asymptotic expansion(s) of the solution about one or more values of the perturbation parameter are obtained using standard perturbation methods. In the second step, the perturbation functions obtained in the first step are used as trial functions in a Bubnov-Galerkin approximation. This semi-analytical, semi-numerical hybrid technique appears to overcome some of the drawbacks of the perturbation and Galerkin methods when they are applied by themselves, while combining some of the good features of each. The technique is illustrated first by a simple example. It is then applied to the problem of determining the flow of a slightly compressible fluid past a circular cylinder and to the problem of determining the shape of a free surface due to a sink above the surface. Solutions obtained by the hybrid method are compared with other approximate solutions, and its possible application to certain problems associated with domain decomposition is discussed.

  4. Numerical modelling of suspended radioactive sediment transport in a stream using matlab

    International Nuclear Information System (INIS)

    Sarpong, Linda

    2017-07-01

    The use of materials that contain radioactive substances has gained grounds in Ghana due to numerous benefits derived from them. These radioactive materials can be found in the areas of medicine, agriculture and industries such as mining. Though there are strict measures to ensure such material do not find its way into the environment, improper management of the waste poses a threat to the environment. To be able to understand the impact the radioactive material has on the environment, mathematical models play a very relevant role in tracking the level of pollution in any medium. This thesis was concerned with the numerical modelling for the transport of the radioactive solute material that suspends in a stream using Matlab at different velocities as a result of flooding or an accident for research purposes. The modelling was done by using partial differential equations describing relevant physical processes evolution which includes water level, dissolved and suspended substances concentration and velocities. The equation system basis are the mass conservation and momentum laws, state equation and state transport equations. The implicit finite difference scheme was used to evaluate the transport equation, Advection-Dispersion Equation (ADE) with respect to time and space. Solution algorithms for Matlab programming were developed and implemented for generating results for analysis. The results obtained showed that the model was able to simulate accurately the various levels of suspended radioactive sediment concentration changes in the flowing stream longitudinally. (au)

  5. The effects of static quartic anharmonicity on the quantum dynamics of a linear oscillator with time-dependent harmonic frequency: Perturbative analysis and numerical calculations

    International Nuclear Information System (INIS)

    Sarkar, P.; Bhattacharyya, S.P.

    1995-01-01

    The effects of quartic anharmonicity on the quantum dynamics of a linear oscillator with time-dependent force constant (K) or harmonic frequency (ω) are studied both perturbatively and numerically by the time-dependent Fourier grid Hamiltonian method. In the absence of anharmonicity, the ground-state population decreases and the population of an accessible excited state (k = 2.4, 6 ... ) increases with time. However, when anharmonicity is introduced, both the ground- and excited-state populations show typical oscillations. For weak coupling, the population of an accessible excited state at a certain instant of time (short) turns out to be a parabolic function of the anharmonic coupling constant (λ), when all other parameters of the system are kept fixed. This parabolic nature of the excited-state population vs. the λ profile is independent of the specific form of the time dependence of the force constant, K t . However, it depends upon the rate at which K t relaxes. For small anharmonic coupling strength and short time scales, the numerical results corroborate expectations based on the first-order time-dependent perturbative analysis, using a suitably repartitioned Hamiltonian that makes H 0 time-independent. Some of the possible experimental implications of our observations are analyzed, especially in relation to intensity oscillations observed in some charge-transfer spectra in systems in which the dephasing rates are comparable with the time scale of the electron transfer. 21 refs., 7 figs., 1 tab

  6. Application of Multistage Homotopy Perturbation Method to the Chaotic Genesio System

    Directory of Open Access Journals (Sweden)

    M. S. H. Chowdhury

    2012-01-01

    Full Text Available Finding accurate solution of chaotic system by using efficient existing numerical methods is very hard for its complex dynamical behaviors. In this paper, the multistage homotopy-perturbation method (MHPM is applied to the Chaotic Genesio system. The MHPM is a simple reliable modification based on an adaptation of the standard homotopy-perturbation method (HPM. The HPM is treated as an algorithm in a sequence of intervals for finding accurate approximate solutions to the Chaotic Genesio system. Numerical comparisons between the MHPM and the classical fourth-order Runge-Kutta (RK4 solutions are made. The results reveal that the new technique is a promising tool for the nonlinear chaotic systems of ordinary differential equations.

  7. Excitation energies from Görling-Levy perturbation theory along the range-separated adiabatic connection

    Science.gov (United States)

    Rebolini, Elisa; Teale, Andrew M.; Helgaker, Trygve; Savin, Andreas; Toulouse, Julien

    2018-06-01

    A Görling-Levy (GL)-based perturbation theory along the range-separated adiabatic connection is assessed for the calculation of electronic excitation energies. In comparison with the Rayleigh-Schrödinger (RS)-based perturbation theory this GL-based perturbation theory keeps the ground-state density constant at each order and thus gives the correct ionisation energy at each order. Excitation energies up to first order in the perturbation have been calculated numerically for the helium and beryllium atoms and the hydrogen molecule without introducing any density-functional approximations. In comparison with the RS-based perturbation theory, the present GL-based perturbation theory gives much more accurate excitation energies for Rydberg states but similar excitation energies for valence states.

  8. Linear analysis on the growth of non-spherical perturbations in supersonic accretion flows

    Energy Technology Data Exchange (ETDEWEB)

    Takahashi, Kazuya; Yamada, Shoichi, E-mail: ktakahashi@heap.phys.waseda.ac.jp [Advanced Research Institute for Science and Engineering, Waseda University, 3-4-1 Okubo, Shinjuku 169-8555 (Japan)

    2014-10-20

    We analyzed the growth of non-spherical perturbations in supersonic accretion flows. We have in mind an application to the post-bounce phase of core-collapse supernovae (CCSNe). Such non-spherical perturbations have been suggested by a series of papers by Arnett, who has numerically investigated violent convections in the outer layers of pre-collapse stars. Moreover, Couch and Ott demonstrated in their numerical simulations that such perturbations may lead to a successful supernova even for a progenitor that fails to explode without fluctuations. This study investigated the linear growth of perturbations during the infall onto a stalled shock wave. The linearized equations are solved as an initial and boundary value problem with the use of a Laplace transform. The background is a Bondi accretion flow whose parameters are chosen to mimic the 15 M {sub ☉} progenitor model by Woosley and Heger, which is supposed to be a typical progenitor of CCSNe. We found that the perturbations that are given at a large radius grow as they flow down to the shock radius; the density perturbations can be amplified by a factor of 30, for example. We analytically show that the growth rate is proportional to l, the index of the spherical harmonics. We also found that the perturbations oscillate in time with frequencies that are similar to those of the standing accretion shock instability. This may have an implication for shock revival in CCSNe, which will be investigated in our forthcoming paper in more detail.

  9. Mono-implicit Runge Kutta schemes for singularly perturbed delay differential equations

    Science.gov (United States)

    Rihan, Fathalla A.; Al-Salti, Nasser S.

    2017-09-01

    In this paper, we adapt Mono-Implicit Runge-Kutta schemes for numerical approximations of singularly perturbed delay differential equations. The schemes are developed to reduce the computational cost of the fully implicit method which combine the accuracy of implicit method and efficient implementation. Numerical stability properties of the schemes are investigated. Numerical simulations are provided to show the effectiveness of the method for both stiff and non-stiff initial value problems.

  10. Numerical analysis of coupled water transport in wood with a focus on the coupling parameter sorption

    DEFF Research Database (Denmark)

    Hozjan, T.; Turk, G.; Rodman, U.

    2011-01-01

    This paper presents a study of sorption rate function in a so-called multi-Fickian or multi-phase model. This model describes the complex moisture transport system in wood, which consists of separate water-vapour and bound-water diffusion interacting through sorption. In the numerical example inf...... influence of the sorption rate function on water transport is presented. It can be seen that the sorption rate function has a noticeable influence on coupled water transport in wood....

  11. Operator Decomposition Framework for Perturbation Theory

    Energy Technology Data Exchange (ETDEWEB)

    Abdel-Khalik, Hany S.; Wang, Congjian; Bang, Young Suk [North Carolina State University, Raleigh (United States)

    2012-05-15

    This summary describes a new framework for perturbation theory intended to improve its performance, in terms of the associated computational cost and the complexity of implementation, for routine reactor calculations in support of design, analysis, and regulation. Since its first introduction in reactor analysis by Winger, perturbation theory has assumed an aura of sophistication with regard to its implementation and its capabilities. Only few reactor physicists, typically mathematically proficient, have contributed to its development, with the general body of the nuclear engineering community remaining unaware of its current status, capabilities, and challenges. Given its perceived sophistication and the small body of community users, the application of perturbation theory has been limited to investigatory analyses only. It is safe to say that the nuclear community is split into two groups, a small one which understands the theory and, and a much bigger group with the perceived notion that perturbation theory is nothing but a fancy mathematical approach that has very little use in practice. Over the past three years, research has demonstrated two goals. First, reduce the computational cost of perturbation theory in order to enable its use for routine reactor calculations. Second, expose some of the myth about perturbation theory and present it in a form that is simple and relatable in order to stimulate the interest of nuclear practitioners, especially those who are currently working on the development of next generation reactor design and analysis tools. The operator decomposition approach has its roots in linear algebra and can be easily understood by code developers, especially those involved in the design of iterative numerical solution strategies

  12. Numerical Simulation of Ion Transport in a Nano-Electrospray Ion Source at Atmospheric Pressure

    Science.gov (United States)

    Wang, Wei; Bajic, Steve; John, Benzi; Emerson, David R.

    2018-03-01

    Understanding ion transport properties from the ion source to the mass spectrometer (MS) is essential for optimizing device performance. Numerical simulation helps in understanding of ion transport properties and, furthermore, facilitates instrument design. In contrast to previously reported numerical studies, ion transport simulations in a continuous injection mode whilst considering realistic space-charge effects have been carried out. The flow field was solved using Reynolds-averaged Navier-Stokes (RANS) equations, and a particle-in-cell (PIC) method was applied to solve a time-dependent electric field with local charge density. A series of ion transport simulations were carried out at different cone gas flow rates, ion source currents, and capillary voltages. A force evaluation analysis reveals that the electric force, the drag force, and the Brownian force are the three dominant forces acting on the ions. Both the experimental and simulation results indicate that cone gas flow rates of ≤250 slph (standard liter per hour) are important for high ion transmission efficiency, as higher cone gas flow rates reduce the ion signal significantly. The simulation results also show that the ion transmission efficiency reduces exponentially with an increased ion source current. Additionally, the ion loss due to space-charge effects has been found to be predominant at a higher ion source current, a lower capillary voltage, and a stronger cone gas counterflow. The interaction of the ion driving force, ion opposing force, and ion dispersion is discussed to illustrate ion transport mechanism in the ion source at atmospheric pressure. [Figure not available: see fulltext.

  13. A perturbative analysis of modulated amplitude waves in Bose-Einstein condensates

    International Nuclear Information System (INIS)

    Porter, Mason A.; Cvitanovic, Predrag

    2004-01-01

    We apply Lindstedt's method and multiple scale perturbation theory to analyze spatio-temporal structures in nonlinear Schroedinger equations and thereby study the dynamics of quasi-one-dimensional Bose-Einstein condensates with mean-field interactions. We determine the dependence of the amplitude of modulated amplitude waves on their wave number. We also explore the band structure of Bose-Einstein condensates in detail using Hamiltonian perturbation theory and supporting numerical simulations

  14. Validation of MORET 4 perturbation against 'physical' type fission products experiments

    International Nuclear Information System (INIS)

    Anno, Jacques; Jacquet, Olivier; Miss, Joachim

    2003-01-01

    After shortly recalling one among the many pertinent recent features of the French criticality CRISTAL package i.e. the perturbation algorithm (so called MORET 4 'Perturbation' or MP), this paper presents original MP validations. Numerical and experimental validations are made using close fission products (FP) experiments. As results, it is shown that, all being equal, MP can detect FP's absorption cross-section variations in the range 0.3-1.2%. (author)

  15. Perturbative calculation of quasinormal modes of AdS Schwarzschild black holes

    International Nuclear Information System (INIS)

    Musiri, Suphot; Ness, Scott; Siopsis, George

    2006-01-01

    We calculate analytically quasinormal modes of AdS Schwarzschild black holes including first-order corrections. We consider massive scalar, gravitational and electromagnetic perturbations. Our results are in good agreement with numerical calculations. In the case of electromagnetic perturbations, ours is the first calculation to provide an analytic expression for quasinormal frequencies, because the effective potential vanishes at zeroth order. We show that the first-order correction is logarithmic

  16. Numerical modelling of solute transport at Forsmark with MIKE SHE. Site descriptive modelling SDM-Site Forsmark

    Energy Technology Data Exchange (ETDEWEB)

    Gustafsson, Lars-Goeran; Sassner, Mona (DHI Sverige AB, Stockholm (Sweden)); Bosson, Emma (Swedish Nuclear Fuel and Waste Management Co., Stockholm (Sweden))

    2008-12-15

    The Swedish Nuclear Fuel and Waste Management Company (SKB) is performing site investigations at two different locations in Sweden, referred to as the Forsmark and Laxemar areas, with the objective of siting a final repository for high-level radioactive waste. Data from the site investigations are used in a variety of modelling activities. This report presents model development and results of numerical transport modelling based on the numerical flow modelling of surface water and near-surface groundwater at the Forsmark site. The numerical modelling was performed using the modelling tool MIKE SHE and is based on the site data and conceptual model of the Forsmark areas. This report presents solute transport applications based on both particle tracking simulations and advection-dispersion calculations. The MIKE SHE model is the basis for the transport modelling presented in this report. Simulation cases relevant for the transport from a deep geological repository have been studied, but also the pattern of near surface recharge and discharge areas. When the main part of the modelling work presented in this report was carried out, the flow modelling of the Forsmark site was not finalised. Thus, the focus of this work is to describe the sensitivity to different transport parameters, and not to point out specific areas as discharge areas from a future repository (this is to be done later, within the framework of the safety assessment). In the last chapter, however, results based on simulations with the re-calibrated MIKE SHE flow model are presented. The results from the MIKE SHE water movement calculations were used by cycling the calculated transient flow field for a selected one-year period as many times as needed to achieve the desired simulation period. The solute source was located either in the bedrock or on top of the model. In total, 15 different transport simulation cases were studied. Five of the simulations were particle tracking simulations, whereas the rest

  17. On the Numerical Modeling of Fluid Instabilities in the Small-Amplitude Limit

    Science.gov (United States)

    Zalesak, Steven; Schmitt, A. J.; Velikovich, A. L.

    2008-11-01

    The problem we wish to address is that of accurately modeling the evolution of small-amplitude perturbations to a time- dependent flow, where the unperturbed flow itself exhibits large-amplitude temporal and spatial variations. In particular, we wish to accurately model the evolution of small-amplitude perturbations to an imploding ICF pellet, which is subject to both Richtmyer-Meshkov and Rayleigh-Taylor instabilities. This modeling is difficult despite the expected linear evolution of the perturbations themselves, because these perturbations are embedded in a highly nonlinear, strongly- shocked, and highly complex flow field which in and of itself stresses numerical computation capabilities, and whose simulation often employs numerical techniques which were not designed with the proper treatment of small-amplitude perturbations in mind. We will review some of the techniques that we have found to be of use toward this end, including the imposition of a ``differentiability condition'' on the component numerical algorithms of the codes which implement such modeling, the appropriate representation of interfaces in an Eulerian hydrodynamics context, and the role of exact energy conservation.

  18. Charged scalar perturbations around Garfinkle–Horowitz–Strominger black holes

    Directory of Open Access Journals (Sweden)

    Cheng-Yong Zhang

    2015-10-01

    Full Text Available We examine the stability of the Garfinkle–Horowitz–Strominger (GHS black hole under charged scalar perturbations. Employing the appropriate numerical methods, we show that the GHS black hole is always stable against charged scalar perturbations. This is different from the results obtained in the de Sitter and anti-de Sitter black holes. Furthermore, we argue that in the GHS black hole background there is no amplification of the incident charged scalar wave to cause the superradiance, so that the superradiant instability cannot exist in this spacetime.

  19. Direct Numerical Simulation of the Rayleigh−Taylor Instability with the Spectral Element Method

    International Nuclear Information System (INIS)

    Xu, Zhang; Duo-Wang, Tan

    2009-01-01

    A novel method is proposed to simulate Rayleigh−Taylor instabilities using a specially-developed unsteady three-dimensional high-order spectral element method code. The numerical model used consists of Navier–Stokes equations and a transport-diffusive equation. The code is first validated with the results of linear stability perturbation theory. Then several characteristics of the Rayleigh−Taylor instabilities are studied using this three-dimensional unsteady code, including instantaneous turbulent structures and statistical turbulent mixing heights under different initial wave numbers. These results indicate that turbulent structures of Rayleigh–Taylor instabilities are strongly dependent on the initial conditions. The results also suggest that a high-order numerical method should provide the capability of simulating small scale fluctuations of Rayleigh−Taylor instabilities of turbulent flows. (fundamental areas of phenomenology (including applications))

  20. Numerical study of the influence of the convective heat transport on acoustic streaming in a standing wave.

    Science.gov (United States)

    Červenka, Milan; Bednařík, Michal

    2018-02-01

    Within this work, acoustic streaming in an air-filled cylindrical resonator with walls supporting a temperature gradient is studied by means of numerical simulations. A set of equations based on successive approximations is derived from the Navier-Stokes equations. The equations take into account the acoustic-streaming-driven convective heat transport; as time-averaged secondary-field quantities are directly calculated, the equations are much easier to integrate than the original fluid-dynamics equations. The model equations are implemented and integrated employing commercial software COMSOL Multiphysics. Numerical calculations are conducted for the case of a resonator with a wall-temperature gradient corresponding to the action of a thermoacoustic effect. It is shown that due to the convective heat transport, the streaming profile is considerably distorted even in the case of weak wall-temperature gradients. The numerical results are consistent with available experimental data.

  1. Electromagnetic transport components and sheared flows in drift-Alfven turbulence

    DEFF Research Database (Denmark)

    Naulin, V.

    2003-01-01

    Results from three-dimensional numerical simulations of drift-Alfven turbulence in a toroidal geometry with sheared magnetic field are presented. The simulations show a relation between self-generated poloidal shear flows and magnetic field perturbations. For large values of the plasma beta we ob...... with a folded Gaussian, while the PDFs of the spatially averaged transport are in good agreement with an extreme value distribution. (C) 2003 American Institute of Physics....... related to magnetic flutter is proposed. The characteristics of the ExB flux are investigated using probability density distribution functions (PDFs). Although they are not Gaussian, no signs of algebraic tails in the PDFs are observed. The PDFs of the pointwise transport are found to agree well...

  2. A non-perturbative operator product expansion

    International Nuclear Information System (INIS)

    Bietenholz, W.; Cundy, N.; Goeckeler, M.

    2009-10-01

    Nucleon structure functions can be observed in Deep Inelastic Scattering experiments, but it is an outstanding challenge to confront them with fully non-perturbative QCD results. For this purpose we investigate the product of electromagnetic currents (with large photonmomenta) between quark states (of low momenta). By means of an Operator Product Expansion the structure function can be decomposed into matrix elements of local operators, and Wilson coefficients. For consistency both have to be computed non-perturbatively. Here we present precision results for a set of Wilson coefficients. They are evaluated from propagators for numerous quark momenta on the lattice, where the use of chiral fermions suppresses undesired operator mixing. This overdetermines the Wilson coefficients, but reliable results can be extracted by means of a Singular Value Decomposition. (orig.)

  3. Stochastic porous media modeling and high-resolution schemes for numerical simulation of subsurface immiscible fluid flow transport

    Science.gov (United States)

    Brantson, Eric Thompson; Ju, Binshan; Wu, Dan; Gyan, Patricia Semwaah

    2018-04-01

    This paper proposes stochastic petroleum porous media modeling for immiscible fluid flow simulation using Dykstra-Parson coefficient (V DP) and autocorrelation lengths to generate 2D stochastic permeability values which were also used to generate porosity fields through a linear interpolation technique based on Carman-Kozeny equation. The proposed method of permeability field generation in this study was compared to turning bands method (TBM) and uniform sampling randomization method (USRM). On the other hand, many studies have also reported that, upstream mobility weighting schemes, commonly used in conventional numerical reservoir simulators do not accurately capture immiscible displacement shocks and discontinuities through stochastically generated porous media. This can be attributed to high level of numerical smearing in first-order schemes, oftentimes misinterpreted as subsurface geological features. Therefore, this work employs high-resolution schemes of SUPERBEE flux limiter, weighted essentially non-oscillatory scheme (WENO), and monotone upstream-centered schemes for conservation laws (MUSCL) to accurately capture immiscible fluid flow transport in stochastic porous media. The high-order schemes results match well with Buckley Leverett (BL) analytical solution without any non-oscillatory solutions. The governing fluid flow equations were solved numerically using simultaneous solution (SS) technique, sequential solution (SEQ) technique and iterative implicit pressure and explicit saturation (IMPES) technique which produce acceptable numerical stability and convergence rate. A comparative and numerical examples study of flow transport through the proposed method, TBM and USRM permeability fields revealed detailed subsurface instabilities with their corresponding ultimate recovery factors. Also, the impact of autocorrelation lengths on immiscible fluid flow transport were analyzed and quantified. A finite number of lines used in the TBM resulted into visual

  4. The bispectrum of matter perturbations from cosmic strings

    Energy Technology Data Exchange (ETDEWEB)

    Regan, Donough; Hindmarsh, Mark, E-mail: d.regan@sussex.ac.uk, E-mail: m.b.hindmarsh@sussex.ac.uk [Astronomy Centre, University of Sussex, Falmer, Brighton, BN1 9QH (United Kingdom)

    2015-03-01

    We present the first calculation of the bispectrum of the matter perturbations induced by cosmic strings. The calculation is performed in two different ways: the first uses the unequal time correlators (UETCs) of the string network - computed using a Gaussian model previously employed for cosmic string power spectra. The second approach uses the wake model, where string density perturbations are concentrated in sheet-like structures whose surface density grows with time. The qualitative and quantitative agreement of the two gives confidence to the results. An essential ingredient in the UETC approach is the inclusion of compensation factors in the integration with the Green's function of the matter and radiation fluids, and we show that these compensation factors must be included in the wake model also. We also present a comparison of the UETCs computed in the Gaussian model, and those computed in the unconnected segment model (USM) used by the standard cosmic string perturbation package CMBACT. We compare numerical estimates for the bispectrum of cosmic strings to those produced by perturbations from an inflationary era, and discover that, despite the intrinsically non-Gaussian nature of string-induced perturbations, the matter bispectrum is unlikely to produce competitive constraints on a population of cosmic strings.

  5. Effects of stratospheric perturbations on the solar radiation budget

    International Nuclear Information System (INIS)

    Luther, F.M.

    1978-04-01

    The changes in solar absorption and in local heating rates due to perturbations to O 3 and NO 2 concentrations caused by stratospheric injection of NO/sub x/ and CFM pollutants are assessed. The changes in species concentration profiles are derived from theoretical calculations using a transport-kinetics model. Because of significant changes in our understanding of stratospheric chemistry during the past year, the assessment of the effect of stratospheric perturbations on the solar radiation budget differs from previous assessments. Previously, a reduction in O 3 due to an NO/sub x/ injection caused a net decrease in the gaseous solar absorption;now the same perturbation leads to a net increase. The implication of these changes on the surface temperature is also discussed

  6. Perturbations and quasi-normal modes of black holes in Einstein-Aether theory

    International Nuclear Information System (INIS)

    Konoplya, R.A.; Zhidenko, A.

    2007-01-01

    We develop a new method for calculation of quasi-normal modes of black holes, when the effective potential, which governs black hole perturbations, is known only numerically in some region near the black hole. This method can be applied to perturbations of a wide class of numerical black hole solutions. We apply it to the black holes in the Einstein-Aether theory, a theory where general relativity is coupled to a unit time-like vector field, in order to observe local Lorentz symmetry violation. We found that in the non-reduced Einstein-Aether theory, real oscillation frequency and damping rate of quasi-normal modes are larger than those of Schwarzschild black holes in the Einstein theory

  7. Exponential discontinuous numerical scheme for electron transport in the continuous slowing down approximation

    International Nuclear Information System (INIS)

    Prinja, A.K.

    1997-01-01

    A nonlinear discretization scheme in space and energy, based on the recently developed exponential discontinuous method, is applied to continuous slowing down dominated electron transport (i.e., in the absence of scattering.) Numerical results for dose and charge deposition are obtained and compared against results from the ONELD and ONEBFP codes, and against exact results from an adjoint Monte Carlo code. It is found that although the exponential discontinuous scheme yields strictly positive and monotonic solutions, the dose profile is considerably straggled when compared to results from the linear codes. On the other hand, the linear schemes produce negative results which, furthermore, do not damp effectively in some cases. A general conclusion is that while yielding strictly positive solutions, the exponential discontinuous method does not show the crude cell accuracy for charged particle transport as was apparent for neutral particle transport problems

  8. Gravitational radiation and 3D numerical relativity

    International Nuclear Information System (INIS)

    Nakamura, T.

    1986-01-01

    Study of Numerical Relativity in Kyoto is reviewed. Main topics discussed are 2D rotating collapse, phase cancellation effects and perturbation calculation of the gravitational radiation from a particle falling into a black hole. New numerical results on 3D time evolution of pure gravitational waves are also presented

  9. Searching Less Perturbed Circular Orbits for a Spacecraft Travelling around Europa

    Directory of Open Access Journals (Sweden)

    J. P. S. Carvalho

    2014-01-01

    Full Text Available Space missions to visit the natural satellite of Jupiter, Europa, constitute an important topic in space activities today, because missions to this moon are under study now. Several considerations have to be made for these missions. The present paper searches for less perturbed circular orbits around Europa. This search is made based on the total effects of the perturbing forces over the time, evaluated by the integral of those forces over the time. This value depends on the dynamical model and on the orbit of the spacecraft. The perturbing forces considered are the third-body perturbation that comes from Jupiter and the J2, J3, and C22 terms of the gravitational potential of Europa. Several numerical studies are performed and the results show the locations of the less perturbed orbits. Using those results, it is possible to find near-circular frozen orbits with smaller amplitudes of variations of the orbital elements.

  10. Numerical modeling of coupled water flow and heat transport in soil and snow

    Science.gov (United States)

    Thijs J. Kelleners; Jeremy Koonce; Rose Shillito; Jelle Dijkema; Markus Berli; Michael H. Young; John M. Frank; William Massman

    2016-01-01

    A one-dimensional vertical numerical model for coupled water flow and heat transport in soil and snow was modified to include all three phases of water: vapor, liquid, and ice. The top boundary condition in the model is driven by incoming precipitation and the surface energy balance. The model was applied to three different terrestrial systems: A warm desert bare...

  11. Numerical modelling of solute transport at Forsmark with MIKE SHE. Site descriptive modelling SDM-Site Forsmark

    International Nuclear Information System (INIS)

    Gustafsson, Lars-Goeran; Sassner, Mona; Bosson, Emma

    2008-12-01

    The Swedish Nuclear Fuel and Waste Management Company (SKB) is performing site investigations at two different locations in Sweden, referred to as the Forsmark and Laxemar areas, with the objective of siting a final repository for high-level radioactive waste. Data from the site investigations are used in a variety of modelling activities. This report presents model development and results of numerical transport modelling based on the numerical flow modelling of surface water and near-surface groundwater at the Forsmark site. The numerical modelling was performed using the modelling tool MIKE SHE and is based on the site data and conceptual model of the Forsmark areas. This report presents solute transport applications based on both particle tracking simulations and advection-dispersion calculations. The MIKE SHE model is the basis for the transport modelling presented in this report. Simulation cases relevant for the transport from a deep geological repository have been studied, but also the pattern of near surface recharge and discharge areas. When the main part of the modelling work presented in this report was carried out, the flow modelling of the Forsmark site was not finalised. Thus, the focus of this work is to describe the sensitivity to different transport parameters, and not to point out specific areas as discharge areas from a future repository (this is to be done later, within the framework of the safety assessment). In the last chapter, however, results based on simulations with the re-calibrated MIKE SHE flow model are presented. The results from the MIKE SHE water movement calculations were used by cycling the calculated transient flow field for a selected one-year period as many times as needed to achieve the desired simulation period. The solute source was located either in the bedrock or on top of the model. In total, 15 different transport simulation cases were studied. Five of the simulations were particle tracking simulations, whereas the rest

  12. Selberg zeta functions and transfer operators an experimental approach to singular perturbations

    CERN Document Server

    Fraczek, Markus Szymon

    2017-01-01

    This book presents a method for evaluating Selberg zeta functions via transfer operators for the full modular group and its congruence subgroups with characters. Studying zeros of Selberg zeta functions for character deformations allows us to access the discrete spectra and resonances of hyperbolic Laplacians under both singular and non-singular perturbations. Areas in which the theory has not yet been sufficiently developed, such as the spectral theory of transfer operators or the singular perturbation theory of hyperbolic Laplacians, will profit from the numerical experiments discussed in this book. Detailed descriptions of numerical approaches to the spectra and eigenfunctions of transfer operators and to computations of Selberg zeta functions will be of value to researchers active in analysis, while those researchers focusing more on numerical aspects will benefit from discussions of the analytic theory, in particular those concerning the transfer operator method and the spectral theory of hyperbolic spac...

  13. Curvature perturbation spectra from waterfall transition, black hole constraints and non-Gaussianity

    Energy Technology Data Exchange (ETDEWEB)

    Bugaev, Edgar; Klimai, Peter, E-mail: bugaev@pcbai10.inr.ruhep.ru, E-mail: pklimai@gmail.com [Institute for Nuclear Research, Russian Academy of Sciences, 60th October Anniversary Prospect 7a, 117312 Moscow (Russian Federation)

    2011-11-01

    We carried out numerical calculations of a contribution of the waterfall field to the primordial curvature perturbation (on uniform density hypersurfaces) ζ, which is produced during waterfall transition in hybrid inflation scenario. The calculation is performed for a broad interval of values of the model parameters. We show that there is a strong growth of amplitudes of the curvature perturbation spectrum in the limit when the bare mass-squared of the waterfall field becomes comparable with the square of Hubble parameter. We show that in this limit the primordial black hole constraints on the curvature perturbations must be taken into account. It is shown that, in the same limit, peak values of the curvature perturbation spectra are far beyond horizon, and the spectra are strongly non-Gaussian.

  14. Curvature perturbation spectra from waterfall transition, black hole constraints and non-Gaussianity

    International Nuclear Information System (INIS)

    Bugaev, Edgar; Klimai, Peter

    2011-01-01

    We carried out numerical calculations of a contribution of the waterfall field to the primordial curvature perturbation (on uniform density hypersurfaces) ζ, which is produced during waterfall transition in hybrid inflation scenario. The calculation is performed for a broad interval of values of the model parameters. We show that there is a strong growth of amplitudes of the curvature perturbation spectrum in the limit when the bare mass-squared of the waterfall field becomes comparable with the square of Hubble parameter. We show that in this limit the primordial black hole constraints on the curvature perturbations must be taken into account. It is shown that, in the same limit, peak values of the curvature perturbation spectra are far beyond horizon, and the spectra are strongly non-Gaussian

  15. Acoustic wavefield evolution as a function of source location perturbation

    KAUST Repository

    Alkhalifah, Tariq Ali

    2010-01-01

    differential equations have the same structure as the wave equation with a source function that depends on the background (original source) wavefield. The similarity in form implies that we can use familiar numerical methods to solve the perturbation equations

  16. Peristaltic transport of Bingham plastic fluid considering magnetic field, Soret and Dufour effects

    Directory of Open Access Journals (Sweden)

    T. Hayat

    Full Text Available Current attempt addresses the peristaltic transport of Bingham plastic fluid under the influence of magnetic force. Space dependent viscosity is considered. Novel Soret and Dufour effects are retained in the mathematical model. Problem formulation is presented through the conventional lubrication approach. Series solutions of the arising non-linear problem are developed via regular perturbation approach. Special attention is given to the role of embedded parameters on the axial velocity, temperature, concentration and pressure distributions. Furthermore the numerical solution of pressure rise per wavelength is obtained through numerical integration because its analytical solution seems impossible. Keywords: Bingham fluid, Variable viscosity, MHD and Joule heating, Soret and Dufour effects

  17. A Finite-Difference Solution of Solute Transport through a Membrane Bioreactor

    Directory of Open Access Journals (Sweden)

    B. Godongwana

    2015-01-01

    Full Text Available The current paper presents a theoretical analysis of the transport of solutes through a fixed-film membrane bioreactor (MBR, immobilised with an active biocatalyst. The dimensionless convection-diffusion equation with variable coefficients was solved analytically and numerically for concentration profiles of the solutes through the MBR. The analytical solution makes use of regular perturbation and accounts for radial convective flow as well as axial diffusion of the substrate species. The Michaelis-Menten (or Monod rate equation was assumed for the sink term, and the perturbation was extended up to second-order. In the analytical solution only the first-order limit of the Michaelis-Menten equation was considered; hence the linearized equation was solved. In the numerical solution, however, this restriction was lifted. The solution of the nonlinear, elliptic, partial differential equation was based on an implicit finite-difference method (FDM. An upwind scheme was employed for numerical stability. The resulting algebraic equations were solved simultaneously using the multivariate Newton-Raphson iteration method. The solution allows for the evaluation of the effect on the concentration profiles of (i the radial and axial convective velocity, (ii the convective mass transfer rates, (iii the reaction rates, (iv the fraction retentate, and (v the aspect ratio.

  18. An Analytic Approach to Developing Transport Threshold Models of Neoclassical Tearing Modes in Tokamaks

    International Nuclear Information System (INIS)

    Mikhailovskii, A.B.; Shirokov, M.S.; Konovalov, S.V.; Tsypin, V.S.

    2005-01-01

    Transport threshold models of neoclassical tearing modes in tokamaks are investigated analytically. An analysis is made of the competition between strong transverse heat transport, on the one hand, and longitudinal heat transport, longitudinal heat convection, longitudinal inertial transport, and rotational transport, on the other hand, which leads to the establishment of the perturbed temperature profile in magnetic islands. It is shown that, in all these cases, the temperature profile can be found analytically by using rigorous solutions to the heat conduction equation in the near and far regions of a chain of magnetic islands and then by matching these solutions. Analytic expressions for the temperature profile are used to calculate the contribution of the bootstrap current to the generalized Rutherford equation for the island width evolution with the aim of constructing particular transport threshold models of neoclassical tearing modes. Four transport threshold models, differing in the underlying competing mechanisms, are analyzed: collisional, convective, inertial, and rotational models. The collisional model constructed analytically is shown to coincide exactly with that calculated numerically; the reason is that the analytical temperature profile turns out to be the same as the numerical profile. The results obtained can be useful in developing the next generation of general threshold models. The first steps toward such models have already been made

  19. A numerical model of non-equilibrium thermal plasmas. I. Transport properties

    Energy Technology Data Exchange (ETDEWEB)

    Zhang XiaoNing; Xia WeiDong [Department of Thermal Science and Energy Engineering, University of Science and Technology of China, Hefei, Anhui Province 230026 (China); Li HePing [Department of Engineering Physics, Tsinghua University, Beijing 100084 (China); Murphy, Anthony B. [CSIRO Materials Science and Engineering, PO Box 218, Lindfield NSW 2070 (Australia)

    2013-03-15

    A self-consistent and complete numerical model for investigating the fundamental processes in a non-equilibrium thermal plasma system consists of the governing equations and the corresponding physical properties of the plasmas. In this paper, a new kinetic theory of the transport properties of two-temperature (2-T) plasmas, based on the solution of the Boltzmann equation using a modified Chapman-Enskog method, is presented. This work is motivated by the large discrepancies between the theories for the calculation of the transport properties of 2-T plasmas proposed by different authors in previous publications. In the present paper, the coupling between electrons and heavy species is taken into account, but reasonable simplifications are adopted, based on the physical fact that m{sub e}/m{sub h} Much-Less-Than 1, where m{sub e} and m{sub h} are, respectively, the masses of electrons and heavy species. A new set of formulas for the transport coefficients of 2-T plasmas is obtained. The new theory has important physical and practical advantages over previous approaches. In particular, the diffusion coefficients are complete and satisfy the mass conversation law due to the consideration of the coupling between electrons and heavy species. Moreover, this essential requirement is satisfied without increasing the complexity of the transport coefficient formulas. Expressions for the 2-T combined diffusion coefficients are obtained. The expressions for the transport coefficients can be reduced to the corresponding well-established expressions for plasmas in local thermodynamic equilibrium for the case in which the electron and heavy-species temperatures are equal.

  20. A numerical model of non-equilibrium thermal plasmas. I. Transport properties

    Science.gov (United States)

    Zhang, Xiao-Ning; Li, He-Ping; Murphy, Anthony B.; Xia, Wei-Dong

    2013-03-01

    A self-consistent and complete numerical model for investigating the fundamental processes in a non-equilibrium thermal plasma system consists of the governing equations and the corresponding physical properties of the plasmas. In this paper, a new kinetic theory of the transport properties of two-temperature (2-T) plasmas, based on the solution of the Boltzmann equation using a modified Chapman-Enskog method, is presented. This work is motivated by the large discrepancies between the theories for the calculation of the transport properties of 2-T plasmas proposed by different authors in previous publications. In the present paper, the coupling between electrons and heavy species is taken into account, but reasonable simplifications are adopted, based on the physical fact that me/mh ≪ 1, where me and mh are, respectively, the masses of electrons and heavy species. A new set of formulas for the transport coefficients of 2-T plasmas is obtained. The new theory has important physical and practical advantages over previous approaches. In particular, the diffusion coefficients are complete and satisfy the mass conversation law due to the consideration of the coupling between electrons and heavy species. Moreover, this essential requirement is satisfied without increasing the complexity of the transport coefficient formulas. Expressions for the 2-T combined diffusion coefficients are obtained. The expressions for the transport coefficients can be reduced to the corresponding well-established expressions for plasmas in local thermodynamic equilibrium for the case in which the electron and heavy-species temperatures are equal.

  1. Numerical modeling of water-vapor transport during pre-storm and COHMEX

    Science.gov (United States)

    Djuric, Dusan

    1986-01-01

    Initial conditions are designed for numerical simulation of mesocale processes in the atmosphere using the Limited Area Mesoscale Prediction System (LAMPS) model. These initial conditions represent an idealized baroclinic wave in which the transport of water vapor can be simulated. The constructed atmosphere has two homogeneous air masses, polar front, polar jet stream and a stratosphere. All these simulate the basic structure of the earth's atmosphere. The hydrostatic and geostrophic balances make it possible to evaluate mutually consistent fields of wind and of the height of isobaric surfaces.

  2. Numerical studies of unsteady coherent structures and transport in two-dimensional flows

    Energy Technology Data Exchange (ETDEWEB)

    Hesthaven, J.S.

    1995-08-01

    The dynamics of unsteady two-dimensional coherent structures in various physical systems is studied through direct numerical solution of the dynamical equations using spectral methods. The relation between the Eulerian and the Lagrangian auto-correlation functions in two-dimensional homogeneous, isotropic turbulence is studied. A simple analytic expression for the Eulerian and Lagrangian auto-correlation function for the fluctuating velocity field is derived solely on the basis of the one-dimensional power spectrum. The long-time evolution of monopolar and dipolar vortices in anisotropic systems relevant for geophysics and plasma physics is studied by direct numerical solution. Transport properties and spatial reorganization of vortical structures are found to depend strongly on the initial conditions. Special attention is given to the dynamics of strong monopoles and the development of unsteady tripolar structures. The development of coherent structures in fluid flows, incompressible as well as compressible, is studied by novel numerical schemes. The emphasis is on the development of spectral methods sufficiently advanced as to allow for detailed and accurate studies of the self-organizing processes. (au) 1 ill., 94 refs.

  3. Applicability of numerical model for seabed topography changes by tsunami flow. Analysis of formulae for sediment transport and simulations in a rectangular harbor

    International Nuclear Information System (INIS)

    Matsuyama, Masafumi

    2009-01-01

    Characteristics of formulae for bed-load transport and pick-up rate in suspended transport are investigated in order to clarify the impact on seabed topography changes by tsunami flow. The impact by bed-load transport was depended on Froude number and water surface slope. Bed-load transport causes deposition under Fr 6/7 at face front of tsunami wave. Pick-up rate has more predominant influences for seabed topography changes than that of one brought by bed-load transport. 2-D Numerical simulations with formulae by Ikeno et.al were carried out to simulate topography changes around harbor by tsunami flow in the flume. The result indicated that the numerical model is more applicable than a numerical model with previous formulae for estimation of deposit and erosion by topography changes. It is for this reason that the formula of pick-up rate is adaptable for wide-range diameter of sand, from 0.08mm to 0.2mm. Upper limit of suspended sediment concentration is needed to set due to avoid overlarge concentration in the numerical model. Comparison between numerical results in a real scale with 1% and 5% upper limits clearly shows topography changes have a deep relevance with the upper limit value. The upper limit value is one of dominant factors for evaluating seabed topography changes by the 2-D Numerical simulations with the formulae by Ikeno et.al in a real scale. (author)

  4. A statistical study of gyro-averaging effects in a reduced model of drift-wave transport

    Science.gov (United States)

    da Fonseca, J. D.; del-Castillo-Negrete, D.; Sokolov, I. M.; Caldas, I. L.

    2016-08-01

    A statistical study of finite Larmor radius (FLR) effects on transport driven by electrostatic drift-waves is presented. The study is based on a reduced discrete Hamiltonian dynamical system known as the gyro-averaged standard map (GSM). In this system, FLR effects are incorporated through the gyro-averaging of a simplified weak-turbulence model of electrostatic fluctuations. Formally, the GSM is a modified version of the standard map in which the perturbation amplitude, K0, becomes K0J0(ρ ̂ ) , where J0 is the zeroth-order Bessel function and ρ ̂ is the Larmor radius. Assuming a Maxwellian probability density function (pdf) for ρ ̂ , we compute analytically and numerically the pdf and the cumulative distribution function of the effective drift-wave perturbation amplitude K0J0(ρ ̂ ) . Using these results, we compute the probability of loss of confinement (i.e., global chaos), Pc, and the probability of trapping in the main drift-wave resonance, Pt. It is shown that Pc provides an upper bound for the escape rate, and that Pt provides a good estimate of the particle trapping rate. The analytical results are compared with direct numerical Monte-Carlo simulations of particle transport.

  5. Application of numerical environment system to regional atmospheric radioactivity transport simulations

    International Nuclear Information System (INIS)

    Yamazawa, H.; Ohkura, T.; Iida, T.; Chino, M.; Nagai, H.

    2003-01-01

    Main functions of the Numerical Environment System (NES), as a part of the Information Technology Based Laboratory (ITBL) project implemented by Japan Atomic Energy Research Institute, became available for test use purposes although the development of the system is still underway. This system consists of numerical models of meteorology and atmospheric dispersion, database necessary for model simulations, post- and pre-processors such as data conversion and visualization, and a suite of system software which provide the users with system functions through a web page access. The system utilizes calculation servers such as vector- and scalar-parallel processors for numerical model execution, a EWS which serves as a hub of the system. This system provides users in the field of nuclear emergency preparedness and atmospheric environment with easy-to-use functions of atmospheric dispersion simulations including input meteorological data preparation and visualization of simulation results. The performance of numerical models in the system was examined with observation data of long-range transported radon-222. The models in the system reproduced quite well temporal variations in the observed radon-222 concentrations in air which were caused by changes in the meteorological field in the synoptic scale. By applying the NES models in combination with the idea of backward-in-time atmospheric dispersion simulation, seasonal shift of source areas of radon-222 in the eastern Asian regions affecting the concentrations in Japan was quantitatively illustrated. (authors)

  6. Monte Carlo perturbation theory in neutron transport calculations

    International Nuclear Information System (INIS)

    Hall, M.C.G.

    1980-01-01

    The need to obtain sensitivities in complicated geometrical configurations has resulted in the development of Monte Carlo sensitivity estimation. A new method has been developed to calculate energy-dependent sensitivities of any number of responses in a single Monte Carlo calculation with a very small time penalty. This estimation typically increases the tracking time per source particle by about 30%. The method of estimation is explained. Sensitivities obtained are compared with those calculated by discrete ordinates methods. Further theoretical developments, such as second-order perturbation theory and application to k/sub eff/ calculations, are discussed. The application of the method to uncertainty analysis and to the analysis of benchmark experiments is illustrated. 5 figures

  7. A mass conservative numerical solution of vertical water flow and mass transport equations in unsaturated porous media

    International Nuclear Information System (INIS)

    Lim, S.C.; Lee, K.J.

    1993-01-01

    The Galerkin finite element method is used to solve the problem of one-dimensional, vertical flow of water and mass transport of conservative-nonconservative solutes in unsaturated porous media. Numerical approximations based on different forms of the governing equation, although they are equivalent in continuous forms, can result in remarkably different solutions in an unsaturated flow problem. Solutions given by a simple Galerkin method based on the h-based Richards equation yield a large mass balance error and an underestimation of the infiltration depth. With the employment of the ROMV (restoration of main variable) concept in the discretization step, the mass conservative numerical solution algorithm for water flow has been derived. The resulting computational schemes for water flow and mass transport are applied to sandy soil. The ROMV method shows good mass conservation in water flow analysis, whereas it seems to have a minor effect on mass transport. However, it may relax the time-step size restriction and so ensure an improved calculation output. (author)

  8. Approximations for transport parameters and self-averaging properties for point-like injections in heterogeneous media

    International Nuclear Information System (INIS)

    Eberhard, Jens

    2004-01-01

    We focus on transport parameters in heterogeneous media with a flow modelled by an ensemble of periodic and Gaussian random fields. The parameters are determined by ensemble averages. We study to what extent these averages represent the behaviour in a single realization. We calculate the centre-of-mass velocity and the dispersion coefficient using approximations based on a perturbative expansion for the transport equation, and on the iterative solution of the Langevin equation. Compared with simulations, the perturbation theory reproduces the numerical results only poorly, whereas the iterative solution yields good results. Using these approximations, we investigate the self-averaging properties. The ensemble average of the velocity characterizes the behaviour of a realization for large times in both ensembles. The dispersion coefficient is not self-averaging in the ensemble of periodic fields. For the Gaussian ensemble the asymptotic dispersion coefficient is self-averaging. For finite times, however, the fluctuations are so large that the average does not represent the behaviour in a single realization

  9. Improving estimates of subsurface gas transport in unsaturated fractured media using experimental Xe diffusion data and numerical methods

    Science.gov (United States)

    Ortiz, J. P.; Ortega, A. D.; Harp, D. R.; Boukhalfa, H.; Stauffer, P. H.

    2017-12-01

    Gas transport in unsaturated fractured media plays an important role in a variety of applications, including detection of underground nuclear explosions, transport from volatile contaminant plumes, shallow CO2 leakage from carbon sequestration sites, and methane leaks from hydraulic fracturing operations. Gas breakthrough times are highly sensitive to uncertainties associated with a variety of hydrogeologic parameters, including: rock type, fracture aperture, matrix permeability, porosity, and saturation. Furthermore, a couple simplifying assumptions are typically employed when representing fracture flow and transport. Aqueous phase transport is typically considered insignificant compared to gas phase transport in unsaturated fracture flow regimes, and an assumption of instantaneous dissolution/volatilization of radionuclide gas is commonly used to reduce computational expense. We conduct this research using a twofold approach that combines laboratory gas experimentation and numerical modeling to verify and refine these simplifying assumptions in our current models of gas transport. Using a gas diffusion cell, we are able to measure air pressure transmission through fractured tuff core samples while also measuring Xe gas breakthrough measured using a mass spectrometer. We can thus create synthetic barometric fluctuations akin to those observed in field tests and measure the associated gas flow through the fracture and matrix pore space for varying degrees of fluid saturation. We then attempt to reproduce the experimental results using numerical models in PLFOTRAN and FEHM codes to better understand the importance of different parameters and assumptions on gas transport. Our numerical approaches represent both single-phase gas flow with immobile water, as well as full multi-phase transport in order to test the validity of assuming immobile pore water. Our approaches also include the ability to simulate the reaction equilibrium kinetics of dissolution

  10. Experimental and Numerical Investigations on Colloid-facilitated Plutonium Reactive Transport in Fractured Tuffaceous Rocks

    Science.gov (United States)

    Dai, Z.; Wolfsberg, A. V.; Zhu, L.; Reimus, P. W.

    2017-12-01

    Colloids have the potential to enhance mobility of strongly sorbing radionuclide contaminants in fractured rocks at underground nuclear test sites. This study presents an experimental and numerical investigation of colloid-facilitated plutonium reactive transport in fractured porous media for identifying plutonium sorption/filtration processes. The transport parameters for dispersion, diffusion, sorption, and filtration are estimated with inverse modeling for minimizing the least squares objective function of multicomponent concentration data from multiple transport experiments with the Shuffled Complex Evolution Metropolis (SCEM). Capitalizing on an unplanned experimental artifact that led to colloid formation and migration, we adopt a stepwise strategy to first interpret the data from each experiment separately and then to incorporate multiple experiments simultaneously to identify a suite of plutonium-colloid transport processes. Nonequilibrium or kinetic attachment and detachment of plutonium-colloid in fractures was clearly demonstrated and captured in the inverted modeling parameters along with estimates of the source plutonium fraction that formed plutonium-colloids. The results from this study provide valuable insights for understanding the transport mechanisms and environmental impacts of plutonium in fractured formations and groundwater aquifers.

  11. Image Reconstruction Based on Homotopy Perturbation Inversion Method for Electrical Impedance Tomography

    Directory of Open Access Journals (Sweden)

    Jing Wang

    2013-01-01

    Full Text Available The image reconstruction for electrical impedance tomography (EIT mathematically is a typed nonlinear ill-posed inverse problem. In this paper, a novel iteration regularization scheme based on the homotopy perturbation technique, namely, homotopy perturbation inversion method, is applied to investigate the EIT image reconstruction problem. To verify the feasibility and effectiveness, simulations of image reconstruction have been performed in terms of considering different locations, sizes, and numbers of the inclusions, as well as robustness to data noise. Numerical results indicate that this method can overcome the numerical instability and is robust to data noise in the EIT image reconstruction. Moreover, compared with the classical Landweber iteration method, our approach improves the convergence rate. The results are promising.

  12. A Schwarz alternating procedure for singular perturbation problems

    Energy Technology Data Exchange (ETDEWEB)

    Garbey, M. [Universit Claude Bernard Lyon, Villeurbanne (France); Kaper, H.G. [Argonne National Lab., IL (United States)

    1994-12-31

    The authors show that the Schwarz alternating procedure offers a good algorithm for the numerical solution of singular perturbation problems, provided the domain decomposition is properly designed to resolve the boundary and transition layers. They give sharp estimates for the optimal position of the domain boundaries and present convergence rates of the algorithm for various second-order singular perturbation problems. The splitting of the operator is domain-dependent, and the iterative solution of each subproblem is based on a modified asymptotic expansion of the operator. They show that this asymptotic-induced method leads to a family of efficient massively parallel algorithms and report on implementation results for a turning-point problem and a combustion problem.

  13. A study on tokamak fusion reactor - Numerical analyses of MHD equilibrium= and edge plasma transport in tokamak fusion reactor with divertor configurations

    Energy Technology Data Exchange (ETDEWEB)

    Hong, Sang Hee; Lim, Ki Hang; Kang, Kyung Doo; Ryu, Ji Myung; Kim, Duk Kyu [Seoul National University, Seoul (Korea, Republic of); Cho, Soo Won [Kyungki Unviersity, Suwon (Korea, Republic of)

    1995-08-01

    In the present project for developing the numerical codes of 2-DMHD equilibrium, edge plasma transport and neutral particle transport for the tokamak plasmas, we compute the plasma equilibrium of double null type and calculate the external coil currents and the plasma parameters used for operation and control data. Also the numerical algorithm is developed to analyse the behavior of edge plasmas in poloidal and radial directions and the programming and debugging of a 2-D transport code are completed. Furthermore, a neutral particle transport code for the edge region is developed and then used for the analysis of the neutral transport phenomena giving the sources in the fluid equations, and expected to supply the input parameters for the edge plasma transport code. 34 refs., 5 tabs., 28 figs. (author)

  14. Adaptative numerical methods for transport problems in safety nuclear reactors by the use of perturbations signatures and processes

    International Nuclear Information System (INIS)

    Doriath, J.Y.

    1983-05-01

    The need for increasingly accurate nuclear reactor performance data has led to increasingly sophisticated methods for solving the Boltzmann transport equation. This work has revealed the need for analyzing the functional signatures of the neutron flux using pattern recognition techniques to relate the local and overall phases of reactor calculations according to the desired parameters. This approach makes it possible to develop procedures based on a reference calculations and designed to evaluate the disturbances due to changes in physical media and to media interface modifications [fr

  15. Numerical modelling of cuttings transport in horizontal wells using conventional drilling fluids

    Energy Technology Data Exchange (ETDEWEB)

    Li, Y.; Bjorndalen, E.; Kuru, E. [Alberta Univ., Edmonton, AB (Canada)

    2004-07-01

    Some of the problems associated with poor wellbore cleaning include high drag or torque, slower rate of penetration, formation fractures and difficulty in wellbore steering. Some of the factors that affect cuttings transport include drilling fluid velocity, inclination angle, drilling fluid viscosity and drilling rate. The general practice is to stop drilling when necessary to clean boreholes with viscous pills, pipe rotation or drilling fluid circulation. It is important to predict when drilling should be stopped for remedial wellbore cleaning. This can be accomplished with a transient cuttings transport model which can improve drilling hydraulics, particularly in long horizontal well sections and extended reach (ERD) wells. This paper presents a newly developed 1-dimensional transient mechanistic model of cuttings transport with conventional (incompressible) drilling fluids in horizontal wells. The numerically solved model predicts the height of cutting beds as a function of different drilling operational parameters such as fluid flow rate and rheological characteristics, drilling rates, wellbore geometry and drillpipe eccentricity. Sensitivity analysis has demonstrated the effects of these parameters on the efficiency of solids transport. The proposed model can be used in the creation of computer programs designed to optimize drilling fluid rheology and flow rates for horizontal well drilling. 29 refs., 3 tabs., 12 figs.

  16. Control of nonlinear systems using periodic parametric perturbations with application to a reversed field pinch

    International Nuclear Information System (INIS)

    Mirus, K.A.

    1998-06-01

    In this thesis, the possibility of controlling low- and high-dimensional chaotic systems by periodically driving an accessible system parameter is examined. This method has been carried out on several numerical systems and the MST Reversed Field Pinch. The numerical systems investigated include the logistic equation, the Lorenz equations, the Roessler equations, a coupled lattice of logistic equations, a coupled lattice of Lorenz equations, the Yoshida equations, which model tearing mode fluctuations in a plasma, and a neural net model for magnetic fluctuations on MST. This method was tested on the MST by sinusoidally driving a magnetic flux through the toroidal gap of the device. Numerically, periodic drives were found to be most effective at producing limit cycle behavior or significantly reducing the dimension of the system when the perturbation frequency was near natural frequencies of unstable periodic orbits embedded in the attractor of the unperturbed system. Several different unstable periodic orbits have been stabilized in this way for the low-dimensional numerical systems, sometimes with perturbation amplitudes that were less than 5% of the nominal value of the parameter being perturbed. In high-dimensional systems, limit cycle behavior and significant decreases in the system dimension were also achieved using perturbations with frequencies near the natural unstable periodic orbit frequencies. Results for the MST were not this encouraging, most likely because of an insufficient drive amplitude, the extremely high dimension of the plasma behavior, large amounts of noise, and a lack of stationarity in the transient plasma pulses

  17. Control of nonlinear systems using periodic parametric perturbations with application to a reversed field pinch

    Energy Technology Data Exchange (ETDEWEB)

    Mirus, Kevin A. [Univ. of Wisconsin, Madison, WI (United States)

    1998-01-01

    In this thesis, the possibility of controlling low- and high-dimensional chaotic systems by periodically driving an accessible system parameter is examined. This method has been carried out on several numerical systems and the MST Reversed Field Pinch. The numerical systems investigated include the logistic equation, the Lorenz equations, the Roessler equations, a coupled lattice of logistic equations, a coupled lattice of Lorenz equations, the Yoshida equations, which model tearing mode fluctuations in a plasma, and a neural net model for magnetic fluctuations on MST. This method was tested on the MST by sinusoidally driving a magnetic flux through the toroidal gap of the device. Numerically, periodic drives were found to be most effective at producing limit cycle behavior or significantly reducing the dimension of the system when the perturbation frequency was near natural frequencies of unstable periodic orbits embedded in the attractor of the unperturbed system. Several different unstable periodic orbits have been stabilized in this way for the low-dimensional numerical systems, sometimes with perturbation amplitudes that were less than 5% of the nominal value of the parameter being perturbed. In high-dimensional systems, limit cycle behavior and significant decreases in the system dimension were also achieved using perturbations with frequencies near the natural unstable periodic orbit frequencies. Results for the MST were not this encouraging, most likely because of an insufficient drive amplitude, the extremely high dimension of the plasma behavior, large amounts of noise, and a lack of stationarity in the transient plasma pulses.

  18. Control of nonlinear systems using periodic parametric perturbations with application to a reversed field pinch

    Science.gov (United States)

    Mirus, Kevin Andrew

    In this thesis, the possibility of controlling low- and high-dimensional chaotic systems by periodically driving an accessible system parameter is examined. This method has been carried out on several numerical systems and the MST Reversed Field Pinch. The numerical systems investigated include the logistic equation, the Lorenz equations, the Rossler equations, a coupled lattice of logistic equations, a coupled lattice of Lorenz equations, the Yoshida equations, which model tearing mode fluctuations in a plasma, and a neural net model for magnetic fluctuations on MST. This method was tested on the MST by sinusoidally driving a magnetic flux through the toroidal gap of the device. Numerically, periodic drives were found to be most effective at producing limit cycle behavior or significantly reducing the dimension of the system when the perturbation frequency was near natural frequencies of unstable periodic orbits embedded in the attractor of the unperturbed system. Several different unstable periodic orbits have been stabilized in this way for the low-dimensional numerical systems, sometimes with perturbation amplitudes that were less than 5% of the nominal value of the parameter being perturbed. In high- dimensional systems, limit cycle behavior and significant decreases in the system dimension were also achieved using perturbations with frequencies near the natural unstable periodic orbit frequencies. Results for the MST were not this encouraging, most likely because of an insufficient drive amplitude, the extremely high dimension of the plasma behavior, large amounts of noise, and a lack of stationarity in the transient plasma pulses.

  19. Effects of Time-Dependent Inflow Perturbations on Turbulent Flow in a Street Canyon

    Science.gov (United States)

    Duan, G.; Ngan, K.

    2017-12-01

    Urban flow and turbulence are driven by atmospheric flows with larger horizontal scales. Since building-resolving computational fluid dynamics models typically employ steady Dirichlet boundary conditions or forcing, the accuracy of numerical simulations may be limited by the neglect of perturbations. We investigate the sensitivity of flow within a unit-aspect-ratio street canyon to time-dependent perturbations near the inflow boundary. Using large-eddy simulation, time-periodic perturbations to the streamwise velocity component are incorporated via the nudging technique. Spatial averages of pointwise differences between unperturbed and perturbed velocity fields (i.e., the error kinetic energy) show a clear dependence on the perturbation period, though spatial structures are largely insensitive to the time-dependent forcing. The response of the error kinetic energy is maximized for perturbation periods comparable to the time scale of the mean canyon circulation. Frequency spectra indicate that this behaviour arises from a resonance between the inflow forcing and the mean motion around closed streamlines. The robustness of the results is confirmed using perturbations derived from measurements of roof-level wind speed.

  20. MS-2 and poliovirus transport in porous media: Hydrophobic effects and chemical perturbations

    Science.gov (United States)

    Bales, Roger C.; Li, Shimin; Maguire, Kimberly M.; Yahya, Moyasar T.; Gerba, Charles P.

    1993-04-01

    In a series of pH 7 continuous-flow column experiments, removal of the bacteriophage MS-2 by attachment to silica beads had a strong, systematic dependence on the amount of hydrophobic surface present on the beads. With no hydrophobic surface, removal of phage at pH 5 was much greater than at pH 7. Release of attached phage at both pH values did occur, but was slow; breakthrough curves exhibited tailing. Poliovirus attached to silica beads at pH 5.5 much more than at pH 7.0, and attachment was also slowly reversible. Time scales for phage and poliovinis attachment were of the order of hours. The sticking efficiency factor (α), reflecting microscaie physicochemical influences on virus attachment, was in the range of 0.0007-0.02. Phage release was small but measurable under steady state conditions. Release was enhanced by lowering ionic strength and by introducing beef extract, a high-ionic-strength protein solution. Results show that viruses experience reversible attachment/detachment (sometimes termed sorption), that large chemical perturbations are needed to induce rapid virus detachment, and that viruses should be quite mobile in sandy porous media. Even small amounts of hydrophobic organic material in the porous media (≥0.001%) can retard virus transport.

  1. Asymptotic solutions of numerical transport problems in optically thick, diffusive regimes

    International Nuclear Information System (INIS)

    Larsen, E.W.; Morel, J.E.; Miller, W.F. Jr.

    1987-01-01

    We present an asymptotic analysis of spatial differencing schemes for the discrete-ordinates equations, for diffusive media with spatial cells that are not optically thin. Our theoretical tool is an asymptotic expansion that has previously been used to describe the transform from analytic transport to analytic diffusion theory for such media. To introduce this expansion and its physical rationale, we first describe it for the analytic discrete-ordinates equations. Then, we apply the expansion to the spatially discretized discrete-ordinates equations, with the spatial mesh scaled in either of two physically relevant ways such that the optical thickness of the spatial cells is not small. If the result of either expansion is a legitimate diffusion description for either the cell-averaged or cell-edge fluxes, then we say that the approximate flux has the appropriate diffusion limit; otherwise, we say it does not. We consider several transport differencing schemes that are applicable in neutron transport and thermal radiation applications. We also include numerical results which demonstrate the validity of our theory and show that differencing schemes that do have a particular diffusion limit are substantially more accurate, in the regime described by the limit, than those that do not. copyright 1987 Academic Press, Inc

  2. A study on the fusion reactor - Numerical analyses of MHD equilibrium and= edge plasma transport in tokamak fusion reactor with divertor configurations

    Energy Technology Data Exchange (ETDEWEB)

    Hong, Sang Hee; Kang, Kyung Doo; Ryu, Ji Myung; Kim, Deok Kyu; Chung, TaeKyun; Chung, Mo Se [Seoul National University, Seoul (Korea, Republic of); Cho, Su Won [Kyungki University, Suwon (Korea, Republic of)

    1995-08-01

    In the present project for developing the numerical codes of 2-D MHD equilibrium, edge plasma transport and neutral particle transport for the tokamak plasmas, we computed the MHD equilibria of single and double null configurations and determined the external coil currents and the plasma parameters used for operation and control data. Also we numerically acquired the distributions of edge plasma parameters in poloidal and radial directions= and the design-related values according to the various operating conditions using the developed plasma transport code. Furthermore, a neutral particle transport code for the edge region is developed and them used for the analysis of the neutral particle behavior yielding the source terms in the fluid transport equations, and expected to supply the input parameters for the edge plasma transport code. 53 refs., 12 tabs., 44 figs. (author)

  3. Contribution to the study of perturbed planetary and protoplanetary disks

    International Nuclear Information System (INIS)

    Charnoz, Sebastien

    2000-01-01

    We studied some dynamical and photometric aspects of perturbed planetary and protoplanetary disks. In the first part of this work, using simple numerical models, the thermodynamic evolution of a colliding planetesimal disk perturbed by a giant planet core was studied. As soon as a giant planet embryo (- 15 earth masses) appears, a heat transfer is triggered in the disk, increasing strongly random velocities over a few astronomical units. The long term evolution of this transitory mechanism was investigated as well as its dependence to the perturber's mass. This is a generic mechanism that may have played an important role during the accretion of both terrestrial and giant planet embryos. Consequences concerning the origin of the Asteroid Belt are discussed, as well as the effect of fragmentation that could not been considered, because of numerical limitations. The second part of this work is a photometric study of Saturn's F ring, that is perturbed by its two nearby shepherding satellites. A 300 images data set, obtained at CFH telescope, was used. We put in evidence the presence of some elongated structures in the F ring, which origin is still a matter of debate. By combining our data set with some other spatial telescope images, new accurate orbital solutions for the F ring were derived, yielding a new radius of 140060 Angstroms ±60 km, that is 150 km smaller than the orbit derived in 1980-81. This may be the sign that the F ring suffered an important radial re-structuration during the last twenty years, which possible cause is also discussed. (author) [fr

  4. A simplified numerical analysis of helical instabilities of arcs in axial magnetic field

    International Nuclear Information System (INIS)

    Gong Ye; Lu Wenyan; Liu Jinyuan; Zheng Shu; Gong Jiquan

    2002-01-01

    The energy equations were simplified by the correct electrostatic ordering under electrostatic approximation. The effects of the external axial magnetic field, the current profiles and arc currents on the helical instabilities of arcs were studied by using numerical method. In the presence of the external magnetic field, numerical results show that when the current profile of an arc column is the uniform distribution, the short wavelength perturbation can be stabilized by positive direction magnetic field, whereas the long wavelength perturbation can be stabilized by reverse magnetic field. When the current profile of an arc column has a parabolic distribution, in the short wavelength perturbation case, the effect of positive direction magnetic field on the arc stability is very small. However, its stabilizing effect is enhanced for the long wavelength perturbation. The intermediate and long wavelength perturbations can also be stabilized by reverse magnetic field

  5. Supersingular quantum perturbations

    International Nuclear Information System (INIS)

    Detwiler, L.C.; Klauder, J.R.

    1975-01-01

    A perturbation potential is called supersingular whenever generally every matrix element of the perturbation in the unperturbed eigenstates is infinite. It follows that supersingular perturbations do not have conventional perturbation expansions, say for energy eigenvalues. By invoking variational arguments, we determine the asymptotic behavior of the energy eigenvalues for asymptotically small values of the coupling constant of the supersingular perturbation

  6. A numerical assessment of rough surface scattering theories. I - Horizontal polarization. II - Vertical polarization

    Science.gov (United States)

    Rodriguez, Ernesto; Kim, Yunjin; Durden, Stephen L.

    1992-01-01

    A numerical evaluation is presented of the regime of validity for various rough surface scattering theories against numerical results obtained by employing the method of moments. The contribution of each theory is considered up to second order in the perturbation expansion for the surface current. Considering both vertical and horizontal polarizations, the unified perturbation method provides best results among all theories weighed.

  7. B-spline solution of a singularly perturbed boundary value problem arising in biology

    International Nuclear Information System (INIS)

    Lin Bin; Li Kaitai; Cheng Zhengxing

    2009-01-01

    We use B-spline functions to develop a numerical method for solving a singularly perturbed boundary value problem associated with biology science. We use B-spline collocation method, which leads to a tridiagonal linear system. The accuracy of the proposed method is demonstrated by test problems. The numerical result is found in good agreement with exact solution.

  8. Computational singular perturbation analysis of stochastic chemical systems with stiffness

    Science.gov (United States)

    Wang, Lijin; Han, Xiaoying; Cao, Yanzhao; Najm, Habib N.

    2017-04-01

    Computational singular perturbation (CSP) is a useful method for analysis, reduction, and time integration of stiff ordinary differential equation systems. It has found dominant utility, in particular, in chemical reaction systems with a large range of time scales at continuum and deterministic level. On the other hand, CSP is not directly applicable to chemical reaction systems at micro or meso-scale, where stochasticity plays an non-negligible role and thus has to be taken into account. In this work we develop a novel stochastic computational singular perturbation (SCSP) analysis and time integration framework, and associated algorithm, that can be used to not only construct accurately and efficiently the numerical solutions to stiff stochastic chemical reaction systems, but also analyze the dynamics of the reduced stochastic reaction systems. The algorithm is illustrated by an application to a benchmark stochastic differential equation model, and numerical experiments are carried out to demonstrate the effectiveness of the construction.

  9. A novel numerical method for the analysis of electron transport in the presence of pointlike magnetic scatterers

    International Nuclear Information System (INIS)

    Miyagawa, Yuu; Ueta, Tsuyoshi

    2008-01-01

    The boundary element method (BEM) is so extended as to treat two-dimensional (2D) electron systems in the presence of pointlike islands of magnetic moment. In the present paper, the pointlike magnetic scatterer is modeled by a cylindrical barrier. The radius of the cylindrical barrier is assumed to be so small, keeping the volume definite, that the pointlike magnetic scatterer is approximated by a Dirac δ function. Then, we make an approximation on the BEM formulation, wherefore we derive a novel numerical method for electron transport in the presence of pointlike magnetic scatterers. In a numerical implementation of the method extended here, the numerical errors of probability conservation are less than 1% for any cases and the computational costs, that is, the required memory amount and CPU time, are much reduced. As examples, the proposed method is applied to transport problems through a quantum wire with four pointlike magnetic scatterers. It is clearly shown that magnetic scatterers, even pointlike magnetic moments, lead to spin flip-flop, localization and resonance

  10. Qualitative dynamical analysis of chaotic plasma perturbations model

    Science.gov (United States)

    Elsadany, A. A.; Elsonbaty, Amr; Agiza, H. N.

    2018-06-01

    In this work, an analytical framework to understand nonlinear dynamics of plasma perturbations model is introduced. In particular, we analyze the model presented by Constantinescu et al. [20] which consists of three coupled ODEs and contains three parameters. The basic dynamical properties of the system are first investigated by the ways of bifurcation diagrams, phase portraits and Lyapunov exponents. Then, the normal form technique and perturbation methods are applied so as to the different types of bifurcations that exist in the model are investigated. It is proved that pitcfork, Bogdanov-Takens, Andronov-Hopf bifurcations, degenerate Hopf and homoclinic bifurcation can occur in phase space of the model. Also, the model can exhibit quasiperiodicity and chaotic behavior. Numerical simulations confirm our theoretical analytical results.

  11. Optimal Linear Responses for Markov Chains and Stochastically Perturbed Dynamical Systems

    Science.gov (United States)

    Antown, Fadi; Dragičević, Davor; Froyland, Gary

    2018-03-01

    The linear response of a dynamical system refers to changes to properties of the system when small external perturbations are applied. We consider the little-studied question of selecting an optimal perturbation so as to (i) maximise the linear response of the equilibrium distribution of the system, (ii) maximise the linear response of the expectation of a specified observable, and (iii) maximise the linear response of the rate of convergence of the system to the equilibrium distribution. We also consider the inhomogeneous, sequential, or time-dependent situation where the governing dynamics is not stationary and one wishes to select a sequence of small perturbations so as to maximise the overall linear response at some terminal time. We develop the theory for finite-state Markov chains, provide explicit solutions for some illustrative examples, and numerically apply our theory to stochastically perturbed dynamical systems, where the Markov chain is replaced by a matrix representation of an approximate annealed transfer operator for the random dynamical system.

  12. Theoretical and Numerical Properties of a Gyrokinetic Plasma: Issues Related to Transport Time Scale Simulation

    International Nuclear Information System (INIS)

    Lee, W.W.

    2003-01-01

    Particle simulation has played an important role for the recent investigations on turbulence in magnetically confined plasmas. In this paper, theoretical and numerical properties of a gyrokinetic plasma as well as its relationship with magnetohydrodynamics (MHD) are discussed with the ultimate aim of simulating microturbulence in transport time scale using massively parallel computers

  13. Modelling and numerical simulation of the corrosion product transport in the pressurised water reactor primary circuit

    International Nuclear Information System (INIS)

    Marchetto, C.

    2002-05-01

    During operation of pressurised water reactor, corrosion of the primary circuit alloys leads to the release of metallic species such as iron, nickel and cobalt in the primary fluid. These corrosion products are implicated in different transport phenomena and are activated in the reactor core where they are submitted to neutron flux. The radioactive corrosion products are afterwards present in the out of flux parts of primary circuit where they generate a radiation field. The first part of this study deals with the modelling of the corrosion: product transport phenomena. In particular, considering the current state of the art, corrosion and release mechanisms are described empirically, which allows to take into account the material surface properties. New mass balance equations describing the corrosion product behaviour are thus obtained. The numerical resolution of these equations is implemented in the second part of this work. In order to obtain large time steps, we choose an implicit time scheme. The associated system is linearized from the Newton method and is solved by a preconditioned GMRES method. Moreover, a time step auto-adaptive management based on Newton iterations is performed. Consequently, an efficient resolution has been implemented, allowing to describe not only the quasi-steady evolutions but also the fast transients. In a last step, numerical simulations are carried out in order to validate the new corrosion product transport modelling and to illustrate the capabilities of this modelling. Notably, the numerical results obtained indicate that the code allows to restore the on-site observations underlining the influence of material surface properties on reactor contamination. (author)

  14. Analytic perturbation theory in analyzing some QCD observables

    International Nuclear Information System (INIS)

    Shirkov, D.V.

    2001-01-01

    The paper is devoted to application of recently devised ghost-free Analytic Perturbation Theory (APT) for analysis of some QCD observables. We start with the discussion of the main problem of the perturbative QCD - ghost singularities and with the resume of this trouble solution within the APT. By a few examples in the various energy and momentum transfer regions (with the flavor number f = 3, 4 and 5) we demonstrate the effect of improved convergence of the APT modified perturbative QCD expansion. Our first observation is that in the APT analysis the three-loop contribution (of an order of α s 3 ) is as a rule numerically inessential. This raises hope for practical solving the well-known problem of asymptotic nature of common QFT perturbation series. The second conclusion is that a common perturbative analysis of time-like events with the big π 2 term in the π 2 coefficient is not adequate at s ≤ 2 GeV 2 . In particular, this relates to τ decay. Then, for the 'high' (f = 5) region it is shown that the common two-loop (NLO, NLLA) perturbation approximation widely used there (at 10 GeV ≤ √s ≤ 170 GeV) for analysis of shape/events data contains a systematic negative error of a 1 - 2 per cent level for the extracted α bar s (2) values. Our physical conclusion is that the α bar s (M Z 2 ) value averaged over the f = 5 data s (M Z 2 )> APT; f= 5 ≅ 0.124 appreciably differs from the currently accepted 'world average' (= 0.118)

  15. Numerical simulation of mass and energy transport phenomena in solid oxide fuel cells

    Energy Technology Data Exchange (ETDEWEB)

    Arpino, F. [Dipartimento di Meccanica, Strutture, Ambiente e Territorio (DiMSAT), University of Cassino, via Di Biasio 43, Cassino (Italy); Massarotti, N. [Dipertimento per le Tecnologie (DiT), University of Naples ' ' Parthenope' ' , Centro Direzionale, isola C4, 80143 Napoli (Italy)

    2009-12-15

    Solid Oxide Fuel Cells (SOFCs) represent a very promising technology for near future energy conversion thanks to a number of advantages, including the possibility of using different fuels. In this paper, a detailed numerical model, based on a general mathematical description and on a finite element Characteristic based Split (CBS) algorithm code is employed to simulate mass and energy transport phenomena in SOFCs. The model predicts the thermodynamic quantity of interest in the fuel cell. Full details of the numerical solution obtained are presented both in terms of heat and mass transfer in the cell and in terms of electro-chemical reactions that occur in the system considered. The results obtained with the present algorithm is compared with the experimental data available in the literature for validation, showing an excellent agreement. (author)

  16. Numerical investigations of passive scalar transport in Taylor-Couette flows: Counter-rotation effect

    Science.gov (United States)

    Ouazib, Nabila; Salhi, Yacine; Si-Ahmed, El-Khider; Legrand, Jack; Degrez, G.

    2017-07-01

    Numerical methods for solving convection-diffusion-reaction (CDR) scalar transport equation in three-dimensional flow are used in the present investigation. The flow is confined between two concentric cylinders both the inner cylinder and the outer one are allowed to rotate. Direct numerical simulations (DNS) have been achieved to study the effects of the gravitational and the centrifugal potentials on the stability of incompressible Taylor-Couette flow. The Navier-Stokes equations and the uncoupled convection-diffusion-reaction equation are solved using a spectral development in one direction combined together with a finite element discretization in the two remaining directions. The complexity of the patterns is highlighted. Since, it increases as the rotation rates of the cylinders increase. In addition, the effect of the counter-rotation of the cylinders on the mass transfer is pointed out.

  17. Impact d'une perturbation mécanique ou photo-chimique sur le trafic intracellulaire

    OpenAIRE

    Aubertin , Kelly

    2014-01-01

    The cell cytoplasm is crowded with membrane-delimited compartments, permanently communicatingwith each other. Such communication is permitted by active transport, also called intracellulartrafficking, of vesicles along the cytoskeleton (actin filaments, microtubules), and mediated bymolecular motors. In order to perturbate this intracellular trafficking, two different ways to applycontrolled physical stresses have been performed. The first perturbation is a mechanical one : weused magnetic en...

  18. Stochastic perturbations in open chaotic systems: random versus noisy maps.

    Science.gov (United States)

    Bódai, Tamás; Altmann, Eduardo G; Endler, Antonio

    2013-04-01

    We investigate the effects of random perturbations on fully chaotic open systems. Perturbations can be applied to each trajectory independently (white noise) or simultaneously to all trajectories (random map). We compare these two scenarios by generalizing the theory of open chaotic systems and introducing a time-dependent conditionally-map-invariant measure. For the same perturbation strength we show that the escape rate of the random map is always larger than that of the noisy map. In random maps we show that the escape rate κ and dimensions D of the relevant fractal sets often depend nonmonotonically on the intensity of the random perturbation. We discuss the accuracy (bias) and precision (variance) of finite-size estimators of κ and D, and show that the improvement of the precision of the estimations with the number of trajectories N is extremely slow ([proportionality]1/lnN). We also argue that the finite-size D estimators are typically biased. General theoretical results are combined with analytical calculations and numerical simulations in area-preserving baker maps.

  19. A perturbational h4 exponential finite difference scheme for the convective diffusion equation

    International Nuclear Information System (INIS)

    Chen, G.Q.; Gao, Z.; Yang, Z.F.

    1993-01-01

    A perturbational h 4 compact exponential finite difference scheme with diagonally dominant coefficient matrix and upwind effect is developed for the convective diffusion equation. Perturbations of second order are exerted on the convective coefficients and source term of an h 2 exponential finite difference scheme proposed in this paper based on a transformation to eliminate the upwind effect of the convective diffusion equation. Four numerical examples including one- to three-dimensional model equations of fluid flow and a problem of natural convective heat transfer are given to illustrate the excellent behavior of the present exponential schemes. Besides, the h 4 accuracy of the perturbational scheme is verified using double precision arithmetic

  20. Numerical simulations for radiation hydrodynamics. 2: Transport limit

    International Nuclear Information System (INIS)

    Dai, W.W.; Woodward, P.R.

    2000-01-01

    A finite difference scheme is proposed for two-dimensional radiation hydrodynamical equations in the transport limit. The scheme is of Godunov-type, in which the set of time-averaged flux needed in the scheme is calculated through Riemann problems solved. In the scheme, flow signals are explicitly treated, while radiation signals are implicitly treated. Flow fields and radiation fields are updated simultaneously. An iterative approach is proposed to solve the set of nonlinear algebraic equations arising from the implicitness of the scheme. The sweeping method used in the scheme significantly reduces the number of iterations or computer CPU time needed. A new approach to further accelerate the convergence is proposed, which further reduces the number of iterations needed by more than one order. No matter how many cells radiation signals propagate in one time step, only an extremely small number of iterations are needed in the scheme, and each iteration costs only about 0.8% of computer CPU time which is needed for one time step of a second order accurate and fully explicit scheme. Two-dimensional problems are treated through a dimensionally split technique. Therefore, iterations for solving the set of algebraic equations are carried out only in each one-dimensional sweep. Through numerical examples it is shown that the scheme keeps the principle advantages of Godunov schemes for flow motion. In the time scale of flow motion numerical results are the same as those obtained from a second order accurate and fully explicit scheme. The acceleration of the convergence proposed in this paper may be directly applied to other hyperbolic systems. This study is important for laser fusion and astrophysics

  1. Finite volume at two-loops in chiral perturbation theory

    International Nuclear Information System (INIS)

    Bijnens, Johan; Rössler, Thomas

    2015-01-01

    We calculate the finite volume corrections to meson masses and decay constants in two and three flavour Chiral Perturbation Theory to two-loop order. The analytical results are compared with the existing result for the pion mass in two-flavour ChPT and the partial results for the other quantities. We present numerical results for all quantities.

  2. Application of synthetic diffusion method in the numerical solution of the equations of neutron transport in slab geometry

    International Nuclear Information System (INIS)

    Valdes Parra, J.J.

    1986-01-01

    One of the main problems in reactor physics is to determine the neutron distribution in reactor core, since knowing that, it is possible to calculate the rapidity of occurrence of different nuclear reaction inside the reactor core. Within different theories existing in nuclear reactor physics, is neutron transport the one in which equation who govern the exact behavior of neutronic distribution are developed even inside the proper neutron transport theory, there exist different methods of solution which are approximations to exact solution; still more, with the purpose to reach a more precise solution, the majority of methods have been approached to the obtention of solutions in numerical form with the aim of take the advantages of modern computers, and for this reason a great deal of effort is dedicated to numerical solution of the equations of neutron transport. In agreement with the above mentioned, in this work has been developed a computer program which uses a relatively new techniques known as 'acceleration of synthetic diffusion' which has been applied to solve the neutron transport equation with 'classical schemes of spatial integration' obtaining results with a smaller quantity of interactions, if they compare to done without using such equation (Author)

  3. Numerical solutions of the monoenergetic neutron transport equation with anisotropic scattering

    International Nuclear Information System (INIS)

    Dahl, B.

    1985-01-01

    The Boltzmann equation for monoenergetic neutrons has been solved numerically with high accuracy for homogeneous slabs and spheres with various degree of linear anisotropy. Vacuum boundary conditions are used. The numerical method is based on previous work by Carlvik. Benchmark values of the criticality factor and higher order eigenvalues are given for multiplying systems of thickness or diameter from 10 -5 to 20 mean free paths and with anisotropy coefficients from 0.0 to 0.3. For slab geometry, both even and odd mode eigenvalues are treated. With increasing anisotropy, an increasing number of complex eigenvalues is observer. The total flux is calculated from the eigenvector and tables of the fundamental mode flux are given. Accurate extrapolation distances are derived for various dimensions and anisotropy coefficients from our eigenvalue results on slabs and spheres and from the work by Sanchez on infinite cylinders.The time eigenvalue spectrum in subcritical systems has also been studied. First, the connection between the eigenvalues arising from the time dependent and stationary transport equation is established. Based on this, the spectrum of real time eigenvalues in slabs and spheres is calculated. For spheres, the existence of complex time eigenvalues in the region beyond the value corresponding to the Corngold limit is numerically established. The presence of such eigenvalues has earlier not been proved. It is further shown that the Boltzmann equation for a sphere is significantly simplified when the decay constant is at the Corngold limit. The spectrum of sphere diameters corresponding to this decay constant is calculated for various linear anisotropies, and detailed numerical results are given. (Author)

  4. Meridional transport of salt in the global ocean from an eddy-resolving model

    Science.gov (United States)

    Treguier, A. M.; Deshayes, J.; Le Sommer, J.; Lique, C.; Madec, G.; Penduff, T.; Molines, J.-M.; Barnier, B.; Bourdalle-Badie, R.; Talandier, C.

    2014-04-01

    The meridional transport of salt is computed in a global eddy-resolving numerical model (1/12° resolution) in order to improve our understanding of the ocean salinity budget. A methodology is proposed that allows a global analysis of the salinity balance in relation to surface water fluxes, without defining a "freshwater anomaly" based on an arbitrary reference salinity. The method consists of a decomposition of the meridional transport into (i) the transport by the time-longitude-depth mean velocity, (ii) time-mean velocity recirculations and (iii) transient eddy perturbations. Water is added (rainfall and rivers) or removed (evaporation) at the ocean surface at different latitudes, which creates convergences and divergences of mass transport with maximum and minimum values close to ±1 Sv. The resulting meridional velocity effects a net transport of salt at each latitude (±30 Sv PSU), which is balanced by the time-mean recirculations and by the net effect of eddy salinity-velocity correlations. This balance ensures that the total meridional transport of salt is close to zero, a necessary condition for maintaining a quasi-stationary salinity distribution. Our model confirms that the eddy salt transport cannot be neglected: it is comparable to the transport by the time-mean recirculation (up to 15 Sv PSU) at the poleward and equatorial boundaries of the subtropical gyres. Two different mechanisms are found: eddy contributions are localized in intense currents such as the Kuroshio at the poleward boundary of the subtropical gyres, while they are distributed across the basins at the equatorward boundaries. Closer to the Equator, salinity-velocity correlations are mainly due to the seasonal cycle and large-scale perturbations such as tropical instability waves.

  5. Numerical modeling of solute transport in a sand tank physical model under varying hydraulic gradient and hydrological stresses

    Science.gov (United States)

    Atlabachew, Abunu; Shu, Longcang; Wu, Peipeng; Zhang, Yongjie; Xu, Yang

    2018-03-01

    This laboratory study improves the understanding of the impacts of horizontal hydraulic gradient, artificial recharge, and groundwater pumping on solute transport through aquifers. Nine experiments and numerical simulations were carried out using a sand tank. The variable-density groundwater flow and sodium chloride transport were simulated using the three-dimensional numerical model SEAWAT. Numerical modelling results successfully reproduced heads and concentrations observed in the sand tank. A higher horizontal hydraulic gradient enhanced the migration of sodium chloride, particularly in the groundwater flow direction. The application of constant artificial recharge increased the spread of the sodium chloride plume in both the longitudinal and lateral directions. In addition, groundwater pumping accelerated spreading of the sodium chloride plume towards the pumping well. Both higher hydraulic gradient and pumping rate generated oval-shaped plumes in the horizontal plane. However, the artificial recharge process produced stretched plumes. These effects of artificial recharge and groundwater pumping were greater under higher hydraulic gradient. The concentration breakthrough curves indicated that emerging solutions never attained the concentration of the originally injected solution. This is probably because of sorption of sodium chloride onto the silica sand and/or the exchange of sodium chloride between the mobile and immobile liquid domains. The fingering and protruding plume shapes in the numerical models constitute instability zones produced by buoyancy-driven flow. Overall, the results have substantiated the influences of hydraulic gradient, boundary condition, artificial recharge, pumping rate and density differences on solute transport through a homogeneous unconfined aquifer. The implications of these findings are important for managing liquid wastes.

  6. Multiphoton transitions in semiconductors in the non-perturbative approach

    International Nuclear Information System (INIS)

    Iqbal, M.Z.; Hassan, A.R.

    1987-09-01

    Transition rates for multiphoton absorption via direct band-to-band excitation have been calculated using a non-perturbative approach due to Jones and Reiss, based on the Volkov type final state wave functions. Both cases of parabolic and non-parabolic energy bands have been included in our calculations. Absorption coefficients have been obtained for the cases of plane polarized and circularly polarized light. In particular, two-photon absorption coefficients are derived for the two cases of polarization for the parabolic band approximation as well as for non-parabolic bands and compared with the results based on perturbation theory. Numerical estimates of the two photon absorption coefficients resulting from our calculations are also provided. (author). 10 refs, 1 tab

  7. Non-perturbative versus perturbative renormalization of lattice operators

    International Nuclear Information System (INIS)

    Goeckeler, M.; Technische Hochschule Aachen; Horsley, R.; Ilgenfritz, E.M.; Oelrich, H.; Forschungszentrum Juelich GmbH; Schierholz, G.; Forschungszentrum Juelich GmbH; Perlt, H.; Schiller, A.; Rakow, P.

    1995-09-01

    Our objective is to compute the moments of the deep-inelastic structure functions of the nucleon on the lattice. A major source of uncertainty is the renormalization of the lattice operators that enter the calculation. In this talk we compare the renormalization constants of the most relevant twist-two bilinear quark operators which we have computed non-perturbatively and perturbatively to one loop order. Furthermore, we discuss the use of tadpole improved perturbation theory. (orig.)

  8. Effects of core perturbations on the structure of the sun

    International Nuclear Information System (INIS)

    Sweigart, A.V.

    1983-01-01

    A number of numerical experiments have been carried out in order to investigate the sensivity of the solar luminosity and radius to perturbations within the radiative core. In these experiments the core was perturbed by suddenly mixing various parts of the composition profile during evolutionary sequences for the present Sun. The hydrostatic readjustment caused by these ''mixing events'' induced an immediate change in the surface luminosity and radius on both the hydrodynamic time scale (approx.15 minutes) and the thermal time scale of the superadiabatic layers (approx.1 day). The subsequent evolution of the luminosity and radius perturbations was followed for 5 x 10 5 yr after each mixing event. The time-dependent behavior of these perturbations was found to depend on where the mixing event occurred. In all cases, however, the ratio W(t) = Δ log R/Δ log L had an initial value of 0.71 and showed only a mild time dependence during the first several thousand years. Two other relationships between the luminosity and radius perturbations are also discussed. One of these, V(t) = (d log R/dd)/(d log L/dt), has a fairly constant value of 0.3 +- 0.1. Both perturbations in the mixing-length ratio α and perturbations in the magnetic pressure within the solar convective envelope yield the same value for V/(t). During the normal unperturbed evolution of the present Sun, V(t) = 0.4. Our results show that core perturbations such as the present mixing events cannot explain the decrease in the solar radius indicated by the solar eclipse data between 1925 and 1980

  9. Singular perturbation theory mathematical and analytical techniques with applications to engineering

    CERN Document Server

    Johnson, RS

    2005-01-01

    Written in a form that should enable the relatively inexperienced (or new) worker in the field of singular perturbation theory to learn and apply all the essential ideasDesigned as a learning tool. The numerous examples and set exercises are intended to aid this process.

  10. Development of numerical methods for reactive transport; Developpement de methodes numeriques pour le transport reactif

    Energy Technology Data Exchange (ETDEWEB)

    Bouillard, N

    2006-12-15

    When a radioactive waste is stored in deep geological disposals, it is expected that the waste package will be damaged under water action (concrete leaching, iron corrosion). Then, to understand these damaging processes, chemical reactions and solutes transport are modelled. Numerical simulations of reactive transport can be done sequentially by the coupling of several codes. This is the case of the software platform ALLIANCES which is developed jointly with CEA, ANDRA and EDF. Stiff reactions like precipitation-dissolution are crucial for the radioactive waste storage applications, but standard sequential iterative approaches like Picard's fail in solving rapidly reactive transport simulations with such stiff reactions. In the first part of this work, we focus on a simplified precipitation and dissolution process: a system made up with one solid species and two aqueous species moving by diffusion is studied mathematically. It is assumed that a precipitation dissolution reaction occurs in between them, and it is modelled by a discontinuous kinetics law of unknown sign. By using monotonicity properties, the convergence of a finite volume scheme on admissible mesh is proved. Existence of a weak solution is obtained as a by-product of the convergence of the scheme. The second part is dedicated to coupling algorithms which improve Picard's method and can be easily used in an existing coupling code. By extending previous works, we propose a general and adaptable framework to solve nonlinear systems. Indeed by selecting special options, we can either recover well known methods, like nonlinear conjugate gradient methods, or design specific method. This algorithm has two main steps, a preconditioning one and an acceleration one. This algorithm is tested on several examples, some of them being rather academical and others being more realistic. We test it on the 'three species model'' example. Other reactive transport simulations use an external

  11. Development of numerical methods for reactive transport; Developpement de methodes numeriques pour le transport reactif

    Energy Technology Data Exchange (ETDEWEB)

    Bouillard, N

    2006-12-15

    When a radioactive waste is stored in deep geological disposals, it is expected that the waste package will be damaged under water action (concrete leaching, iron corrosion). Then, to understand these damaging processes, chemical reactions and solutes transport are modelled. Numerical simulations of reactive transport can be done sequentially by the coupling of several codes. This is the case of the software platform ALLIANCES which is developed jointly with CEA, ANDRA and EDF. Stiff reactions like precipitation-dissolution are crucial for the radioactive waste storage applications, but standard sequential iterative approaches like Picard's fail in solving rapidly reactive transport simulations with such stiff reactions. In the first part of this work, we focus on a simplified precipitation and dissolution process: a system made up with one solid species and two aqueous species moving by diffusion is studied mathematically. It is assumed that a precipitation dissolution reaction occurs in between them, and it is modelled by a discontinuous kinetics law of unknown sign. By using monotonicity properties, the convergence of a finite volume scheme on admissible mesh is proved. Existence of a weak solution is obtained as a by-product of the convergence of the scheme. The second part is dedicated to coupling algorithms which improve Picard's method and can be easily used in an existing coupling code. By extending previous works, we propose a general and adaptable framework to solve nonlinear systems. Indeed by selecting special options, we can either recover well known methods, like nonlinear conjugate gradient methods, or design specific method. This algorithm has two main steps, a preconditioning one and an acceleration one. This algorithm is tested on several examples, some of them being rather academical and others being more realistic. We test it on the 'three species model'' example. Other reactive transport simulations use an external chemical code CHESS. For a

  12. Passive heat transfer augmentation in a cylindrical annulus utilizing multiple perturbations on the inner and outer cylinders

    International Nuclear Information System (INIS)

    Iyer, S.V.; Vafai, K.

    1999-01-01

    The study of natural convection flow and heat transfer within a cylindrical annulus has received considerable attention because of its numerous applications, such as in nuclear reactor design, electronic component cooling, thermal storage systems, energy conservation, energy storage, and energy transmission. Here, the effects of multiple geometric perturbations on the inner and outer cylinders of an annulus with impermeable end walls are investigated in this work. A three-dimensional study was done using a numerical scheme based on a Galerkin method of finite element formulation. The nature of the buoyancy-induced flow field has been analyzed in detail. The flow fields for the cases considered were found to be qualitatively similar, and the introduction of each additional perturbation altered the flow field in a regular and recurring manner. The introduction of each perturbation on the outer cylinder causes clockwise and counterclock-wise rotating patterns on either side of the perturbation in the upper circumferential regions of the annulus. The motion of the fluid entrained by these circulatory patterns constitutes the key features of the flow pattern observed in the annulus. It is observed that the presence of multiple perturbations on the inner and outer cylinders substantially increases the overall heat transfer rate as compared to the regular annulus without any perturbation. Key qualitative and quantitative effects of the introduction of perturbations on both the inner and outer cylinders of the annulus are discussed

  13. Computational Flame Diagnostics for Direct Numerical Simulations with Detailed Chemistry of Transportation Fuels

    Energy Technology Data Exchange (ETDEWEB)

    Lu, Tianfeng [Univ. of Connecticut, Storrs, CT (United States)

    2017-02-16

    The goal of the proposed research is to create computational flame diagnostics (CFLD) that are rigorous numerical algorithms for systematic detection of critical flame features, such as ignition, extinction, and premixed and non-premixed flamelets, and to understand the underlying physicochemical processes controlling limit flame phenomena, flame stabilization, turbulence-chemistry interactions and pollutant emissions etc. The goal has been accomplished through an integrated effort on mechanism reduction, direct numerical simulations (DNS) of flames at engine conditions and a variety of turbulent flames with transport fuels, computational diagnostics, turbulence modeling, and DNS data mining and data reduction. The computational diagnostics are primarily based on the chemical explosive mode analysis (CEMA) and a recently developed bifurcation analysis using datasets from first-principle simulations of 0-D reactors, 1-D laminar flames, and 2-D and 3-D DNS (collaboration with J.H. Chen and S. Som at Argonne, and C.S. Yoo at UNIST). Non-stiff reduced mechanisms for transportation fuels amenable for 3-D DNS are developed through graph-based methods and timescale analysis. The flame structures, stabilization mechanisms, local ignition and extinction etc., and the rate controlling chemical processes are unambiguously identified through CFLD. CEMA is further employed to segment complex turbulent flames based on the critical flame features, such as premixed reaction fronts, and to enable zone-adaptive turbulent combustion modeling.

  14. Nonlinear ordinary differential equations analytical approximation and numerical methods

    CERN Document Server

    Hermann, Martin

    2016-01-01

    The book discusses the solutions to nonlinear ordinary differential equations (ODEs) using analytical and numerical approximation methods. Recently, analytical approximation methods have been largely used in solving linear and nonlinear lower-order ODEs. It also discusses using these methods to solve some strong nonlinear ODEs. There are two chapters devoted to solving nonlinear ODEs using numerical methods, as in practice high-dimensional systems of nonlinear ODEs that cannot be solved by analytical approximate methods are common. Moreover, it studies analytical and numerical techniques for the treatment of parameter-depending ODEs. The book explains various methods for solving nonlinear-oscillator and structural-system problems, including the energy balance method, harmonic balance method, amplitude frequency formulation, variational iteration method, homotopy perturbation method, iteration perturbation method, homotopy analysis method, simple and multiple shooting method, and the nonlinear stabilized march...

  15. Propagation Dynamics Associated with Resonant Magnetic Perturbation Fields in High-Confinement Mode Plasmas inside the KSTAR Tokamak.

    Science.gov (United States)

    Xiao, W W; Evans, T E; Tynan, G R; Yoon, S W; Jeon, Y M; Ko, W H; Nam, Y U; Oh, Y K

    2017-11-17

    The propagation dynamics of resonant magnetic perturbation fields in KSTAR H-mode plasmas with injection of small edge perturbations produced by a supersonic molecular beam injection is reported for the first time. The results show that the perturbation field first excites a plasma response on the q=3 magnetic surface and then propagates inward to the q=2 surface with a radially averaged propagation velocity of resonant magnetic perturbations field equal to 32.5  m/ s. As a result, the perturbation field brakes the toroidal rotation on the q=3 surface first causing a momentum transport perturbation that propagates both inward and outward. A higher density fluctuation level is observed. The propagation velocity of the resonant magnetic perturbations field is larger than the radial propagation velocity of the perturbation in the toroidal rotation.

  16. A Study of Single- and Double-Averaged Second-Order Models to Evaluate Third-Body Perturbation Considering Elliptic Orbits for the Perturbing Body

    Directory of Open Access Journals (Sweden)

    R. C. Domingos

    2013-01-01

    Full Text Available The equations for the variations of the Keplerian elements of the orbit of a spacecraft perturbed by a third body are developed using a single average over the motion of the spacecraft, considering an elliptic orbit for the disturbing body. A comparison is made between this approach and the more used double averaged technique, as well as with the full elliptic restricted three-body problem. The disturbing function is expanded in Legendre polynomials up to the second order in both cases. The equations of motion are obtained from the planetary equations, and several numerical simulations are made to show the evolution of the orbit of the spacecraft. Some characteristics known from the circular perturbing body are studied: circular, elliptic equatorial, and frozen orbits. Different initial eccentricities for the perturbed body are considered, since the effect of this variable is one of the goals of the present study. The results show the impact of this parameter as well as the differences between both models compared to the full elliptic restricted three-body problem. Regions below, near, and above the critical angle of the third-body perturbation are considered, as well as different altitudes for the orbit of the spacecraft.

  17. Time dependent AN neutron transport calculations in finite media using a numerical inverse Laplace transform technique

    International Nuclear Information System (INIS)

    Ganapol, B.D.; Sumini, M.

    1990-01-01

    The time dependent space second order discrete form of the monokinetic transport equation is given an analytical solution, within the Laplace transform domain. Th A n dynamic model is presented and the general resolution procedure is worked out. The solution in the time domain is then obtained through the application of a numerical transform inversion technique. The justification of the research relies in the need to produce reliable and physically meaningful transport benchmarks for dynamic calculations. The paper is concluded by a few results followed by some physical comments

  18. A model to quantify the resilience of mass railway transportation systems

    International Nuclear Information System (INIS)

    Adjetey-Bahun, Kpotissan; Birregah, Babiga; Châtelet, Eric; Planchet, Jean-Luc

    2016-01-01

    Traditional risk management approaches focus on perturbation events' likelihood and their consequences. However, recent events show that not all perturbation events can be foreseen. The concept of resilience has been introduced to measure not only the system's ability to absorb perturbations, but also its ability to rapidly recover from perturbations. In this work, we propose a simulation-based model for quantifying resilience in mass railway transportation systems by quantifying passenger delay and passenger load as the system's performance indicators. We integrate all subsystems that make up mass railway transportation systems (transportation, power, telecommunication and organisation subsystems) and their interdependencies. The model is applied to the Paris mass railway transportation system. The model's results show that since trains continue running within the system even by decreasing their speed, the system remains resilient. During the normal operation of the system as well as during perturbation, the model shows similarities with reality. The perturbation management plan that consists of setting up temporary train services on part of the impacted line while repairing the failed system's component is considered in this work. We also assess the extent to which some resilient system's capacities (i.e. absorption, adaptation and recovery) can increase the resilience of the system. - Highlights: • The need of resilience quantification models in sociotechnical systems. • We propose a simulation-based model. • This model is applied to Paris mass railway transportation system.

  19. Numerical study of criticality of the slab reactors with three regions in one-group transport theory

    International Nuclear Information System (INIS)

    Santos, A. dos.

    1979-01-01

    The criticality of slab reactors consisting of core, blanket, and reflector is studied numerically based on the singular-eigenfunction-expansion method in one-group transport theory. The purpose of this work is three-fold: (1) it is shown that the three-media problem can be converted, using a recently developed method, to a set of regular integral equations for the expansion coefficients, such that numerical solutions can be obtained for the first time based on an exact theory; (2) highly accurate numerical results that can serve as standards of comparison for various approximate methods are reported for representative sets of parameters; and (3) the accuracy of the P sub(N) approximation, one of the more often used methods, is analyzed compared to the exact results [pt

  20. Sensitivity calculations of integral parameters by a generalyzed perturbation theory

    International Nuclear Information System (INIS)

    Santo, A.C.F. de.

    1981-12-01

    In this work, we first revise some concepts, concerning the neutron transport in nuclear systems. We derive the balance and importance equation. Then we discuss the neutron importance in subcritical, critical and supercritical systems. The adjoint flux is estabilished as the neutron importance for the fission process. The conventional perturbation theory is later presented. We developed a sistematic perturbative formulation in the first order variation in the distribution functions calculate the reactivity due to a system perturbation. We present in detail the flux difference and generalized functions methos. The above formulation is then extended for altered systems. We consider integral parameters of the type ratio of bilinear functionals (for which the reactivity is a particular case). We define sensitivity coeficients, for any integral parameter, corresponding to a especific system alterations. Possible aplication of the method are also discussed. In the last part of this work, we apply the perturbative formulation to the doppler reacitivity sensibility calculation, utilizing the generalized functions method. We describe in detail the compiler program written for this and some other possible aplications. (Author) [pt

  1. Perturbative construction of self-dual configurations on the torus

    International Nuclear Information System (INIS)

    Garcia Perez, M.; Gonzalez-Arroyo, A.; Pena, C.

    2000-01-01

    We develop a perturbative expansion which allows the construction of non-abelian self-dual SU(2) Yang-Mills field configurations on the four-dimensional torus with topological charge 1/2. The expansion is performed around the constant field strength abelian solutions found by 't Hooft. Next to leading order calculations are compared with numerical results obtained with lattice gauge theory techniques. (author)

  2. Transcendental smallness in singularly perturbed equations of volterra type

    International Nuclear Information System (INIS)

    Bijura, Angelina M.

    2003-11-01

    The application of different limit processes to a physical problem is an important tool in layer type techniques. Hence the study of initial layer correction functions is of central importance for understanding layer-type problems. It is shown that for singularly perturbed problems of Volterra type, the concept of transcendental smallness is an asymptotic one. Transcendentally small terms may be numerically important. (author)

  3. Gyrokinetic Simulations with External Resonant Magnetic Perturbations: Island Torque and Nonambipolar Transport with Rotation

    Science.gov (United States)

    Waltz, R. E.; Waelbroeck, F. L.

    2012-03-01

    Static external resonant magnetic perturbations (RMPs) have been added to the δf gyrokinetic code GYRO. This allows nonlinear gyrokinetic simulations of the nonambipolar radial current flow jr and the corresponding plasma torque (density) R[jrBθ/c], induced by islands that break the toroidal symmetry of a tokamak. This extends previous GYRO simulations for the transport of toroidal angular momentum (TAM) [1,2]. The focus is on full torus radial slice electrostatic simulations of induced q=m/n=6/3 islands with widths 5% of the minor radius. The island torque scales with the radial electric field Er the island width w, and the intensity I of the high-n micro-turbulence, as wErI^1/2. The net island torque is null at zero Er rather than at zero toroidal rotation. This means that there is a small co-directed magnetic acceleration to the small diamagnetic co-rotation corresponding to the zero Er which can be called the residual stress [2] from an externally induced island. Finite-beta GYRO simulations of a core radial slice demonstrate island unlocking and the RMP screening. 6pt[1] R.E. Waltz, et al., Phys. Plasmas 14, 122507 (2007). [2] R.E. Waltz, et al., Phys. Plasmas 18, 042504 (2011).

  4. The multistage homotopy-perturbation method: A powerful scheme for handling the Lorenz system

    International Nuclear Information System (INIS)

    Chowdhury, M.S.H.; Hashim, I.; Momani, S.

    2009-01-01

    In this paper, a new reliable algorithm based on an adaptation of the standard homotopy-perturbation method (HPM) is presented. The HPM is treated as an algorithm in a sequence of intervals (i.e. time step) for finding accurate approximate solutions to the famous Lorenz system. Numerical comparisons between the multistage homotopy-perturbation method (MHPM) and the classical fourth-order Runge-Kutta (RK4) method reveal that the new technique is a promising tool for the nonlinear systems of ODEs.

  5. Systems of evolution equations and the singular perturbation method

    International Nuclear Information System (INIS)

    Mika, J.

    Several fundamental theorems are presented important for the solution of linear evolution equations in the Banach space. The algorithm is deduced extending the solution of the system of singularly perturbed evolution equations into an asymptotic series with respect to a small positive parameter. The asymptotic convergence is shown of an approximate solution to the accurate solution. Singularly perturbed evolution equations of the resonance type were analysed. The special role is considered of the asymptotic equivalence of P1 equations obtained as the first order approximation if the spherical harmonics method is applied to the linear Boltzmann equation, and the diffusion equations of the linear transport theory where the small parameter approaches zero. (J.B.)

  6. Numerical study of thermal test of a cask of transportation for radioactive material; Estudo numérico do ensaio térmico de um casco de transporte para material radioativo

    Energy Technology Data Exchange (ETDEWEB)

    Vieira, Tiago A.S.; Santos, André A.C. dos; Vidal, Guilherme A.M.; Silva Junior, Geraldo E., E-mail: tiago.vieira.eng@gmail.com, E-mail: gvidal.ufmg@gmail.com, E-mail: aacs@cdtn.br, E-mail: geraldo.esilva@yahoo.com.br [Centro de Desenvolvimento da Tecnologia Nuclear (CDTN/CNEN-MG), Belo Horizonte, MG (Brazil)

    2017-07-01

    In this study numerical simulations of a transport cask for radioactive material were made and the numerical results were compared with experimental results of tests carried out in two different opportunities. A mesh study was also made regarding the previously designed geometry of the same cask, in order to evaluate its impact in relation to the stability of numerical results for this type of problem. The comparison of the numerical and experimental results allowed to evaluate the need to plan and carry out a new test in order to validate the CFD codes used in the numerical simulations.

  7. Numerical modeling of solute transport in deformable unsaturated layered soil

    Directory of Open Access Journals (Sweden)

    Sheng Wu

    2017-07-01

    Full Text Available The effect of soil stratification was studied through numerical investigation based on the coupled model of solute transport in deformable unsaturated soil. The theoretical model implied two-way coupled excess pore pressure and soil deformation based on Biot's consolidation theory as well as a one-way coupled volatile pollutant concentration field developed from the advection-diffusion theory. Embedded in the model, the degree of saturation, fluid compressibility, self-weight of the soil matrix, porosity variance, longitudinal dispersion, and linear sorption were computed. Based on simulation results of a proposed three-layer landfill model using the finite element method, the multi-layer effects are discussed with regard to the hydraulic conductivity, shear modulus, degree of saturation, molecular diffusion coefficient, and thickness of each layer. Generally speaking, contaminants spread faster in a stratified field with a soft and highly permeable top layer; soil parameters of the top layer are more critical than the lower layers but controlling soil thicknesses will alter the results. This numerical investigation showed noticeable impacts of stratified soil properties on solute migration results, demonstrating the importance of correctly modeling layered soil instead of simply assuming the averaged properties across the soil profile.

  8. Numerical modelling of solid transport caused by an extreme flood: Case of the Hamiz dam failure (Algeria

    Directory of Open Access Journals (Sweden)

    Haddad Ali

    2017-07-01

    Full Text Available Study of solid transport caused by the flow of an extreme flood such as the propagation of dam failure wave aims to simulate the hydrodynamics behaviour of the solid particles contained in the valley during the flood passage. With this intention, we have developed a numerical model which is based on the resolution of the one-dimensional Saint Venant–Exner equations by the implicit finite difference scheme. Numerical stability of liquid phase calculation is checked by the Courant number and De Vries condition for the solid phase. The model has been applied to the Hamiz dam (Algeria which is built in the semi arid zone and presents a major risk of failure. The simulation of several scenarios of dam failure has allowed us to trace the cartography of sediment transport in the valley which is induced by the flood of dam failure.

  9. International Winter Workshop on Differential Equations and Numerical Analysis

    CERN Document Server

    Miller, John; Narasimhan, Ramanujam; Mathiazhagan, Paramasivam; Victor, Franklin

    2016-01-01

    This book offers an ideal introduction to singular perturbation problems, and a valuable guide for researchers in the field of differential equations. It also includes chapters on new contributions to both fields: differential equations and singular perturbation problems. Written by experts who are active researchers in the related fields, the book serves as a comprehensive source of information on the underlying ideas in the construction of numerical methods to address different classes of problems with solutions of different behaviors, which will ultimately help researchers to design and assess numerical methods for solving new problems. All the chapters presented in the volume are complemented by illustrations in the form of tables and graphs.

  10. Solution methods for compartment models of transport through the environment using numerical inversion of Laplace transforms

    International Nuclear Information System (INIS)

    Garratt, T.J.

    1989-05-01

    Compartment models for the transport of radionuclides in the biosphere are conventionally solved using a numerical time-stepping procedure. This report examines an alternative method based on the numerical inversion of Laplace transforms, which is potentially more efficient and accurate for some classes of problem. The central problem considered is the most efficient and robust technique for solving the Laplace-transformed rate equations. The conclusion is that Gaussian elimination is the most efficient and robust solution method. A general compartment model has been implemented on a personal computer and used to solve a realistic case including radionuclide decay chains. (author)

  11. A new perturbative treatment of pentadiagonal Hamiltonians

    International Nuclear Information System (INIS)

    Znojil, M.

    1987-01-01

    A new formulation of the Rayleich - Schroedinger perturbation theory is proposed. It is inspired by a recurent construction of propagators, and its main idea lies in a replacement of the auxiliary matrix elements (generalized continued fractions) by their non-numerical approximants. In a test of convergence (the anharmonic oscillator), the asymptotic fixed-point approximation scheme is used. The results indicate a good applicability of this fixed-point version of our formalism to systems with a band-matrix structure of the Hamiltonian

  12. Scalar-gravitational perturbations and quasi normal modes in the five dimensional Schwarzschild black hole

    International Nuclear Information System (INIS)

    Cardoso, Vitor; Lemos, Jose P.S.; Yoshida, Shijun

    2003-01-01

    We calculate the quasi normal modes (QNMs) for gravitational perturbations of the Schwarzschild black hole in the five dimensional (5D) spacetime with a continued fraction method. For all the types of perturbations (scalar-gravitational, vector-gravitational, and tensor-gravitational perturbations), the QNMs associated with l = 2, l 3, and l = 4 are calculated. Our numerical results are summarized as follows: (i) The three types of gravitational perturbations associated with the same angular quantum number l have a different set of the quasi normal (QN) frequencies; (ii) There is no purely imaginary frequency mode; (iii) The three types of gravitational perturbations have the same asymptotic behavior of the QNMs in the limit of the large imaginary frequencies, which are given by ωT H -1 → log 3+ 2πi(n+1/2) as n → ∞, where ω, T H , and n are the oscillation frequency, the Hawking temperature of the black hole, and the mode number, respectively. (author)

  13. Data Shuffling--A New Masking Approach for Numerical Data

    OpenAIRE

    Krishnamurty Muralidhar; Rathindra Sarathy

    2006-01-01

    This study discusses a new procedure for masking confidential numerical data--a procedure called data shuffling--in which the values of the confidential variables are "shuffled" among observations. The shuffled data provides a high level of data utility and minimizes the risk of disclosure. From a practical perspective, data shuffling overcomes reservations about using perturbed or modified confidential data because it retains all the desirable properties of perturbation methods and performs ...

  14. Numerical simulation of pollutant transport in fractured vuggy porous karstic aquifers

    KAUST Repository

    Sun, S.

    2011-01-01

    This paper begins with presenting a mathematical model for contaminant transport in the fractured vuggy porous media of a species of contaminant (PCP). Two phases are numerically simulated for a process of contaminant and clean water infiltrated in the fractured vuggy porous media by coupling mixed finite element (MFE) method and finite volume method (FVM), both of which are locally conservative, to approximate the model. A hybrid mixed finite element (HMFE) method is applied to approximate the velocity field for the model. The convection and diffusion terms are approached by FVM and the standard MFE, respectively. The pressure distribution and temporary evolution of the concentration profiles are obtained for two phases. The average effluent concentration on the outflow boundary is obtained at different time and shows some different features from the matrix porous media. The temporal multiscale phenomena of the effluent concentration on the outlet are observed. The results show how the different distribution of the vugs and the fractures impacts on the contaminant transport and the effluent concentration on the outlet. This paper sheds light on certain features of karstic groundwater are obtained.

  15. Numerical Simulation of Pollutant Transport in Fractured Vuggy Porous Karstic Aquifers

    Directory of Open Access Journals (Sweden)

    Xiaolin Fan

    2011-01-01

    Full Text Available This paper begins with presenting a mathematical model for contaminant transport in the fractured vuggy porous media of a species of contaminant (PCP. Two phases are numerically simulated for a process of contaminant and clean water infiltrated in the fractured vuggy porous media by coupling mixed finite element (MFE method and finite volume method (FVM, both of which are locally conservative, to approximate the model. A hybrid mixed finite element (HMFE method is applied to approximate the velocity field for the model. The convection and diffusion terms are approached by FVM and the standard MFE, respectively. The pressure distribution and temporary evolution of the concentration profiles are obtained for two phases. The average effluent concentration on the outflow boundary is obtained at different time and shows some different features from the matrix porous media. The temporal multiscale phenomena of the effluent concentration on the outlet are observed. The results show how the different distribution of the vugs and the fractures impacts on the contaminant transport and the effluent concentration on the outlet. This paper sheds light on certain features of karstic groundwater are obtained.

  16. Conceptual and Numerical Modeling of Radionuclide Transport and Retention in Near-Surface Systems

    International Nuclear Information System (INIS)

    Pique, Angels; Arcos, David; Grandia, Fidel; Molinero, Jorge; Duro, Lara; Berglund, Sten

    2013-01-01

    Scenarios of barrier failure and radionuclide release to the near-surface environment are important to consider within performance and safety assessments of repositories for nuclear waste. A geological repository for spent nuclear fuel is planned at Forsmark, Sweden. Conceptual and numerical reactive transport models were developed in order to assess the retention capacity of the Quaternary till and clay deposits for selected radionuclides, in the event of an activity release from the repository. The elements considered were carbon (C), chlorine (Cl), cesium (Cs), iodine (I), molybdenum (Mo), niobium (Nb), nickel (Ni), radium (Ra), selenium (Se), strontium (Sr), technetium (Tc), thorium (Th), and uranium (U). According to the numerical predictions, the repository-derived nuclides that would be most significantly retained are Th, Ni, and Cs, mainly through sorption onto clays, followed by U, C, Sr, and Ra, trapped by sorption and/or incorporation into mineral phases

  17. Bounded Perturbation Regularization for Linear Least Squares Estimation

    KAUST Repository

    Ballal, Tarig

    2017-10-18

    This paper addresses the problem of selecting the regularization parameter for linear least-squares estimation. We propose a new technique called bounded perturbation regularization (BPR). In the proposed BPR method, a perturbation with a bounded norm is allowed into the linear transformation matrix to improve the singular-value structure. Following this, the problem is formulated as a min-max optimization problem. Next, the min-max problem is converted to an equivalent minimization problem to estimate the unknown vector quantity. The solution of the minimization problem is shown to converge to that of the ℓ2 -regularized least squares problem, with the unknown regularizer related to the norm bound of the introduced perturbation through a nonlinear constraint. A procedure is proposed that combines the constraint equation with the mean squared error (MSE) criterion to develop an approximately optimal regularization parameter selection algorithm. Both direct and indirect applications of the proposed method are considered. Comparisons with different Tikhonov regularization parameter selection methods, as well as with other relevant methods, are carried out. Numerical results demonstrate that the proposed method provides significant improvement over state-of-the-art methods.

  18. tran-SAS v1.0: a numerical model to compute catchment-scale hydrologic transport using StorAge Selection functions

    Directory of Open Access Journals (Sweden)

    P. Benettin

    2018-04-01

    Full Text Available This paper presents the tran-SAS package, which includes a set of codes to model solute transport and water residence times through a hydrological system. The model is based on a catchment-scale approach that aims at reproducing the integrated response of the system at one of its outlets. The codes are implemented in MATLAB and are meant to be easy to edit, so that users with minimal programming knowledge can adapt them to the desired application. The problem of large-scale solute transport has both theoretical and practical implications. On the one side, the ability to represent the ensemble of water flow trajectories through a heterogeneous system helps unraveling streamflow generation processes and allows us to make inferences on plant–water interactions. On the other side, transport models are a practical tool that can be used to estimate the persistence of solutes in the environment. The core of the package is based on the implementation of an age master equation (ME, which is solved using general StorAge Selection (SAS functions. The age ME is first converted into a set of ordinary differential equations, each addressing the transport of an individual precipitation input through the catchment, and then it is discretized using an explicit numerical scheme. Results show that the implementation is efficient and allows the model to run in short times. The numerical accuracy is critically evaluated and it is shown to be satisfactory in most cases of hydrologic interest. Additionally, a higher-order implementation is provided within the package to evaluate and, if necessary, to improve the numerical accuracy of the results. The codes can be used to model streamflow age and solute concentration, but a number of additional outputs can be obtained by editing the codes to further advance the ability to understand and model catchment transport processes.

  19. tran-SAS v1.0: a numerical model to compute catchment-scale hydrologic transport using StorAge Selection functions

    Science.gov (United States)

    Benettin, Paolo; Bertuzzo, Enrico

    2018-04-01

    This paper presents the tran-SAS package, which includes a set of codes to model solute transport and water residence times through a hydrological system. The model is based on a catchment-scale approach that aims at reproducing the integrated response of the system at one of its outlets. The codes are implemented in MATLAB and are meant to be easy to edit, so that users with minimal programming knowledge can adapt them to the desired application. The problem of large-scale solute transport has both theoretical and practical implications. On the one side, the ability to represent the ensemble of water flow trajectories through a heterogeneous system helps unraveling streamflow generation processes and allows us to make inferences on plant-water interactions. On the other side, transport models are a practical tool that can be used to estimate the persistence of solutes in the environment. The core of the package is based on the implementation of an age master equation (ME), which is solved using general StorAge Selection (SAS) functions. The age ME is first converted into a set of ordinary differential equations, each addressing the transport of an individual precipitation input through the catchment, and then it is discretized using an explicit numerical scheme. Results show that the implementation is efficient and allows the model to run in short times. The numerical accuracy is critically evaluated and it is shown to be satisfactory in most cases of hydrologic interest. Additionally, a higher-order implementation is provided within the package to evaluate and, if necessary, to improve the numerical accuracy of the results. The codes can be used to model streamflow age and solute concentration, but a number of additional outputs can be obtained by editing the codes to further advance the ability to understand and model catchment transport processes.

  20. Modelling of ion thermal transport in ergodic region of collisionless toroidal plasma

    International Nuclear Information System (INIS)

    Kanno, Ryutaro; Nunami, Masanori; Satake, Shinsuke; Ohyabu, Nobuyoshi; Takamaru, Hisanori; Okamoto, Masao

    2009-09-01

    In recent tokamak experiments it has been found that so-called diffusion theory based on the 'diffusion of magnetic field lines' overestimates the radial energy transport in the ergodic region of the collisionless plasma affected by resonant magnetic perturbations (RMPs), though the RMPs induce chaotic behavior of the magnetic field lines. The result implies that the modelling of the transport should be reconsidered for low collisionality cases. A computer simulation study of transport in the ergodic region is required for understanding fundamental properties of collisionless ergodized-plasmas, estimating the transport coefficients, and reconstructing the modelling of the transport. In this paper, we report the simulation study of thermal transport in the ergodic region under the assumption of neglecting effects of an electric field, impurities and neutrals. Because of the simulations neglecting interactions with different particle-species and saving the computational time, we treat ions (protons) in our numerical-study of the transport. We find that the thermal diffusivity in the ergodic region is extremely small compared to the one predicted by the theory of field-line diffusion and that the diffusivity depends on both the collision frequency and the strength of RMPs even for the collisionless ergodized-plasma. (author)

  1. Linear perturbation growth at the trailing edge of a rarefaction wave

    International Nuclear Information System (INIS)

    Wouchuk, J.G.; Carretero, R.

    2003-01-01

    An analytic model for the perturbation growth inside a rarefaction wave is presented. The objective of the work is to calculate the growth of the perturbations at the trailing edge of a simple expanding wave in planar geometry. Previous numerical and analytical works have shown that the ripples at the rarefaction tail exhibit linear growth asymptotically in time [Yang et al., Phys. Fluids 6, 1856 (1994), A. Velikovich and L. Phillips, ibid. 8, 1107 (1996)]. However, closed expressions for the asymptotic value of the perturbed velocity of the trailing edge have not been reported before, except for very weak rarefactions. Explicit analytic solutions for the perturbations growing at the rarefaction trailing edge as a function of time and also for the asymptotic perturbed velocity are given, for fluids with γ<3. The limits of weak and strong rarefactions are considered and the corresponding scaling laws are given. A semi-qualitative discussion of the late time linear growth at the trailing edge ripple is presented and it is seen that the lateral mass flow induced by the sound wave fluctuations is solely responsible for that behavior. Only the rarefactions generated after the interaction of a shock wave with a contact discontinuity are considered

  2. Perturbation theory for the effective diffusion constant in a medium of random scatterers

    International Nuclear Information System (INIS)

    Dean, D S; Drummond, I T; Horgan, R R; Lefevre, A

    2004-01-01

    We develop perturbation theory and physically motivated resummations of the perturbation theory for the problem of a tracer particle diffusing in a random medium. The random medium contains point scatterers of density ρ uniformly distributed throughout the material. The tracer is a Langevin particle subjected to the quenched random force generated by the scatterers. Via our perturbative analysis, we determine when the random potential can be approximated by a Gaussian random potential. We also develop a self-similar renormalization group approach based on thinning out the scatterers; this scheme is similar to that used with success for diffusion in Gaussian random potentials and agrees with known exact results. To assess the accuracy of this approximation scheme, its predictions are confronted with results obtained by numerical simulation

  3. Numerical simulation of two-phase multicomponent flow with reactive transport in porous media

    International Nuclear Information System (INIS)

    Vostrikov, Viatcheslav

    2014-01-01

    The subject of this thesis is the numerical simulation of water-gas flow in the subsurface together with chemical reactions. The subject has applications to various situations in environmental modeling, though we are mainly concerned with CO 2 storage in deep saline aquifers. In Carbon Capture and Storage studies, CO 2 is first captured from its sources of origin, transport in liquefied form and injected as gas under high pressure in deep saline aquifers. Numerical simulation is an essential tool to make sure that gaseous CO 2 will remain trapped for several hundreds or thousands of years. Several trapping mechanisms can be brought to bear to achieve this goal. Of particular interest in this thesis are solubility trapping (whereby gaseous CO 2 dissolves in the brine as it moves upward) and, on a longer term, mineral trapping (which causes CO 2 to react with the surrounding rock to form minerals such as calcite). Thus, understanding how CO 2 reacts chemically becomes an important issue for its long term fate. The thesis is composed of four chapters. The first chapter is an introduction to multicomponent two-phase flow in porous media, with or without chemical reactions. It presents a review of the existing literature, and gives an outline of the whole thesis. Chapter 2 presents a quantitative discussion of the physical and chemical phenomena involved, and of their mathematical modeling. The model we use is that of two-phase two-component flow in porous media, coupled to reactive transport. This model leads to a large set of partial differential equations, coupled to algebraic equations, describing the evolution of the concentration of each species at each grid point. A direct solution of this problem (a fully coupled solution) is possible, but presents many difficulties form the numerical point of view. Moreover, it makes it difficult to reuse codes already written, and validated, to simulate the simpler phenomena of (uncoupled) two-phase flow and reactive transport

  4. Unified description of perturbation theory and band center anomaly in one-dimensional Anderson localization

    International Nuclear Information System (INIS)

    Kang, Kai; Qin, Shaojing; Wang, Chuilin

    2011-01-01

    We calculated numerically the localization length of one-dimensional Anderson model with diagonal disorder. For weak disorder, we showed that the localization length changes continuously as the energy changes from the band center to the boundary of the anomalous region near the band edge. We found that all the localization lengths for different disorder strengths and different energies collapse onto a single curve, which can be fitted by a simple equation. Thus the description of the perturbation theory and the band center anomaly were unified into this equation. -- Highlights: → We study the band center anomaly of one-dimensional Anderson localization. → We study numerically the Lyapunov exponent through a parametrization method of the transfer matrix. → We give a unified equation to describe the band center anomaly and perturbation theory.

  5. The effect of resonant magnetic perturbations on the impurity transport in TEXTOR-DED plasmas

    International Nuclear Information System (INIS)

    Greiche, Albert Josef

    2009-01-01

    Thermonuclear fusion provides a new mechanism for the generation of electrical power which has the perspective to serve humanity for several millions of years. One possibility to implement fusion on earth is to magnetically confine hot deuterium tritium plasmas in so called tokamaks. The fusion reactions take place in the hot plasma core. Each of the fusion reactions between deuterium and tritium yields 17.6 MeV which can be used in the process of generating electrical power. Impurities contaminate the plasma which then is cooled down and diluted. This leads to a reduction of the fusion reactions and in consequence the energy yield. The transport behaviour of the impurities in the plasma is not fully understood up to now. Nevertheless, experiments have shown that the application of resonant magnetic perturbations (RMP) can control the impurity content in the plasma. The dynamic ergodic divertor (DED) on the tokamak Textor is able to induce static and dynamic RMPs. During the application of RMPs transient impurity transport experiments with argon have been performed and the time evolution of the impurity concentrations have been monitored. The line emission intensity of the impurities in the plasma is measured in the vacuum ultraviolet (VUV) and in the soft X-ray (SXR) with the absolutely calibrated VUV spectrometer Hexos and SXR PIN diodes, respectively. The analysis of the transient impurity transport experiments is performed with the help of the transport code Strahl. The impurity flows in Strahl are described by a combination of a diffusive and a convective flow. In the computing process the code solves the coupled set of continuity equations of each of the ionization stages of an impurity. With this method the time evolution of the impurity ion densities and the line emission intensities of the ionization stages can be computed. The adaption to the experimental measurements is performed with the help of the diffusion coefficient and the drift velocity which

  6. Enhanced Multistage Homotopy Perturbation Method: Approximate Solutions of Nonlinear Dynamic Systems

    Directory of Open Access Journals (Sweden)

    Daniel Olvera

    2014-01-01

    Full Text Available We introduce a new approach called the enhanced multistage homotopy perturbation method (EMHPM that is based on the homotopy perturbation method (HPM and the usage of time subintervals to find the approximate solution of differential equations with strong nonlinearities. We also study the convergence of our proposed EMHPM approach based on the value of the control parameter h by following the homotopy analysis method (HAM. At the end of the paper, we compare the derived EMHPM approximate solutions of some nonlinear physical systems with their corresponding numerical integration solutions obtained by using the classical fourth order Runge-Kutta method via the amplitude-time response curves.

  7. Resonant interaction of energetic ions with Alfven-like perturbations in stellarators

    International Nuclear Information System (INIS)

    Karulin, N.; Wobig, H.

    1994-04-01

    The modification of passing guiding center orbits of 3.5 MeV alpha particles and 45 keV protons in the presence of global Alfven eigenmodes (GAE's) is studied in modular advanced stellarators. It is found that if resonances between particles and waves occur, drift surfaces form a set of island structures. The mode numbers of the perturbations, which are dangerous for the energetic particle confinement, are discussed for two particular stellarators (Helias reactor and Wendelstein 7-AS). The perturbation amplitudes corresponding to the onset of orbit stochasticity are studied numerically. The coefficient of the collisionless stochastic diffusion is estimated using the island width derived analytically. (orig.)

  8. Application of the perturbation iteration method to boundary layer type problems.

    Science.gov (United States)

    Pakdemirli, Mehmet

    2016-01-01

    The recently developed perturbation iteration method is applied to boundary layer type singular problems for the first time. As a preliminary work on the topic, the simplest algorithm of PIA(1,1) is employed in the calculations. Linear and nonlinear problems are solved to outline the basic ideas of the new solution technique. The inner and outer solutions are determined with the iteration algorithm and matched to construct a composite expansion valid within all parts of the domain. The solutions are contrasted with the available exact or numerical solutions. It is shown that the perturbation-iteration algorithm can be effectively used for solving boundary layer type problems.

  9. Non-perturbative description of quantum systems

    CERN Document Server

    Feranchuk, Ilya; Le, Van-Hoang; Ulyanenkov, Alexander

    2015-01-01

    This book introduces systematically the operator method for the solution of the Schrödinger equation. This method permits to describe the states of quantum systems in the entire range of parameters of Hamiltonian with a predefined accuracy. The operator method is unique compared with other non-perturbative methods due to its ability to deliver in zeroth approximation the uniformly suitable estimate for both ground and excited states of quantum system. The method has been generalized for the application to quantum statistics and quantum field theory.  In this book, the numerous applications of operator method for various physical systems are demonstrated. Simple models are used to illustrate the basic principles of the method which are further used for the solution of complex problems of quantum theory for many-particle systems. The results obtained are supplemented by numerical calculations, presented as tables and figures.

  10. Shielding of External Magnetic Perturbations By Torque In Rotating Tokamak Plasmas

    International Nuclear Information System (INIS)

    Park, Jong-Kyu; Boozer, Allen H.; Menard, Jonathan E.; Gerhardt, Stefan P.; Sabbagh, Steve A.

    2009-01-01

    The imposition of a nonaxisymmetric magnetic perturbation on a rotating tokamak plasma requires energy and toroidal torque. Fundamental electrodynamics implies that the torque is essentially limited and must be consistent with the external response of a plasma equilibrium (rvec f) = (rvec j) x (rvec B). Here magnetic measurements on National Spherical Torus eXperiment (NSTX) device are used to derive the energy and the torque, and these empirical evaluations are compared with theoretical calculations based on perturbed scalar pressure equilibria (rvec f) = (rvec (del))p coupled with the theory of nonambipolar transport. The measurement and the theory are consistent within acceptable uncertainties, but can be largely inconsistent when the torque is comparable to the energy. This is expected since the currents associated with the torque are ignored in scalar pressure equilibria, but these currents tend to shield the perturbation.

  11. A numerical simulation of pre-big bang cosmology

    CERN Document Server

    Maharana, J P; Veneziano, Gabriele

    1998-01-01

    We analyse numerically the onset of pre-big bang inflation in an inhomogeneous, spherically symmetric Universe. Adding a small dilatonic perturbation to a trivial (Milne) background, we find that suitable regions of space undergo dilaton-driven inflation and quickly become spatially flat ($\\Omega \\to 1$). Numerical calculations are pushed close enough to the big bang singularity to allow cross checks against previously proposed analytic asymptotic solutions.

  12. A Perturbation Analysis of Harmonics Generation from Saturated Elements in Power Systems

    Science.gov (United States)

    Kumano, Teruhisa

    Nonlinear phenomena such as saturation in magnetic flux give considerable effects in power system analysis. It is reported that a failure in a real 500kV system triggered islanding operation, where resultant even harmonics caused malfunctions in protective relays. It is also reported that the major origin of this wave distortion is nothing but unidirectional magnetization of the transformer iron core. Time simulation is widely used today to analyze this type of phenomena, but it has basically two shortcomings. One is that the time simulation takes two much computing time in the vicinity of inflection points in the saturation characteristic curve because certain iterative procedure such as N-R (Newton-Raphson) should be used and such methods tend to be caught in an ill conditioned numerical hunting. The other is that such simulation methods sometimes do not help intuitive understanding of the studied phenomenon because the whole nonlinear equations are treated in a matrix form and not properly divided into understandable parts as done in linear systems. This paper proposes a new computation scheme which is based on so called perturbation method. Magnetic saturation in iron cores in a generator and a transformer are taken into account. The proposed method has a special feature against the first shortcoming of the N-R based time simulation method stated above. In the proposed method no iterative process is used to reduce the equation residue but uses perturbation series, which means free from the ill condition problem. Users have only to calculate each perturbation terms one by one until he reaches necessary accuracy. In a numerical example treated in the present paper the first order perturbation can make reasonably high accuracy, which means very fast computing. In numerical study three nonlinear elements are considered. Calculated results are almost identical to the conventional Newton-Raphson based time simulation, which shows the validity of the method. The

  13. Lagrangian transport and chaos in the near wake of the flow around an obstacle: a numerical implementation of lobe dynamics

    Directory of Open Access Journals (Sweden)

    J. Duan

    1997-01-01

    Full Text Available In this paper we study Lagrangian transport in the near wake of the flow around an obstacle, which we take to be a cylinder. In this case, for the range of Reynolds numbers investigated, the flow is two-dimensional and time periodic. We use ideas and methods from transport theory in dynamical systems to describe and quantify transport in the near wake. We numerically solve the Navier-Stokes equations for the velocity field and apply these methods to the resulting numerical representation of the velocity field. We show that the method of lobe dynamics can be used in conjunction with computational fluid dynamics methods to give very detailed and quantitative information about Lagrangian transport. In particular, we show how the stable and unstable manifolds of certain saddle-type stagnation points on the cylinder, and one in the wake, can be used to divide the flow into three distinct regions, an upper wake, a lower wake, and a wake cavity. The significance of the division using stable and unstable manifolds lies in the fact that these invariant manifolds form a template on which the transport occurs. Using this, we compute fluxes from the upper and lower wakes into the wake cavity using the associated turnstile lobes. We also compute escape time distributions as well as compare transport properties for two different Reynolds numbers.

  14. Stability under scalar perturbations and quasinormal modes of 4D Einstein-Born-Infeld dilaton spacetime. Exact spectrum

    International Nuclear Information System (INIS)

    Destounis, Kyriakos; Panotopoulos, Grigoris; Rincon, Angel

    2018-01-01

    We study the stability under scalar perturbations, and we compute the quasinormal modes of the Einstein-Born-Infeld dilaton spacetime in 1 + 3 dimensions. Solving the full radial equation in terms of hypergeometric functions, we provide an exact analytical expression for the spectrum. We find that the frequencies are purely imaginary, and we confirm our results by computing them numerically. Although the scalar field that perturbs the black hole is electrically neutral, an instability similar to that seen in charged scalar perturbations of the Reissner-Nordstroem black hole is observed. (orig.)

  15. Stability under scalar perturbations and quasinormal modes of 4D Einstein-Born-Infeld dilaton spacetime. Exact spectrum

    Energy Technology Data Exchange (ETDEWEB)

    Destounis, Kyriakos; Panotopoulos, Grigoris [Universidade de Lisboa, Centro Multidisciplinar de Astrofisica, Instituto Superior Tecnico, Lisbon (Portugal); Rincon, Angel [Pontificia Universidad Catolica de Chile, Instituto de Fisica, Santiago (Chile)

    2018-02-15

    We study the stability under scalar perturbations, and we compute the quasinormal modes of the Einstein-Born-Infeld dilaton spacetime in 1 + 3 dimensions. Solving the full radial equation in terms of hypergeometric functions, we provide an exact analytical expression for the spectrum. We find that the frequencies are purely imaginary, and we confirm our results by computing them numerically. Although the scalar field that perturbs the black hole is electrically neutral, an instability similar to that seen in charged scalar perturbations of the Reissner-Nordstroem black hole is observed. (orig.)

  16. "Phonon" scattering beyond perturbation theory

    Science.gov (United States)

    Qiu, WuJie; Ke, XueZhi; Xi, LiLi; Wu, LiHua; Yang, Jiong; Zhang, WenQing

    2016-02-01

    Searching and designing materials with intrinsically low lattice thermal conductivity (LTC) have attracted extensive consideration in thermoelectrics and thermal management community. The concept of part-crystalline part-liquid state, or even part-crystalline part-amorphous state, has recently been proposed to describe the exotic structure of materials with chemical- bond hierarchy, in which a set of atoms is weakly bonded to the rest species while the other sublattices retain relatively strong rigidity. The whole system inherently manifests the coexistence of rigid crystalline sublattices and fluctuating noncrystalline substructures. Representative materials in the unusual state can be classified into two categories, i.e., caged and non-caged ones. LTCs in both systems deviate from the traditional T -1 relationship ( T, the absolute temperature), which can hardly be described by small-parameter-based perturbation approaches. Beyond the classical perturbation theory, an extra rattling-like scattering should be considered to interpret the liquid-like and sublattice-amorphization-induced heat transport. Such a kind of compounds could be promising high-performance thermoelectric materials, due to the extremely low LTCs. Other physical properties for these part-crystalline substances should also exhibit certain novelty and deserve further exploration.

  17. Perturbed rhythmic activation of signaling pathways in mice deficient for Sterol Carrier Protein 2-dependent diurnal lipid transport and metabolism.

    Science.gov (United States)

    Jouffe, Céline; Gobet, Cédric; Martin, Eva; Métairon, Sylviane; Morin-Rivron, Delphine; Masoodi, Mojgan; Gachon, Frédéric

    2016-04-21

    Through evolution, most of the living species have acquired a time keeping system to anticipate daily changes caused by the rotation of the Earth. In all of the systems this pacemaker is based on a molecular transcriptional/translational negative feedback loop able to generate rhythmic gene expression with a period close to 24 hours. Recent evidences suggest that post-transcriptional regulations activated mostly by systemic cues play a fundamental role in the process, fine tuning the time keeping system and linking it to animal physiology. Among these signals, we consider the role of lipid transport and metabolism regulated by SCP2. Mice harboring a deletion of the Scp2 locus present a modulated diurnal accumulation of lipids in the liver and a perturbed activation of several signaling pathways including PPARα, SREBP, LRH-1, TORC1 and its upstream regulators. This defect in signaling pathways activation feedbacks upon the clock by lengthening the circadian period of animals through post-translational regulation of core clock regulators, showing that rhythmic lipid transport is a major player in the establishment of rhythmic mRNA and protein expression landscape.

  18. Entanglement dynamics in critical random quantum Ising chain with perturbations

    Energy Technology Data Exchange (ETDEWEB)

    Huang, Yichen, E-mail: ychuang@caltech.edu

    2017-05-15

    We simulate the entanglement dynamics in a critical random quantum Ising chain with generic perturbations using the time-evolving block decimation algorithm. Starting from a product state, we observe super-logarithmic growth of entanglement entropy with time. The numerical result is consistent with the analytical prediction of Vosk and Altman using a real-space renormalization group technique. - Highlights: • We study the dynamical quantum phase transition between many-body localized phases. • We simulate the dynamics of a very long random spin chain with matrix product states. • We observe numerically super-logarithmic growth of entanglement entropy with time.

  19. Non perturbative analysis of an N=2 Landau-Ginsburg model

    International Nuclear Information System (INIS)

    Leaf Herrmann, W.A.

    1993-01-01

    We analyze the topological sector of an N=2 Landau-Ginsburg model using nonperturbative methods. In particular, we study the renormalization group flow between two superconformal minimal models, numerically compute the correlation functions along this trajectory, and compare the results to semi-classical calculations. We also study some aspects of arbitrary supersymmetric perturbations of the Landau-Ginsburg model. 20 refs, 4 figs

  20. Investigation of solutions of boundary-value singular perturbated problem for Schroedinger equation of 4th order

    International Nuclear Information System (INIS)

    Amirkhanov, I.V.; Zhidkov, E.P.; Konnova, S.V.

    2000-01-01

    For the case of spherical-symmetrical potential we have considered the convergence of the solution of singular-perturbated Schroedinger equation of the 4th order to the solution of the corresponding standard nonrelativistic Schroedinger equation by numerical and analytical methods. The questions of existence of the solutions are explored. Numerical results are given. (author)

  1. Numerical fluid solutions for nonlocal electron transport in hot plasmas: Equivalent diffusion versus nonlocal source

    International Nuclear Information System (INIS)

    Colombant, Denis; Manheimer, Wallace

    2010-01-01

    Flux limitation and preheat are important processes in electron transport occurring in laser produced plasmas. The proper calculation of both of these has been a subject receiving much attention over the entire lifetime of the laser fusion project. Where nonlocal transport (instead of simple single flux limit) has been modeled, it has always been with what we denote the equivalent diffusion solution, namely treating the transport as only a diffusion process. We introduce here a new approach called the nonlocal source solution and show it is numerically viable for laser produced plasmas. It turns out that the equivalent diffusion solution generally underestimates preheat. Furthermore, the advance of the temperature front, and especially the preheat, can be held up by artificial 'thermal barriers'. The nonlocal source method of solution, on the other hand more accurately describes preheat and can stably calculate the solution for the temperature even if the heat flux is up the gradient.

  2. Non-perturbative aspects of nonlinear sigma models

    Energy Technology Data Exchange (ETDEWEB)

    Flore, Raphael

    2012-12-07

    The aim of this thesis was the study and further development of non-perturbative methods of quantum field theory by means of their application to nonlinear sigma models. While a large part of the physical phenomena of quantum field theory can be successfully predicted by the perturbation theory, some aspects in the region of large coupling strengths are not definitively understood and require suited non-perturbative methods for its analysis. This thesis is concentrated on two approaches, the numerical treatment of field theories on discrete space-time lattices and the functional renormalization group (FRG) as description of the renormalization flux of effective actions. Considerations of the nonlinear O(N) models have shown that for the correct analysis of the critical properties in the framework of the FRG an approach must be chosen, which contained fourth-derivation orders. For this a covariant formalism was developed, which is based on a background-field expansion and the development of a heat kernel. Apart from a destabilizing coupling the results suggest a nontrivial fixed point and by this a non-perturbative renormalizability of these models. The resulting flow diagrams were finally still compared with the results of a numerical analysis of the renormalization flow by means of the Monte-Carlo renormalization group, and hereby qualitative agreement was found. Furthermore an alternative formulation of the FRG in phase-space coordinates was studied and their consistency tested on simple examples. Beyond this an alternative expansion of the effective action in orders of the canonical momenta was applied to the nonlinear O(N) models with the result of a stable non-trivial fixed point, the critical properties of which however show not the expected N-dependence. By means of the FRG finally still the renormalization of topological operators was studied by means of the winding number of the O(3){approx_equal}CP{sup 1} model. By the generalization of the topological

  3. Non-perturbative aspects of nonlinear sigma models

    International Nuclear Information System (INIS)

    Flore, Raphael

    2012-01-01

    The aim of this thesis was the study and further development of non-perturbative methods of quantum field theory by means of their application to nonlinear sigma models. While a large part of the physical phenomena of quantum field theory can be successfully predicted by the perturbation theory, some aspects in the region of large coupling strengths are not definitively understood and require suited non-perturbative methods for its analysis. This thesis is concentrated on two approaches, the numerical treatment of field theories on discrete space-time lattices and the functional renormalization group (FRG) as description of the renormalization flux of effective actions. Considerations of the nonlinear O(N) models have shown that for the correct analysis of the critical properties in the framework of the FRG an approach must be chosen, which contained fourth-derivation orders. For this a covariant formalism was developed, which is based on a background-field expansion and the development of a heat kernel. Apart from a destabilizing coupling the results suggest a nontrivial fixed point and by this a non-perturbative renormalizability of these models. The resulting flow diagrams were finally still compared with the results of a numerical analysis of the renormalization flow by means of the Monte-Carlo renormalization group, and hereby qualitative agreement was found. Furthermore an alternative formulation of the FRG in phase-space coordinates was studied and their consistency tested on simple examples. Beyond this an alternative expansion of the effective action in orders of the canonical momenta was applied to the nonlinear O(N) models with the result of a stable non-trivial fixed point, the critical properties of which however show not the expected N-dependence. By means of the FRG finally still the renormalization of topological operators was studied by means of the winding number of the O(3)≅CP 1 model. By the generalization of the topological operator and the

  4. A Comparison of Analytical and Numerical Methods for Modeling Dissolution and Other Reactions in Transport Limited Systems

    Science.gov (United States)

    Hochstetler, D. L.; Kitanidis, P. K.

    2009-12-01

    Modeling the transport of reactive species is a computationally demanding problem, especially in complex subsurface media, where it is crucial to improve understanding of geochemical processes and the fate of groundwater contaminants. In most of these systems, reactions are inherently fast and actual rates of transformations are limited by the slower physical transport mechanisms. There have been efforts to reformulate multi-component reactive transport problems into systems that are simpler and less demanding to solve. These reformulations include defining conservative species and decoupling of reactive transport equations so that fewer of them must be solved, leaving mostly conservative equations for transport [e.g., De Simoni et al., 2005; De Simoni et al., 2007; Kräutle and Knabner, 2007; Molins et al., 2004]. Complex and computationally cumbersome numerical codes used to solve such problems have also caused De Simoni et al. [2005] to develop more manageable analytical solutions. Furthermore, this work evaluates reaction rates and has reaffirmed that the mixing rate,▽TuD▽u, where u is a solute concentration and D is the dispersion tensor, as defined by Kitanidis [1994], is an important and sometimes dominant factor in determining reaction rates. Thus, mixing of solutions is often reaction-limiting. We will present results from analytical and computational modeling of multi-component reactive-transport problems. The results have applications to dissolution of solid boundaries (e.g., calcite), dissolution of non-aqueous phase liquids (NAPLs) in separate phases, and mixing of saltwater and freshwater (e.g. saltwater intrusion in coastal carbonate aquifers). We quantify reaction rates, compare numerical and analytical results, and analyze under what circumstances which approach is most effective for a given problem. References: DeSimoni, M., et al. (2005), A procedure for the solution of multicomponent reactive transport problems, Water Resources Research, 41

  5. Flow in a circular expansion pipe flow: effect of a vortex perturbation on localised turbulence

    Energy Technology Data Exchange (ETDEWEB)

    Selvam, Kamal; Peixinho, Jorge [Laboratoire Ondes Milieux Complexes, CNRS and Université du Havre, F-76600 Le Havre (France); Willis, Ashley P, E-mail: jorge.peixinho@univ-lehavre.fr [School of Mathematics and Statistics, University of Sheffield, Sheffield S3 7RH (United Kingdom)

    2016-12-15

    We report the results of three-dimensional direct numerical simulations for incompressible viscous fluid in a circular pipe flow with a sudden expansion. At the inlet, a parabolic velocity profile is applied together with a finite amplitude perturbation in the form of a vortex with its axis parallel to the axis of the pipe. At sufficiently high Reynolds numbers the recirculation region breaks into a turbulent patch that changes position axially, depending on the strength of the perturbation. This vortex perturbation is believed to produce a less abrupt transition than in previous studies, which applied a tilt perturbation, as the localised turbulence is observed via the formation of a wavy structure at a low order azimuthal mode, which resembles an optimally amplified perturbation. For large vortex amplitude, the localised turbulence remains at a constant axial position. It is further investigated using proper orthogonal decomposition, which indicates that the centre region close to the expansion is highly energetic. (paper)

  6. Numerical Study of the Ghost-Ghost-Gluon Vertex on the Lattice

    International Nuclear Information System (INIS)

    Mihara, A.; Cucchieri, A.; Mendes, T.

    2004-01-01

    It is well known that, in Landau gauge, the renormalization function of the ghost-ghost-gluon vertex Z-tilde1 (p2) is finite and constant, at least to all orders of perturbation theory. On the other hand, a direct non-perturbative verification of this result using numerical simulations of lattice QCD is still missing. Here we present a preliminary numerical study of the ghost-ghost-gluon vertex and of its corresponding renormalization function using Monte Carlo simulations in SU(2) lattice Landau gauge. Data were obtained in 4 dimensions for lattice couplings β = 2.2, 2.3, 2.4 and lattice sides N = 4, 8, 16

  7. Numerical study of the ghost-ghost-gluon vertex on the lattice

    International Nuclear Information System (INIS)

    Mihara, A.; Cucchieri, A.; Mendes, T.

    2004-01-01

    It is well known that, in Landau gauge, the renormalization function of the ghost-ghost-gluon vertex Z∼ 1 1(p 2 ) is finite and constant, at least to all orders of perturbation theory. On the other hand, a direct non-perturbative verification of this result using numerical simulations of lattice QCD is still missing. Here we present a preliminary numerical study of the ghost-ghost-gluon vertex and of its corresponding renormalization function using Monte Carlo simulations in SU(2) lattice Landau gauge. Data were obtained in 4 dimensions for lattice couplings β= 2.2, 2.3, 2.4 and lattice sides N = 4, 8, 16. (author)

  8. Numerical Experiments on Advective Transport in Large Three-Dimensional Discrete Fracture Networks

    Science.gov (United States)

    Makedonska, N.; Painter, S. L.; Karra, S.; Gable, C. W.

    2013-12-01

    Modeling of flow and solute transport in discrete fracture networks is an important approach for understanding the migration of contaminants in impermeable hard rocks such as granite, where fractures provide dominant flow and transport pathways. The discrete fracture network (DFN) model attempts to mimic discrete pathways for fluid flow through a fractured low-permeable rock mass, and may be combined with particle tracking simulations to address solute transport. However, experience has shown that it is challenging to obtain accurate transport results in three-dimensional DFNs because of the high computational burden and difficulty in constructing a high-quality unstructured computational mesh on simulated fractures. An integrated DFN meshing [1], flow, and particle tracking [2] simulation capability that enables accurate flow and particle tracking simulation on large DFNs has recently been developed. The new capability has been used in numerical experiments on advective transport in large DFNs with tens of thousands of fractures and millions of computational cells. The modeling procedure starts from the fracture network generation using a stochastic model derived from site data. A high-quality computational mesh is then generated [1]. Flow is then solved using the highly parallel PFLOTRAN [3] code. PFLOTRAN uses the finite volume approach, which is locally mass conserving and thus eliminates mass balance problems during particle tracking. The flow solver provides the scalar fluxes on each control volume face. From the obtained fluxes the Darcy velocity is reconstructed for each node in the network [4]. Velocities can then be continuously interpolated to any point in the domain of interest, thus enabling random walk particle tracking. In order to describe the flow field on fractures intersections, the control volume cells on intersections are split into four planar polygons, where each polygon corresponds to a piece of a fracture near the intersection line. Thus

  9. Perturbed Strong Stability Preserving Time-Stepping Methods For Hyperbolic PDEs

    KAUST Repository

    Hadjimichael, Yiannis

    2017-09-30

    A plethora of physical phenomena are modelled by hyperbolic partial differential equations, for which the exact solution is usually not known. Numerical methods are employed to approximate the solution to hyperbolic problems; however, in many cases it is difficult to satisfy certain physical properties while maintaining high order of accuracy. In this thesis, we develop high-order time-stepping methods that are capable of maintaining stability constraints of the solution, when coupled with suitable spatial discretizations. Such methods are called strong stability preserving (SSP) time integrators, and we mainly focus on perturbed methods that use both upwind- and downwind-biased spatial discretizations. Firstly, we introduce a new family of third-order implicit Runge–Kuttas methods with arbitrarily large SSP coefficient. We investigate the stability and accuracy of these methods and we show that they perform well on hyperbolic problems with large CFL numbers. Moreover, we extend the analysis of SSP linear multistep methods to semi-discretized problems for which different terms on the right-hand side of the initial value problem satisfy different forward Euler (or circle) conditions. Optimal perturbed and additive monotonicity-preserving linear multistep methods are studied in the context of such problems. Optimal perturbed methods attain augmented monotonicity-preserving step sizes when the different forward Euler conditions are taken into account. On the other hand, we show that optimal SSP additive methods achieve a monotonicity-preserving step-size restriction no better than that of the corresponding non-additive SSP linear multistep methods. Furthermore, we develop the first SSP linear multistep methods of order two and three with variable step size, and study their optimality. We describe an optimal step-size strategy and demonstrate the effectiveness of these methods on various one- and multi-dimensional problems. Finally, we establish necessary conditions

  10. Amplification of curvature perturbations in cyclic cosmology

    International Nuclear Information System (INIS)

    Zhang Jun; Liu Zhiguo; Piao Yunsong

    2010-01-01

    We analytically and numerically show that through the cycles with nonsingular bounce, the amplitude of curvature perturbation on a large scale will be amplified and the power spectrum will redden. In some sense, this amplification will eventually destroy the homogeneity of the background, which will lead to the ultimate end of cycles of the global universe. We argue that for the model with increasing cycles, it might be possible that a fissiparous multiverse will emerge after one or several cycles, in which the cycles will continue only at corresponding local regions.

  11. Quasi-B-mode generated by high-frequency gravitational waves and corresponding perturbative photon fluxes

    Energy Technology Data Exchange (ETDEWEB)

    Li, Fangyu, E-mail: cqufangyuli@hotmail.com [Institute of Gravitational Physics, Department of Physics, Chongqing University, Chongqing 400044 (China); Wen, Hao [Institute of Gravitational Physics, Department of Physics, Chongqing University, Chongqing 400044 (China); State Key Laboratory of Theoretical Physics, Institute of Theoretical Physics, Chinese Academy of Sciences, Beijing 100190 (China); Fang, Zhenyun [Institute of Gravitational Physics, Department of Physics, Chongqing University, Chongqing 400044 (China); Wei, Lianfu; Wang, Yiwen; Zhang, Miao [Quantum Optoelectronics Laboratory, Southwest Jiaotong University, Chengdu 610031 (China)

    2016-10-15

    Interaction of very low-frequency primordial (relic) gravitational waves (GWs) to cosmic microwave background (CMB) can generate B-mode polarization. Here, for the first time we point out that the electromagnetic (EM) response to high-frequency GWs (HFGWs) would produce quasi-B-mode distribution of the perturbative photon fluxes. We study the duality and high complementarity between such two B-modes, and it is shown that such two effects are from the same physical origin: the tensor perturbation of the GWs and not the density perturbation. Based on this quasi-B-mode in HFGWs and related numerical calculation, it is shown that the distinguishing and observing of HFGWs from the braneworld would be quite possible due to their large amplitude, higher frequency and very different physical behaviors between the perturbative photon fluxes and background photons, and the measurement of relic HFGWs may also be possible though face to enormous challenge.

  12. Acoustic wavefield evolution as a function of source location perturbation

    KAUST Repository

    Alkhalifah, Tariq Ali

    2010-12-01

    The wavefield is typically simulated for seismic exploration applications through solving the wave equation for a specific seismic source location. The direct relation between the form (or shape) of the wavefield and the source location can provide insights useful for velocity estimation and interpolation. As a result, I derive partial differential equations that relate changes in the wavefield shape to perturbations in the source location, especially along the Earth\\'s surface. These partial differential equations have the same structure as the wave equation with a source function that depends on the background (original source) wavefield. The similarity in form implies that we can use familiar numerical methods to solve the perturbation equations, including finite difference and downward continuation. In fact, we can use the same Green\\'s function to solve the wave equation and its source perturbations by simply incorporating source functions derived from the background field. The solutions of the perturbation equations represent the coefficients of a Taylor\\'s series type expansion of the wavefield as a function of source location. As a result, we can speed up the wavefield calculation as we approximate the wavefield shape for sources in the vicinity of the original source. The new formula introduces changes to the background wavefield only in the presence of lateral velocity variation or in general terms velocity variations in the perturbation direction. The approach is demonstrated on the smoothed Marmousi model.

  13. Solution to the Diffusion equation for multi groups in X Y geometry using Linear Perturbation theory

    International Nuclear Information System (INIS)

    Mugica R, C.A.

    2004-01-01

    Diverse methods exist to solve numerically the neutron diffusion equation for several energy groups in stationary state among those that highlight those of finite elements. In this work the numerical solution of this equation is presented using Raviart-Thomas nodal methods type finite element, the RT0 and RT1, in combination with iterative techniques that allow to obtain the approached solution in a quick form. Nevertheless the above mentioned, the precision of a method is intimately bound to the dimension of the approach space by cell, 5 for the case RT0 and 12 for the RT1, and/or to the mesh refinement, that makes the order of the problem of own value to solve to grow considerably. By this way if it wants to know an acceptable approach to the value of the effective multiplication factor of the system when this it has experimented a small perturbation it was appeal to the Linear perturbation theory with which is possible to determine it starting from the neutron flow and of the effective multiplication factor of the not perturbed case. Results are presented for a reference problem in which a perturbation is introduced in an assemble that simulates changes in the control bar. (Author)

  14. A Double Perturbation Method for Reducing Dynamical Degradation of the Digital Baker Map

    Science.gov (United States)

    Liu, Lingfeng; Lin, Jun; Miao, Suoxia; Liu, Bocheng

    2017-06-01

    The digital Baker map is widely used in different kinds of cryptosystems, especially for image encryption. However, any chaotic map which is realized on the finite precision device (e.g. computer) will suffer from dynamical degradation, which refers to short cycle lengths, low complexity and strong correlations. In this paper, a novel double perturbation method is proposed for reducing the dynamical degradation of the digital Baker map. Both state variables and system parameters are perturbed by the digital logistic map. Numerical experiments show that the perturbed Baker map can achieve good statistical and cryptographic properties. Furthermore, a new image encryption algorithm is provided as a simple application. With a rather simple algorithm, the encrypted image can achieve high security, which is competitive to the recently proposed image encryption algorithms.

  15. Perturbation analysis of octupoles in circular accelerators

    International Nuclear Information System (INIS)

    Moohyun Yoon

    1998-01-01

    The octupole effects in a circular accelerator are analyzed using a first-order canonical perturbation theory. It is shown that, to the first order, the nonlinear amplitude-dependent tune shifts due to an octupole are composed of two types: terms of second order and terms of fourth order in betatron-oscillation amplitudes. The fourth-order part of tune shifts is expressed in terms of distortion functions. Distortion functions are also expanded in harmonics to express the higher-order tune shifts in harmonically expanded form. Finally, the results are applied to an accelerator and compared with the results of numerical tracking of particles. Laskar's algorithm for numerical analysis of the fundamental frequency is used to determine tunes from the tracking data, in which the error becomes inversely proportional to the cube of the number of data points. (author)

  16. Gauge-invariant non-spherical metric perturbations of Schwarzschild black-hole spacetimes

    International Nuclear Information System (INIS)

    Nagar, Alessandro; Rezzolla, Luciano

    2005-01-01

    The theory of gauge-invariant non-spherical metric perturbations of Schwarzschild black-hole spacetimes is now well established. Yet, as different notations and conventions have been used throughout the years, the literature on the subject is often confusing and sometimes confused. The purpose of this review is to review and collect the relevant expressions related to the Regge-Wheeler and Zerilli equations for the odd and even-parity perturbations of a Schwarzschild spacetime. Special attention is paid to the form they assume in the presence of matter-sources and, for the two most popular conventions in the literature, to the asymptotic expressions and gravitational-wave amplitudes. Besides pointing out some inconsistencies in the literature, the expressions collected here could serve as a quick reference for the calculation of the perturbations of a Schwarzschild black-hole spacetime driven by generic sources and for those approaches in which gravitational waves are extracted from numerically generated spacetimes. (topical review)

  17. Exact-to-precision generalized perturbation theory for source-driven systems

    International Nuclear Information System (INIS)

    Wang Congjian; Abdel-Khalik, Hany S.

    2011-01-01

    Highlights: ► We present a new development in higher order generalized perturbation theory. ► The method addresses the explosion in the flux phase space, input parameters, and responses. ► The method hybridizes first-order GPT and proper orthogonal decomposition snapshots method. ► A simplified 1D and realistic 2D assembly models demonstrate applicability of the method. ► The accuracy of the method is compared to exact direct perturbations and first-order GPT. - Abstract: Presented in this manuscript are new developments to perturbation theory which are intended to extend its applicability to estimate, with quantifiable accuracy, the exact variations in all responses calculated by the model with respect to all possible perturbations in the model's input parameters. The new developments place high premium on reducing the associated computational overhead in order to enable the use of perturbation theory in routine reactor design calculations. By way of examples, these developments could be employed in core simulation to accurately estimate the few-group cross-sections variations resulting from perturbations in neutronics and thermal-hydraulics core conditions. These variations are currently being described using a look-up table approach, where thousands of assembly calculations are performed to capture few-group cross-sections variations for the downstream core calculations. Other applications include the efficient evaluation of surrogates for applications that require repeated model runs such as design optimization, inverse studies, uncertainty quantification, and online core monitoring. The theoretical background of these developments applied to source-driven systems and supporting numerical experiments are presented in this manuscript. Extension to eigenvalue problems will be presented in a future article.

  18. Application of He's homotopy perturbation method to boundary layer flow and convection heat transfer over a flat plate

    International Nuclear Information System (INIS)

    Esmaeilpour, M.; Ganji, D.D.

    2007-01-01

    In this Letter, the problem of forced convection over a horizontal flat plate is presented and the homotopy perturbation method (HPM) is employed to compute an approximation to the solution of the system of nonlinear differential equations governing on the problem. It has been attempted to show the capabilities and wide-range applications of the homotopy perturbation method in comparison with the previous ones in solving heat transfer problems. The obtained solutions, in comparison with the exact solutions admit a remarkable accuracy. A clear conclusion can be drawn from the numerical results that the HPM provides highly accurate numerical solutions for nonlinear differential equations

  19. Heat transfer enhancement through control of added perturbation velocity in flow field

    International Nuclear Information System (INIS)

    Wang, Jiansheng; Wu, Cui; Li, Kangning

    2013-01-01

    Highlights: ► Three strategies which restrain the flow drag in heat transfer are proposed. ► Added perturbation induces quasi-streamwise vortices around controlled zone. ► The flow and heat transfer features depend on induced quasi-streamwise vortices. ► Vertical strategy has the best synthesis performance of three control strategies. ► Synthesis performance with control strategy is superior to that without strategy. - Abstract: The characteristics of heat transfer and flow, through an added perturbation velocity, in a rectangle channel, are investigated by Large Eddy Simulation (LES). The downstream, vertical, and upstream control strategy, which can suppress the lift of low speed streaks in the process of improving the performance of heat transfer, are adopted in numerical investigation. Taking both heat transfer and flow properties into consideration, the synthesis performance of heat transfer and flow of three control strategies are evaluated. The numerical results show that the flow structure in boundary layer has been varied obviously for the effect of perturbation velocity and induced quasi-streamwise vortices emerging around the controlled zone. The results indicate that the vertical control strategy has the best synthesis performance of the three control strategies, which also has the least skin frication coefficient. The upstream and downstream strategies can improve the heat transfer performance, but the skin frication coefficient is higher than that with vertical control strategy

  20. ELM suppression in low edge collisionality H-mode discharges using n = 3 magnetic perturbations

    Energy Technology Data Exchange (ETDEWEB)

    Burrell, K H [General Atomics, PO Box 85608, San Diego, CA 92186-9784 (United States); Evans, T E [General Atomics, PO Box 85608, San Diego, CA 92186-9784 (United States); Doyle, E J [University of California, Los Angeles, California (United States); Fenstermacher, M E [Lawrence Livermore National Laboratory, Livermore, California (United States); Groebner, R J [General Atomics, PO Box 85608, San Diego, CA 92186-9784 (United States); Leonard, A W [General Atomics, PO Box 85608, San Diego, CA 92186-9784 (United States); Moyer, R A [University of California, San Diego, California (United States); Osborne, T H; Schaffer, M J; Snyder, P B [General Atomics, PO Box 85608, San Diego, CA 92186-9784 (United States); Thomas, P R [CEA Cadarache EURATOM Association, Cadarache (France); West, W P [General Atomics, PO Box 85608, San Diego, CA 92186-9784 (United States); Boedo, J A [University of California, San Diego, California (United States); Garofalo, A M [Columbia University, New York, New York (United States); Gohil, P; Jackson, G L; La Haye, R J [General Atomics, PO Box 85608, San Diego, CA 92186-9784 (United States); Lasnier, C J [Lawrence Livermore National Laboratory, Livermore, California (United States); Reimerdes, H [Columbia University, New York, New York (United States); Rhodes, T L [University of California, Los Angeles, California (United States); Scoville, J T [General Atomics, PO Box 85608, San Diego, CA 92186-9784 (United States); Solomon, W M [Princeton Plasma Physics Laboratory, Princeton, New Jersey (United States); Thomas, D M [General Atomics, PO Box 85608, San Diego, CA 92186-9784 (United States); Wang, G [University of California, Los Angeles, California (United States); Watkins, J G [Sandia National Laboratories, Albuquerque, New Mexico (United States); Zeng, L [University of California, Los Angeles, California (United States)

    2005-12-15

    Using resonant magnetic perturbations with toroidal mode number n = 3, we have produced H-mode discharges without edge localized modes (ELMs) which run with constant density and radiated power for periods up to about 2550 ms (17 energy confinement times). These ELM suppression results are achieved at pedestal collisionalities close to those desired for next step burning plasma experiments such as ITER and provide a means of eliminating the rapid erosion of divertor components in such machines which could be caused by giant ELMs. The ELM suppression is due to an enhancement in the edge particle transport which reduces pedestal current density and maximum edge pressure gradient below the threshold for peeling-ballooning modes. These n = 3 magnetic perturbations provide a means of active control of edge plasma transport.

  1. ELM suppression in low edge collisionality H-mode discharges using n = 3 magnetic perturbations

    International Nuclear Information System (INIS)

    Burrell, K H; Evans, T E; Doyle, E J; Fenstermacher, M E; Groebner, R J; Leonard, A W; Moyer, R A; Osborne, T H; Schaffer, M J; Snyder, P B; Thomas, P R; West, W P; Boedo, J A; Garofalo, A M; Gohil, P; Jackson, G L; La Haye, R J; Lasnier, C J; Reimerdes, H; Rhodes, T L; Scoville, J T; Solomon, W M; Thomas, D M; Wang, G; Watkins, J G; Zeng, L

    2005-01-01

    Using resonant magnetic perturbations with toroidal mode number n = 3, we have produced H-mode discharges without edge localized modes (ELMs) which run with constant density and radiated power for periods up to about 2550 ms (17 energy confinement times). These ELM suppression results are achieved at pedestal collisionalities close to those desired for next step burning plasma experiments such as ITER and provide a means of eliminating the rapid erosion of divertor components in such machines which could be caused by giant ELMs. The ELM suppression is due to an enhancement in the edge particle transport which reduces pedestal current density and maximum edge pressure gradient below the threshold for peeling-ballooning modes. These n = 3 magnetic perturbations provide a means of active control of edge plasma transport

  2. Numerical investigations of solute transport in bimodal porous media under dynamic boundary conditions

    Science.gov (United States)

    Cremer, Clemens; Neuweiler, Insa; Bechtold, Michel; Vanderborght, Jan

    2016-04-01

    Quantification of flow and solute transport in the shallow subsurface adjacent to the atmosphere is decisive to prevent groundwater pollution and conserve groundwater quality, to develop successful remediation strategies and to understand nutrient cycling. In nature, due to erratic precipitation-evaporation patterns, soil moisture content and related hydraulic conductivity in the vadose zone are not only variable in space but also in time. Flow directions and flow paths locally change between precipitation and evaporation periods. This makes the identification and description of solute transport processes in the vadose zone a complex problem. Recent studies (Lehmann and Or, 2009; Bechtold et al., 2011a) focused on the investigation of upward transport of solutes during evaporation in heterogeneous soil columns, where heterogeneity was introduced by a sharp vertical material interface between two types of sand. Lateral solute transport through the interface in both (lateral) directions was observed at different depths of the investigated soil columns. Following recent approaches, we conduct two-dimensional numerical simulations in a similar setup which is composed of two sands with a sharp vertical material interface. The investigation is broadened from the sole evaporation to combined precipitation-evaporation cycles in order to quantify transport processes resulting from the combined effects of heterogeneous soil structure and dynamic flow conditions. Simulations are performed with a coupled finite volume and random walk particle tracking algorithm (Ippisch et al., 2006; Bechtold et al., 2011b). By comparing scenarios with cyclic boundary conditions and stationary counterparts with the same net flow rate, we found that duration and intensity of precipitation and evaporation periods potentially have an influence on lateral redistribution of solutes and thus leaching rates. Whether or not dynamic boundary conditions lead to significant deviations in the transport

  3. The statistics of maxima in primordial density perturbations

    International Nuclear Information System (INIS)

    Peacock, J.A.; Heavens, A.F.

    1985-01-01

    An investigation has been made of the hypothesis that protogalaxies/protoclusters form at the sites of maxima in a primordial field of normally distributed density perturbations. Using a mixture of analytic and numerical techniques, the properties of the maxima, have been studied. The results provide a natural mechanism for biased galaxy formation in which galaxies do not necessarily follow the large-scale density. Methods for obtained the true autocorrelation function of the density field and implications for Microwave Background studies are discussed. (author)

  4. Global gravitational anomalies and transport

    Energy Technology Data Exchange (ETDEWEB)

    Chowdhury, Subham Dutta; David, Justin R. [Centre for High Energy Physics, Indian Institute of Science,C. V. Raman Avenue, Bangalore 560012 (India)

    2016-12-21

    We investigate the constraints imposed by global gravitational anomalies on parity odd induced transport coefficients in even dimensions for theories with chiral fermions, gravitinos and self dual tensors. The η-invariant for the large diffeomorphism corresponding to the T transformation on a torus constraints the coefficients in the thermal effective action up to mod 2. We show that the result obtained for the parity odd transport for gravitinos using global anomaly matching is consistent with the direct perturbative calculation. In d=6 we see that the second Pontryagin class in the anomaly polynomial does not contribute to the η-invariant which provides a topological explanation of this observation in the ‘replacement rule’. We then perform a direct perturbative calculation for the contribution of the self dual tensor in d=6 to the parity odd transport coefficient using the Feynman rules proposed by Gaumé and Witten. The result for the transport coefficient agrees with that obtained using matching of global anomalies.

  5. Perturbation of a Schwarzschild Black Hole Due to a Rotating Thin Disk

    Energy Technology Data Exchange (ETDEWEB)

    Čížek, P.; Semerák, O., E-mail: oldrich.semerak@mff.cuni.cz [Institute of Theoretical Physics, Faculty of Mathematics and Physics, Charles University, Prague (Czech Republic)

    2017-09-01

    Will, in 1974, treated the perturbation of a Schwarzschild black hole due to a slowly rotating, light, concentric thin ring by solving the perturbation equations in terms of a multipole expansion of the mass-and-rotation perturbation series. In the Schwarzschild background, his approach can be generalized to perturbation by a thin disk (which is more relevant astrophysically), but, due to rather bad convergence properties, the resulting expansions are not suitable for specific (numerical) computations. However, we show that Green’s functions, represented by Will’s result, can be expressed in closed form (without multipole expansion), which is more useful. In particular, they can be integrated out over the source (a thin disk in our case) to yield good converging series both for the gravitational potential and for the dragging angular velocity. The procedure is demonstrated, in the first perturbation order, on the simplest case of a constant-density disk, including the physical interpretation of the results in terms of a one-component perfect fluid or a two-component dust in a circular orbit about the central black hole. Free parameters are chosen in such a way that the resulting black hole has zero angular momentum but non-zero angular velocity, as it is just carried along by the dragging effect of the disk.

  6. The Numerical Tokamak Project (NTP) simulation of turbulent transport in the core plasma: A grand challenge in plasma physics

    International Nuclear Information System (INIS)

    1993-12-01

    The long-range goal of the Numerical Tokamak Project (NTP) is the reliable prediction of tokamak performance using physics-based numerical tools describing tokamak physics. The NTP is accomplishing the development of the most advanced particle and extended fluid model's on massively parallel processing (MPP) environments as part of a multi-institutional, multi-disciplinary numerical study of tokamak core fluctuations. The NTP is a continuing focus of the Office of Fusion Energy's theory and computation program. Near-term HPCC work concentrates on developing a predictive numerical description of the core plasma transport in tokamaks driven by low-frequency collective fluctuations. This work addresses one of the greatest intellectual challenges to our understanding of the physics of tokamak performance and needs the most advanced computational resources to progress. We are conducting detailed comparisons of kinetic and fluid numerical models of tokamak turbulence. These comparisons are stimulating the improvement of each and the development of hybrid models which embody aspects of both. The combination of emerging massively parallel processing hardware and algorithmic improvements will result in an estimated 10**2--10**6 performance increase. Development of information processing and visualization tools is accelerating our comparison of computational models to one another, to experimental data, and to analytical theory, providing a bootstrap effect in our understanding of the target physics. The measure of success is the degree to which the experimentally observed scaling of fluctuation-driven transport may be predicted numerically. The NTP is advancing the HPCC Initiative through its state-of-the-art computational work. We are pushing the capability of high performance computing through our efforts which are strongly leveraged by OFE support

  7. Perturbed effects at radiation physics

    International Nuclear Information System (INIS)

    Külahcı, Fatih; Şen, Zekâi

    2013-01-01

    Perturbation methodology is applied in order to assess the linear attenuation coefficient, mass attenuation coefficient and cross-section behavior with random components in the basic variables such as the radiation amounts frequently used in the radiation physics and chemistry. Additionally, layer attenuation coefficient (LAC) and perturbed LAC (PLAC) are proposed for different contact materials. Perturbation methodology provides opportunity to obtain results with random deviations from the average behavior of each variable that enters the whole mathematical expression. The basic photon intensity variation expression as the inverse exponential power law (as Beer–Lambert's law) is adopted for perturbation method exposition. Perturbed results are presented not only in terms of the mean but additionally the standard deviation and the correlation coefficients. Such perturbation expressions provide one to assess small random variability in basic variables. - Highlights: • Perturbation methodology is applied to Radiation Physics. • Layer attenuation coefficient (LAC) and perturbed LAC are proposed for contact materials. • Perturbed linear attenuation coefficient is proposed. • Perturbed mass attenuation coefficient (PMAC) is proposed. • Perturbed cross-section is proposed

  8. Contaminant transport in the sub-surface soil of an uncontrolled landfill site in China: site investigation and two-dimensional numerical analysis.

    Science.gov (United States)

    Xie, Haijian; Chen, Yunmin; Thomas, Hywel R; Sedighi, Majid; Masum, Shakil A; Ran, Qihua

    2016-02-01

    A field investigation of contaminant transport beneath and around an uncontrolled landfill site in Huainan in China is presented in this paper. The research aimed at studying the migration of some chemicals present in the landfill leachate into the surrounding clayey soils after 17 years of landfill operation. The concentrations of chloride and sodium ions in the pore water of soil samples collected at depths up to 15 m were obtained through an extensive site investigation. The contents of organic matter in the soil samples were also determined. A two-dimensional numerical study of the reactive transport of sodium and chloride ion in the soil strata beneath and outside the landfill is also presented. The numerical modelling approach adopted is based on finite element/finite difference techniques. The domain size of approximately 300 × 30 m has been analysed and major chemical transport parameters/mechanisms are established via a series of calibration exercises. Numerical simulations were then performed to predict the long-term behaviour of the landfill in relation to the chemicals studied. The lateral migration distance of the chloride ions was more than 40 m which indicates that the advection and mechanical dispersion are the dominant mechanism controlling the contaminant transport at this site. The results obtained from the analysis of chloride and sodium migration also indicated a non-uniform advective flow regime of ions with depth, which were localised in the first few metres of the soil beneath the disposal site. The results of long-term simulations of contaminant transport indicated that the concentrations of ions can be 10 to 30 times larger than that related to the allowable limit of concentration values. The results of this study may be of application and interest in the assessment of potential groundwater and soil contamination at this site with a late Pleistocene clayey soil. The obtained transport properties of the soils and the contaminant transport

  9. Rapid Charged Geosynchronous Debris Perturbation Modeling of Electrodynamic Disturbances

    Science.gov (United States)

    Hughes, Joseph; Schaub, Hanspeter

    2018-04-01

    Charged space objects experience small perturbative torques and forces from their interaction with Earth's magnetic field. These small perturbations can change the orbits of lightweight, uncontrolled debris objects dramatically even over short periods. This paper investigates the effects of the isolated Lorentz force, the effects of including or neglecting this and other electromagnetic perturbations in a full propagation, and then analyzes for which objects electromagnetic effects have the most impact. It is found that electromagnetic forces have a negligible impact on their own. However, if the center of charge is not collocated with the center of mass, electromagnetic torques are produced which do impact the attitude, and thus the position by affecting the direction and magnitude of the solar radiation pressure force. The objects for which electrostatic torques have the most influence are charged above the kilovolt level, have a difference between their center of mass and center of charge, have highly attitude-dependent cross-sectional area, and are not spinning stably about an axis of maximum inertia. Fully coupled numerical simulation illustrate the impact of electromagnetic disturbances through the solar radiation pressure coupling.

  10. Perturbation analysis of the TRIGA Mark II reactor Vienna

    Energy Technology Data Exchange (ETDEWEB)

    Khan, R. [Pakistan Institute of Engineering and Applied Sciences (PIEAS), Islamabad (Pakistan); Villa, M.; Stummer, T.; Boeck, H. [Vienna Univ. of Technology (Austria). Atominstitut; Saeedbadshah [International Islamic Univ., Islamabad (Pakistan)

    2013-04-15

    The safety design of a nuclear reactor needs to maintain the steady state operation at desired power level. The safe and reliable reactor operation demands the complete knowledge of the core multiplication and its changes during the reactor operation. Therefore it is frequently of interest to compute the changes in core multiplication caused by small disturbances in the field of reactor physics. These disturbances can be created either by geometry or composition changes of the core. Fortunately if these changes (or perturbations) are very small, one does not have to repeat the reactivity calculations. This article focuses the study of small perturbations created in the Central Irradiation Channel (CIC) of the TRIGA mark II core to investigate their reactivity influences on the core reactivity. For this purpose, 3 different kinds of perturbations are created by inserting 3 different samples in the CIC. The cylindrical void (air), heavy water (D2O) and Cadmium (Cd) samples are inserted into the CIC separately to determine their neutronics behavior along the length of the core. The Monte Carlo N-Particle radiation transport code (MCNP) is applied to simulate these perturbations in the CIC. The MCNP theoretical predictions are verified by the experiments performed on the current reactor core. The behavior of void in the whole core and its dependence on position and water fraction is also presented in this article. (orig.)

  11. Uncertainty Quantification in Numerical Aerodynamics

    KAUST Repository

    Litvinenko, Alexander

    2017-05-16

    We consider uncertainty quantification problem in aerodynamic simulations. We identify input uncertainties, classify them, suggest an appropriate statistical model and, finally, estimate propagation of these uncertainties into the solution (pressure, velocity and density fields as well as the lift and drag coefficients). The deterministic problem under consideration is a compressible transonic Reynolds-averaged Navier-Strokes flow around an airfoil with random/uncertain data. Input uncertainties include: uncertain angle of attack, the Mach number, random perturbations in the airfoil geometry, mesh, shock location, turbulence model and parameters of this turbulence model. This problem requires efficient numerical/statistical methods since it is computationally expensive, especially for the uncertainties caused by random geometry variations which involve a large number of variables. In numerical section we compares five methods, including quasi-Monte Carlo quadrature, polynomial chaos with coefficients determined by sparse quadrature and gradient-enhanced version of Kriging, radial basis functions and point collocation polynomial chaos, in their efficiency in estimating statistics of aerodynamic performance upon random perturbation to the airfoil geometry [D.Liu et al \\'17]. For modeling we used the TAU code, developed in DLR, Germany.

  12. Matrix-oriented implementation for the numerical solution of the partial differential equations governing flows and transport in porous media

    KAUST Repository

    Sun, Shuyu; Salama, Amgad; El-Amin, Mohamed

    2012-01-01

    In this paper we introduce a new technique for the numerical solution of the various partial differential equations governing flow and transport phenomena in porous media. This method is proposed to be used in high level programming languages like

  13. Thermal gluons beyond pure perturbation theory

    International Nuclear Information System (INIS)

    Reinbach, J.

    2000-01-01

    The perturbative treatment of non-abelian gauge theory at high temperature leads to a threshold in calculation because of chromomagnetic effects. Infinitely many terms of the same order of magnitude arise. The numerical series to be summed is contained in the part of the theory reduced on 3D, which was recently treated non-perturbative as 2+1D Yang-Mills theory at T=0 by Karabali, Kim and Nair. In the thesis in question the exact 3D results are combined with the thermal 4D diagrammatic. In particular the splitting of the space-part of the transverse self-energy in the static limit is treated. As expected, the 3D subsystem can separate as regularized 3D Yang-Mills theory from the 4D structure. In 1-loop order the regulators are received explicit. For 2-loop order it can be shown amongst other things, that the generic contribution with hard inner momenta vanishes. It is examined, how the magnetic mass could follow. Under pressure it is possible to separate the 3D part in 1- and 2-loop order and to receive regulators [de

  14. Comparison of two numerical modelling approaches to a field experiment of unsaturated radon transport in a covered uranium mill tailings soil (Lavaugrasse, France)

    Energy Technology Data Exchange (ETDEWEB)

    Saadi, Zakaria; Guillevic, Jerome [Institut de Radioprotection et de Surete Nucleaire (IRSN), PRP-DGE/SEDRAN/BRN, 31 avenue de la Division Leclerc, B.P. 17, 92262, Fontenay-aux-Roses, Cedex (France)

    2014-07-01

    Uncertainties on the mathematical modelling of radon transport in an unsaturated covered uranium mill tailings (UMT) soil at field scale can have a great impact on the estimation of the average measured radon flux to the atmosphere at the landfill cover, which must be less than the threshold value 0.74 Bq.m{sup -2}.s{sup -1}recommended by the federal standard (EPA 40 CFR 192). These uncertainties are usually attributed to the numerical errors from the numerical schemes dealing with soil layering and to inadequate representations of the modelling of physical processes at the soil/plant/atmosphere interface and of the soil hydraulic and transport properties, as well as their parameterization. In this work, we compare one-dimensional simulation results from two numerical models of two-phase (water-air) porous media flow and radon transport to the data of radon activity exhalation flux and depth-volumetric concentration measured during a field campaign from June to November of 1999 in a two-layered soil of 1.3 m thickness (i.e., cover material/UMT: 0.5/0.8 m) of an experimental pond located at the Lavaugrasse UMT-landfill site (France). The first numerical modelling approach is a coupled finite volume compositional (i.e., water, radon, air) transport model (TOUGH2/EOS7Rn code, Saadi et al., 2013), while the second one is a decoupled finite difference one-component (i.e., radon) transport model (TRACI code, Ferry et al., 2001). Transient simulations during six month of hourly rainfall and atmospheric pressure variations showed that calculations from the one-component transport model usually overestimate both measured radon exhalation flux and depth-concentration. However, considering the effective unsaturated pore air-component diffusivity to be different from that of the radon-component in the compositional transport model allowed to significantly enhancing the modelling of these radon experimental data. The time-averaged radon flux calculated by EOS7Rn (3.42 Bq

  15. Generalized perturbation theory based on the method of cyclic characteristics

    Energy Technology Data Exchange (ETDEWEB)

    Assawaroongruengchot, M.; Marleau, G. [Institut de Genie Nucleaire, Departement de Genie Physique, Ecole Polytechnique de Montreal, 2900 Boul. Edouard-Montpetit, Montreal, Que. H3T 1J4 (Canada)

    2006-07-01

    A GPT algorithm for estimation of eigenvalues and reaction-rate ratios is developed for the neutron transport problems in 2D fuel assemblies with isotropic scattering. In our study the GPT formulation is based on the integral transport equations. The mathematical relationship between the generalized flux importance and generalized source importance functions is applied to transform the generalized flux importance transport equations into the integro-differential forms. The resulting adjoint and generalized adjoint transport equations are then solved using the method of cyclic characteristics (MOCC). Because of the presence of negative adjoint sources, a biasing/decontamination scheme is applied to make the generalized adjoint functions positive in such a way that it can be used for the multigroup re-balance technique. To demonstrate the efficiency of the algorithms, perturbative calculations are performed on a 17 x 17 PWR lattice. (authors)

  16. Generalized perturbation theory based on the method of cyclic characteristics

    International Nuclear Information System (INIS)

    Assawaroongruengchot, M.; Marleau, G.

    2006-01-01

    A GPT algorithm for estimation of eigenvalues and reaction-rate ratios is developed for the neutron transport problems in 2D fuel assemblies with isotropic scattering. In our study the GPT formulation is based on the integral transport equations. The mathematical relationship between the generalized flux importance and generalized source importance functions is applied to transform the generalized flux importance transport equations into the integro-differential forms. The resulting adjoint and generalized adjoint transport equations are then solved using the method of cyclic characteristics (MOCC). Because of the presence of negative adjoint sources, a biasing/decontamination scheme is applied to make the generalized adjoint functions positive in such a way that it can be used for the multigroup re-balance technique. To demonstrate the efficiency of the algorithms, perturbative calculations are performed on a 17 x 17 PWR lattice. (authors)

  17. Quasi-B-mode generated by high-frequency gravitational waves and corresponding perturbative photon fluxes

    Directory of Open Access Journals (Sweden)

    F.Y. Fangyu Li

    2016-10-01

    Full Text Available Interaction of very low-frequency primordial (relic gravitational waves (GWs to cosmic microwave background (CMB can generate B-mode polarization. Here, for the first time we point out that the electromagnetic (EM response to high-frequency GWs (HFGWs would produce quasi-B-mode distribution of the perturbative photon fluxes. We study the duality and high complementarity between such two B-modes, and it is shown that such two effects are from the same physical origin: the tensor perturbation of the GWs and not the density perturbation. Based on this quasi-B-mode in HFGWs and related numerical calculation, it is shown that the distinguishing and observing of HFGWs from the braneworld would be quite possible due to their large amplitude, higher frequency and very different physical behaviors between the perturbative photon fluxes and background photons, and the measurement of relic HFGWs may also be possible though face to enormous challenge.

  18. Finite difference numerical method for the superlattice Boltzmann transport equation and case comparison of CPU(C) and GPU(CUDA) implementations

    Energy Technology Data Exchange (ETDEWEB)

    Priimak, Dmitri

    2014-12-01

    We present a finite difference numerical algorithm for solving two dimensional spatially homogeneous Boltzmann transport equation which describes electron transport in a semiconductor superlattice subject to crossed time dependent electric and constant magnetic fields. The algorithm is implemented both in C language targeted to CPU and in CUDA C language targeted to commodity NVidia GPU. We compare performances and merits of one implementation versus another and discuss various software optimisation techniques.

  19. Finite difference numerical method for the superlattice Boltzmann transport equation and case comparison of CPU(C) and GPU(CUDA) implementations

    International Nuclear Information System (INIS)

    Priimak, Dmitri

    2014-01-01

    We present a finite difference numerical algorithm for solving two dimensional spatially homogeneous Boltzmann transport equation which describes electron transport in a semiconductor superlattice subject to crossed time dependent electric and constant magnetic fields. The algorithm is implemented both in C language targeted to CPU and in CUDA C language targeted to commodity NVidia GPU. We compare performances and merits of one implementation versus another and discuss various software optimisation techniques

  20. Perturbative anyon gas

    International Nuclear Information System (INIS)

    Dasnieres de Veigy, A.; Ouvry, S.; Paris-6 Univ., 75

    1992-06-01

    The problem of the statistical mechanics of an anyon gas is addressed. A perturbative analysis in the anyonic coupling constant α is reviewed, and the thermodynamical potential is computed at first and second order. An adequate second quantized formalism (field theory at finite temperature) is proposed. At first order in perturbation theory, the results are strikingly simple: only the second virial coefficient close to bosonic statistics is corrected. At second order, however, the complexity of the anyon model appears. One can compute exactly the perturbative correction to each cluster coefficient. However, and contrary to first order, a closed expression for the equation of state seems out of reach. As an illustration, the perturbative expressions of a 3 , a 4 , a 5 and a 6 are given at second order. Finally, using the same formalism, the equation of state of an anyon gas in a constant magnetic field is analyzed at first order in perturbation theory. (K.A.) 16 refs.; 3 figs.; 7 tabs

  1. Perturbation theory

    International Nuclear Information System (INIS)

    Bartlett, R.; Kirtman, B.; Davidson, E.R.

    1978-01-01

    After noting some advantages of using perturbation theory some of the various types are related on a chart and described, including many-body nonlinear summations, quartic force-field fit for geometry, fourth-order correlation approximations, and a survey of some recent work. Alternative initial approximations in perturbation theory are also discussed. 25 references

  2. Uncertainty Quantification in Numerical Aerodynamics

    KAUST Repository

    Litvinenko, Alexander; Matthies, Hermann G.; Liu, Dishi; Schillings, Claudia; Schulz, Volker

    2017-01-01

    In numerical section we compares five methods, including quasi-Monte Carlo quadrature, polynomial chaos with coefficients determined by sparse quadrature and gradient-enhanced version of Kriging, radial basis functions and point collocation polynomial chaos, in their efficiency in estimating statistics of aerodynamic performance upon random perturbation to the airfoil geometry [D.Liu et al '17]. For modeling we used the TAU code, developed in DLR, Germany.

  3. A discrete homotopy perturbation method for non-linear Schrodinger equation

    Directory of Open Access Journals (Sweden)

    H. A. Wahab

    2015-12-01

    Full Text Available A general analysis is made by homotopy perturbation method while taking the advantages of the initial guess, appearance of the embedding parameter, different choices of the linear operator to the approximated solution to the non-linear Schrodinger equation. We are not dependent upon the Adomian polynomials and find the linear forms of the components without these calculations. The discretised forms of the nonlinear Schrodinger equation allow us whether to apply any numerical technique on the discritisation forms or proceed for perturbation solution of the problem. The discretised forms obtained by constructed homotopy provide the linear parts of the components of the solution series and hence a new discretised form is obtained. The general discretised form for the NLSE allows us to choose any initial guess and the solution in the closed form.

  4. Collisional dynamics of perturbed particle disks in the solar system

    Science.gov (United States)

    Roberts, W. W.; Stewart, G. R.

    1987-01-01

    Investigations of the collisional evolution of particulate disks subject to the gravitational perturbation of a more massive particle orbiting within the disk are underway. Both numerical N-body simulations using a novel collision algorithm and analytical kinetic theory are being employed to extend our understanding of perturbed disks in planetary rings and during the formation of the solar system. Particular problems proposed for investigation are: (1) The development and testing of general criteria for a small moonlet to clear a gap and produce observable morphological features in planetary rings; (2) The development of detailed models of collisional damping of the wavy edges observed on the Encke division of Saturn's A ring; and (3) The determination of the extent of runaway growth of the few largest planetesimals during the early stages of planetary accretion.

  5. Numerical investigations of Z-pinch plasma instabilities

    International Nuclear Information System (INIS)

    Duan Yaoyong; Guo Yonghui; Wang Wensheng; Qiu Aici

    2004-01-01

    A two-dimensional, radiation magneto-hydrodynamics model is applied to the simulation of Z-pinch plasma sausage instability. Different implosion mechanisms in the cases of the existence and the non-existence of instability are analyzed, and the effects of various initial density perturbation levels on the x-ray power and energy are investigated. Numerical results show that x-ray energy output is not susceptive to sausage instabilities in a certain extent but x-ray power versus time is evidently dependent on the instabilities. In addition, this paper also studies the effects of numerical treatment of extreme low density in Z-pinch simulations on numerical results

  6. Some robust numerical methods for flow and transport in porous media; Quelques methodes numeriques robustes pour l'ecoulement et le transport en milieu poreux

    Energy Technology Data Exchange (ETDEWEB)

    Sboui, A

    2007-01-15

    The aim of this thesis is to model and develop numerical tools adapted to study underground water flow and the propagation of pollutants in a porous medium. The main motivation of this work is a benchmark from GDR Momas and ANDRA to simulate the 3-D propagation of radionuclides around a deep disposal of nuclear waste. Firstly, we construct a new mixed finite elements method suitable for general hexahedral meshes. Convergence of the method is proved and shown in numerical experiments. Secondly, we present a method of time discretization for the advection equation which allows for the use of different time steps in different sub-domains in order to take into account of strong heterogeneities. Finally a numerical method for the calculation of the transport of contaminants is proposed. The techniques above were implemented in a 3-D code and simulation results are shown on the 3-D far field benchmark from GDR Momas and ANDRA. (author)

  7. Nonlinear optimal perturbations in a curved pipe

    Science.gov (United States)

    Rinaldi, Enrico; Canton, Jacopo; Marin, Oana; Schanen, Michel; Schlatter, Philipp

    2017-11-01

    We investigate the effect of curvature on transition to turbulence in pipes by comparing optimal perturbations of finite amplitude that maximise their energy growth in a toroidal geometry to the ones calculated in the absence of curvature. Our interest is motivated by the fact that even small curvatures, of the order of d =Rpipe /Rtorus art numerical algorithms, capable of tackling the optimisation problem on large computational domains, coupled to a high-order spectral-element code, which is used to perform direct numerical simulations (DNS) of the full Navier-Stokes and their adjoint equations. Results are compared to the corresponding states in straight pipes and differences in their structure and evolution are discussed. Furthermore, the newly calculated initial conditions are used to identify coherent flow structures that are compared to the ones observed in recent DNS of weakly turbulent and relaminarising flows in the same toroidal geometry.

  8. Approximate Solution of Schrödinger Equation with Pseudo-Gaussian Potential Viewed as a Perturbation

    Directory of Open Access Journals (Sweden)

    Iacob Theodor-Felix

    2015-12-01

    Full Text Available We consider the Schrödinger equation with pseudo-Gaussian potential and point out that it is basically made up by a term representing the harmonic oscillator potential and an additional term, which is actually a power series that converges rapidly. Based on this observation the system can be considered as a perturbation of harmonic oscillator. The perturbation method is used to approximate the energy levels of pseudo- Gaussian oscillator. The results are compared with those obtained in the analytic and numeric case.

  9. Formation of magnetic islands due to field perturbations in toroidal stellarator configurations

    International Nuclear Information System (INIS)

    Lee, D.K.; Harris, J.H.; Lee, G.S.

    1990-06-01

    An explicit formulation is developed to determine the width of a magnetic island separatrix generated by magnetic field perturbations in a general toroidal stellarator geometry. A conventional method is employed to recast the analysis in a magnetic flux coordinate system without using any simplifying approximations. The island width is seen to be proportional to the square root of the Fourier harmonic of B ρ /B ζ that is in resonance with the rational value of the rotational transform, where B ρ and B ζ are contravariant normal and toroidal components of the perturbed magnetic field, respectively. The procedure, which is based on a representation of three-dimensional flux surfaces by double Fourier series, allows rapid and fairly accurate calculation of the island widths in real vacuum field configurations, without the need to follow field lines through numerical integration of the field line equations. Numerical results of the island width obtained in the flux coordinate representation for the Advanced Toroidal Facility agree closely with those determined from Poincare puncture points obtained by following field lines. 22 refs., 5 tabs

  10. Three dimensional numerical modeling of flow and pollutant transport in a flooding area of 2008 US Midwest Flood

    Science.gov (United States)

    This paper presents the development and application of a three-dimensional numerical model for simulating the flow field and pollutant transport in a flood zone near the confluence of the Mississippi River and Iowa River in Oakville, Iowa. Due to a levee breaching along the Iowa River during the US ...

  11. Numerical analysis of quasiperiodic perturbations for the Alfven wave

    International Nuclear Information System (INIS)

    Yamakoshi, Y.; Muto, K.; Yoshida, Z.

    1994-01-01

    The Alfven wave may have a localized eigenfunction when it propagates on a chaotic magnetic field. The Arnold-Beltrami-Childress (ABC) flow is a paradigm of chaotic stream lines and is a simple exact solution to the three-dimensional force-free plasma equilibrium equations. The three-dimensional structure of the magnetic field is represented by sinusoidal quasiperiodic modulation. The short wavelength Alfven wave equation for the ABC-flow magnetic field has a quasiperiodic potential term, which induces interference among ''Bragg-reflected'' waves with irregular phases. Then the eigenfunction decays at long distance and a point spectrum occurs. Two different types of short wavelength modes have numerically analyzed to demonstrate the existence of localized Alfven wave eigenmodes

  12. Application of perturbation theory to lattice calculations based on method of cyclic characteristics

    Science.gov (United States)

    Assawaroongruengchot, Monchai

    Perturbation theory is a technique used for the estimation of changes in performance functionals, such as linear reaction rate ratio and eigenvalue affected by small variations in reactor core compositions. Here the algorithm of perturbation theory is developed for the multigroup integral neutron transport problems in 2D fuel assemblies with isotropic scattering. The integral transport equation is used in the perturbative formulation because it represents the interconnecting neutronic systems of the lattice assemblies via the tracking lines. When the integral neutron transport equation is used in the formulation, one needs to solve the resulting integral transport equations for the flux importance and generalized flux importance functions. The relationship between the generalized flux importance and generalized source importance functions is defined in order to transform the generalized flux importance transport equations into the integro-differential equations for the generalized adjoints. Next we develop the adjoint and generalized adjoint transport solution algorithms based on the method of cyclic characteristics (MOCC) in DRAGON code. In the MOCC method, the adjoint characteristics equations associated with a cyclic tracking line are formulated in such a way that a closed form for the adjoint angular function can be obtained. The MOCC method then requires only one cycle of scanning over the cyclic tracking lines in each spatial iteration. We also show that the source importance function by CP method is mathematically equivalent to the adjoint function by MOCC method. In order to speed up the MOCC solution algorithm, a group-reduction and group-splitting techniques based on the structure of the adjoint scattering matrix are implemented. A combined forward flux/adjoint function iteration scheme, based on the group-splitting technique and the common use of a large number of variables storing tracking-line data and exponential values, is proposed to reduce the

  13. Application of perturbation theory to lattice calculations based on method of cyclic characteristics

    Energy Technology Data Exchange (ETDEWEB)

    Assawaroongruengchot, M

    2007-07-01

    Perturbation theory is a technique used for the estimation of changes in performance functionals, such as linear reaction rate ratio and eigenvalue affected by small variations in reactor core compositions. Here the algorithm of perturbation theory is developed for the multigroup integral neutron transport problems in 2D fuel assemblies with isotropic scattering. The integral transport equation is used in the perturbative formulation because it represents the interconnecting neutronic systems of the lattice assemblies via the tracking lines. When the integral neutron transport equation is used in the formulation, one needs to solve the resulting integral transport equations for the flux importance and generalized flux importance functions. The relationship between the generalized flux importance and generalized source importance functions is defined in order to transform the generalized flux importance transport equations into the integro-differential equations for the generalized adjoints. Next we develop the adjoint and generalized adjoint transport solution algorithms based on the method of cyclic characteristics (MOCC) in DRAGON code. In the MOCC method, the adjoint characteristics equations associated with a cyclic tracking line are formulated in such a way that a closed form for the adjoint angular function can be obtained. The MOCC method then requires only one cycle of scanning over the cyclic tracking lines in each spatial iteration. We also show that the source importance function by CP method is mathematically equivalent to the adjoint function by MOCC method. In order to speed up the MOCC solution algorithm, a group-reduction and group-splitting techniques based on the structure of the adjoint scattering matrix are implemented. A combined forward flux/adjoint function iteration scheme, based on the group-splitting technique and the common use of a large number of variables storing tracking-line data and exponential values, is proposed to reduce the

  14. Application of perturbation theory to lattice calculations based on method of cyclic characteristics

    International Nuclear Information System (INIS)

    Assawaroongruengchot, M.

    2007-01-01

    Perturbation theory is a technique used for the estimation of changes in performance functionals, such as linear reaction rate ratio and eigenvalue affected by small variations in reactor core compositions. Here the algorithm of perturbation theory is developed for the multigroup integral neutron transport problems in 2D fuel assemblies with isotropic scattering. The integral transport equation is used in the perturbative formulation because it represents the interconnecting neutronic systems of the lattice assemblies via the tracking lines. When the integral neutron transport equation is used in the formulation, one needs to solve the resulting integral transport equations for the flux importance and generalized flux importance functions. The relationship between the generalized flux importance and generalized source importance functions is defined in order to transform the generalized flux importance transport equations into the integro-differential equations for the generalized adjoints. Next we develop the adjoint and generalized adjoint transport solution algorithms based on the method of cyclic characteristics (MOCC) in DRAGON code. In the MOCC method, the adjoint characteristics equations associated with a cyclic tracking line are formulated in such a way that a closed form for the adjoint angular function can be obtained. The MOCC method then requires only one cycle of scanning over the cyclic tracking lines in each spatial iteration. We also show that the source importance function by CP method is mathematically equivalent to the adjoint function by MOCC method. In order to speed up the MOCC solution algorithm, a group-reduction and group-splitting techniques based on the structure of the adjoint scattering matrix are implemented. A combined forward flux/adjoint function iteration scheme, based on the group-splitting technique and the common use of a large number of variables storing tracking-line data and exponential values, is proposed to reduce the

  15. Structural-change localization and monitoring through a perturbation-based inverse problem.

    Science.gov (United States)

    Roux, Philippe; Guéguen, Philippe; Baillet, Laurent; Hamze, Alaa

    2014-11-01

    Structural-change detection and characterization, or structural-health monitoring, is generally based on modal analysis, for detection, localization, and quantification of changes in structure. Classical methods combine both variations in frequencies and mode shapes, which require accurate and spatially distributed measurements. In this study, the detection and localization of a local perturbation are assessed by analysis of frequency changes (in the fundamental mode and overtones) that are combined with a perturbation-based linear inverse method and a deconvolution process. This perturbation method is applied first to a bending beam with the change considered as a local perturbation of the Young's modulus, using a one-dimensional finite-element model for modal analysis. Localization is successful, even for extended and multiple changes. In a second step, the method is numerically tested under ambient-noise vibration from the beam support with local changes that are shifted step by step along the beam. The frequency values are revealed using the random decrement technique that is applied to the time-evolving vibrations recorded by one sensor at the free extremity of the beam. Finally, the inversion method is experimentally demonstrated at the laboratory scale with data recorded at the free end of a Plexiglas beam attached to a metallic support.

  16. PerturbationAnalyzer: a tool for investigating the effects of concentration perturbation on protein interaction networks.

    Science.gov (United States)

    Li, Fei; Li, Peng; Xu, Wenjian; Peng, Yuxing; Bo, Xiaochen; Wang, Shengqi

    2010-01-15

    The propagation of perturbations in protein concentration through a protein interaction network (PIN) can shed light on network dynamics and function. In order to facilitate this type of study, PerturbationAnalyzer, which is an open source plugin for Cytoscape, has been developed. PerturbationAnalyzer can be used in manual mode for simulating user-defined perturbations, as well as in batch mode for evaluating network robustness and identifying significant proteins that cause large propagation effects in the PINs when their concentrations are perturbed. Results from PerturbationAnalyzer can be represented in an intuitive and customizable way and can also be exported for further exploration. PerturbationAnalyzer has great potential in mining the design principles of protein networks, and may be a useful tool for identifying drug targets. PerturbationAnalyzer can be accessed from the Cytoscape web site http://www.cytoscape.org/plugins/index.php or http://biotech.bmi.ac.cn/PerturbationAnalyzer. Supplementary data are available at Bioinformatics online.

  17. Numerical tilting compensation in microscopy based on wavefront sensing using transport of intensity equation method

    Science.gov (United States)

    Hu, Junbao; Meng, Xin; Wei, Qi; Kong, Yan; Jiang, Zhilong; Xue, Liang; Liu, Fei; Liu, Cheng; Wang, Shouyu

    2018-03-01

    Wide-field microscopy is commonly used for sample observations in biological research and medical diagnosis. However, the tilting error induced by the oblique location of the image recorder or the sample, as well as the inclination of the optical path often deteriorates the imaging quality. In order to eliminate the tilting in microscopy, a numerical tilting compensation technique based on wavefront sensing using transport of intensity equation method is proposed in this paper. Both the provided numerical simulations and practical experiments prove that the proposed technique not only accurately determines the tilting angle with simple setup and procedures, but also compensates the tilting error for imaging quality improvement even in the large tilting cases. Considering its simple systems and operations, as well as image quality improvement capability, it is believed the proposed method can be applied for tilting compensation in the optical microscopy.

  18. The reverse effects of random perturbation on discrete systems for single and multiple population models

    International Nuclear Information System (INIS)

    Kang, Li; Tang, Sanyi

    2016-01-01

    Highlights: • The discrete single species and multiple species models with random perturbation are proposed. • The complex dynamics and interesting bifurcation behavior have been investigated. • The reverse effects of random perturbation on discrete systems have been discussed and revealed. • The main results can be applied for pest control and resources management. - Abstract: The natural species are likely to present several interesting and complex phenomena under random perturbations, which have been confirmed by simple mathematical models. The important questions are: how the random perturbations influence the dynamics of the discrete population models with multiple steady states or multiple species interactions? and is there any different effects for single species and multiple species models with random perturbation? To address those interesting questions, we have proposed the discrete single species model with two stable equilibria and the host-parasitoid model with Holling type functional response functions to address how the random perturbation affects the dynamics. The main results indicate that the random perturbation does not change the number of blurred orbits of the single species model with two stable steady states compared with results for the classical Ricker model with same random perturbation, but it can strength the stability. However, extensive numerical investigations depict that the random perturbation does not influence the complexities of the host-parasitoid models compared with the results for the models without perturbation, while it does increase the period of periodic orbits doubly. All those confirm that the random perturbation has a reverse effect on the dynamics of the discrete single and multiple population models, which could be applied in reality including pest control and resources management.

  19. Spatial perturbation of a wing-tip vortex using pulsed span-wise jets

    Science.gov (United States)

    Heyes, A. L.; Smith, D. A. R.

    The separation distance required between transport aircraft to avoid wake vortices remains a limiting factor on airport capacity. The dissipation of the wake can be accelerated by perturbing co-operative instabilities between multiple pairs of vortices. This paper presents the results of a preliminary experimental investigation into the use of pulsed span-wise air jets in the wing tip to perturb a single tip vortex in the very near field. Velocity measurements were made using PIV and hot-wire anemometry. The results demonstrate that the vortex position can be modulated at frequencies up to 50 Hz and, as such, the method shows promise for forcing instability in multiple vortex wakes.

  20. Bounds and estimates for the linearly perturbed eigenvalue problem

    International Nuclear Information System (INIS)

    Raddatz, W.D.

    1983-01-01

    This thesis considers the problem of bounding and estimating the discrete portion of the spectrum of a linearly perturbed self-adjoint operator, M(x). It is supposed that one knows an incomplete set of data consisting in the first few coefficients of the Taylor series expansions of one or more of the eigenvalues of M(x) about x = 0. The foundations of the variational study of eigen-values are first presented. These are then used to construct the best possible upper bounds and estimates using various sets of given information. Lower bounds are obtained by estimating the error in the upper bounds. The extension of these bounds and estimates to the eigenvalues of the doubly-perturbed operator M(x,y) is discussed. The results presented have numerous practical application in the physical sciences, including problems in atomic physics and the theory of vibrations of acoustical and mechanical systems

  1. Numerical prediction of cavitating flow around a hydrofoil using pans and improved shear stress transport k-omega model

    Directory of Open Access Journals (Sweden)

    Zhang De-Sheng

    2015-01-01

    Full Text Available The prediction accuracies of partially-averaged Navier-Stokes model and improved shear stress transport k-ω turbulence model for simulating the unsteady cavitating flow around the hydrofoil were discussed in this paper. Numerical results show that the two turbulence models can effectively reproduce the cavitation evolution process. The numerical prediction for the cycle time of cavitation inception, development, detachment, and collapse agrees well with the experimental data. It is found that the vortex pair induced by the interaction between the re-entrant jet and mainstream is responsible for the instability of the cavitation shedding flow.

  2. Selection of doublet cellular patterns in directional solidification through spatially periodic perturbations

    International Nuclear Information System (INIS)

    Losert, W.; Stillman, D.A.; Cummins, H.Z.; Kopczynski, P.; Rappel, W.; Karma, A.

    1998-01-01

    Pattern formation at the solid-liquid interface of a growing crystal was studied in directional solidification using a perturbation technique. We analyzed both experimentally and numerically the stability range and dynamical selection of cellular arrays of 'doublets' with asymmetric tip shapes, separated by alternate deep and shallow grooves. Applying an initial periodic perturbation of arbitrary wavelength to the unstable planar interface allowed us to force the interface to evolve into doublet states that would not otherwise be dynamically accessible from a planar interface. We determined systematically the ranges of wavelength corresponding to stable singlets, stable doublets, and transient unstable patterns. Experimentally, this was accomplished by applying a brief UV light pulse of a desired spatial periodicity to the planar interface during the planar-cellular transient using the model alloy Succinonitrile-Coumarin 152. Numerical simulations of the nonlinear evolution of the interface were performed starting from a small sinusoidal perturbation of the steady-state planar interface. These simulations were carried out using a computationally efficient phase-field symmetric model of directional solidification with recently reformulated asymptotics and vanishing kinetics [A. Karma and W.-J. Rappel, Phys. Rev. E 53 R3017 (1996); Phys. Rev. Lett. 77, 4050 (1996); Phys. Rev. E 57, 4323 (1998)], which allowed us to simulate spatially extended arrays that can be meaningfully compared to experiments. Simulations and experiments show remarkable qualitative agreement in the dynamic evolution, steady-state structure, and instability mechanisms of doublet cellular arrays. copyright 1998 The American Physical Society

  3. Modeling of amorphous pocket formation in silicon by numerical solution of the heat transport equation

    International Nuclear Information System (INIS)

    Kovac, D.; Otto, G.; Hobler, G.

    2005-01-01

    In this paper we present a model of amorphous pocket formation that is based on binary collision simulations to generate the distribution of deposited energy, and on numerical solution of the heat transport equation to describe the quenching process. The heat transport equation is modified to consider the heat of melting when the melting temperature is crossed at any point in space. It is discretized with finite differences on grid points that coincide with the crystallographic lattice sites, which allows easy determination of molten atoms. Atoms are considered molten if the average of their energy and the energy of their neighbors meets the melting criterion. The results obtained with this model are in good overall agreement with published experimental data on P, As, Te and Tl implantations in Si and with data on the polyatomic effect at cryogenic temperature

  4. Numerical and analytical treatment on peristaltic flow of Williamson fluid in the occurrence of induced magnetic field

    Energy Technology Data Exchange (ETDEWEB)

    Akram, Safia, E-mail: safia_akram@yahoomail.com [Department of Basic Sciences, Military College of Signals, National University of Sciences and Technology (Pakistan); Nadeem, S. [Department of Mathematics, Quaid-i-Azam University 45320, Islamabad 44000 (Pakistan); Hanif, M. [Department of Basic Sciences, Military College of Signals, National University of Sciences and Technology (Pakistan)

    2013-11-15

    In this paper the effects of induced magnetic field on the peristaltic transport of a Williamson fluid model in an asymmetric channel has been investigated. The problem is simplified by using long wave length and low Reynolds number approximations. The perturbation and numerical solutions have been presented. The expressions for pressure rise, pressure gradient, stream function, magnetic force function, current density distribution have been computed. The results of pertinent parameters have been discussed graphically. The trapping phenomena for different wave forms have been also discussed. - highlights: • The main motivation of this work is that we want to see the behavior of peristaltic flow of Williamson fluid in the occurrence of induced magnetic field. In literature no attempt is taken to discuss the lateral Numerical and analytical treatment on peristaltic flow of Williamson fluid in the occurrence of induced magnetic field. • We do not want to fill the gap in literature after studying this.

  5. Numerical and analytical treatment on peristaltic flow of Williamson fluid in the occurrence of induced magnetic field

    International Nuclear Information System (INIS)

    Akram, Safia; Nadeem, S.; Hanif, M.

    2013-01-01

    In this paper the effects of induced magnetic field on the peristaltic transport of a Williamson fluid model in an asymmetric channel has been investigated. The problem is simplified by using long wave length and low Reynolds number approximations. The perturbation and numerical solutions have been presented. The expressions for pressure rise, pressure gradient, stream function, magnetic force function, current density distribution have been computed. The results of pertinent parameters have been discussed graphically. The trapping phenomena for different wave forms have been also discussed. - highlights: • The main motivation of this work is that we want to see the behavior of peristaltic flow of Williamson fluid in the occurrence of induced magnetic field. In literature no attempt is taken to discuss the lateral Numerical and analytical treatment on peristaltic flow of Williamson fluid in the occurrence of induced magnetic field. • We do not want to fill the gap in literature after studying this

  6. Stabilization of spiral wave and turbulence in the excitable media using parameter perturbation scheme

    International Nuclear Information System (INIS)

    Ma Jun; Wang Chunni; Li Yanlong; Pu Zhongsheng; Jin Wuyin

    2008-01-01

    This paper proposes a scheme of parameter perturbation to suppress the stable rotating spiral wave, meandering spiral wave and turbulence in the excitable media, which is described by the modified Fitzhugh–Nagumo (MFHN) model. The controllable parameter in the MFHN model is perturbed with a weak pulse and the pulse period is decided by the rotating period of the spiral wave approximatively. It is confirmed that the spiral wave and spiral turbulence can be suppressed greatly. Drift and instability of spiral wave can be observed in the numerical simulation tests before the whole media become homogeneous finally. (general)

  7. Numerical solution of fractured horizontal wells in shale gas reservoirs considering multiple transport mechanisms

    Science.gov (United States)

    Zhao, Yu-long; Tang, Xu-chuan; Zhang, Lie-hui; Tang, Hong-ming; Tao, Zheng-Wu

    2018-06-01

    The multiscale pore size and specific gas storage mechanism in organic-rich shale gas reservoirs make gas transport in such reservoirs complicated. Therefore, a model that fully incorporates all transport mechanisms and employs an accurate numerical method is urgently needed to simulate the gas production process. In this paper, a unified model of apparent permeability was first developed, which took into account multiple influential factors including slip flow, Knudsen diffusion (KD), surface diffusion, effects of the adsorbed layer, permeability stress sensitivity, and ad-/desorption phenomena. Subsequently, a comprehensive mathematical model, which included the model of apparent permeability, was derived to describe gas production behaviors. Thereafter, on the basis of unstructured perpendicular bisection grids and finite volume method, a fully implicit numerical simulator was developed using Matlab software. The validation and application of the new model were confirmed using a field case reported in the literature. Finally, the impacts of related influencing factors on gas production were analyzed. The results showed that KD resulted in a negligible impact on gas production in the proposed model. The smaller the pore size was, the more obvious the effects of the adsorbed layer on the well production rate would be. Permeability stress sensitivity had a slight effect on well cumulative production in shale gas reservoirs. Adsorbed gas made a major contribution to the later flow period of the well; the greater the adsorbed gas content, the greater the well production rate would be. This paper can improve the understanding of gas production in shale gas reservoirs for petroleum engineers.

  8. Numerical orbit generators of artificial earth satellites

    Science.gov (United States)

    Kugar, H. K.; Dasilva, W. C. C.

    1984-04-01

    A numerical orbit integrator containing updatings and improvements relative to the previous ones that are being utilized by the Departmento de Mecanica Espacial e Controle (DMC), of INPE, besides incorporating newer modellings resulting from the skill acquired along the time is presented. Flexibility and modularity were taken into account in order to allow future extensions and modifications. Characteristics of numerical accuracy, processing quickness, memory saving as well as utilization aspects were also considered. User's handbook, whole program listing and qualitative analysis of accuracy, processing time and orbit perturbation effects were included as well.

  9. Effects of the underlying topology on perturbation spreading in the Axelrod model for cultural dissemination

    Science.gov (United States)

    Kim, Yup; Cho, Minsoo; Yook, Soon-Hyung

    2011-10-01

    We study the effects of the underlying topologies on a single feature perturbation imposed to the Axelrod model of consensus formation. From the numerical simulations we show that there are successive updates which are similar to avalanches in many self-organized criticality systems when a perturbation is imposed. We find that the distribution of avalanche size satisfies the finite-size scaling (FSS) ansatz on two-dimensional lattices and random networks. However, on scale-free networks with the degree exponent γ≤3 we show that the avalanche size distribution does not satisfy the FSS ansatz. The results indicate that the disordered configurations on two-dimensional lattices or on random networks are still stable against the perturbation in the limit N (network size) →∞. However, on scale-free networks with γ≤3 the perturbation always drives the disordered phase into an ordered phase. The possible relationship between the properties of phase transition of the Axelrod model and the avalanche distribution is also discussed.

  10. A SCILAB Program for Computing General-Relativistic Models of Rotating Neutron Stars by Implementing Hartle's Perturbation Method

    Science.gov (United States)

    Papasotiriou, P. J.; Geroyannis, V. S.

    We implement Hartle's perturbation method to the computation of relativistic rigidly rotating neutron star models. The program has been written in SCILAB (© INRIA ENPC), a matrix-oriented high-level programming language. The numerical method is described in very detail and is applied to many models in slow or fast rotation. We show that, although the method is perturbative, it gives accurate results for all practical purposes and it should prove an efficient tool for computing rapidly rotating pulsars.

  11. Micromagnetic simulations with thermal noise: Physical and numerical aspects

    Energy Technology Data Exchange (ETDEWEB)

    Martinez, E. [Dept. de Ingenieria Electromecanica, Universidad de Burgos, Plaza Misael Banuelos, s/n, E-09001, Burgos (Spain)]. E-mail: emvecino@ubu.es; Lopez-Diaz, L. [Dept. de Fisica Aplicada, Universidad Salamanca, Plaza de la Merced s/n, Salamanca E-37008 (Spain); Torres, L. [Dept. de Fisica Aplicada, Universidad Salamanca, Plaza de la Merced s/n, Salamanca E-37008 (Spain); Garcia-Cervera, C.J. [Department of Mathematics, University of California, Santa Barbara, CA 93106 (United States)

    2007-09-15

    Langevin dynamics treats finite temperature effects in micromagnetics framework by adding a thermal fluctuation field to the local effective field. Several works have addressed that the numerical results depend on the cell size used to split the ferromagnetic samples on the nanoscale regime. In this short paper, we analyze a thermally perturbed micromagnetic problem by using an implicit unconditionally stable numerical scheme to integrate the Langevin equation at room temperature. The obtained micromagnetic results for several cell sizes inside the validity range of the micromagnetic formalism, indicate that the addressed cell size dependence could be associated to numerical limitations of the commonly used numerical schemes.

  12. Micromagnetic simulations with thermal noise: Physical and numerical aspects

    International Nuclear Information System (INIS)

    Martinez, E.; Lopez-Diaz, L.; Torres, L.; Garcia-Cervera, C.J.

    2007-01-01

    Langevin dynamics treats finite temperature effects in micromagnetics framework by adding a thermal fluctuation field to the local effective field. Several works have addressed that the numerical results depend on the cell size used to split the ferromagnetic samples on the nanoscale regime. In this short paper, we analyze a thermally perturbed micromagnetic problem by using an implicit unconditionally stable numerical scheme to integrate the Langevin equation at room temperature. The obtained micromagnetic results for several cell sizes inside the validity range of the micromagnetic formalism, indicate that the addressed cell size dependence could be associated to numerical limitations of the commonly used numerical schemes

  13. Internal wave energy flux from density perturbations in nonlinear stratifications

    Science.gov (United States)

    Lee, Frank M.; Allshouse, Michael R.; Swinney, Harry L.; Morrison, P. J.

    2017-11-01

    Tidal flow over the topography at the bottom of the ocean, whose density varies with depth, generates internal gravity waves that have a significant impact on the energy budget of the ocean. Thus, understanding the energy flux (J = p v) is important, but it is difficult to measure simultaneously the pressure and velocity perturbation fields, p and v . In a previous work, a Green's-function-based method was developed to calculate the instantaneous p, v , and thus J , given a density perturbation field for a constant buoyancy frequency N. Here we extend the previous analytic Green's function work to include nonuniform N profiles, namely the tanh-shaped and linear cases, because background density stratifications that occur in the ocean and some experiments are nonlinear. In addition, we present a finite-difference method for the general case where N has an arbitrary profile. Each method is validated against numerical simulations. The methods we present can be applied to measured density perturbation data by using our MATLAB graphical user interface EnergyFlux. PJM was supported by the U.S. Department of Energy Contract DE-FG05-80ET-53088. HLS and MRA were supported by ONR Grant No. N000141110701.

  14. Searching for Orbits with Minimum Fuel Consumption for Station-Keeping Maneuvers: An Application to Lunisolar Perturbations

    Directory of Open Access Journals (Sweden)

    Antonio Fernando Bertachini de Almeida Prado

    2013-01-01

    Full Text Available The present paper has the goal of developing a new criterion to search for orbits that minimize the fuel consumption for station-keeping maneuvers. This approach is based on the integral over the time of the perturbing forces. This integral measures the total variation of velocity caused by the perturbations in the spacecraft, which corresponds to the equivalent variation of velocity that an engine should deliver to the spacecraft to compensate the perturbations and to keep its orbit Keplerian all the time. This integral is a characteristic of the orbit and the set of perturbations considered and does not depend on the type of engine used. In this sense, this integral can be seen as a criterion to select the orbit of the spacecraft. When this value becomes larger, more consumption of fuel is required for the station keeping, and, in this sense, less interesting is the orbit. This concept can be applied to any perturbation. In the present research, as an example, the perturbation caused by a third body is considered. Then, numerical simulations considering the effects of the Sun and the Moon in a satellite around the Earth are shown to exemplify the method.

  15. Development and implementation of a set of numerical quadratures SQN and EQN type in the transport code AZTRAN

    International Nuclear Information System (INIS)

    Chepe P, M.; Xolocostli M, J. V.; Gomez T, A. M.; Del Valle G, E.

    2015-09-01

    The deterministic transport codes for analysis of nuclear reactors have been used for several years already, these codes have evolved in terms of the methodology used and the degree of accuracy, because at the present time has more computer power. In this paper, the transport code used considers the classical technique of multi-group for discretization energy, for space discretization uses the nodal methods, while for the angular discretization the discrete ordinates method is used; so that presents the development and implementation of a set of numerical quadratures of SQ N type symmetrical with the same weight for each angular direction and these are compared with the quadratures of EQ N type. The two sets of numerical quadratures were implemented in the program AZTRAN to a problem with isotropic medium in XYZ geometry, in steady state using the nodal method RTN-0 (Raviart-Thomas-Nedelec). The analyzed results correspond to the effective multiplication factor k eff and neutron angular flux with approximations from S 4 to S 16 . (Author)

  16. Radionuclide Transport in Fractured Rock: Numerical Assessment for High Level Waste Repository

    Directory of Open Access Journals (Sweden)

    Claudia Siqueira da Silveira

    2013-01-01

    Full Text Available Deep and stable geological formations with low permeability have been considered for high level waste definitive repository. A common problem is the modeling of radionuclide migration in a fractured medium. Initially, we considered a system consisting of a rock matrix with a single planar fracture in water saturated porous rock. Transport in the fracture is assumed to obey an advection-diffusion equation, while molecular diffusion is considered the dominant mechanism of transport in porous matrix. The partial differential equations describing the movement of radionuclides were discretized by finite difference methods, namely, fully explicit, fully implicit, and Crank-Nicolson schemes. The convective term was discretized by the following numerical schemes: backward differences, centered differences, and forward differences. The model was validated using an analytical solution found in the literature. Finally, we carried out a simulation with relevant spent fuel nuclide data with a system consisting of a horizontal fracture and a vertical fracture for assessing the performance of a hypothetical repository inserted into the host rock. We have analysed the bentonite expanded performance at the beginning of fracture, the quantified radionuclide released from a borehole, and an estimated effective dose to an adult, obtained from ingestion of well water during one year.

  17. Numerical computation of the transport matrix in toroidal plasma with a stochastic magnetic field

    Science.gov (United States)

    Zhu, Siqiang; Chen, Dunqiang; Dai, Zongliang; Wang, Shaojie

    2018-04-01

    A new numerical method, based on integrating along the full orbit of guiding centers, to compute the transport matrix is realized. The method is successfully applied to compute the phase-space diffusion tensor of passing electrons in a tokamak with a stochastic magnetic field. The new method also computes the Lagrangian correlation function, which can be used to evaluate the Lagrangian correlation time and the turbulence correlation length. For the case of the stochastic magnetic field, we find that the order of magnitude of the parallel correlation length can be estimated by qR0, as expected previously.

  18. Electron transport in the plasma edge with rotating resonant magnetic perturbations at the TEXTOR tokamak

    International Nuclear Information System (INIS)

    Stoschus, Henning

    2011-01-01

    Small three-dimensional (3D) magnetic perturbations can be used as a tool to control the edge plasma parameters in magnetically confined plasmas in high confinement mode (''H-mode'') to suppress edge instabilities inherent to this regime, the Edge Localized Modes (ELMs). In this work, the impact of rotating 3D resonant magnetic perturbation (RMP) fields on the edge plasma structure characterized by electron density and temperature fields is investigated. We study a low confinement (L-mode) edge plasma (r/a>0.9) with high resistivity (edge electron collisionality ν * e >4) at the TEXTOR tokamak. The plasma structure in the plasma edge is measured by a set of high resolution diagnostics: a fast CCD camera (Δt=20 μs) is set up in order to visualize the plasma structure in terms of electron density variations. A supersonic helium beam diagnostic is established as standard diagnostic at TEXTOR to measure electron density n e and temperature T e with high spatial (Δr=2 mm) and temporal resolution (Δt=20 μs). The measured plasma structure is compared to modeling results from the fluid plasma and kinetic neutral transport code EMC3-EIRENE. A sequence of five new observations is discussed: (1) Imaging of electron density variations in the plasma edge shows that a fast rotating RMP field imposes an edge plasma structure, which rotates with the external RMP rotation frequency of vertical stroke ν RMP vertical stroke =1 kHz. (2) Measurements of the electron density and temperature provide strong experimental evidence that in the far edge a rotating 3D scrape-off layer (SOL) exists with helical exhaust channels to the plasma wall components. (3) Radially inward, the plasma structure at the next rational flux surface is found to depend on the relative rotation between external RMP field and intrinsic plasma rotation. For low relative rotation the plasma structure is dominated by a particle and energy loss along open magnetic field lines to the wall components. For high

  19. Electron transport in the plasma edge with rotating resonant magnetic perturbations at the TEXTOR tokamak

    Energy Technology Data Exchange (ETDEWEB)

    Stoschus, Henning

    2011-10-13

    Small three-dimensional (3D) magnetic perturbations can be used as a tool to control the edge plasma parameters in magnetically confined plasmas in high confinement mode (''H-mode'') to suppress edge instabilities inherent to this regime, the Edge Localized Modes (ELMs). In this work, the impact of rotating 3D resonant magnetic perturbation (RMP) fields on the edge plasma structure characterized by electron density and temperature fields is investigated. We study a low confinement (L-mode) edge plasma (r/a>0.9) with high resistivity (edge electron collisionality {nu}{sup *}{sub e}>4) at the TEXTOR tokamak. The plasma structure in the plasma edge is measured by a set of high resolution diagnostics: a fast CCD camera ({delta}t=20 {mu}s) is set up in order to visualize the plasma structure in terms of electron density variations. A supersonic helium beam diagnostic is established as standard diagnostic at TEXTOR to measure electron density n{sub e} and temperature T{sub e} with high spatial ({delta}r=2 mm) and temporal resolution ({delta}t=20 {mu}s). The measured plasma structure is compared to modeling results from the fluid plasma and kinetic neutral transport code EMC3-EIRENE. A sequence of five new observations is discussed: (1) Imaging of electron density variations in the plasma edge shows that a fast rotating RMP field imposes an edge plasma structure, which rotates with the external RMP rotation frequency of vertical stroke {nu}{sub RMP} vertical stroke =1 kHz. (2) Measurements of the electron density and temperature provide strong experimental evidence that in the far edge a rotating 3D scrape-off layer (SOL) exists with helical exhaust channels to the plasma wall components. (3) Radially inward, the plasma structure at the next rational flux surface is found to depend on the relative rotation between external RMP field and intrinsic plasma rotation. For low relative rotation the plasma structure is dominated by a particle and energy loss

  20. Some robust numerical methods for flow and transport in porous media; Quelques methodes numeriques robustes pour l'ecoulement et le transport en milieu poreux

    Energy Technology Data Exchange (ETDEWEB)

    Sboui, A

    2007-01-15

    The aim of this thesis is to model and develop numerical tools adapted to study underground water flow and the propagation of pollutants in a porous medium. The main motivation of this work is a benchmark from GDR Momas and ANDRA to simulate the 3-D propagation of radionuclides around a deep disposal of nuclear waste. Firstly, we construct a new mixed finite elements method suitable for general hexahedral meshes. Convergence of the method is proved and shown in numerical experiments. Secondly, we present a method of time discretization for the advection equation which allows for the use of different time steps in different sub-domains in order to take into account of strong heterogeneities. Finally a numerical method for the calculation of the transport of contaminants is proposed. The techniques above were implemented in a 3-D code and simulation results are shown on the 3-D far field benchmark from GDR Momas and ANDRA. (author)

  1. Analytic-continuation approach to the resummation of divergent series in Rayleigh-Schrödinger perturbation theory

    Science.gov (United States)

    Mihálka, Zsuzsanna É.; Surján, Péter R.

    2017-12-01

    The method of analytic continuation is applied to estimate eigenvalues of linear operators from finite order results of perturbation theory even in cases when the latter is divergent. Given a finite number of terms E(k ),k =1 ,2 ,⋯M resulting from a Rayleigh-Schrödinger perturbation calculation, scaling these numbers by μk (μ being the perturbation parameter) we form the sum E (μ ) =∑kμkE(k ) for small μ values for which the finite series is convergent to a certain numerical accuracy. Extrapolating the function E (μ ) to μ =1 yields an estimation of the exact solution of the problem. For divergent series, this procedure may serve as resummation tool provided the perturbation problem has a nonzero radius of convergence. As illustrations, we treat the anharmonic (quartic) oscillator and an example from the many-electron correlation problem.

  2. The numerical parallel computing of photon transport

    International Nuclear Information System (INIS)

    Huang Qingnan; Liang Xiaoguang; Zhang Lifa

    1998-12-01

    The parallel computing of photon transport is investigated, the parallel algorithm and the parallelization of programs on parallel computers both with shared memory and with distributed memory are discussed. By analyzing the inherent law of the mathematics and physics model of photon transport according to the structure feature of parallel computers, using the strategy of 'to divide and conquer', adjusting the algorithm structure of the program, dissolving the data relationship, finding parallel liable ingredients and creating large grain parallel subtasks, the sequential computing of photon transport into is efficiently transformed into parallel and vector computing. The program was run on various HP parallel computers such as the HY-1 (PVP), the Challenge (SMP) and the YH-3 (MPP) and very good parallel speedup has been gotten

  3. Investigation of ELM [edge localized mode] Dynamics with the Resonant Magnetic Perturbation Effects

    International Nuclear Information System (INIS)

    Pankin, Alexei Y.; Kritz, Arnold H.

    2011-01-01

    Topics covered are: anomalous transport and E f- B flow shear effects in the H-mode pedestal; RMP (resonant magnetic perturbation) effects in NSTX discharges; development of a scaling of H-mode pedestal in tokamak plasmas with type I ELMs (edge localized modes); and divertor heat load studies

  4. Investigation of ELM [edge localized mode] Dynamics with the Resonant Magnetic Perturbation Effects

    Energy Technology Data Exchange (ETDEWEB)

    Pankin, Alexei Y.; Kritz, Arnold H.

    2011-07-19

    Topics covered are: anomalous transport and E x B flow shear effects in the H-mode pedestal; RMP (resonant magnetic perturbation) effects in NSTX discharges; development of a scaling of H-mode pedestal in tokamak plasmas with type I ELMs (edge localized modes); and divertor heat load studies.

  5. Lattice dynamics calculations based on density-functional perturbation theory in real space

    Science.gov (United States)

    Shang, Honghui; Carbogno, Christian; Rinke, Patrick; Scheffler, Matthias

    2017-06-01

    A real-space formalism for density-functional perturbation theory (DFPT) is derived and applied for the computation of harmonic vibrational properties in molecules and solids. The practical implementation using numeric atom-centered orbitals as basis functions is demonstrated exemplarily for the all-electron Fritz Haber Institute ab initio molecular simulations (FHI-aims) package. The convergence of the calculations with respect to numerical parameters is carefully investigated and a systematic comparison with finite-difference approaches is performed both for finite (molecules) and extended (periodic) systems. Finally, the scaling tests and scalability tests on massively parallel computer systems demonstrate the computational efficiency.

  6. Effects of Nonlinear Inhomogeneity on the Cosmic Expansion with Numerical Relativity.

    Science.gov (United States)

    Bentivegna, Eloisa; Bruni, Marco

    2016-06-24

    We construct a three-dimensional, fully relativistic numerical model of a universe filled with an inhomogeneous pressureless fluid, starting from initial data that represent a perturbation of the Einstein-de Sitter model. We then measure the departure of the average expansion rate with respect to this homogeneous and isotropic reference model, comparing local quantities to the predictions of linear perturbation theory. We find that collapsing perturbations reach the turnaround point much earlier than expected from the reference spherical top-hat collapse model and that the local deviation of the expansion rate from the homogeneous one can be as high as 28% at an underdensity, for an initial density contrast of 10^{-2}. We then study, for the first time, the exact behavior of the backreaction term Q_{D}. We find that, for small values of the initial perturbations, this term exhibits a 1/a scaling, and that it is negative with a linearly growing absolute value for larger perturbation amplitudes, thereby contributing to an overall deceleration of the expansion. Its magnitude, on the other hand, remains very small even for relatively large perturbations.

  7. Spatio-temporal effects in a perturbed Sine-Gordan system: A long Josephson junction

    International Nuclear Information System (INIS)

    Nana, L.; Crepin Kofane, T.

    2003-12-01

    A collective coordinate approach is applied to study chaotic responses induced by an applied driven signal on the long Josephson junction influenced by a constant dc-driven field. We derive a nonlinear equation for a collective variable of the breather and the Melnikov method is then used to demonstrate the existence of irregular behavior in breather-fluxon-antifluxon pair transitions. Additionally, numerical simulations show that the theoretical predictions are well reproduced. Results obtained using these perturbative analysis are in good agreement with numerical simulations of the dynamics of the junction. (author)

  8. Modeling of Low Frequency MHD Induced Beam Ion Transport In NSTX

    International Nuclear Information System (INIS)

    Gorelenkov, N.N.; Medley, S.S.

    2004-01-01

    Beam ion transport in the presence of low frequency MHD activity in National Spherical Tokamak Experiment (NSTX) plasma is modeled numerically and analyzed theoretically in order to understand basic underlying physical mechanisms responsible for the observed fast ion redistribution and losses. Numerical modeling of the beam ions flux into the NPA in NSTX shows that after the onset of low frequency MHD activity high energy part of beam ion distribution, E b > 40keV, is redistributed radially due to stochastic diffusion. Such diffusion is caused by high order harmonics of the transit frequency resonance overlap in the phase space. Large drift orbit radial width induces such high order resonances. Characteristic confinement time is deduced from the measured NPA energy spectrum and is typically ∼ 4msec. Considered MHD activity may induce losses on the order of 10% at the internal magnetic field perturbation (delta)B/B = Ο (10 -3 ), which is comparable to the prompt orbit losses

  9. Numerical-analytic implementation of the higher-order canonical Van Vleck perturbation theory for the interpretation of medium-sized molecule vibrational spectra.

    Science.gov (United States)

    Krasnoshchekov, Sergey V; Isayeva, Elena V; Stepanov, Nikolay F

    2012-04-12

    Anharmonic vibrational states of semirigid polyatomic molecules are often studied using the second-order vibrational perturbation theory (VPT2). For efficient higher-order analysis, an approach based on the canonical Van Vleck perturbation theory (CVPT), the Watson Hamiltonian and operators of creation and annihilation of vibrational quanta is employed. This method allows analysis of the convergence of perturbation theory and solves a number of theoretical problems of VPT2, e.g., yields anharmonic constants y(ijk), z(ijkl), and allows the reliable evaluation of vibrational IR and Raman anharmonic intensities in the presence of resonances. Darling-Dennison and higher-order resonance coupling coefficients can be reliably evaluated as well. The method is illustrated on classic molecules: water and formaldehyde. A number of theoretical conclusions results, including the necessity of using sextic force field in the fourth order (CVPT4) and the nearly vanishing CVPT4 contributions for bending and wagging modes. The coefficients of perturbative Dunham-type Hamiltonians in high-orders of CVPT are found to conform to the rules of equality at different orders as earlier proven analytically for diatomic molecules. The method can serve as a good substitution of the more traditional VPT2.

  10. Linear perturbation of spherically symmetric flows: a first-order upwind scheme for the gas dynamics equations in Lagrangian coordinates

    International Nuclear Information System (INIS)

    Clarisse, J.M.

    2007-01-01

    A numerical scheme for computing linear Lagrangian perturbations of spherically symmetric flows of gas dynamics is proposed. This explicit first-order scheme uses the Roe method in Lagrangian coordinates, for computing the radial spherically symmetric mean flow, and its linearized version, for treating the three-dimensional linear perturbations. Fulfillment of the geometric conservation law discrete formulations for both the mean flow and its perturbation is ensured. This scheme capabilities are illustrated by the computation of free-surface mode evolutions at the boundaries of a spherical hollow shell undergoing an homogeneous cumulative compression, showing excellent agreement with reference results. (author)

  11. Loschmidt echo for local perturbations: non-monotonic cross-over from the Fermi-golden-rule to the escape-rate regime

    International Nuclear Information System (INIS)

    Goussev, Arseni; Waltner, Daniel; Richter, Klaus; Jalabert, Rodolfo A

    2008-01-01

    We address the sensitivity of quantum mechanical time evolution by considering the time decay of the Loschmidt echo (LE) (or fidelity) for local perturbations of the Hamiltonian. Within a semiclassical approach, we derive analytical expressions for the LE decay for chaotic systems for the whole range from weak to strong local perturbations and identify different decay regimes which complement those known for the case of global perturbations. For weak perturbations, a Fermi-golden-rule (FGR)-type behavior is recovered. For strong perturbations, the escape-rate regime is reached, where the LE decays exponentially with a rate independent of the perturbation strength. The transition between the FGR regime and the escape-rate regime is non-monotonic, i.e. the rate of the exponential time-decay of the LE oscillates as a function of the perturbation strength. We further perform extensive quantum mechanical calculations of the LE based on numerical wave packet evolution, which strongly support our semiclassical theory. Finally, we discuss in some detail possible experimental realizations for observing the predicted behavior of the LE

  12. Quark mass corrections to the perturbative thrust and its effect on the ...

    Indian Academy of Sciences (India)

    atic approach for handling power corrections using perturbation theory. ... The numerator of the above is given up to З(αs) and to З(ξ) by (σ0 = (4πα2/s)e2 i is the .... MARK II. AMY. ALEPH. DELPHI. OPAL. Massless formula. Massive formula ... We can also estimate the theoretical uncertainties on these quantities by vary-.

  13. SedFoam-2.0: a 3-D two-phase flow numerical model for sediment transport

    Directory of Open Access Journals (Sweden)

    J. Chauchat

    2017-11-01

    Full Text Available In this paper, a three-dimensional two-phase flow solver, SedFoam-2.0, is presented for sediment transport applications. The solver is extended from twoPhaseEulerFoam available in the 2.1.0 release of the open-source CFD (computational fluid dynamics toolbox OpenFOAM. In this approach the sediment phase is modeled as a continuum, and constitutive laws have to be prescribed for the sediment stresses. In the proposed solver, two different intergranular stress models are implemented: the kinetic theory of granular flows and the dense granular flow rheology μ(I. For the fluid stress, laminar or turbulent flow regimes can be simulated and three different turbulence models are available for sediment transport: a simple mixing length model (one-dimensional configuration only, a k − ε, and a k − ω model. The numerical implementation is demonstrated on four test cases: sedimentation of suspended particles, laminar bed load, sheet flow, and scour at an apron. These test cases illustrate the capabilities of SedFoam-2.0 to deal with complex turbulent sediment transport problems with different combinations of intergranular stress and turbulence models.

  14. SedFoam-2.0: a 3-D two-phase flow numerical model for sediment transport

    Science.gov (United States)

    Chauchat, Julien; Cheng, Zhen; Nagel, Tim; Bonamy, Cyrille; Hsu, Tian-Jian

    2017-11-01

    In this paper, a three-dimensional two-phase flow solver, SedFoam-2.0, is presented for sediment transport applications. The solver is extended from twoPhaseEulerFoam available in the 2.1.0 release of the open-source CFD (computational fluid dynamics) toolbox OpenFOAM. In this approach the sediment phase is modeled as a continuum, and constitutive laws have to be prescribed for the sediment stresses. In the proposed solver, two different intergranular stress models are implemented: the kinetic theory of granular flows and the dense granular flow rheology μ(I). For the fluid stress, laminar or turbulent flow regimes can be simulated and three different turbulence models are available for sediment transport: a simple mixing length model (one-dimensional configuration only), a k - ɛ, and a k - ω model. The numerical implementation is demonstrated on four test cases: sedimentation of suspended particles, laminar bed load, sheet flow, and scour at an apron. These test cases illustrate the capabilities of SedFoam-2.0 to deal with complex turbulent sediment transport problems with different combinations of intergranular stress and turbulence models.

  15. Non-standard perturbative methods for the effective potential in λφ4 QFT

    International Nuclear Information System (INIS)

    Okopinska, A.

    1986-07-01

    The effective potential in scalar QFT is calculated in the non-standard perturbative methods and compared with the conventional loop expansion. In the space time dimensions 0 and 1 the results are compared with the ''exact'' effective potential obtained numerically. In 4 dimensions we show that λφ 4 theory is non-interacting. (author)

  16. Numerical Calculation of Transport Based on the Drift Kinetic Equation for plasmas in General Toroidal Magnetic Geometry

    International Nuclear Information System (INIS)

    Reynolds, J. M.; Lopez-Bruna, D.

    2009-01-01

    This report is the first of a series dedicated to the numerical calculation of the evolution of fusion plasmas in general toroidal geometry, including TJ-II plasmas. A kinetic treatment has been chosen: the evolution equation of the distribution function of one or several plasma species is solved in guiding center coordinates. The distribution function is written as a Maxwellian one modulated by polynomial series in the kinetic coordinates with no other approximations than those of the guiding center itself and the computation capabilities. The code allows also for the inclusion of the three-dimensional electrostatic potential in a self-consistent manner, but the initial objective has been set to solving only the neoclassical transport. A high order conservative method (Spectral Difference Method) has been chosen in order to discretized the equation for its numerical solution. In this first report, in addition to justifying the work, the evolution equation and its approximations are described, as well as the baseline of the numerical procedures. (Author) 28 refs

  17. Tangent Orbital Rendezvous Using Linear Relative Motion with J2 Perturbations

    Directory of Open Access Journals (Sweden)

    Gang Zhang

    2013-01-01

    Full Text Available The tangent-impulse coplanar orbit rendezvous problem is studied based on the linear relative motion for J2-perturbed elliptic orbits. There are three cases: (1 only the first impulse is tangent; (2 only the second impulse is tangent; (3 both impulses are tangent. For a given initial impulse point, the first two problems can be transformed into finding all roots of a single variable function about the transfer time, which can be done by the secant method. The bitangent rendezvous problem requires the same solution for the first two problems. By considering the initial coasting time, the bitangent rendezvous solution is obtained with a difference function. A numerical example for two coplanar elliptic orbits with J2 perturbations is given to verify the efficiency of these proposed techniques.

  18. Stationary axially symmetric perturbations of a rotating black hole. [Space-time perturbation, Newman-Penrose formalism

    Energy Technology Data Exchange (ETDEWEB)

    Demianski, M [California Inst. of Tech., Pasadena (USA)

    1976-07-01

    A stationary axially symmetric perturbation of a rotating black hole due to a distribution of test matter is investigated. The Newman-Penrose spin coefficient formalism is used to derive a general set of equations describing the perturbed space-time. In a linear approximation it is shown that the mass and angular momentum of a rotating black hole is not affected by the perturbation. The metric perturbations near the horizon are given. It is concluded that given a perturbing test fluid distribution, one can always find a corresponding metric perturbation such that the mass and angular momentum of the black hole are not changed. It was also noticed that when a tends to M, those perturbed spin coefficients and components of the Weyl tensor which determine the intrinsic properties of the incoming null cone near the horizon grow indefinitely.

  19. 2D numerical comparison between S{sub n} and M{sub 1} radiation transport methods

    Energy Technology Data Exchange (ETDEWEB)

    Gonzalez, Matthias [Instituto de Fusion Nuclear, Universidad Politecnica de Madrid, calle Jose Gutierrez Abascal 2, 28006 Madrid (Spain)], E-mail: matthias@din.upm.es; Garcia-Fernandez, Carlos [Instituto de Fusion Nuclear, Universidad Politecnica de Madrid, calle Jose Gutierrez Abascal 2, 28006 Madrid (Spain)], E-mail: carlos@din.upm.es; Velarde, Pedro [Instituto de Fusion Nuclear, Universidad Politecnica de Madrid, calle Jose Gutierrez Abascal 2, 28006 Madrid (Spain)], E-mail: velarde@din.upm.es

    2009-07-15

    In this article we study the accuracy of the M{sub 1} method to solve some relevant radiation transport problems in 2D. We compare two radiation models (S{sub n} and M{sub 1}) with analytical and numerical tests to highlight the strengths and limitations of each method. These methods give comparable results except when sharp geometry effects are present. We have used these methods in a test that mimics, without fluid motion or electron heat conduction, the cone-target interaction relevant to inertial confinement fusion physics. In this case, we show that S{sub n} and M{sub 1} models agree with a quite good accuracy but shows differences in the temperature profiles and heating times inside the target. These results point out that M{sub 1} is a possible alternative candidate for 3D simulations, where full energy transport methods are extremely computer time consuming.

  20. Development of computation model on the GoldSim platform for the radionuclide transport in the geosphere with the time-dependent parameters

    International Nuclear Information System (INIS)

    Koo, Shigeru; Inagaki, Manabu

    2010-06-01

    In the high-level radioactive waste (HLW) disposal system, numerical evaluation for radionuclide transport with the time-dependent parameters is necessary to evaluate various scenarios. In H12 report, numerical calculation code MESHNOTE and TIGER were used for the evaluation of some natural phenomena scenarios that had to handle the time-dependent parameters. In the future, the necessity of handling the time-dependent parameters will be expected to increase, and more efficient calculation and improvement of quality control of input/output parameters will be required. Therefore, for the purpose of corresponding this requirement, a radionuclide transport model has been developed on the GoldSim platform. The GoldSim is a general simulation software, that was used for the computation modeling of Yucca Mountain Project. The conceptual model, the mathematical model and the verification of the GoldSim model are described in this report. In the future, application resources on this report will be able to upgrade for perturbation scenarios analysis model and other conceptual models. (author)

  1. A Numerical Study of Hydrodynamics and Sediment Transport in Fourleague Bay, Louisiana

    Science.gov (United States)

    Hu, K.; Chen, Q. J.; Xu, K.; Bentley, S. J.; WANG, J.

    2017-12-01

    Fourleague Bay is a shallow and vertically well-mixed estuary in south-central Louisiana. This estuary is highly impacted by wind (e.g., cold fronts and tropical storms), river discharge from the Atchafalaya River and tides from the Gulf of Mexico, and is being used as an analog site to study impacts of sediment-diversion restoration strategies in the Mississippi River Delta. In this study, a coupled flow-wave Delft3D model was setup and applied to study hydrodynamics and sediment transport in this area. The model grid size is 1071x631 with a 50-m resolution in the bay. Vegetation is considered by rigid cylinders in both flow and wave modules. The offshore water level boundary conditions were provided by a Gulf-scale Delft3D model. Model parameters, especially for cohesive sediment transport such as settling velocity, erosion rate and critical bottom shear stress, were calibrated using the field observation data during three seasons from May 2015 to March 2016. The modeled water levels, currents, significant wave heights and suspended sediment concentrations agreed fairly well with measurements, which suggests a reasonable model performance. Seasonal variations were analyzed based on different scenarios. A series of numerical experiments were set up to quantify the contributions of different factors, such as river discharge, tides and waves to sediment transport in this area. This model will be further applied to be part of a landscape ecosystem model to test landscape and population change over time with manipulations to sediment delivery. This study was funded by the National Science Foundation (SEES-1427389 and CCF-1539567).

  2. Numerical studies of transport processes in Tokamak plasma

    International Nuclear Information System (INIS)

    Spineanu, F.; Vlad, M.

    1984-09-01

    The paper contains the summary of a set of studies of the transport processes in tokamak plasma, performed with a one-dimensional computer code. The various transport models (which are implemented by the expressions of the transport coefficients) are presented in connection with the regimes of the dynamical development of the discharge. Results of studies concerning the skin effect and the large scale MHD instabilities are also included

  3. Turbulence, transport, and zonal flows in the Madison symmetric torus reversed-field pinch

    Science.gov (United States)

    Williams, Z. R.; Pueschel, M. J.; Terry, P. W.; Hauff, T.

    2017-12-01

    The robustness and the effect of zonal flows in trapped electron mode (TEM) turbulence and Ion Temperature Gradient (ITG) turbulence in the reversed-field pinch (RFP) are investigated from numerical solutions of the gyrokinetic equations with and without magnetic external perturbations introduced to model tearing modes. For simulations without external magnetic field perturbations, zonal flows produce a much larger reduction of transport for the density-gradient-driven TEM turbulence than they do for the ITG turbulence. Zonal flows are studied in detail to understand the nature of their strong excitation in the RFP and to gain insight into the key differences between the TEM- and ITG-driven regimes. The zonal flow residuals are significantly larger in the RFP than in tokamak geometry due to the low safety factor. Collisionality is seen to play a significant role in the TEM zonal flow regulation through the different responses of the linear growth rate and the size of the Dimits shift to collisionality, while affecting the ITG only minimally. A secondary instability analysis reveals that the TEM turbulence drives zonal flows at a rate that is twice that of the ITG turbulence. In addition to interfering with zonal flows, the magnetic perturbations are found to obviate an energy scaling relation for fast particles.

  4. A fast direct solver for boundary value problems on locally perturbed geometries

    Science.gov (United States)

    Zhang, Yabin; Gillman, Adrianna

    2018-03-01

    Many applications including optimal design and adaptive discretization techniques involve solving several boundary value problems on geometries that are local perturbations of an original geometry. This manuscript presents a fast direct solver for boundary value problems that are recast as boundary integral equations. The idea is to write the discretized boundary integral equation on a new geometry as a low rank update to the discretized problem on the original geometry. Using the Sherman-Morrison formula, the inverse can be expressed in terms of the inverse of the original system applied to the low rank factors and the right hand side. Numerical results illustrate for problems where perturbation is localized the fast direct solver is three times faster than building a new solver from scratch.

  5. A Newton-Based Extremum Seeking MPPT Method for Photovoltaic Systems with Stochastic Perturbations

    Directory of Open Access Journals (Sweden)

    Heng Li

    2014-01-01

    Full Text Available Microcontroller based maximum power point tracking (MPPT has been the most popular MPPT approach in photovoltaic systems due to its high flexibility and efficiency in different photovoltaic systems. It is well known that PV systems typically operate under a range of uncertain environmental parameters and disturbances, which implies that MPPT controllers generally suffer from some unknown stochastic perturbations. To address this issue, a novel Newton-based stochastic extremum seeking MPPT method is proposed. Treating stochastic perturbations as excitation signals, the proposed MPPT controller has a good tolerance of stochastic perturbations in nature. Different from conventional gradient-based extremum seeking MPPT algorithm, the convergence rate of the proposed controller can be totally user-assignable rather than determined by unknown power map. The stability and convergence of the proposed controller are rigorously proved. We further discuss the effects of partial shading and PV module ageing on the proposed controller. Numerical simulations and experiments are conducted to show the effectiveness of the proposed MPPT algorithm.

  6. Numerical Verification Of Equilibrium Chemistry

    International Nuclear Information System (INIS)

    Piro, Markus; Lewis, Brent; Thompson, William T.; Simunovic, Srdjan; Besmann, Theodore M.

    2010-01-01

    A numerical tool is in an advanced state of development to compute the equilibrium compositions of phases and their proportions in multi-component systems of importance to the nuclear industry. The resulting software is being conceived for direct integration into large multi-physics fuel performance codes, particularly for providing boundary conditions in heat and mass transport modules. However, any numerical errors produced in equilibrium chemistry computations will be propagated in subsequent heat and mass transport calculations, thus falsely predicting nuclear fuel behaviour. The necessity for a reliable method to numerically verify chemical equilibrium computations is emphasized by the requirement to handle the very large number of elements necessary to capture the entire fission product inventory. A simple, reliable and comprehensive numerical verification method is presented which can be invoked by any equilibrium chemistry solver for quality assurance purposes.

  7. A stochastic perturbation theory for non-autonomous systems

    Energy Technology Data Exchange (ETDEWEB)

    Moon, W., E-mail: wm275@damtp.cam.ac.uk [Yale University, New Haven, Connecticut 06520-8109 (United States); Wettlaufer, J. S., E-mail: wettlaufer@maths.ox.ac.uk [Yale University, New Haven, Connecticut 06520-8109 (United States); Mathematical Institute, University of Oxford, Oxford OX2 6GG (United Kingdom)

    2013-12-15

    We develop a perturbation theory for a class of first order nonlinear non-autonomous stochastic ordinary differential equations that arise in climate physics. The perturbative procedure produces moments in terms of integral delay equations, whose order by order decay is characterized in a Floquet-like sense. Both additive and multiplicative sources of noise are discussed and the question of how the nature of the noise influences the results is addressed theoretically and numerically. By invoking the Martingale property, we rationalize the transformation of the underlying Stratonovich form of the model to an Ito form, independent of whether the noise is additive or multiplicative. The generality of the analysis is demonstrated by developing it both for a Brownian particle moving in a periodically forced quartic potential, which acts as a simple model of stochastic resonance, as well as for our more complex climate physics model. The validity of the approach is shown by comparison with numerical solutions. The particular climate dynamics problem upon which we focus involves a low-order model for the evolution of Arctic sea ice under the influence of increasing greenhouse gas forcing ΔF{sub 0}. The deterministic model, developed by Eisenman and Wettlaufer [“Nonlinear threshold behavior during the loss of Arctic sea ice,” Proc. Natl. Acad. Sci. U.S.A. 106(1), 28–32 (2009)] exhibits several transitions as ΔF{sub 0} increases and the stochastic analysis is used to understand the manner in which noise influences these transitions and the stability of the system.

  8. Linear perturbation of spherically symmetric flows: a first-order upwind scheme for the gas dynamics equations in Lagrangian coordinates; Perturbation lineaire d'ecoulements a symetrie spherique: schema decentre d'ordre 1 pour les equations de la dynamique des gaz en variables de Lagrange

    Energy Technology Data Exchange (ETDEWEB)

    Clarisse, J.M

    2007-07-01

    A numerical scheme for computing linear Lagrangian perturbations of spherically symmetric flows of gas dynamics is proposed. This explicit first-order scheme uses the Roe method in Lagrangian coordinates, for computing the radial spherically symmetric mean flow, and its linearized version, for treating the three-dimensional linear perturbations. Fulfillment of the geometric conservation law discrete formulations for both the mean flow and its perturbation is ensured. This scheme capabilities are illustrated by the computation of free-surface mode evolutions at the boundaries of a spherical hollow shell undergoing an homogeneous cumulative compression, showing excellent agreement with reference results. (author)

  9. A numerical analysis of antithetic variates in Monte Carlo radiation transport with geometrical surface splitting

    International Nuclear Information System (INIS)

    Sarkar, P.K.; Prasad, M.A.

    1989-01-01

    A numerical study for effective implementation of the antithetic variates technique with geometric splitting/Russian roulette in Monte Carlo radiation transport calculations is presented. The study is based on the theory of Monte Carlo errors where a set of coupled integral equations are solved for the first and second moments of the score and for the expected number of flights per particle history. Numerical results are obtained for particle transmission through an infinite homogeneous slab shield composed of an isotropically scattering medium. Two types of antithetic transformations are considered. The results indicate that the antithetic transformations always lead to reduction in variance and increase in efficiency provided optimal antithetic parameters are chosen. A substantial gain in efficiency is obtained by incorporating antithetic transformations in rule of thumb splitting. The advantage gained for thick slabs (∼20 mfp) with low scattering probability (0.1-0.5) is attractively large . (author). 27 refs., 9 tabs

  10. Theory of deep inelastic neutron scattering: Hard-core perturbation theory

    International Nuclear Information System (INIS)

    Silver, R.N.

    1988-01-01

    Details are presented of a new many-body theory for deep inelastic neutron scattering (DINS) experiments to measure momentum distributions in quantum fluids and solids. The high-momentum and energy-transfer scattering law in helium is shown to be a convolution of the impulse approximation with a final-state broadening function which depends on the scattering phase shifts and the radial distribution function. The predicted broadening satisfies approximate Y scaling, is neither Lorentzian nor Gaussian, and obeys the f, ω 2 , and ω 3 sum rules. The derivation uses a combination of Liouville perturbation theory, projection superoperators, and semiclassical methods which I term ''hard-core perturbation theory.'' A review is presented of the predictions of prior theories for DINS experiments in relation to the present work. A subsequent paper will present massive numerical predictions and a discussion of DINS experiments on superfluid 4 He

  11. Conceptual and numerical models of groundwater flow and solute transport in fracture zones: Application to the Aspo Island (Sweden)

    International Nuclear Information System (INIS)

    Molinero, J.; Samper, J.

    2003-01-01

    Several countries around the world are considering the final disposal of high-level radioactive waste in deep repositories located in fractured granite formations. Evaluating the long term safety of such repositories requires sound conceptual and numerical models which must consider simultaneously groundwater flow, solute transport and chemical and radiological processes. These models are being developed from data and knowledge gained from in situ experiments carried out at deep underground laboratories such as that of Aspo, Sweden, constructed in fractured granite. The Redox Zone Experiment is one of such experiments performed at Aspo in order to evaluate the effects of the construction of the access tunnel on the hydrogeological and hydrochemical conditions of a fracture zone intersected by the tunnel. Previous authors interpreted hydrochemical and isotopic data of this experiment using a mass-balance approach based on a qualitative description of groundwater flow conditions. Such an interpretation, however, is subject to uncertainties related to an over-simplified conceptualization of groundwater flow. Here we present numerical models of groundwater flow and solute transport for this fracture zone. The first model is based on previously published conceptual model. It presents noticeable un consistencies and fails to match simultaneously observed draw downs and chloride breakthrough curves. To overcome its limitations, a revised flow and transport model is presented which relies directly on available hydrodynamic and transport parameters, is based on the identification of appropriate flow and transport boundary conditions and uses, when needed, solute data extrapolated from nearby fracture zones. A significant quantitative improvement is achieved with the revised model because its results match simultaneously drawdown and chloride data. Other improvements are qualitative and include: ensuring consistency of hydrodynamic and hydrochemical data and avoiding

  12. Perturbation studies on KAHTER

    Energy Technology Data Exchange (ETDEWEB)

    Rueckert, M.; Jonas, H.; Neef, R. D.

    1974-10-15

    The paper describes experimental and analytical results by both transport theory and diffusion theory calculations of perturbation tests in the KAHTER pebble bed critical experiment. The fission-weighted adjoint flux is measured from in-core detector responses by introducing a Cf-source into the core. Adjoint-weighted reactivities are calculated and compared to reactivity measurements for the introduction of a fuel and graphite pebble onto the top of the critical pile, the central rod worth, and the effect of replacing B4C with varying amounts of HfC in the central rod. In addition, analytical studies were made of the sensitivity of criticality to the fuel to graphite pebble ratio as measured in tests and of the effect of the upper void cavity as simulated in tests by placing cadmium layer across the top of the pebble pile to force a zero flux boundary condition.

  13. Numerical simulations of self-pinched transport of intense ion beams in low-pressure gases

    International Nuclear Information System (INIS)

    Rose, D.V.; Ottinger, P.F.; Welch, D.R.; Oliver, B.V.; Olson, C.L.

    1999-01-01

    The self-pinched transport of intense ion beams in low-pressure background gases is studied using numerical simulations and theoretical analysis. The simulations are carried out in a parameter regime that is similar to proton beam experiments being fielded on the Gamble II pulsed power generator [J. D. Shipman, Jr., IEEE Trans. Nucl. Sci. NS-18, 243 (1971)] at the Naval Research Laboratory. Simulation parameter variations provide information on scaling with background gas species, gas pressure, beam current, beam energy, injection angles, and boundaries. The simulation results compare well with simple analytic scaling arguments for the gas pressure at which the effective net current should peak and with estimates for the required confinement current. The analysis indicates that the self-pinched transport of intense proton beams produced on Gamble II (1.5 MeV, 100 kA, 3 cm radius) is expected to occur at gas pressures between 30 and 80 mTorr of He or between 3 and 10 mTorr of Ar. The significance of these results to ion-driven inertial confinement fusion is discussed. copyright 1999 American Institute of Physics

  14. Numerical simulation of advective-dispersive multisolute transport with sorption, ion exchange and equilibrium chemistry

    Science.gov (United States)

    Lewis, F.M.; Voss, C.I.; Rubin, Jacob

    1986-01-01

    A model was developed that can simulate the effect of certain chemical and sorption reactions simultaneously among solutes involved in advective-dispersive transport through porous media. The model is based on a methodology that utilizes physical-chemical relationships in the development of the basic solute mass-balance equations; however, the form of these equations allows their solution to be obtained by methods that do not depend on the chemical processes. The chemical environment is governed by the condition of local chemical equilibrium, and may be defined either by the linear sorption of a single species and two soluble complexation reactions which also involve that species, or binary ion exchange and one complexation reaction involving a common ion. Partial differential equations that describe solute mass balance entirely in the liquid phase are developed for each tenad (a chemical entity whose total mass is independent of the reaction process) in terms of their total dissolved concentration. These equations are solved numerically in two dimensions through the modification of an existing groundwater flow/transport computer code. (Author 's abstract)

  15. Stochastic foundations of undulatory transport phenomena: generalized Poisson-Kac processes—part III extensions and applications to kinetic theory and transport

    Science.gov (United States)

    Giona, Massimiliano; Brasiello, Antonio; Crescitelli, Silvestro

    2017-08-01

    This third part extends the theory of Generalized Poisson-Kac (GPK) processes to nonlinear stochastic models and to a continuum of states. Nonlinearity is treated in two ways: (i) as a dependence of the parameters (intensity of the stochastic velocity, transition rates) of the stochastic perturbation on the state variable, similarly to the case of nonlinear Langevin equations, and (ii) as the dependence of the stochastic microdynamic equations of motion on the statistical description of the process itself (nonlinear Fokker-Planck-Kac models). Several numerical and physical examples illustrate the theory. Gathering nonlinearity and a continuum of states, GPK theory provides a stochastic derivation of the nonlinear Boltzmann equation, furnishing a positive answer to the Kac’s program in kinetic theory. The transition from stochastic microdynamics to transport theory within the framework of the GPK paradigm is also addressed.

  16. Stochastic foundations of undulatory transport phenomena: generalized Poisson–Kac processes—part III extensions and applications to kinetic theory and transport

    International Nuclear Information System (INIS)

    Giona, Massimiliano; Brasiello, Antonio; Crescitelli, Silvestro

    2017-01-01

    This third part extends the theory of Generalized Poisson–Kac (GPK) processes to nonlinear stochastic models and to a continuum of states. Nonlinearity is treated in two ways: (i) as a dependence of the parameters (intensity of the stochastic velocity, transition rates) of the stochastic perturbation on the state variable, similarly to the case of nonlinear Langevin equations, and (ii) as the dependence of the stochastic microdynamic equations of motion on the statistical description of the process itself (nonlinear Fokker–Planck–Kac models). Several numerical and physical examples illustrate the theory. Gathering nonlinearity and a continuum of states, GPK theory provides a stochastic derivation of the nonlinear Boltzmann equation, furnishing a positive answer to the Kac’s program in kinetic theory. The transition from stochastic microdynamics to transport theory within the framework of the GPK paradigm is also addressed. (paper)

  17. Hybrid perturbation methods based on statistical time series models

    Science.gov (United States)

    San-Juan, Juan Félix; San-Martín, Montserrat; Pérez, Iván; López, Rosario

    2016-04-01

    In this work we present a new methodology for orbit propagation, the hybrid perturbation theory, based on the combination of an integration method and a prediction technique. The former, which can be a numerical, analytical or semianalytical theory, generates an initial approximation that contains some inaccuracies derived from the fact that, in order to simplify the expressions and subsequent computations, not all the involved forces are taken into account and only low-order terms are considered, not to mention the fact that mathematical models of perturbations not always reproduce physical phenomena with absolute precision. The prediction technique, which can be based on either statistical time series models or computational intelligence methods, is aimed at modelling and reproducing missing dynamics in the previously integrated approximation. This combination results in the precision improvement of conventional numerical, analytical and semianalytical theories for determining the position and velocity of any artificial satellite or space debris object. In order to validate this methodology, we present a family of three hybrid orbit propagators formed by the combination of three different orders of approximation of an analytical theory and a statistical time series model, and analyse their capability to process the effect produced by the flattening of the Earth. The three considered analytical components are the integration of the Kepler problem, a first-order and a second-order analytical theories, whereas the prediction technique is the same in the three cases, namely an additive Holt-Winters method.

  18. Introduction to non-perturbative quantum chromodynamics

    International Nuclear Information System (INIS)

    Pene, O.

    1995-01-01

    Quantum chromodynamics is considered to be the theory of strong interaction. The main peculiarity of this theory is that its asymptotic states (hadrons) are different from its elementary fields (quarks and gluons). This property plays a great part in any physical process involving small momentum-energy transfers. In such a range perturbative methods are no longer allowed. This work focuses on other tools such as QCD symmetry, the quark model, Green functions and the sum rules. To get hadron characteristics numerically, QCD on lattices is used but only in the case of simple process involving no more than one hadron in the initial and final states because of the complexity of the Green function. Some examples using a Monte-Carlo simulation are given. (A.C.)

  19. Perturbative and constructive renormalization

    International Nuclear Information System (INIS)

    Veiga, P.A. Faria da

    2000-01-01

    These notes are a survey of the material treated in a series of lectures delivered at the X Summer School Jorge Andre Swieca. They are concerned with renormalization in Quantum Field Theories. At the level of perturbation series, we review classical results as Feynman graphs, ultraviolet and infrared divergences of Feynman integrals. Weinberg's theorem and Hepp's theorem, the renormalization group and the Callan-Symanzik equation, the large order behavior and the divergence of most perturbation series. Out of the perturbative regime, as an example of a constructive method, we review Borel summability and point out how it is possible to circumvent the perturbation diseases. These lectures are a preparation for the joint course given by professor V. Rivasseau at the same school, where more sophisticated non-perturbative analytical methods based on rigorous renormalization group techniques are presented, aiming at furthering our understanding about the subject and bringing field theoretical models to a satisfactory mathematical level. (author)

  20. Perturbative Heat Transport Experiments on TJ-II

    International Nuclear Information System (INIS)

    Eguilor, S.; Castejon, F.; Luna, E. de la; Cappa, A.; Likin, K.; Fernandez, A.; Tj-II, T.

    2002-01-01

    Heat wave experiments are performed on TJ-II stellarator plasmas to estimate both heat diffusivity and power deposition profiles. High frequency ECRH modulation experiments are used to obtain the power deposition profiles, which is observed to be wider and duller than estimated by tracing techniques. The causes of this difference are discussed in the paper. Fourier analysis techniques are used to estimate the heat diffusivity in low frequency ECRH modulation experiments. This include the power deposition profile as a new ingredient. ECHR switch on/off experiments are exploited to obtain power deposition and heat diffusivities profile. Those quantities are compared with the obtained by modulation experiments and transport analysis, showing a good agreement. (Author) 18 refs