New class of accelerating black hole solutions

International Nuclear Information System (INIS)

Camps, Joan; Emparan, Roberto

2010-01-01

We construct several new families of vacuum solutions that describe black holes in uniformly accelerated motion. They generalize the C metric to the case where the energy density and tension of the strings that pull (or push) on the black holes are independent parameters. These strings create large curvatures near their axis and when they have infinite length they modify the asymptotic properties of the spacetime, but we discuss how these features can be dealt with physically, in particular, in terms of 'wiggly cosmic strings'. We comment on possible extensions and extract lessons for the problem of finding higher-dimensional accelerating black hole solutions.

Accelerated FRW solutions in Chern-Simons gravity

International Nuclear Information System (INIS)

Cataldo, Mauricio; Crisostomo, Juan; Gomez, Fernando; Salgado, Patricio; Campo, Sergio del; Quinzacara, Cristian C.

2014-01-01

We consider a five-dimensional Einstein-Chern-Simons action which is composed of a gravitational sector and a sector of matter where the gravitational sector is given by a Chern-Simons gravity action instead of the Einstein-Hilbert action and where the matter sector is given by the so-called perfect fluid. It is shown that (i) the Einstein-Chern-Simons (EChS) field equations subject to suitable conditions can be written in a similar way to the Einstein-Maxwell field equations; (ii) these equations have solutions that describe an accelerated expansion for the three possible cosmological models of the universe, namely, spherical expansion, flat expansion, and hyperbolic expansion when α a parameter of the theory, is greater than zero. This result allows us to conjecture that these solutions are compatible with the era of dark energy and that the energy-momentum tensor for the field h a , a bosonic gauge field from the Chern-Simons gravity action, corresponds to a form of positive cosmological constant. It is also shown that the EChS field equations have solutions compatible with the era of matter: (i) In the case of an open universe, the solutions correspond to an accelerated expansion (α > 0) with a minimum scale factor at initial time that, when time goes to infinity, the scale factor behaves as a hyperbolic sine function. (ii) In the case of a flat universe, the solutions describe an accelerated expansion whose scale factor behaves as an exponential function of time. (iii) In the case of a closed universe there is found only one solution for a universe in expansion, which behaves as a hyperbolic cosine function of time. (orig.)

Numerical integration of asymptotic solutions of ordinary differential equations

Science.gov (United States)

Thurston, Gaylen A.

1989-01-01

Classical asymptotic analysis of ordinary differential equations derives approximate solutions that are numerically stable. However, the analysis also leads to tedious expansions in powers of the relevant parameter for a particular problem. The expansions are replaced with integrals that can be evaluated by numerical integration. The resulting numerical solutions retain the linear independence that is the main advantage of asymptotic solutions. Examples, including the Falkner-Skan equation from laminar boundary layer theory, illustrate the method of asymptotic analysis with numerical integration.

Numerical solution of non-linear diffusion problems

International Nuclear Information System (INIS)

Carmen, A. del; Ferreri, J.C.

1998-01-01

This paper presents a method for the numerical solution of non-linear diffusion problems using finite-differences in moving grids. Due to the presence of steep fronts in the solution domain and to the presence of advective terms originating in the grid movement, an implicit TVD scheme, first order in time and second order in space has been developed. Some algebraic details of the derivation are given. Results are shown for the pure advection of a scalar as a test case and an example dealing with the slow spreading of viscous fluids over plane surfaces. The agreement between numerical and analytical solutions is excellent. (author). 8 refs., 3 figs

Stochastic coalescence in finite systems: an algorithm for the numerical solution of the multivariate master equation.

Science.gov (United States)

Alfonso, Lester; Zamora, Jose; Cruz, Pedro

2015-04-01

The stochastic approach to coagulation considers the coalescence process going in a system of a finite number of particles enclosed in a finite volume. Within this approach, the full description of the system can be obtained from the solution of the multivariate master equation, which models the evolution of the probability distribution of the state vector for the number of particles of a given mass. Unfortunately, due to its complexity, only limited results were obtained for certain type of kernels and monodisperse initial conditions. In this work, a novel numerical algorithm for the solution of the multivariate master equation for stochastic coalescence that works for any type of kernels and initial conditions is introduced. The performance of the method was checked by comparing the numerically calculated particle mass spectrum with analytical solutions obtained for the constant and sum kernels, with an excellent correspondence between the analytical and numerical solutions. In order to increase the speedup of the algorithm, software parallelization techniques with OpenMP standard were used, along with an implementation in order to take advantage of new accelerator technologies. Simulations results show an important speedup of the parallelized algorithms. This study was funded by a grant from Consejo Nacional de Ciencia y Tecnologia de Mexico SEP-CONACYT CB-131879. The authors also thanks LUFAC® Computacion SA de CV for CPU time and all the support provided.

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

JDiffraction: A GPGPU-accelerated JAVA library for numerical propagation of scalar wave fields

Science.gov (United States)

Piedrahita-Quintero, Pablo; Trujillo, Carlos; Garcia-Sucerquia, Jorge

2017-05-01

JDiffraction, a GPGPU-accelerated JAVA library for numerical propagation of scalar wave fields, is presented. Angular spectrum, Fresnel transform, and Fresnel-Bluestein transform are the numerical algorithms implemented in the methods and functions of the library to compute the scalar propagation of the complex wavefield. The functionality of the library is tested with the modeling of easy to forecast numerical experiments and also with the numerical reconstruction of a digitally recorded hologram. The performance of JDiffraction is contrasted with a library written for C++, showing great competitiveness in the apparently less complex environment of JAVA language. JDiffraction also includes JAVA easy-to-use methods and functions that take advantage of the computation power of the graphic processing units to accelerate the processing times of 2048×2048 pixel images up to 74 frames per second.

Numerically satisfactory solutions of Kummer recurrence relations

NARCIS (Netherlands)

J. Segura (Javier); N.M. Temme (Nico)

2008-01-01

textabstractPairs of numerically satisfactory solutions as $n\\rightarrow \\infty$ for the three-term recurrence relations satisfied by the families of functions $_1\\mbox{F}_1(a+\\epsilon_1 n; b +\\epsilon_2 n;z)$, $\\epsilon_i \\in {\\mathbb Z}$, are given. It is proved that minimal solutions always

Constructing exact symmetric informationally complete measurements from numerical solutions

Science.gov (United States)

Appleby, Marcus; Chien, Tuan-Yow; Flammia, Steven; Waldron, Shayne

2018-04-01

Recently, several intriguing conjectures have been proposed connecting symmetric informationally complete quantum measurements (SIC POVMs, or SICs) and algebraic number theory. These conjectures relate the SICs to their minimal defining algebraic number field. Testing or sharpening these conjectures requires that the SICs are expressed exactly, rather than as numerical approximations. While many exact solutions of SICs have been constructed previously using Gröbner bases, this method has probably been taken as far as is possible with current computer technology (except in special cases where there are additional symmetries). Here, we describe a method for converting high-precision numerical solutions into exact ones using an integer relation algorithm in conjunction with the Galois symmetries of an SIC. Using this method, we have calculated 69 new exact solutions, including nine new dimensions, where previously only numerical solutions were known—which more than triples the number of known exact solutions. In some cases, the solutions require number fields with degrees as high as 12 288. We use these solutions to confirm that they obey the number-theoretic conjectures, and address two questions suggested by the previous work.

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)

Archimedean-type force in a cosmic dark fluid. I. Exact solutions for the late-time accelerated expansion

International Nuclear Information System (INIS)

Balakin, Alexander B.; Bochkarev, Vladimir V.

2011-01-01

We establish a new self-consistent model in order to explain from a unified viewpoint two key features of the cosmological evolution: the inflation in the early Universe and the late-time accelerated expansion. The key element of this new model is the Archimedean-type coupling of the dark matter with dark energy, which form the so-called cosmic dark fluid. We suppose that dark matter particles immersed into the dark energy reservoir are affected by the force proportional to the four-gradient of the dark energy pressure. The Archimedean-type coupling is shown to play a role of effective energy-momentum redistributor between the dark matter and the dark energy components of the dark fluid, thus providing the Universe evolution to be a quasiperiodic and/or multistage process. In the first part of the work we discuss a theoretical base and new exact solutions of the model master equations. Special attention is focused on the exact solutions, for which the scale factor is presented by the anti-Gaussian function: these solutions describe the late-time acceleration and are characterized by a nonsingular behavior in the early Universe. The second part contains qualitative and numerical analysis of the master equations; we focus there on the solutions describing a multi-inflationary Universe.

Temperature Profile of the Solution Vessel of an Accelerator-Driven Subcritical Fissile Solution System

Energy Technology Data Exchange (ETDEWEB)

Klein, Steven Karl [Los Alamos National Lab. (LANL), Los Alamos, NM (United States); Determan, John C. [Los Alamos National Lab. (LANL), Los Alamos, NM (United States)

2015-09-14

Dynamic System Simulation (DSS) models of fissile solution systems have been developed and verified against a variety of historical configurations. DSS techniques have been applied specifically to subcritical accelerator-driven systems using fissile solution fuels of uranium. Initial DSS models were developed in DESIRE, a specialized simulation scripting language. In order to tailor the DSS models to specifically meet needs of system designers they were converted to a Visual Studio implementation, and one of these subsequently to National Instrument’s LabVIEW for human factors engineering and operator training. Specific operational characteristics of subcritical accelerator-driven systems have been examined using a DSS model tailored to this particular class using fissile fuel.

Temperature Profile of the Solution Vessel of an Accelerator-Driven Subcritical Fissile Solution System

International Nuclear Information System (INIS)

Klein, Steven Karl; Determan, John C.

2015-01-01

Dynamic System Simulation (DSS) models of fissile solution systems have been developed and verified against a variety of historical configurations. DSS techniques have been applied specifically to subcritical accelerator-driven systems using fissile solution fuels of uranium. Initial DSS models were developed in DESIRE, a specialized simulation scripting language. In order to tailor the DSS models to specifically meet needs of system designers they were converted to a Visual Studio implementation, and one of these subsequently to National Instrument's LabVIEW for human factors engineering and operator training. Specific operational characteristics of subcritical accelerator-driven systems have been examined using a DSS model tailored to this particular class using fissile fuel.

Numerical solution of Boltzmann's equation

International Nuclear Information System (INIS)

Sod, G.A.

1976-04-01

The numerical solution of Boltzmann's equation is considered for a gas model consisting of rigid spheres by means of Hilbert's expansion. If only the first two terms of the expansion are retained, Boltzmann's equation reduces to the Boltzmann-Hilbert integral equation. Successive terms in the Hilbert expansion are obtained by solving the same integral equation with a different source term. The Boltzmann-Hilbert integral equation is solved by a new very fast numerical method. The success of the method rests upon the simultaneous use of four judiciously chosen expansions; Hilbert's expansion for the distribution function, another expansion of the distribution function in terms of Hermite polynomials, the expansion of the kernel in terms of the eigenvalues and eigenfunctions of the Hilbert operator, and an expansion involved in solving a system of linear equations through a singular value decomposition. The numerical method is applied to the study of the shock structure in one space dimension. Numerical results are presented for Mach numbers of 1.1 and 1.6. 94 refs, 7 tables, 1 fig

Late time solution for interacting scalar in accelerating spaces

Energy Technology Data Exchange (ETDEWEB)

Prokopec, Tomislav, E-mail: t.prokopec@uu.nl [Institute for Theoretical Physics, Spinoza Institute and EMME$\\Phi$, Utrecht University, Postbus 80.195, Utrecht, 3508 TD The Netherlands (Netherlands)

2015-11-01

We consider stochastic inflation in an interacting scalar field in spatially homogeneous accelerating space-times with a constant principal slow roll parameter ε. We show that, if the scalar potential is scale invariant (which is the case when scalar contains quartic self-interaction and couples non-minimally to gravity), the late-time solution on accelerating FLRW spaces can be described by a probability distribution function (PDF) ρ which is a function of φ/H only, where φ=φ( x-vector ) is the scalar field and H=H(t) denotes the Hubble parameter. We give explicit late-time solutions for ρarrow ρ{sub ∞}(φ/H), and thereby find the order ε corrections to the Starobinsky-Yokoyama result. This PDF can then be used to calculate e.g. various n-point functions of the (self-interacting) scalar field, which are valid at late times in arbitrary accelerating space-times with ε= constant.

A theoretical response of the electrostatic parallel plate to constant and low-frequency accelerations

International Nuclear Information System (INIS)

Lee, Ki Bang

2009-01-01

A theoretical response of an electrostatic gap-closing actuator based on parallel plates to constant and low-frequency accelerations has been derived as a function of the applied acceleration and voltage. The nonlinear equation of motion is obtained in a dimensionless form from the fact that the inertial and damping forces are neglected at a frequency much less than the resonant frequency of the parallel plate, and thereafter the nonlinear equation is solved for the stable inter-plate gap at the acceleration and voltage. From the derived solution, the pull-in acceleration is obtained as a function of the applied voltage, and the pull-in voltage is also expressed as a function of the acceleration. The closed-form solution is validated by comparison with a numerical solution. The theoretical solution is in excellent agreement with the numerical results when the actuator is exposed to a constant acceleration as well as a low-frequency acceleration. The theoretical solution and pull-in acceleration and voltage thus provide guidance to prescribe operational constraints for devices that use the parallel plate actuator and to predict the response of the electrostatic gap-closing parallel plates to constant and low-frequency acceleration

Pierce electrodes for a multigap accelerating system

International Nuclear Information System (INIS)

Davydenko, V.I.; Ivanov, A.A.; Kotelnikov, I.A.; Tiunov, M.A.

2007-01-01

A well-known Pierce's solution that allows to focus a beam of charged particles using properly shaped electrodes outside the beam is generalized to the case of multigap accelerating system. Simple parametric formulae for Pierce electrodes are derived for an accelerating system with current density, limited either by space charge or by emitting property of the cathode. As an example of general approach, Pierce electrodes shape is analyzed for a system with two accelerating gaps. It is shown that precise Pierce's solution exists if acceleration rate within second gap is lower than within first gap. In the opposite case quasi-Pierce solution can be implemented using non-equipotential electrode between the gaps, and guidelines, based on numerical simulations, for the design of equipotential focusing electrodes are given

The numerical simulation of accelerator components

International Nuclear Information System (INIS)

Herrmannsfeldt, W.B.; Hanerfeld, H.

1987-05-01

The techniques of the numerical simulation of plasmas can be readily applied to problems in accelerator physics. Because the problems usually involve a single component ''plasma,'' and times that are at most, a few plasma oscillation periods, it is frequently possible to make very good simulations with relatively modest computation resources. We will discuss the methods and illustrate them with several examples. One of the more powerful techniques of understanding the motion of charged particles is to view computer-generated motion pictures. We will show several little movie strips to illustrate the discussions. The examples will be drawn from the application areas of Heavy Ion Fusion, electron-positron linear colliders and injectors for free-electron lasers. 13 refs., 10 figs., 2 tabs

Introduction to the numerical solutions of Markov chains

CERN Document Server

Stewart, Williams J

1994-01-01

A cornerstone of applied probability, Markov chains can be used to help model how plants grow, chemicals react, and atoms diffuse - and applications are increasingly being found in such areas as engineering, computer science, economics, and education. To apply the techniques to real problems, however, it is necessary to understand how Markov chains can be solved numerically. In this book, the first to offer a systematic and detailed treatment of the numerical solution of Markov chains, William Stewart provides scientists on many levels with the power to put this theory to use in the actual world, where it has applications in areas as diverse as engineering, economics, and education. His efforts make for essential reading in a rapidly growing field. Here, Stewart explores all aspects of numerically computing solutions of Markov chains, especially when the state is huge. He provides extensive background to both discrete-time and continuous-time Markov chains and examines many different numerical computing metho...

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.

Numerical Solution of Stochastic Nonlinear Fractional Differential Equations

KAUST Repository

El-Beltagy, Mohamed A.

2015-01-07

Using Wiener-Hermite expansion (WHE) technique in the solution of the stochastic partial differential equations (SPDEs) has the advantage of converting the problem to a system of deterministic equations that can be solved efficiently using the standard deterministic numerical methods [1]. WHE is the only known expansion that handles the white/colored noise exactly. This work introduces a numerical estimation of the stochastic response of the Duffing oscillator with fractional or variable order damping and driven by white noise. The WHE technique is integrated with the Grunwald-Letnikov approximation in case of fractional order and with Coimbra approximation in case of variable-order damping. The numerical solver was tested with the analytic solution and with Monte-Carlo simulations. The developed mixed technique was shown to be efficient in simulating SPDEs.

Numerical Solution of Stochastic Nonlinear Fractional Differential Equations

KAUST Repository

El-Beltagy, Mohamed A.; Al-Juhani, Amnah

2015-01-01

Using Wiener-Hermite expansion (WHE) technique in the solution of the stochastic partial differential equations (SPDEs) has the advantage of converting the problem to a system of deterministic equations that can be solved efficiently using the standard deterministic numerical methods [1]. WHE is the only known expansion that handles the white/colored noise exactly. This work introduces a numerical estimation of the stochastic response of the Duffing oscillator with fractional or variable order damping and driven by white noise. The WHE technique is integrated with the Grunwald-Letnikov approximation in case of fractional order and with Coimbra approximation in case of variable-order damping. The numerical solver was tested with the analytic solution and with Monte-Carlo simulations. The developed mixed technique was shown to be efficient in simulating SPDEs.

Rotationally symmetric numerical solutions to the sine-Gordon equation

DEFF Research Database (Denmark)

Olsen, O. H.; Samuelsen, Mogens Rugholm

1981-01-01

We examine numerically the properties of solutions to the spherically symmetric sine-Gordon equation given an initial profile which coincides with the one-dimensional breather solution and refer to such solutions as ring waves. Expanding ring waves either exhibit a return effect or expand towards...

On numerical solution of Burgers' equation by homotopy analysis method

International Nuclear Information System (INIS)

Inc, Mustafa

2008-01-01

In this Letter, we present the Homotopy Analysis Method (shortly HAM) for obtaining the numerical solution of the one-dimensional nonlinear Burgers' equation. The initial approximation can be freely chosen with possible unknown constants which can be determined by imposing the boundary and initial conditions. Convergence of the solution and effects for the method is discussed. The comparison of the HAM results with the Homotopy Perturbation Method (HPM) and the results of [E.N. Aksan, Appl. Math. Comput. 174 (2006) 884; S. Kutluay, A. Esen, Int. J. Comput. Math. 81 (2004) 1433; S. Abbasbandy, M.T. Darvishi, Appl. Math. Comput. 163 (2005) 1265] are made. The results reveal that HAM is very simple and effective. The HAM contains the auxiliary parameter h, which provides us with a simple way to adjust and control the convergence region of solution series. The numerical solutions are compared with the known analytical and some numerical solutions

Numerical Study of Correlation of Fluid Particle Acceleration and Turbulence Intensity in Swirling Flow

Directory of Open Access Journals (Sweden)

Nan Gui

2015-01-01

Full Text Available Numerical investigation of correlation between the fluid particle acceleration and the intensity of turbulence in swirling flows at a large Reynolds number is carried out via direct numerical simulation. A weak power-law form correlation ur.m.sE~C(aLφ between the Lagrangian acceleration and the Eulerian turbulence intensity is derived. It is found that the increase of the swirl level leads to the increase of the exponent φ and the trajectory-conditioned correlation coefficient ρ(aL,uE and results in a weak power-law augmentation of the acceleration intermittency. The trajectory-conditioned convection of turbulence fluctuation in the Eulerian viewpoint is generally linearly proportional to the fluctuation of Lagrangian accelerations, indicating a weak but clear relation between the Lagrangian intermittency and Eulerian intermittency effects. Moreover, except the case with vortex breakdown, the weak linear dependency is maintained when the swirl levels change, only with the coefficient of slope varied.

Numerical modeling of accelerated, pre-compressed CTs in RACE

International Nuclear Information System (INIS)

Eddleman, J.L.; Hammer, J.H.; Hartman, C.W.; Logan, B.G.; McLean, H.S.; Molvik, A.W.

1990-01-01

Numerical modeling of accelerated compact toroids in the RACE experiment has motivated the development and application of a wide range of computational tools. These tools have included the zero-dimensional RAC code for fast parameter and design studies, and the two-dimensional, Eulerian, axisymmetric, magneto-hydrodynamic code, HAM, used to model plasma ring formation in magnetized plasma guns and acceleration in straight cylindrical electrodes. Extension of the RACE geometry to include converging conical electrodes motivated the development of a new two-dimensional, Lagrangian, axisymmetric, magnetohydrodynamic code, TRAC. The code includes optional initialization of the ring magnetic fields to a Taylor-equilibrium profile as well as self-consistent external capacitor bank driving circuit. Stability of initial field configurations with toroidal mode number > 0 may also be determined. The new code is particularly suited for predicting the behavior of accelerated plasma rings in arbitrarily shaped conical electrodes, since the restriction to a rectilinear mesh is removed. In particular, application of the code to the new pre-compression geometry in the RACE experiment is discussed and compared with experimental results

Application of Fourier transform to MHD flow over an accelerated plate with partial-slippage

Directory of Open Access Journals (Sweden)

Salman Ahmad

2014-06-01

Full Text Available Magneto-Hydrodynamic (MHD flow over an accelerated plate is investigated with partial slip conditions. Generalized Fourier Transform is used to get the exact solution not only for uniform acceleration but also for variable acceleration. The numerical solution is obtained by using linear finite element method in space and One-Step-θ-scheme in time. The resulting discretized algebraic systems are solved by applying geometric-multigrid approach. Numerical solutions are compared with the obtained Fourier transform results. Many interesting results related with slippage and MHD effects are discussed in detail through graphical sketches and tables. Application of Dirac-Delta function is one of the main features of present work.

Explicit appropriate basis function method for numerical solution of stiff systems

International Nuclear Information System (INIS)

Chen, Wenzhen; Xiao, Hongguang; Li, Haofeng; Chen, Ling

2015-01-01

Highlights: • An explicit numerical method called the appropriate basis function method is presented. • The method differs from the power series method for obtaining approximate numerical solutions. • Two cases show the method is fit for linear and nonlinear stiff systems. • The method is very simple and effective for most of differential equation systems. - Abstract: In this paper, an explicit numerical method, called the appropriate basis function method, is presented. The explicit appropriate basis function method differs from the power series method because it employs an appropriate basis function such as the exponential function, or periodic function, other than a polynomial, to obtain approximate numerical solutions. The method is successful and effective for the numerical solution of the first order ordinary differential equations. Two examples are presented to show the ability of the method for dealing with linear and nonlinear systems of differential equations

Automatic validation of numerical solutions

DEFF Research Database (Denmark)

Stauning, Ole

1997-01-01

This thesis is concerned with ``Automatic Validation of Numerical Solutions''. The basic theory of interval analysis and self-validating methods is introduced. The mean value enclosure is applied to discrete mappings for obtaining narrow enclosures of the iterates when applying these mappings...... differential equations, but in this thesis, we describe how to use the methods for enclosing iterates of discrete mappings, and then later use them for discretizing solutions of ordinary differential equations. The theory of automatic differentiation is introduced, and three methods for obtaining derivatives...... are described: The forward, the backward, and the Taylor expansion methods. The three methods have been implemented in the C++ program packages FADBAD/TADIFF. Some examples showing how to use the three metho ds are presented. A feature of FADBAD/TADIFF not present in other automatic differentiation packages...

Computer simulation of dynamic processes on accelerators

International Nuclear Information System (INIS)

Kol'ga, V.V.

1979-01-01

The problems of computer numerical investigation of motion of accelerated particles in accelerators and storages, an effect of different accelerator systems on the motion, determination of optimal characteristics of accelerated charged particle beams are considered. Various simulation representations are discussed which describe the accelerated particle dynamics, such as the enlarged particle method, the representation where a great number of discrete particle is substituted for a field of continuously distributed space charge, the method based on determination of averaged beam characteristics. The procedure is described of numerical studies involving the basic problems, viz. calculation of closed orbits, establishment of stability regions, investigation of resonance propagation determination of the phase stability region, evaluation of the space charge effect the problem of beam extraction. It is shown that most of such problems are reduced to solution of the Cauchy problem using a computer. The ballistic method which is applied to solution of the boundary value problem of beam extraction is considered. It is shown that introduction into the equation under study of additional members with the small positive regularization parameter is a general idea of the methods for regularization of noncorrect problems [ru

Theoretical and numerical studies on the transport of transverse beam quality in plasma-based accelerators

International Nuclear Information System (INIS)

Mehrling, Timon Johannes

2014-11-01

This work examines effects, which impact the transverse quality of electron-beams in plasma-based accelerators, by means of theoretical and numerical methods. Plasma-based acceleration is a promising candidate for future particle accelerator technologies. In plasma-based acceleration, highly intense laser beams or high-current relativistic particle beams are focused into a plasma to excite plasma-waves with extreme transverse and longitudinal electric fields. The amplitude of these fields exceed with 10-100 GV/m the ones in today's radio-frequency accelerators by several orders of magnitude, hence, in principle allowing for accordingly shorter and cheaper accelerators based on plasma. Despite the tremendous progress in the recent decade, beams from plasma accelerators are not yet achieving the quality as demanded for pivotal applications of relativistic electron-beams, e.g. free-electron lasers (FELs).Studies within this work examine how the quality can be optimized in the production of the beams and preserved during the acceleration and transport to the interaction region. Such studies cannot be approached purely analytical but necessitate numerical methods, such as the Particle-In-Cell (PIC) method, which can model kinetic, electrodynamic and relativistic plasma phenomena. However, this method is computationally too expensive for parameter-scans in three-dimensional geometries. Hence, a quasi-static PIC code was developed in connection with this work, which is significantly more effective than the full PIC method for a class of problems in plasma-based acceleration.The evolution of the emittance of beams which are injected into plasma modules was studied in this work by means of theoretical and the above numerical methods. It was shown that the beam parameters need to be matched accurately into the focusing plasma-channel in order to allow for beam-quality preservation. This suggested that new extraction and injection-techniques are required in staged plasma-acceleration

Merging AI and numerical modeling for accelerator control

International Nuclear Information System (INIS)

Schultz, D.E.; Silbar, R.R.

1987-01-01

The authors report the beginnings of an experiment to evaluate the power and limitations of artificial intelligence techniques combined with beam-line modeling for solving problems in accelerator control. Using the Knowledge Engineering Environment (KEE) system, they have built a knowledge base that describes the characteristics and the relationships of about 30 devices in a typical accelerator beam line. Each device in the line is categorized and pertinent attributes for each category are defined. Specific values for each device are assigned in the knowledge base to represent static characteristics. Device-specific slots are also provided for dynamic attributes. The definition of these slots reflects the data type and any limitations or restrictions on the range of the data. The authors model relationships between the various beam-line devices using the techniques of rules, active values, and object-oriented models. The knowledge base provides a framework for analyzing faults and offering suggestions to assist in tuning, based on information provided by the accelerator physicists (domain experts) responsible for designing and tuning this beam line. Our knowledge base has a powerful graphical interface. It allows the operator to mouse on an icon for a particular icon in the schematic of the beam line and obtain device-specific information and control over that device. The beam optics code Transport is used to model the beam line numerically. 11 refs., 7 figs

The solution of the point kinetics equations via converged accelerated Taylor series (CATS)

Energy Technology Data Exchange (ETDEWEB)

Ganapol, B.; Picca, P. [Dept. of Aerospace and Mechanical Engineering, Univ. of Arizona (United States); Previti, A.; Mostacci, D. [Laboratorio di Montecuccolino, Alma Mater Studiorum - Universita di Bologna (Italy)

2012-07-01

This paper deals with finding accurate solutions of the point kinetics equations including non-linear feedback, in a fast, efficient and straightforward way. A truncated Taylor series is coupled to continuous analytical continuation to provide the recurrence relations to solve the ordinary differential equations of point kinetics. Non-linear (Wynn-epsilon) and linear (Romberg) convergence accelerations are employed to provide highly accurate results for the evaluation of Taylor series expansions and extrapolated values of neutron and precursor densities at desired edits. The proposed Converged Accelerated Taylor Series, or CATS, algorithm automatically performs successive mesh refinements until the desired accuracy is obtained, making use of the intermediate results for converged initial values at each interval. Numerical performance is evaluated using case studies available from the literature. Nearly perfect agreement is found with the literature results generally considered most accurate. Benchmark quality results are reported for several cases of interest including step, ramp, zigzag and sinusoidal prescribed insertions and insertions with adiabatic Doppler feedback. A larger than usual (9) number of digits is included to encourage honest benchmarking. The benchmark is then applied to the enhanced piecewise constant algorithm (EPCA) currently being developed by the second author. (authors)

Numerical solution of the equation of neutrons transport on plane geometry by analytical schemes using acceleration by synthetic diffusion

International Nuclear Information System (INIS)

Alonso-Vargas, G.

1991-01-01

A computer program has been developed which uses a technique of synthetic acceleration by diffusion by analytical schemes. Both in the diffusion equation as in that of transport, analytical schemes were used which allowed a substantial time saving in the number of iterations required by source iteration method to obtain the K e ff. The program developed ASD (Synthetic Diffusion Acceleration) by diffusion was written in FORTRAN and can be executed on a personal computer with a hard disc and mathematical O-processor. The program is unlimited as to the number of regions and energy groups. The results obtained by the ASD program for K e ff is nearly completely concordant with those of obtained utilizing the ANISN-PC code for different analytical type problems in this work. The ASD program allowed obtention of an approximate solution of the neutron transport equation with a relatively low number of internal reiterations with good precision. One of its applications would be in the direct determinations of axial distribution neutronic flow in a fuel assembly as well as in the obtention of the effective multiplication factor. (Author)

Spurious solutions in few-body equations. II. Numerical investigations

International Nuclear Information System (INIS)

Adhikari, S.K.

1979-01-01

A recent analytic study of spurious solutions in few-body equations by Adhikari and Gloeckle is here complemented by numerical investigations. As proposed by Adhikari and Gloeckle we study numerically the spurious solutions in the three-body Weinberg type equations and draw some general conclusions about the existence of spurious solutions in three-body equations with the Weinberg kernel and in other few-body formulations. In particular we conclude that for most of the potentials we encounter in problems of nuclear physics the three-body Weinberg type equation will not have a spurious solution which may interfere with the bound state or scattering calculation. Hence, if proven convenient, the three-body Weinberg type equation can be used in practical calculations. The same conclusion is true for the three-body channel coupling array scheme of Kouri, Levin, and Tobocman. In the case of the set of six coupled four-body equations proposed by Rosenberg et al. and the set of the Bencze-Redish-Sloan equations a careful study of the possible spurious solutions is needed before using these equations in practical calculations

Efficient numerical solution to vacuum decay with many fields

Energy Technology Data Exchange (ETDEWEB)

Masoumi, Ali; Olum, Ken D.; Shlaer, Benjamin, E-mail: ali@cosmos.phy.tufts.edu, E-mail: kdo@cosmos.phy.tufts.edu, E-mail: shlaer@cosmos.phy.tufts.edu [Institute of Cosmology, Department of Physics and Astronomy, Tufts University, Medford, MA 02155 (United States)

2017-01-01

Finding numerical solutions describing bubble nucleation is notoriously difficult in more than one field space dimension. Traditional shooting methods fail because of the extreme non-linearity of field evolution over a macroscopic distance as a function of initial conditions. Minimization methods tend to become either slow or imprecise for larger numbers of fields due to their dependence on the high dimensionality of discretized function spaces. We present a new method for finding solutions which is both very efficient and able to cope with the non-linearities. Our method directly integrates the equations of motion except at a small number of junction points, so we do not need to introduce a discrete domain for our functions. The method, based on multiple shooting, typically finds solutions involving three fields in around a minute, and can find solutions for eight fields in about an hour. We include a numerical package for Mathematica which implements the method described here.

Numerical soliton-like solutions of the potential Kadomtsev-Petviashvili equation by the decomposition method

International Nuclear Information System (INIS)

Kaya, Dogan; El-Sayed, Salah M.

2003-01-01

In this Letter we present an Adomian's decomposition method (shortly ADM) for obtaining the numerical soliton-like solutions of the potential Kadomtsev-Petviashvili (shortly PKP) equation. We will prove the convergence of the ADM. We obtain the exact and numerical solitary-wave solutions of the PKP equation for certain initial conditions. Then ADM yields the analytic approximate solution with fast convergence rate and high accuracy through previous works. The numerical solutions are compared with the known analytical solutions

Matching of analytical and numerical solutions for neutron stars of arbitrary rotation

International Nuclear Information System (INIS)

Pappas, George

2009-01-01

We demonstrate the results of an attempt to match the two-soliton analytical solution with the numerically produced solutions of the Einstein field equations, that describe the spacetime exterior of rotating neutron stars, for arbitrary rotation. The matching procedure is performed by equating the first four multipole moments of the analytical solution to the multipole moments of the numerical one. We then argue that in order to check the effectiveness of the matching of the analytical with the numerical solution we should compare the metric components, the radius of the innermost stable circular orbit (R ISCO ), the rotation frequency and the epicyclic frequencies Ω ρ , Ω z . Finally we present some results of the comparison.

Matching of analytical and numerical solutions for neutron stars of arbitrary rotation

Energy Technology Data Exchange (ETDEWEB)

Pappas, George, E-mail: gpappas@phys.uoa.g [Section of Astrophysics, Astronomy, and Mechanics, Department of Physics, University of Athens, Panepistimiopolis Zografos GR15783, Athens (Greece)

2009-10-01

We demonstrate the results of an attempt to match the two-soliton analytical solution with the numerically produced solutions of the Einstein field equations, that describe the spacetime exterior of rotating neutron stars, for arbitrary rotation. The matching procedure is performed by equating the first four multipole moments of the analytical solution to the multipole moments of the numerical one. We then argue that in order to check the effectiveness of the matching of the analytical with the numerical solution we should compare the metric components, the radius of the innermost stable circular orbit (R{sub ISCO}), the rotation frequency and the epicyclic frequencies {Omega}{sub {rho}}, {Omega}{sub z}. Finally we present some results of the comparison.

Numerical simulation of spin motion in circular accelerators using spinor formulation

International Nuclear Information System (INIS)

Nghiem, P.; Tkatchenko, A.

1992-07-01

A simple method is presented based on spinor algebra formalism for tracking the spin motion in circular accelerators. Using an analytical expression of the one-turn transformation matrix including the effects of perturbating fields or of siberian snakes, a simple and very fast numerical code has been written for studying spin motion in various circumstances. In particular, effects of synchrotron oscillations on final polarization after one isolated resonance crossing are simulated. Results of these calculations agree very well with those which have been obtained previously from analytical approaches or from other numerical-simulation programs. (author) 8 refs.; 14 figs

Numerical solution of distributed order fractional differential equations

Science.gov (United States)

Katsikadelis, John T.

2014-02-01

In this paper a method for the numerical solution of distributed order FDEs (fractional differential equations) of a general form is presented. The method applies to both linear and nonlinear equations. The Caputo type fractional derivative is employed. The distributed order FDE is approximated with a multi-term FDE, which is then solved by adjusting appropriately the numerical method developed for multi-term FDEs by Katsikadelis. Several example equations are solved and the response of mechanical systems described by such equations is studied. The convergence and the accuracy of the method for linear and nonlinear equations are demonstrated through well corroborated numerical results.

Numerical solution of ordinary differential equations. For classical, relativistic and nano systems

International Nuclear Information System (INIS)

Greenspan, D.

2006-01-01

An up-to-date survey on numerical solutions with theory, intuition and applications. Ordinary differential equations (ODE) play a significant role in mathematics, physics and engineering sciences, and thus are part of relevant college and university courses. Many problems, however, both traditional and modern, do not possess exact solutions, and must be treated numerically. Usually this is done with software packages, but for this to be efficient requires a sound understanding of the mathematics involved. This work meets the need for an affordable textbook that helps in understanding numerical solutions of ODE. Carefully structured by an experienced textbook author, it provides a survey of ODE for various applications, both classical and modern, including such special applications as relativistic and nano systems. The examples are carefully explained and compiled into an algorithm, each of which is presented generically, independent of a specific programming language, while each chapter is rounded off with exercises. The text meets the demands of MA200 courses and of the newly created Numerical Solution of Differential Equations courses, making it ideal for both students and lecturers in physics, mathematics, mechanical engineering, electrical engineering, as well as for physicists, mathematicians, engineers, and electrical engineers. From the Contents - Euler's Method - Runge-Kutta Methods - The Method of Taylor Expansions - Large Second Order Systems with Application to Nano Systems - Completely Conservative, Covariant Numerical Methodology - Instability - Numerical Solution of Tridiagonal Linear Algebraic Systems and Related Nonlinear Systems - Approximate Solution of Boundary Value Problems - Special Relativistic Motion - Special Topics - Appendix: Basic Matrix Operations - Bibliography. (orig.) (orig.)

Numerical solutions of the Vlasov equation

International Nuclear Information System (INIS)

Satofuka, Nobuyuki; Morinishi, Koji; Nishida, Hidetoshi

1985-01-01

A numerical procedure is derived for the solutions of the one- and two-dimensional Vlasov-Poisson system equations. This numerical procedure consists of the phase space discretization and the integration of the resulting set of ordinary differential equations. In the phase space discretization, derivatives with respect to the phase space variable are approximated by a weighted sum of the values of the distribution function at properly chosen neighboring points. Then, the resulting set of ordinary differential equations is solved by using an appropriate time integration scheme. The results for linear Landau damping, nonlinear Landau damping and counter-streaming plasmas are investigated and compared with those of the splitting scheme. The proposed method is found to be very accurate and efficient. (author)

Numerical Nudging: Using an Accelerating Score to Enhance Performance.

Science.gov (United States)

Shen, Luxi; Hsee, Christopher K

2017-08-01

People often encounter inherently meaningless numbers, such as scores in health apps or video games, that increase as they take actions. This research explored how the pattern of change in such numbers influences performance. We found that the key factor is acceleration-namely, whether the number increases at an increasing velocity. Six experiments in both the lab and the field showed that people performed better on an ongoing task if they were presented with a number that increased at an increasing velocity than if they were not presented with such a number or if they were presented with a number that increased at a decreasing or constant velocity. This acceleration effect occurred regardless of the absolute magnitude or the absolute velocity of the number, and even when the number was not tied to any specific rewards. This research shows the potential of numerical nudging-using inherently meaningless numbers to strategically alter behaviors-and is especially relevant in the present age of digital devices.

Exact and numerical solutions of generalized Drinfeld-Sokolov equations

International Nuclear Information System (INIS)

Ugurlu, Yavuz; Kaya, Dogan

2008-01-01

In this Letter, we consider a system of generalized Drinfeld-Sokolov (gDS) equations which models one-dimensional nonlinear wave processes in two-component media. We find some exact solutions of gDS by using tanh function method and we also obtain a numerical solution by using the Adomian's Decomposition Method (ADM)

Exact and numerical solutions of generalized Drinfeld-Sokolov equations

Energy Technology Data Exchange (ETDEWEB)

Ugurlu, Yavuz [Firat University, Department of Mathematics, 23119 Elazig (Turkey); Kaya, Dogan [Firat University, Department of Mathematics, 23119 Elazig (Turkey)], E-mail: dkaya36@yahoo.com

2008-04-14

In this Letter, we consider a system of generalized Drinfeld-Sokolov (gDS) equations which models one-dimensional nonlinear wave processes in two-component media. We find some exact solutions of gDS by using tanh function method and we also obtain a numerical solution by using the Adomian's Decomposition Method (ADM)

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.

Solution of Milne problem by Laplace transformation with numerical inversion

International Nuclear Information System (INIS)

Campos Velho, H.F. de.

1987-12-01

The Milne problem for monoenergetic neutrons, by Laplace Transform of the neutron transport integral equation with numerical inversion of the transformed solution by gaussian quadrature, using the fatorization of the dispersion function. The resulted is solved compared its analitical solution. (author) [pt

The response matrix discrete ordinates solution to the 1D radiative transfer equation

International Nuclear Information System (INIS)

Ganapol, Barry D.

2015-01-01

The discrete ordinates method (DOM) of solution to the 1D radiative transfer equation has been an effective method of solution for nearly 70 years. During that time, the method has experienced numerous improvements as numerical and computational techniques have become more powerful and efficient. Here, we again consider the analytical solution to the discrete radiative transfer equation in a homogeneous medium by proposing a new, and consistent, form of solution that improves upon previous forms. Aided by a Wynn-epsilon convergence acceleration, its numerical evaluation can achieve extreme precision as demonstrated by comparison with published benchmarks. Finally, we readily extend the solution to a heterogeneous medium through the star product formulation producing a novel benchmark for closed form Henyey–Greenstein scattering as an example. - Highlights: • Presents a new solution to the RTE called the response matrix DOM (RM/DOM). • Solution representations avoid the instability common in exponential solutions. • Explicit form in terms of matrix hyperbolic functions. • Extreme accuracy through Wynn-epsilon acceleration checked by published benchmarks. • Provides a more transparent numerical evaluation than found previously

Numerical investigation of closed-loop control for Hall accelerators

International Nuclear Information System (INIS)

Barral, S.; Miedzik, J.

2011-01-01

Low frequency discharge current oscillations in Hall accelerators are conventionally damped with external inductor-capacitor (LC) or resistor-inductor-capacitor (RLC) networks. The role of such network in the stabilization of the plasma discharge is investigated with a numerical model and the potential advantages of proportional-integral-derivative (PID) closed-loop control over RLC networks are subsequently assessed using either discharge voltage or magnetic field modulation. Simulations confirm the reduction of current oscillations in the presence of a RLC network, but suggest that PID control could ensure nearly oscillation-free operation with little sensitivity toward the PID settings.

GPU accelerated flow solver for direct numerical simulation of turbulent flows

Energy Technology Data Exchange (ETDEWEB)

Salvadore, Francesco [CASPUR – via dei Tizii 6/b, 00185 Rome (Italy); Bernardini, Matteo, E-mail: matteo.bernardini@uniroma1.it [Department of Mechanical and Aerospace Engineering, University of Rome ‘La Sapienza’ – via Eudossiana 18, 00184 Rome (Italy); Botti, Michela [CASPUR – via dei Tizii 6/b, 00185 Rome (Italy)

2013-02-15

Graphical processing units (GPUs), characterized by significant computing performance, are nowadays very appealing for the solution of computationally demanding tasks in a wide variety of scientific applications. However, to run on GPUs, existing codes need to be ported and optimized, a procedure which is not yet standardized and may require non trivial efforts, even to high-performance computing specialists. In the present paper we accurately describe the porting to CUDA (Compute Unified Device Architecture) of a finite-difference compressible Navier–Stokes solver, suitable for direct numerical simulation (DNS) of turbulent flows. Porting and validation processes are illustrated in detail, with emphasis on computational strategies and techniques that can be applied to overcome typical bottlenecks arising from the porting of common computational fluid dynamics solvers. We demonstrate that a careful optimization work is crucial to get the highest performance from GPU accelerators. The results show that the overall speedup of one NVIDIA Tesla S2070 GPU is approximately 22 compared with one AMD Opteron 2352 Barcelona chip and 11 compared with one Intel Xeon X5650 Westmere core. The potential of GPU devices in the simulation of unsteady three-dimensional turbulent flows is proved by performing a DNS of a spatially evolving compressible mixing layer.

Numerical solution of large sparse linear systems

International Nuclear Information System (INIS)

Meurant, Gerard; Golub, Gene.

1982-02-01

This note is based on one of the lectures given at the 1980 CEA-EDF-INRIA Numerical Analysis Summer School whose aim is the study of large sparse linear systems. The main topics are solving least squares problems by orthogonal transformation, fast Poisson solvers and solution of sparse linear system by iterative methods with a special emphasis on preconditioned conjuguate gradient method [fr

On mesh refinement and accuracy of numerical solutions

NARCIS (Netherlands)

Zhou, Hong; Peters, Maria; van Oosterom, Adriaan

1993-01-01

This paper investigates mesh refinement and its relation with the accuracy of the boundary element method (BEM) and the finite element method (FEM). TO this end an isotropic homogeneous spherical volume conductor, for which the analytical solution is available, wag used. The numerical results

The numerical solution of boundary value problems over an infinite domain

International Nuclear Information System (INIS)

Shepherd, M.; Skinner, R.

1976-01-01

A method is presented for the numerical solution of boundary value problems over infinite domains. An example that illustrates also the strength and accuracy of a numerical procedure for calculating Green's functions is described in detail

Numerical Solution of Inviscid Compressible Steady Flows around the RAE 2822 Airfoil

Science.gov (United States)

Kryštůfek, P.; Kozel, K.

2015-05-01

The article presents results of a numerical solution of subsonic, transonic and supersonic flows described by the system of Euler equations in 2D compressible flows around the RAE 2822 airfoil. Authors used FVM multistage Runge-Kutta method to numerically solve the flows around the RAE 2822 airfoil. The results are compared with the solution using the software Ansys Fluent 15.0.7.

Numerical solution of second-order stochastic differential equations with Gaussian random parameters

Directory of Open Access Journals (Sweden)

Rahman Farnoosh

2014-07-01

Full Text Available In this paper, we present the numerical solution of ordinary differential equations (or SDEs, from each orderespecially second-order with time-varying and Gaussian random coefficients. We indicate a complete analysisfor second-order equations in specially case of scalar linear second-order equations (damped harmonicoscillators with additive or multiplicative noises. Making stochastic differential equations system from thisequation, it could be approximated or solved numerically by different numerical methods. In the case oflinear stochastic differential equations system by Computing fundamental matrix of this system, it could becalculated based on the exact solution of this system. Finally, this stochastic equation is solved by numericallymethod like E.M. and Milstein. Also its Asymptotic stability and statistical concepts like expectationand variance of solutions are discussed.

QUARTZ: a numerical simulation of an asymmetric electrostatic accelerator

International Nuclear Information System (INIS)

Wooten, J.W.; Drooks, L.J.; McCollough, D.H.; McGaffey, R.W.; Whealton, J.H.

1979-01-01

The physics and numerical aspects of the development of the computer code QUARTZ are given. This code includes the (1) use of a finite element code to obtain solutions of Poisson's equation in an asymmetric, three-dimensional volume; (2) inclusion of space charge neutralization by electrons; and (3) inclusion of ion space charge through an iterative procedure

Numerical investigation on complex target geometries in the context of laser-accelerated proton beams

Energy Technology Data Exchange (ETDEWEB)

Deppert, O.; Harres, K.; Busold, S.; Schaumann, G.; Roth, M. [IKP, Technische Universitaet Darmstadt (Germany); Brabetz, C. [IAP, Goethe Universitaet Frankfurt (Germany); Schollmeier, M.; Geissel, M. [Sandia National Laboratories, NM (United States); Bagnoud, V. [GSI - Helmholtzzentrum fuer Schwerionenforschung, Darmstadt (Germany); Neely, D. [Rutherford Appleton Laboratory (United Kingdom); McKenna, P. [University of Strathclyde (United Kingdom)

2012-07-01

The irradiation of thin metal foils by an ultra-intense laser pulse leads to the generation of a highly laminar, intense proton beam accelerated from the target rear side by a mechanism called TNSA. This acceleration mechanism strongly depends on the geometry of the target. The acceleration originates from the formation of a Gaussian-like electron sheath leading to an electric field in the order of TV/m. This sheath field-ionizes the target rear side and is able to accelerate protons from a hydrogen contamination layer. The Gaussian-like sheath adds an energy dependent divergence to the spatial proton beam profile. For future applications it is essential to reduce the divergence already from the source of the acceleration process. Therefore different target geometries were studied numerically with the help of Particle-In-Cell (PIC) simulations. Both, the influence of the target geometry as well as the influence of the laser beam profile onto the proton trajectories are discussed. Furthermore, the first experimental results of a dedicated target geometry for laser-ion acceleration are presented.

Acceleration of criticality analysis solution convergence by matrix eigenvector for a system with weak neutron interaction

Energy Technology Data Exchange (ETDEWEB)

Nomura, Yasushi; Takada, Tomoyuki; Kuroishi, Takeshi [Japan Atomic Energy Research Inst., Tokai, Ibaraki (Japan). Tokai Research Establishment; Kadotani, Hiroyuki [Shizuoka Sangyo Univ., Iwata, Shizuoka (Japan)

2003-03-01

In the case of Monte Carlo calculation to obtain a neutron multiplication factor for a system of weak neutron interaction, there might be some problems concerning convergence of the solution. Concerning this difficulty in the computer code calculations, theoretical derivation was made from the general neutron transport equation and consideration was given for acceleration of solution convergence by using the matrix eigenvector in this report. Accordingly, matrix eigenvector calculation scheme was incorporated together with procedure to make acceleration of convergence into the continuous energy Monte Carlo code MCNP. Furthermore, effectiveness of acceleration of solution convergence by matrix eigenvector was ascertained with the results obtained by applying to the two OECD/NEA criticality analysis benchmark problems. (author)

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

Numerical solution of the resistive magnetohydrodynamic boundary-layer equations

International Nuclear Information System (INIS)

Glasser, A.H.; Jardin, S.C.; Tesauro, G.

1983-10-01

Three different techniques are presented for numerical solution of the equations governing the boundary layer of resistive magnetohydrodynamic tearing and interchange instabilities in toroidal geometry. Excellent agreement among these methods and with analytical results provides confidence in the correctness of the results. Solutions obtained in regimes where analytical medthods fail indicate a new scaling for the tearing mode as well as the existence of a new regime of stability

Drag of a growing bubble at rectilinear accelerated ascension in pure liquids and binary solutions

Directory of Open Access Journals (Sweden)

Ašković Radomir

2003-01-01

Full Text Available The problem of predicting the drag coefficient of a growing bubble at rectilinear accelerated ascension in uniformly super­heated pure liquids and in binary solutions with a non-volatile solute at large Reynolds and Peclet numbers is discussed. In the case of pure liquids, the general solution for the drag coefficient of an accelerated growing bubble from its inception at the critical radius and through the surface-tension-, inertia-, and heat-diffusion-controlled regimes is established, as well as some necessary adaptations in the case of binary solutions with a non-volatile solute. Two particular limiting regimes in the case of pure liquids, inertia-controlled and heat-diffusion-controlled regimes, respectively, are analyzed in details, with satisfactory results. .

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.)

Numerical study of traveling-wave solutions for the Camassa-Holm equation

International Nuclear Information System (INIS)

Kalisch, Henrik; Lenells, Jonatan

2005-01-01

We explore numerically different aspects of periodic traveling-wave solutions of the Camassa-Holm equation. In particular, the time evolution of some recently found new traveling-wave solutions and the interaction of peaked and cusped waves is studied

Numerical solutions of a three-point boundary value problem with an ...

African Journals Online (AJOL)

Numerical solutions of a three-point boundary value problem with an integral condition for a third-order partial differential equation by using Laplace transform method Solutions numeriques d'un probleme pour une classe d'equations differentielles d'ordr.

Numerical solution of the polymer system

Energy Technology Data Exchange (ETDEWEB)

Haugse, V.; Karlsen, K.H.; Lie, K.-A.; Natvig, J.R.

1999-05-01

The paper describes the application of front tracking to the polymer system, an example of a nonstrictly hyperbolic system. Front tracking computes piecewise constant approximations based on approximate Remain solutions and exact tracking of waves. It is well known that the front tracking method may introduce a blow-up of the initial total variation for initial data along the curve where the two eigenvalues of the hyperbolic system are identical. It is demonstrated by numerical examples that the method converges to the correct solution after a finite time that decreases with the discretization parameter. For multidimensional problems, front tracking is combined with dimensional splitting and numerical experiments indicate that large splitting steps can be used without loss of accuracy. Typical CFL numbers are in the range of 10 to 20 and comparisons with the Riemann free, high-resolution method confirm the high efficiency of front tracking. The polymer system, coupled with an elliptic pressure equation, models two-phase, tree-component polymer flooding in an oil reservoir. Two examples are presented where this model is solved by a sequential time stepping procedure. Because of the approximate Riemann solver, the method is non-conservative and CFL members must be chosen only moderately larger than unity to avoid substantial material balance errors generated in near-well regions after water breakthrough. Moreover, it is demonstrated that dimensional splitting may introduce severe grid orientation effects for unstable displacements that are accentuated for decreasing discretization parameters. 9 figs., 2 tabs., 26 refs.

On the numerical evaluation of algebro-geometric solutions to integrable equations

International Nuclear Information System (INIS)

Kalla, C; Klein, C

2012-01-01

Physically meaningful periodic solutions to certain integrable partial differential equations are given in terms of multi-dimensional theta functions associated with real Riemann surfaces. Typical analytical problems in the numerical evaluation of these solutions are studied. In the case of hyperelliptic surfaces efficient algorithms exist even for almost degenerate surfaces. This allows the numerical study of solitonic limits. For general real Riemann surfaces, the choice of a homology basis adapted to the anti-holomorphic involution is important for a convenient formulation of the solutions and smoothness conditions. Since existing algorithms for algebraic curves produce a homology basis not related to automorphisms of the curve, we study symplectic transformations to an adapted basis and give explicit formulae for M-curves. As examples we discuss solutions of the Davey–Stewartson and the multi-component nonlinear Schrödinger equations

Numerical Solution of Differential Algebraic Equations and Applications

DEFF Research Database (Denmark)

Thomsen, Per Grove

2005-01-01

These lecture notes have been written as part of a special course on the numerical solution of Differential Algebraic Equations and applications . The course was held at IMM in the spring of 2005. The authors of the different chapters have all taken part in the course and the chapters are written...

Numerical solution of field theories using random walks

International Nuclear Information System (INIS)

Barnes, T.; Daniell, G.J.

1985-01-01

We show how random walks in function space can be employed to evaluate field theoretic vacuum expectation values numerically. Specific applications which we study are the two-point function, mass gap, magnetization and classical solutions. This technique offers the promise of faster calculations using less computer memory than current methods. (orig.)

Numerical double layer solutions with ionization

International Nuclear Information System (INIS)

Andersson, D.; Soerensen, J.

1982-08-01

Maxwell's equation div D = ro in one dimension is solved numerically, taking ionization into account. Time independent anode sheath and double layer solutions are obtained. By varying voltage, neutral gas pressure, temperature of the trapped ions on the cathode side and density and temperature of the trapped electrones on the anode side, diagrams are constructed that show permissible combinations of these parameters. Results from a recent experiment form a subset. Distribution functions, the Langmuir condition, some scaling laws and a possible application to the lower ionosphere are discussed. (Authors)

Numerical solution of dynamic equilibrium models under Poisson uncertainty

DEFF Research Database (Denmark)

Posch, Olaf; Trimborn, Timo

2013-01-01

We propose a simple and powerful numerical algorithm to compute the transition process in continuous-time dynamic equilibrium models with rare events. In this paper we transform the dynamic system of stochastic differential equations into a system of functional differential equations of the retar...... solution to Lucas' endogenous growth model under Poisson uncertainty are used to compute the exact numerical error. We show how (potential) catastrophic events such as rare natural disasters substantially affect the economic decisions of households....

Case studies in the numerical solution of oscillatory integrals

International Nuclear Information System (INIS)

Adam, G.

1992-06-01

A numerical solution of a number of 53,249 test integrals belonging to nine parametric classes was attempted by two computer codes: EAQWOM (Adam and Nobile, IMA Journ. Numer. Anal. (1991) 11, 271-296) and DO1ANF (Mark 13, 1988) from the NAG library software. For the considered test integrals, EAQWOM was found to be superior to DO1ANF as it concerns robustness, reliability, and friendly user information in case of failure. (author). 9 refs, 3 tabs

Solutions manual to accompany An introduction to numerical methods and analysis

CERN Document Server

Epperson, James F

2014-01-01

A solutions manual to accompany An Introduction to Numerical Methods and Analysis, Second Edition An Introduction to Numerical Methods and Analysis, Second Edition reflects the latest trends in the field, includes new material and revised exercises, and offers a unique emphasis on applications. The author clearly explains how to both construct and evaluate approximations for accuracy and performance, which are key skills in a variety of fields. A wide range of higher-level methods and solutions, including new topics such as the roots of polynomials, sp

Numerical Solutions for Convection-Diffusion Equation through Non-Polynomial Spline

Directory of Open Access Journals (Sweden)

Ravi Kanth A.S.V.

2016-01-01

Full Text Available In this paper, numerical solutions for convection-diffusion equation via non-polynomial splines are studied. We purpose an implicit method based on non-polynomial spline functions for solving the convection-diffusion equation. The method is proven to be unconditionally stable by using Von Neumann technique. Numerical results are illustrated to demonstrate the efficiency and stability of the purposed method.

Numerical solution of a reaction-diffusion equation

International Nuclear Information System (INIS)

Moyano, Edgardo A.; Scarpettini, Alberto F.

2000-01-01

The purpose of the present work to continue the observations and the numerical experiences on a reaction-diffusion model, that is a simplified form of the neutronic flux equation. The model is parabolic, nonlinear, with Dirichlet boundary conditions. The purpose is to approximate non trivial solutions, asymptotically stables for t → ∞, that is solutions that tend to the elliptic problem, in the Lyapunov sense. It belongs to the so-called reaction-diffusion equations of semi linear kind, that is, linear equations in the heat operator and they have a nonlinear reaction function, in this case f (u, a, b) = u (a - b u), being u concentration, a and b parameters. The study of the incidence of these parameters take an interest to the neutronic flux physics. So that we search non trivial, positive and bounded solutions. The used algorithm is based on the concept of monotone and ordered sequences, and on the existence theorem of Amann and Sattinger. (author)

An Accelerating Solution for N-Body MOND Simulation with FPGA-SoC

Directory of Open Access Journals (Sweden)

Bo Peng

2016-01-01

Full Text Available As a modified-gravity proposal to handle the dark matter problem on galactic scales, Modified Newtonian Dynamics (MOND has shown a great success. However, the N-body MOND simulation is quite challenged by its computation complexity, which appeals to acceleration of the simulation calculation. In this paper, we present a highly integrated accelerating solution for N-body MOND simulations. By using the FPGA-SoC, which integrates both FPGA and SoC (system on chip in one chip, our solution exhibits potentials for better performance, higher integration, and lower power consumption. To handle the calculation bottleneck of potential summation, on one hand, we develop a strategy to simplify the pipeline, in which the square calculation task is conducted by the DSP48E1 of Xilinx 7 series FPGAs, so as to reduce the logic resource utilization of each pipeline; on the other hand, advantages of particle-mesh scheme are taken to overcome the bottleneck on bandwidth. Our experiment results show that 2 more pipelines can be integrated in Zynq-7020 FPGA-SoC with the simplified pipeline, and the bandwidth requirement is reduced significantly. Furthermore, our accelerating solution has a full range of advantages over different processors. Compared with GPU, our work is about 10 times better in performance per watt and 50% better in performance per cost.

Numerical Solution of Heun Equation Via Linear Stochastic Differential Equation

Directory of Open Access Journals (Sweden)

Hamidreza Rezazadeh

2014-05-01

Full Text Available In this paper, we intend to solve special kind of ordinary differential equations which is called Heun equations, by converting to a corresponding stochastic differential equation(S.D.E.. So, we construct a stochastic linear equation system from this equation which its solution is based on computing fundamental matrix of this system and then, this S.D.E. is solved by numerically methods. Moreover, its asymptotic stability and statistical concepts like expectation and variance of solutions are discussed. Finally, the attained solutions of these S.D.E.s compared with exact solution of corresponding differential equations.

The set of prime numbers: Multiscale analysis and numeric accelerators

International Nuclear Information System (INIS)

Iovane, Gerardo

2009-01-01

In this work, we show that the prime numbers follow a multiscale distribution. Indeed they can be classified thanks to tree structures, which are expressed in terms of two maximal subsets of N and using multilayer selection rules, acting on these sets of prime candidates. Consequently, the prime numbers follow a specific deterministic rules. Indeed, a numeric accelerator for generating primes can be realized in terms of the above mentioned specific rules. From the comparison with the Fibonacci numbers a beautiful harmony comes in terms of the Golden Mean which is relevant to high energy physics and E-Infinity theory too.

2nd International Workshop on the Numerical Solution of Markov Chains

CERN Document Server

1995-01-01

Computations with Markov Chains presents the edited and reviewed proceedings of the Second International Workshop on the Numerical Solution of Markov Chains, held January 16--18, 1995, in Raleigh, North Carolina. New developments of particular interest include recent work on stability and conditioning, Krylov subspace-based methods for transient solutions, quadratic convergent procedures for matrix geometric problems, further analysis of the GTH algorithm, the arrival of stochastic automata networks at the forefront of modelling stratagems, and more. An authoritative overview of the field for applied probabilists, numerical analysts and systems modelers, including computer scientists and engineers.

Numerical Solution of Compressible Steady Flows around the RAE 2822 Airfoil

Science.gov (United States)

Kryštůfek, P.; Kozel, K.

2014-03-01

The article presents results of a numerical solution of subsonic, transonic and supersonic flows described by the system of Navier-Stokes equations in 2D laminar compressible flows around the RAE 2822 airfoil. Authors used FVM multistage Runge-Kutta method to numerically solve the flows around the RAE 2822 airfoil.

Numerical Solution of Compressible Steady Flows around the NACA 0012 Airfoil

Directory of Open Access Journals (Sweden)

Kozel K

2013-04-01

Full Text Available The article presents results of a numerical solution of subsonic and transonic flows described by the system of Navier-Stokes equations in 2D laminar compressible flows around the NACA 0012 airfoil. Authors used Runge-Kutta method to numerically solve the flows around the NACA 0012 airfoil.

Numerical solutions of diffusive logistic equation

International Nuclear Information System (INIS)

Afrouzi, G.A.; Khademloo, S.

2007-01-01

In this paper we investigate numerically positive solutions of a superlinear Elliptic equation on bounded domains. The study of Diffusive logistic equation continues to be an active field of research. The subject has important applications to population migration as well as many other branches of science and engineering. In this paper the 'finite difference scheme' will be developed and compared for solving the one- and three-dimensional Diffusive logistic equation. The basis of the analysis of the finite difference equations considered here is the modified equivalent partial differential equation approach, developed from many authors these years

Numerical Solution of Compressible Steady Flows around the RAE 2822 Airfoil

Directory of Open Access Journals (Sweden)

Kryštůfek P.

2014-03-01

Full Text Available The article presents results of a numerical solution of subsonic, transonic and supersonic flows described by the system of Navier-Stokes equations in 2D laminar compressible flows around the RAE 2822 airfoil. Authors used FVM multistage Runge-Kutta method to numerically solve the flows around the RAE 2822 airfoil.

A numerical guide to the solution of the bidomain equations of cardiac electrophysiology

KAUST Repository

Pathmanathan, Pras

2010-06-01

Simulation of cardiac electrical activity using the bidomain equations can be a massively computationally demanding problem. This study provides a comprehensive guide to numerical bidomain modelling. Each component of bidomain simulations-discretisation, ODE-solution, linear system solution, and parallelisation-is discussed, and previously-used methods are reviewed, new methods are proposed, and issues which cause particular difficulty are highlighted. Particular attention is paid to the choice of stimulus currents, compatibility conditions for the equations, the solution of singular linear systems, and convergence of the numerical scheme. © 2010 Elsevier Ltd.

A numerical guide to the solution of the bidomain equations of cardiac electrophysiology

KAUST Repository

Pathmanathan, Pras; Bernabeu, Miguel O.; Bordas, Rafel; Cooper, Jonathan; Garny, Alan; Pitt-Francis, Joe M.; Whiteley, Jonathan P.; Gavaghan, David J.

2010-01-01

Simulation of cardiac electrical activity using the bidomain equations can be a massively computationally demanding problem. This study provides a comprehensive guide to numerical bidomain modelling. Each component of bidomain simulations-discretisation, ODE-solution, linear system solution, and parallelisation-is discussed, and previously-used methods are reviewed, new methods are proposed, and issues which cause particular difficulty are highlighted. Particular attention is paid to the choice of stimulus currents, compatibility conditions for the equations, the solution of singular linear systems, and convergence of the numerical scheme. © 2010 Elsevier Ltd.

LED-based Photometric Stereo: Modeling, Calibration and Numerical Solutions

DEFF Research Database (Denmark)

Quéau, Yvain; Durix, Bastien; Wu, Tao

2018-01-01

We conduct a thorough study of photometric stereo under nearby point light source illumination, from modeling to numerical solution, through calibration. In the classical formulation of photometric stereo, the luminous fluxes are assumed to be directional, which is very difficult to achieve in pr...

Accelerated corrosion of stainless steel in thiocyanate-containing solutions

Energy Technology Data Exchange (ETDEWEB)

Pistorius, P Chris; Li, Wen

2012-09-19

It is known that reduced sulfur compounds (such as thiocyanate and thiosulfate) can accelerate active corrosion of austenitic stainless steel in acid solutions, but before we started this project the mechanism of acceleration was largely unclear. This work combined electrochemical measurements and analysis using scanning electron microscopy (SEM) and X-ray photo-electron spectroscopy (XPS), which provided a comprehensive understanding of the catalytic effect of reduced sulfur species on the active corrosion of stainless steel. Both the behavior of the pure elements and the steel were studied and the work focused on the interaction between the pure elements of the steel, which is the least understood area. Upon completion of this work, several aspects are now much clearer. The main results from this work can be summarized as follows: The presence of low concentrations (around 0.1 mM) of thiocyanate or tetrathionate in dilute sulfuric acid greatly accelerates the anodic dissolution of chromium and nickel, but has an even stronger effect on stainless steels (iron-chromium-nickel alloys). Electrochemical measurements and surface analyses are in agreement with the suggestion that accelerated dissolution really results from suppressed passivation. Even well below the passivation potential, the electrochemical signature of passivation is evident in the electrode impedance; the electrode impedance shows clearly that this pre-passivation is suppressed in the presence of thiocyanate. For the stainless steels, remarkable changes in the morphology of the corroded metal surface and in the surface concentration of chromium support the suggestion that pre-passivation of stainless steels is suppressed because dissolution of chromium is accelerated. Surface analysis confirmed that adsorbed sulfur / sulfide forms on the metal surfaces upon exposure to solutions containing thiocyanate or thiosulfate. For pure nickel, and steels containing nickel (and residual copper), bulk sulfide

Mining the multigroup-discrete ordinates algorithm for high quality solutions

International Nuclear Information System (INIS)

Ganapol, B.D.; Kornreich, D.E.

2005-01-01

A novel approach to the numerical solution of the neutron transport equation via the discrete ordinates (SN) method is presented. The new technique is referred to as 'mining' low order (SN) numerical solutions to obtain high order accuracy. The new numerical method, called the Multigroup Converged SN (MGCSN) algorithm, is a combination of several sequence accelerators: Romberg and Wynn-epsilon. The extreme accuracy obtained by the method is demonstrated through self consistency and comparison to the independent semi-analytical benchmark BLUE. (authors)

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

Performance analysis of numeric solutions applied to biokinetics of radionuclides

International Nuclear Information System (INIS)

Mingatos, Danielle dos Santos; Bevilacqua, Joyce da Silva

2013-01-01

Biokinetics models for radionuclides applied to dosimetry problems are constantly reviewed by ICRP. The radionuclide trajectory could be represented by compartmental models, assuming constant transfer rates between compartments. A better understanding of physiological or biochemical phenomena, improve the comprehension of radionuclide behavior in the human body and, in general, more complex compartmental models are proposed, increasing the difficulty of obtaining the analytical solution for the system of first order differential equations. Even with constant transfer rates numerical solutions must be carefully implemented because of almost singular characteristic of the matrix of coefficients. In this work we compare numerical methods with different strategies for ICRP-78 models for Thorium-228 and Uranium-234. The impact of uncertainty in the parameters of the equations is also estimated for local and global truncation errors. (author)

Time-dependent diffusive acceleration of test particles at shocks

Energy Technology Data Exchange (ETDEWEB)

Drury, L.O' C. (Dublin Inst. for Advanced Studies (Ireland))

1991-07-15

The acceleration of test particles at a steady plane non-relativistic shock is considered. Analytic expressions are found for the mean and the variance of the acceleration time distribution in the case where the diffusion coefficient has an arbitrary dependence on position and momentum. These expressions are used as the basis for an approximation scheme which is shown, by comparison with numerical solutions, to give an excellent representation of the time-dependent spectrum. (author).

Time-dependent diffusive acceleration of test particles at shocks

International Nuclear Information System (INIS)

Drury, L.O'C.

1991-01-01

The acceleration of test particles at a steady plane non-relativistic shock is considered. Analytic expressions are found for the mean and the variance of the acceleration time distribution in the case where the diffusion coefficient has an arbitrary dependence on position and momentum. These expressions are used as the basis for an approximation scheme which is shown, by comparison with numerical solutions, to give an excellent representation of the time-dependent spectrum. (author)

Acceleration of charged particles by lasers in vacuum

International Nuclear Information System (INIS)

Cicchitelli, L.; Hora, H.; Scheid, W.

1989-01-01

For laser acceleration of electrons (and other charged particles) by lasers to the TeV energy range in vacuum, the scheme of trapping electrons in spatially moving and accelerated intensity gradients or minima of laser fields, the single electron motion in standing wave fields is evaluated in details numerically. Acceleration of the minima results in the acceleration of the electrons as expected from global results of the nonlinear forces. If half-wave length laser pulses propagating in vacuum are used the relativistic exact solutions are derived and evaluated. A disadvantage is the lateral motion requiring a large laser focus. For TeV electron energy, MJ KrF-laser pulses are necessary and the acceleration length is about 10 cm. copyright 1989 American Institute of Physics

Exact and grid-free solutions to the Lighthill-Whitham-Richards traffic flow model with bounded acceleration for a class of fundamental diagrams

KAUST Repository

Qiu, Shanwen

2013-09-01

In this article, we propose a new exact and grid-free numerical scheme for computing solutions associated with an hybrid traffic flow model based on the Lighthill-Whitham-Richards (LWR) partial differential equation, for a class of fundamental diagrams. In this hybrid flow model, the vehicles satisfy the LWR equation whenever possible, and have a constant acceleration otherwise. We first propose a mathematical definition of the solution as a minimization problem. We use this formulation to build a grid-free solution method for this model based on the minimization of component function. We then derive these component functions analytically for triangular fundamental diagrams, which are commonly used to model traffic flow. We also show that the proposed computational method can handle fixed or moving bottlenecks. A toolbox implementation of the resulting algorithm is briefly discussed, and posted at https://dl.dropbox.com/u/1318701/Toolbox.zip. © 2013 Elsevier Ltd.

On the numerical solution of fault trees

International Nuclear Information System (INIS)

Demichela, M.; Piccinini, N.; Ciarambino, I.; Contini, S.

2003-01-01

In this paper an account will be given of the numerical solution of the logic trees directly extracted from the Recursive Operability Analysis. Particular attention will be devoted to the use of the NOT and INH logic gates for correct logical representation of Fault Trees prior to their quantitative resolution. The NOT gate is needed for correct logical representation of events when both non-intervention and correct intervention of a protective system may lead to a Top Event. The INH gate must be used to correctly represent the time link between two events that are both necessary, but must occur in sequence. Some numerical examples will be employed to show both the correct identification of the events entering the INH gates and how use of the AND gate instead of the INH gate leads to overestimation of the probability of occurrence of a Top Event

Analytical and Numerical solutions of a nonlinear alcoholism model via variable-order fractional differential equations

Science.gov (United States)

Gómez-Aguilar, J. F.

2018-03-01

In this paper, we analyze an alcoholism model which involves the impact of Twitter via Liouville-Caputo and Atangana-Baleanu-Caputo fractional derivatives with constant- and variable-order. Two fractional mathematical models are considered, with and without delay. Special solutions using an iterative scheme via Laplace and Sumudu transform were obtained. We studied the uniqueness and existence of the solutions employing the fixed point postulate. The generalized model with variable-order was solved numerically via the Adams method and the Adams-Bashforth-Moulton scheme. Stability and convergence of the numerical solutions were presented in details. Numerical examples of the approximate solutions are provided to show that the numerical methods are computationally efficient. Therefore, by including both the fractional derivatives and finite time delays in the alcoholism model studied, we believe that we have established a more complete and more realistic indicator of alcoholism model and affect the spread of the drinking.

Numerical solutions of ordinary and partial differential equations in the frequency domain

International Nuclear Information System (INIS)

Hazi, G.; Por, G.

1997-01-01

Numerical problems during the noise simulation in a nuclear power plant are discussed. The solutions of ordinary and partial differential equations are studied in the frequency domain. Numerical methods by the transfer function method are applied. It is shown that the correctness of the numerical methods is limited for ordinary differential equations in the frequency domain. To overcome the difficulties, step-size selection is suggested. (author)

The Numerical Solution of an Abelian Ordinary Differential Equation ...

African Journals Online (AJOL)

In this paper we present a relatively new technique call theNew Hybrid of Adomian decomposition method (ADM) for solution of an Abelian Differential equation. The numerical results of the equation have been obtained in terms of convergent series with easily computable component. These methods are applied to solve ...

Diffusion-accelerated solution of the 2-D x-y Sn equations with linear-bilinear nodal differencing

International Nuclear Information System (INIS)

Wareing, T.A.; Walters, W.F.; Morel, J.E.

1994-01-01

Recently a new diffusion-synthetic acceleration scheme was developed for solving the 2-D S n Equations in x-y geometry with bilinear-discontinuous finite element spatial discretization using a bilinear-discontinuous diffusion differencing scheme for the diffusion acceleration equations. This method differs from previous methods in that it is conditional efficient for problems with isotropic or nearly isotropic scattering. We have used the same bilinear-discontinuous diffusion scheme, and associated solution technique, to accelerate the x-y geometry S n equations with linear-bilinear nodal spatial differencing. We find that this leads to an unconditionally efficient solution method for problems with isotropic or nearly isotropic scattering. computational results are given which demonstrate this property

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

Possibilities for beam stripping solutions at a rare isotope accelerator (RIA)

International Nuclear Information System (INIS)

Greife, Uwe; Simmons, Ellen; Erikson, Luke; Jewett, Cybele; Livesay, Jake; Chipps, Kelly

2007-01-01

We investigated the possibilities and problems of beam strippers in the different heavy ion accelerator components of a possible rare isotope accelerator (RIA) facility. We focused on two beam stripping positions in the RIA heavy ion driver where benchmark currents of up to 5 particle μA 238 U were projected at energies of 10.5 MeV/u and 85 MeV/u, respectively. In order to select feasible stripper materials, data from experiments with uranium beams at the Texas A and M cyclotron and the Gesellschaft fuer Schwerionenforschung (GSI) accelerator were evaluated. Based on these results thermal estimates for a possible design were calculated and cooling simulations with commercially available software performed. Additionally, we performed simulations with the GEANT4 code on evaluating the radiation environment for our beam stripping solution at the 85 MeV/u position in the RIA driver

Fast numerical solution of KKR-CPA equations: Testing new algorithms

Energy Technology Data Exchange (ETDEWEB)

Bruno, E.; Florio, G.M.; Ginatempo, B.; Giuliano, E.S. (Universita di Messina (Italy))

1994-04-01

Some numerical methods for the solution of KKR-CPA equations are discussed and tested. New, efficient, computational algorithms are proposed, allowing a remarkable reduction of computing time and a good reliability in evaluating spectral quantities. 16 refs., 7 figs.

A numerical dressing method for the nonlinear superposition of solutions of the KdV equation

International Nuclear Information System (INIS)

Trogdon, Thomas; Deconinck, Bernard

2014-01-01

In this paper we present the unification of two existing numerical methods for the construction of solutions of the Korteweg–de Vries (KdV) equation. The first method is used to solve the Cauchy initial-value problem on the line for rapidly decaying initial data. The second method is used to compute finite-genus solutions of the KdV equation. The combination of these numerical methods allows for the computation of exact solutions that are asymptotically (quasi-)periodic finite-gap solutions and are a nonlinear superposition of dispersive, soliton and (quasi-)periodic solutions in the finite (x, t)-plane. Such solutions are referred to as superposition solutions. We compute these solutions accurately for all values of x and t. (paper)

Numerical computation of gravitational field for general axisymmetric objects

Science.gov (United States)

Fukushima, Toshio

2016-10-01

We developed a numerical method to compute the gravitational field of a general axisymmetric object. The method (I) numerically evaluates a double integral of the ring potential by the split quadrature method using the double exponential rules, and (II) derives the acceleration vector by numerically differentiating the numerically integrated potential by Ridder's algorithm. Numerical comparison with the analytical solutions for a finite uniform spheroid and an infinitely extended object of the Miyamoto-Nagai density distribution confirmed the 13- and 11-digit accuracy of the potential and the acceleration vector computed by the method, respectively. By using the method, we present the gravitational potential contour map and/or the rotation curve of various axisymmetric objects: (I) finite uniform objects covering rhombic spindles and circular toroids, (II) infinitely extended spheroids including Sérsic and Navarro-Frenk-White spheroids, and (III) other axisymmetric objects such as an X/peanut-shaped object like NGC 128, a power-law disc with a central hole like the protoplanetary disc of TW Hya, and a tear-drop-shaped toroid like an axisymmetric equilibrium solution of plasma charge distribution in an International Thermonuclear Experimental Reactor-like tokamak. The method is directly applicable to the electrostatic field and will be easily extended for the magnetostatic field. The FORTRAN 90 programs of the new method and some test results are electronically available.

Dynamics of the east India coastal current. 2. Numerical solutions

Digital Repository Service at National Institute of Oceanography (India)

McCreary, J.P.; Han, W.; Shankar, D.; Shetye, S.R.

A linear, continuously stratified model is used to investigate the dynamics of the East India Coastal Current (EICC). Solutions are found numerically in a basin that resembles the Indian Ocean basin north of 29 degrees S, and they are forced...

Short-term dietary supplementation with fructose accelerates gastric emptying of a fructose but not a glucose solution.

Science.gov (United States)

Yau, Adora M W; McLaughlin, John; Maughan, Ronald J; Gilmore, William; Evans, Gethin H

2014-01-01

Short-term dietary glucose supplementation has been shown to accelerate the gastric emptying rate of both glucose and fructose solutions. The aim of this study was to examine gastric emptying rate responses to monosaccharide ingestion following short-term dietary fructose supplementation. The gastric emptying rate of a fructose solution containing 36 g of fructose and an equicaloric glucose solution containing 39.6 g glucose monohydrate were measured in 10 healthy non-smoking men with and without prior fructose supplementation (water control) using a randomized crossover design. Gastric emptying rate was assessed for a period of 1 h using the [(13)C]breath test with sample collections at baseline and 10-min intervals following drink ingestion. Additionally, appetite ratings of hunger, fullness, and prospective food consumption were recorded at baseline and every 10 min using visual analog scales. Increased dietary fructose ingestion resulted in significantly accelerated half-emptying time of a fructose solution (mean = 48, SD = 6 versus 58, SD = 14 min control; P = 0.037), whereas the emptying of a glucose solution remained unchanged (mean = 85, SD = 31 versus 78, SD = 27 min control; P = 0.273). Time of maximal emptying rate of fructose was also significantly accelerated following increased dietary fructose intake (mean = 33, SD = 6 versus 38, SD = 9 min control; P = 0.042), while it remained unchanged for glucose (mean = 45, SD = 14 versus 44, SD = 14 min control; P = 0.757). No effects of supplementation were observed for appetite measures. Three d of supplementation with 120 g/d of fructose resulted in an acceleration of gastric emptying rate of a fructose solution but not a glucose solution. Copyright © 2014 Elsevier Inc. All rights reserved.

Supplementation of Flow Accelerated Corrosion Prediction Program Using Numerical Analysis Technique

International Nuclear Information System (INIS)

Hwang, Kyeong Mo; Jin, Tae Eun; Park, Won; Oh, Dong Hoon

2010-01-01

Flow-accelerated corrosion (FAC) leads to thinning of steel pipe walls that are exposed to flowing water or wet steam. From experience, it is seen that FAC damage to piping at fossil and nuclear plants can result in outages that require expensive repairs and can affect plant reliability and safety. CHECWORKS have been utilized in domestic nuclear plants as a predictive tool to assist FAC engineers in planning inspections and evaluating the inspection data so that piping failures caused by FAC can be prevented. However, CHECWORKS may be occasionally ignore local susceptible portions when predicting FAC damage in a group of pipelines after constructing a database for all the secondary side piping in nuclear plants. This paper describes the methodologies that can complement CHECWORKS and the verifications of CHECWORKS prediction results using numerical analysis. FAC susceptible locations determined using CHECWORKS for two pipeline groups of a nuclear plant was compared with determined using the numerical-analysis-based FLUENT

Numerical solution of High-kappa model of superconductivity

Energy Technology Data Exchange (ETDEWEB)

Karamikhova, R. [Univ. of Texas, Arlington, TX (United States)

1996-12-31

We present formulation and finite element approximations of High-kappa model of superconductivity which is valid in the high {kappa}, high magnetic field setting and accounts for applied magnetic field and current. Major part of this work deals with steady-state and dynamic computational experiments which illustrate our theoretical results numerically. In our experiments we use Galerkin discretization in space along with Backward-Euler and Crank-Nicolson schemes in time. We show that for moderate values of {kappa}, steady states of the model system, computed using the High-kappa model, are virtually identical with results computed using the full Ginzburg-Landau (G-L) equations. We illustrate numerically optimal rates of convergence in space and time for the L{sup 2} and H{sup 1} norms of the error in the High-kappa solution. Finally, our numerical approximations demonstrate some well-known experimentally observed properties of high-temperature superconductors, such as appearance of vortices, effects of increasing the applied magnetic field and the sample size, and the effect of applied constant current.

Comparing numerical methods for the solutions of the Chen system

International Nuclear Information System (INIS)

Noorani, M.S.M.; Hashim, I.; Ahmad, R.; Bakar, S.A.; Ismail, E.S.; Zakaria, A.M.

2007-01-01

In this paper, the Adomian decomposition method (ADM) is applied to the Chen system which is a three-dimensional system of ODEs with quadratic nonlinearities. The ADM yields an analytical solution in terms of a rapidly convergent infinite power series with easily computable terms. Comparisons between the decomposition solutions and the classical fourth-order Runge-Kutta (RK4) numerical solutions are made. In particular we look at the accuracy of the ADM as the Chen system changes from a non-chaotic system to a chaotic one. To highlight some computational difficulties due to a high Lyapunov exponent, a comparison with the Lorenz system is given

Numerical solutions of multi-order fractional differential equations by Boubaker polynomials

Directory of Open Access Journals (Sweden)

Bolandtalat A.

2016-01-01

Full Text Available In this paper, we have applied a numerical method based on Boubaker polynomials to obtain approximate numerical solutions of multi-order fractional differential equations. We obtain an operational matrix of fractional integration based on Boubaker polynomials. Using this operational matrix, the given problem is converted into a set of algebraic equations. Illustrative examples are are given to demonstrate the efficiency and simplicity of this technique.

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

Second-order numerical methods for multi-term fractional differential equations: Smooth and non-smooth solutions

Science.gov (United States)

Zeng, Fanhai; Zhang, Zhongqiang; Karniadakis, George Em

2017-12-01

Starting with the asymptotic expansion of the error equation of the shifted Gr\\"{u}nwald--Letnikov formula, we derive a new modified weighted shifted Gr\\"{u}nwald--Letnikov (WSGL) formula by introducing appropriate correction terms. We then apply one special case of the modified WSGL formula to solve multi-term fractional ordinary and partial differential equations, and we prove the linear stability and second-order convergence for both smooth and non-smooth solutions. We show theoretically and numerically that numerical solutions up to certain accuracy can be obtained with only a few correction terms. Moreover, the correction terms can be tuned according to the fractional derivative orders without explicitly knowing the analytical solutions. Numerical simulations verify the theoretical results and demonstrate that the new formula leads to better performance compared to other known numerical approximations with similar resolution.

Numerical solution of the full potential equation using a chimera grid approach

Science.gov (United States)

Holst, Terry L.

1995-01-01

A numerical scheme utilizing a chimera zonal grid approach for solving the full potential equation in two spatial dimensions is described. Within each grid zone a fully-implicit approximate factorization scheme is used to advance the solution one interaction. This is followed by the explicit advance of all common zonal grid boundaries using a bilinear interpolation of the velocity potential. The presentation is highlighted with numerical results simulating the flow about a two-dimensional, nonlifting, circular cylinder. For this problem, the flow domain is divided into two parts: an inner portion covered by a polar grid and an outer portion covered by a Cartesian grid. Both incompressible and compressible (transonic) flow solutions are included. Comparisons made with an analytic solution as well as single grid results indicate that the chimera zonal grid approach is a viable technique for solving the full potential equation.

Numerical solution of the ekpyrotic scenario in the moduli space approximation

International Nuclear Information System (INIS)

Soerensen, Torquil MacDonald

2005-01-01

A numerical solution to the equations of motion for the ekpyrotic bulk brane scenario in the moduli space approximation is presented. The visible universe brane has positive tension, and we use a potential that goes to zero exponentially at large distance, and also goes to zero at small distance. In the case considered, no bulk brane, visible brane collision occurs in the solution. This property and the general behavior of the solution is qualitatively the same when the visible brane tension is negative, and for many different parameter choices

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)

Accelerating cosmologies from exponential potentials

International Nuclear Information System (INIS)

Neupane, Ishwaree P.

2003-11-01

It is learnt that exponential potentials of the form V ∼ exp(-2cφ/M p ) arising from the hyperbolic or flux compactification of higher-dimensional theories are of interest for getting short periods of accelerated cosmological expansions. Using a similar potential but derived for the combined case of hyperbolic-flux compactification, we study a four-dimensional flat (or open) FRW cosmologies and give analytic (and numerical) solutions with exponential behavior of scale factors. We show that, for the M-theory motivated potentials, the cosmic acceleration of the universe can be eternal if the spatial curvature of the 4d spacetime is negative, while the acceleration is only transient for a spatially flat universe. We also briefly discuss about the mass of massive Kaluza-Klein modes and the dynamical stabilization of the compact hyperbolic extra dimensions. (author)

special algorithm for the numerical solution of system of initial value ...

African Journals Online (AJOL)

Nwokem et al.

Science World Journal Vol 12(No 4) 2017 ... Over the years, several researchers have considered the collocation method as a way of generating numerical solutions to ... study problems in mathematics, engineering, computer science and.

Numerical Solution and Simulation of Second-Order Parabolic PDEs with Sinc-Galerkin Method Using Maple

Directory of Open Access Journals (Sweden)

Aydin Secer

2013-01-01

Full Text Available An efficient solution algorithm for sinc-Galerkin method has been presented for obtaining numerical solution of PDEs with Dirichlet-type boundary conditions by using Maple Computer Algebra System. The method is based on Whittaker cardinal function and uses approximating basis functions and their appropriate derivatives. In this work, PDEs have been converted to algebraic equation systems with new accurate explicit approximations of inner products without the need to calculate any numeric integrals. The solution of this system of algebraic equations has been reduced to the solution of a matrix equation system via Maple. The accuracy of the solutions has been compared with the exact solutions of the test problem. Computational results indicate that the technique presented in this study is valid for linear partial differential equations with various types of boundary conditions.

Numerical solution of modified differential equations based on symmetry preservation.

Science.gov (United States)

Ozbenli, Ersin; Vedula, Prakash

2017-12-01

In this paper, we propose a method to construct invariant finite-difference schemes for solution of partial differential equations (PDEs) via consideration of modified forms of the underlying PDEs. The invariant schemes, which preserve Lie symmetries, are obtained based on the method of equivariant moving frames. While it is often difficult to construct invariant numerical schemes for PDEs due to complicated symmetry groups associated with cumbersome discrete variable transformations, we note that symmetries associated with more convenient transformations can often be obtained by appropriately modifying the original PDEs. In some cases, modifications to the original PDEs are also found to be useful in order to avoid trivial solutions that might arise from particular selections of moving frames. In our proposed method, modified forms of PDEs can be obtained either by addition of perturbation terms to the original PDEs or through defect correction procedures. These additional terms, whose primary purpose is to enable symmetries with more convenient transformations, are then removed from the system by considering moving frames for which these specific terms go to zero. Further, we explore selection of appropriate moving frames that result in improvement in accuracy of invariant numerical schemes based on modified PDEs. The proposed method is tested using the linear advection equation (in one- and two-dimensions) and the inviscid Burgers' equation. Results obtained for these tests cases indicate that numerical schemes derived from the proposed method perform significantly better than existing schemes not only by virtue of improvement in numerical accuracy but also due to preservation of qualitative properties or symmetries of the underlying differential equations.

Nonlinear reaction-diffusion equations with delay: some theorems, test problems, exact and numerical solutions

Science.gov (United States)

Polyanin, A. D.; Sorokin, V. G.

2017-12-01

The paper deals with nonlinear reaction-diffusion equations with one or several delays. We formulate theorems that allow constructing exact solutions for some classes of these equations, which depend on several arbitrary functions. Examples of application of these theorems for obtaining new exact solutions in elementary functions are provided. We state basic principles of construction, selection, and use of test problems for nonlinear partial differential equations with delay. Some test problems which can be suitable for estimating accuracy of approximate analytical and numerical methods of solving reaction-diffusion equations with delay are presented. Some examples of numerical solutions of nonlinear test problems with delay are considered.

Numerical Solution of Multiterm Fractional Differential Equations Using the Matrix Mittag–Leffler Functions

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Marina Popolizio

2018-01-01

Full Text Available Multiterm fractional differential equations (MTFDEs nowadays represent a widely used tool to model many important processes, particularly for multirate systems. Their numerical solution is then a compelling subject that deserves great attention, not least because of the difficulties to apply general purpose methods for fractional differential equations (FDEs to this case. In this paper, we first transform the MTFDEs into equivalent systems of FDEs, as done by Diethelm and Ford; in this way, the solution can be expressed in terms of Mittag–Leffler (ML functions evaluated at matrix arguments. We then propose to compute it by resorting to the matrix approach proposed by Garrappa and Popolizio. Several numerical tests are presented that clearly show that this matrix approach is very accurate and fast, also in comparison with other numerical methods.

Waves and particles in the Fermi accelerator model. Numerical simulation

International Nuclear Information System (INIS)

Meplan, O.

1996-01-01

This thesis is devoted to a numerical study of the quantum dynamics of the Fermi accelerator which is classically chaotic: it is particle in a one dimensional box with a oscillating wall. First, we study the classical dynamics: we show that the time of impact of the particle with the moving wall and its energy in the wall frame are conjugated variables and that Poincare surface of sections in these variables are more understandable than the usual stroboscopic sections. Then, the quantum dynamics of this systems is studied by the means of two numerical methods. The first one is a generalization of the KKR method in the space-time; it is enough to solve an integral equation on the boundary of a space-time billiard. The second method is faster and is based on successive free propagations and kicks of potential. This allows us to obtain Floquet states which we can on one hand, compare to the classical dynamics with the help of Husimi distributions and on the other hand, study as a function of parameters of the system. This study leads us to nice illustrations of phenomenons such as spatial localizations of a wave packet in a vibrating well or tunnel effects. In the adiabatic situation, we give a formula for quasi-energies which exhibits a phase term independent of states. In this regime, there exist some particular situations where the quasi-energy spectrum presents a total quasi-degeneracy. Then, the wave packet energy can increase significantly. This phenomenon is quite surprising for smooth motion of the wall. The third part deals with the evolution of a classical wave in the Fermi accelerator. Using generalized KKR method, we show a surprising phenomenon: in most of situations (so long as the wall motion is periodic), a wave is localized exponentially in the well and its energy increases in a geometric way. (author). 107 refs., 66 figs., 5 tabs. 2 appends

Numerical solutions of stochastic Lotka-Volterra equations via operational matrices

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F. Hosseini Shekarabi

2016-03-01

Full Text Available In this paper, an efficient and convenient method for numerical solutions of stochastic Lotka-Volterra dynamical system is proposed. Here, we consider block pulse functions and their operational matrices of integration. Illustrative example is included to demonstrate the procedure and accuracy of the operational matrices based on block pulse functions.

Numerical solution for heave of expansive soils

International Nuclear Information System (INIS)

Sadrnezhad, S. A.

1999-01-01

A numerical solution for heave prediction is developed within the context theories for both saturated and unsaturated soil behaviors. Basically, lowering the potential level of compressing on a saturated layer will cause heaving due to water absorption. This water absorption is in an opposite way, similar to water dissipation as what happens during unloading in consolidation process. However, in unsaturated layers any change of the stability of potential energy level will cause the tendency of change in particle interconnection forces. So, any change by either distressing or the variation of moisture ratio will lead to soil heave. In this paper a finite element solution is employed for predicting the heave in saturated soil similar to unloading in consolidation. Also, in the case of unsaturated soil, equivalent soil suction as negative pore water pressures in applied to soil elements as equivalent nodal forces. To show the potential of this method, test results were com pated with those obtained from computations. These comparisons show that the presented method is capable of predicting the heave phenomenon quite well

The numerical solution of ICRF fields in axisymmetric mirrors

International Nuclear Information System (INIS)

Phillips, M.W.; Todd, A.M.M.

1986-01-01

The numerics of a numerical code called GARFIELD (Grumman Aerospace RF fIELD code) designed to calculate the three-dimensional structure of ICRF fields in axisymmetric mirrors is presented. The code solves the electromagnetic wave equation for the electric field using a cold plasma dispersion relation with a small collision term to simulate absorption. The full wave solution including E.B is computed. The fields are Fourier analyzed in the poloidal direction and solved on a grid in the axial and radial directions. A two-dimensional equilibrium can be used as the source of equilibrium data. This allows us to extend previous studies of ICRF wave propagation and absorption in mirrors to include the effect of axial variation of the magnetic field and density. (orig.)

Numerical solutions of the semiclassical Boltzmann ellipsoidal-statistical kinetic model equation

Science.gov (United States)

Yang, Jaw-Yen; Yan, Chin-Yuan; Huang, Juan-Chen; Li, Zhihui

2014-01-01

Computations of rarefied gas dynamical flows governed by the semiclassical Boltzmann ellipsoidal-statistical (ES) kinetic model equation using an accurate numerical method are presented. The semiclassical ES model was derived through the maximum entropy principle and conserves not only the mass, momentum and energy, but also contains additional higher order moments that differ from the standard quantum distributions. A different decoding procedure to obtain the necessary parameters for determining the ES distribution is also devised. The numerical method in phase space combines the discrete-ordinate method in momentum space and the high-resolution shock capturing method in physical space. Numerical solutions of two-dimensional Riemann problems for two configurations covering various degrees of rarefaction are presented and various contours of the quantities unique to this new model are illustrated. When the relaxation time becomes very small, the main flow features a display similar to that of ideal quantum gas dynamics, and the present solutions are found to be consistent with existing calculations for classical gas. The effect of a parameter that permits an adjustable Prandtl number in the flow is also studied. PMID:25104904

Theory and numerical modeling of the accelerated expansion of laser-ablated materials near a solid surface

International Nuclear Information System (INIS)

Chen, K.R.; King, T.C.; Hes, J.H.; Leboeuf, J.N.; Geohegan, D.B.; Wood, R.F.; Puretzky, A.A.; Donato, J.M.

1999-01-01

A self-similar theory and numerical hydrodynamic modeling is developed to investigate the effects of dynamic source and partial ionization on the acceleration of the unsteady expansion of laser-ablated material near a solid target surface. The dynamic source effect accelerates the expansion in the direction perpendicular to the target surface, while the dynamic partial ionization effect accelerates the expansion in all directions. The vaporized material during laser ablation provides a nonadiabatic dynamic source at the target surface into the unsteady expanding fluid. For studying the dynamic source effect, the self-similar theory begins with an assumed profile of plume velocity, u=v/v m =α+(1-α)ξ, where v m is the maximum expansion velocity, α is a constant, and ξ=x/v m t. The resultant profiles of plume density and plume temperature are derived. The relations obtained from the conservations of mass, momentum, and energy, respectively, all show that the maximum expansion velocity is inversely proportional to α, where 1-α is the slope of plume velocity profile. The numerical hydrodynamic simulation is performed with the Rusanov method and the Newton Raphson method. The profiles and scalings obtained from numerical hydrodynamic modeling are in good agreement with the theory. The dynamic partial ionization requires ionization energy from the heat at the expansion front, and thus reduces the increase of front temperature. The reduction of thermal motion would increase the flow velocity to conserve the momentum. This dynamic partial ionization effect is studied with the numerical hydrodynamic simulation including the Saha equation. With these effects, α is reduced from its value of conventional free expansion. This reduction on α increases the flow velocity slope, decreases the flow velocity near the surface, and reduces the thermal motion of plume, such that the maximum expansion velocity is significantly increased over that found from conventional models

Numerical solution of modified fokker-planck equation with poissonian input

Czech Academy of Sciences Publication Activity Database

Náprstek, Jiří; Král, Radomil

2010-01-01

Roč. 17, 3/4 (2010), s. 251-268 ISSN 1802-1484 R&D Projects: GA AV ČR(CZ) IAA200710805; GA ČR(CZ) GA103/09/0094 Institutional research plan: CEZ:AV0Z20710524 Keywords : Fokker-Planck equation * poisson ian exciation * numerical solution * transition effects Subject RIV: JN - Civil Engineering

Intermediate accelerated solutions as generic late-time attractors in a modified Jordan-Brans-Dicke theory

Energy Technology Data Exchange (ETDEWEB)

Cid, Antonella [Grupo de Cosmología y Gravitación GCG-UBB and Departamento de Física, Universidad del Bío-Bío, Casilla 5-C, Concepción (Chile); Leon, Genly [Instituto de Física, Pontificia Universidad Católica de Valparaíso, Casilla 4950, Valparaíso (Chile); Leyva, Yoelsy, E-mail: acidm@ubiobio.cl, E-mail: genly.leon@ucv.cl, E-mail: yoelsy.leyva@uta.cl [Departamento de Física, Facultad de Ciencias, Universidad de Tarapacá, Casilla 7-D, Arica (Chile)

2016-02-01

In this paper we investigate the evolution of a Jordan-Brans-Dicke scalar field, Φ, with a power-law potential in the presence of a second scalar field, φ, with an exponential potential, in both the Jordan and the Einstein frames. We present the relation of our model with the induced gravity model with power-law potential and the integrability of this kind of models is discussed when the quintessence field φ is massless, and has a small velocity. The fact that for some fine-tuned values of the parameters we may get some integrable cosmological models, makes our choice of potentials very interesting. We prove that in Jordan-Brans-Dicke theory, the de Sitter solution is not a natural attractor. Instead, we show that the attractor in the Jordan frame corresponds to an ''intermediate accelerated'' solution of the form a(t) ≅ e{sup α{sub 1} t{sup p{sup {sub 1}}}}, as t → ∞ where α{sub 1} > 0 and 0 < p{sub 1} < 1, for a wide range of parameters. Furthermore, when we work in the Einstein frame we get that the attractor is also an ''intermediate accelerated'' solution of the form a(t) ≅ e{sup α{sub 2} tp{sub 2}} as t → ∞ where α{sub 2} > 0 and 0solutions are of saddle type. These results were proved using the center manifold theorem, which is not based on linear approximation. Finally, we present a specific elaboration of our extension of the induced gravity model in the Jordan frame, which corresponds to a particular choice of a linear potential of Φ. The dynamical system is then reduced to a two dimensional one, and the late-time attractor is linked with the exact solution found for the induced gravity model. In this example the ''intermediate accelerated

Intermediate accelerated solutions as generic late-time attractors in a modified Jordan-Brans-Dicke theory

International Nuclear Information System (INIS)

Cid, Antonella; Leon, Genly; Leyva, Yoelsy

2016-01-01

In this paper we investigate the evolution of a Jordan-Brans-Dicke scalar field, Φ, with a power-law potential in the presence of a second scalar field, φ, with an exponential potential, in both the Jordan and the Einstein frames. We present the relation of our model with the induced gravity model with power-law potential and the integrability of this kind of models is discussed when the quintessence field φ is massless, and has a small velocity. The fact that for some fine-tuned values of the parameters we may get some integrable cosmological models, makes our choice of potentials very interesting. We prove that in Jordan-Brans-Dicke theory, the de Sitter solution is not a natural attractor. Instead, we show that the attractor in the Jordan frame corresponds to an ''intermediate accelerated'' solution of the form a(t) ≅ e α 1  t p 1 , as t → ∞ where α 1  > 0 and 0 < p 1  < 1, for a wide range of parameters. Furthermore, when we work in the Einstein frame we get that the attractor is also an ''intermediate accelerated'' solution of the form a(t) ≅ e α 2  tp 2 as t → ∞ where α 2  > 0 and 0

solutions are of saddle type. These results were proved using the center manifold theorem, which is not based on linear approximation. Finally, we present a specific elaboration of our extension of the induced gravity model in the Jordan frame, which corresponds to a particular choice of a linear potential of Φ. The dynamical system is then reduced to a two dimensional one, and the late-time attractor is linked with the exact solution found for the induced gravity model. In this example the ''intermediate accelerated'' solution does not exist, and the attractor

Numerical tools for musical instruments acoustics: analysing nonlinear physical models using continuation of periodic solutions

OpenAIRE

Karkar , Sami; Vergez , Christophe; Cochelin , Bruno

2012-01-01

International audience; We propose a new approach based on numerical continuation and bifurcation analysis for the study of physical models of instruments that produce self- sustained oscillation. Numerical continuation consists in following how a given solution of a set of equations is modified when one (or several) parameter of these equations are allowed to vary. Several physical models (clarinet, saxophone, and violin) are formulated as nonlinear dynamical systems, whose periodic solution...

Hermite interpolant multiscaling functions for numerical solution of the convection diffusion equations

Directory of Open Access Journals (Sweden)

Elmira Ashpazzadeh

2018-04-01

Full Text Available A numerical technique based on the Hermite interpolant multiscaling functions is presented for the solution of Convection-diusion equations. The operational matrices of derivative, integration and product are presented for multiscaling functions and are utilized to reduce the solution of linear Convection-diusion equation to the solution of algebraic equations. Because of sparsity of these matrices, this method is computationally very attractive and reduces the CPU time and computer memory. Illustrative examples are included to demonstrate the validity and applicability of the new technique.

Numerical benchmarking of SPEEDUP trademark against point kinetics solutions

International Nuclear Information System (INIS)

Gregory, M.V.

1993-02-01

SPEEDUP trademark is a state-of-the-art, dynamic, chemical process modeling package offered by Aspen Technology. In anticipation of new customers' needs for new analytical tools to support the site's waste management activities, SRTC has secured a multiple-user license to SPEEDUP trademark. In order to verify both the installation and mathematical correctness of the algorithms in SPEEDUP trademark, we have performed several numerical benchmarking calculations. These calculations are the first steps in establishing an on-site quality assurance pedigree for SPEEDUP trademark. The benchmark calculations consisted of SPEEDUP trademark Version 5.3L representations of five neutron kinetics benchmarks (each a mathematically stiff system of seven coupled ordinary differential equations), whose exact solutions are documented in the open literature. In all cases, SPEEDUP trademark solutions to be in excellent agreement with the reference solutions. A minor peculiarity in dealing with a non-existent discontinuity in the OPERATION section of the model made itself evident

A note on numerical solution of a parabolic-Schrödinger equation

Science.gov (United States)

Ozdemir, Yildirim; Alp, Mustafa

2016-08-01

In the present study, a nonlocal boundary value problem for a parabolic-Schrödinger equation is considered. The stability estimates for the solution of the given problem is established. The first and second order of difference schemes are presented for approximately solving a specific nonlocal boundary problem. The theoretical statements for the solution of these difference schemes are supported by the result of numerical examples.

A numerical solution for a class of time fractional diffusion equations with delay

Directory of Open Access Journals (Sweden)

Pimenov Vladimir G.

2017-09-01

Full Text Available This paper describes a numerical scheme for a class of fractional diffusion equations with fixed time delay. The study focuses on the uniqueness, convergence and stability of the resulting numerical solution by means of the discrete energy method. The derivation of a linearized difference scheme with convergence order O(τ2−α+ h4 in L∞-norm is the main purpose of this study. Numerical experiments are carried out to support the obtained theoretical results.

Random ordinary differential equations and their numerical solution

CERN Document Server

Han, Xiaoying

2017-01-01

This book is intended to make recent results on the derivation of higher order numerical schemes for random ordinary differential equations (RODEs) available to a broader readership, and to familiarize readers with RODEs themselves as well as the closely associated theory of random dynamical systems. In addition, it demonstrates how RODEs are being used in the biological sciences, where non-Gaussian and bounded noise are often more realistic than the Gaussian white noise in stochastic differential equations (SODEs).   RODEs are used in many important applications and play a fundamental role in the theory of random dynamical systems.  They can be analyzed pathwise with deterministic calculus, but require further treatment beyond that of classical ODE theory due to the lack of smoothness in their time variable. Although classical numerical schemes for ODEs can be used pathwise for RODEs, they rarely attain their traditional order since the solutions of RODEs do not have sufficient smoothness to have Taylor ...

Six-dimensional localized black holes: Numerical solutions

International Nuclear Information System (INIS)

Kudoh, Hideaki

2004-01-01

To test the strong-gravity regime in Randall-Sundrum braneworlds, we consider black holes bound to a brane. In a previous paper, we studied numerical solutions of localized black holes whose horizon radii are smaller than the AdS curvature radius. In this paper, we improve the numerical method and discuss properties of the six-dimensional (6D) localized black holes whose horizon radii are larger than the AdS curvature radius. At a horizon temperature T≅1/2πl, the thermodynamics of the localized black hole undergo a transition with its character changing from a 6D Schwarzschild black hole type to a 6D black string type. The specific heat of the localized black holes is negative, and the entropy is greater than or nearly equal to that of the 6D black strings with the same thermodynamic mass. The large localized black holes show flattened horizon geometries, and the intrinsic curvature of the horizon four-geometry becomes negative near the brane. Our results indicate that the recovery mechanism of lower-dimensional Einstein gravity on the brane works even in the presence of the black holes

A numerical study of the eigenvalues in the neutron diffusion theory

International Nuclear Information System (INIS)

Lima Bezerra, J. de.

1982-12-01

A systematic numerical study for the eigenvalue problem in one dimension was carried out. A computer code RED2G was developed to obtain and to discuss a number of numerical solutions concerning eigenvalues problems originating from the discretization of the two groups neutron diffusion equation in one dimension and steady state. The problem of eigenvalues was created from the discretization by the method of finite differences. The solutions were obtained by four different iterative methods, i.e. Power, Wielandt-1, Wielandt-2 and accelerated Power with the Chebyshev polinomials. The numerical results given by the solution of the two test-problems indicate that the RED2G code is fast and efficient in these calculations and the Wielandt-2 method has been found to be the best both in respect of rapidity of calculations as well as programation effort required. (E.G.) [pt

Numerical solution of matrix exponential in burn-up equation using mini-max polynomial approximation

International Nuclear Information System (INIS)

Kawamoto, Yosuke; Chiba, Go; Tsuji, Masashi; Narabayashi, Tadashi

2015-01-01

Highlights: • We propose a new numerical solution of matrix exponential in burn-up depletion calculations. • The depletion calculation with extremely short half-lived nuclides can be done numerically stable with this method. • The computational time is shorter than the other conventional methods. - Abstract: Nuclear fuel burn-up depletion calculations are essential to compute the nuclear fuel composition transition. In the burn-up calculations, the matrix exponential method has been widely used. In the present paper, we propose a new numerical solution of the matrix exponential, a Mini-Max Polynomial Approximation (MMPA) method. This method is numerically stable for burn-up matrices with extremely short half-lived nuclides as the Chebyshev Rational Approximation Method (CRAM), and it has several advantages over CRAM. We also propose a multi-step calculation, a computational time reduction scheme of the MMPA method, which can perform simultaneously burn-up calculations with several time periods. The applicability of these methods has been theoretically and numerically proved for general burn-up matrices. The numerical verification has been performed, and it has been shown that these methods have high precision equivalent to CRAM

Approximate Analytic and Numerical Solutions to Lane-Emden Equation via Fuzzy Modeling Method

Directory of Open Access Journals (Sweden)

De-Gang Wang

2012-01-01

Full Text Available A novel algorithm, called variable weight fuzzy marginal linearization (VWFML method, is proposed. This method can supply approximate analytic and numerical solutions to Lane-Emden equations. And it is easy to be implemented and extended for solving other nonlinear differential equations. Numerical examples are included to demonstrate the validity and applicability of the developed technique.

Effects of Turbulent Magnetic Fields on the Transport and Acceleration of Energetic Charged Particles: Numerical Simulations with Application to Heliospheric Physics

Science.gov (United States)

Guo, Fan

2012-11-01

Turbulent magnetic fields are ubiquitous in space physics and astrophysics. The influence of magnetic turbulence on the motions of charged particles contains the essential physics of the transport and acceleration of energetic charged particles in the heliosphere, which is to be explored in this thesis. After a brief introduction on the energetic charged particles and magnetic fields in the heliosphere, the rest of this dissertation focuses on three specific topics: 1. the transport of energetic charged particles in the inner heliosphere, 2. the acceleration of ions at collisionless shocks, and 3. the acceleration of electrons at collisionless shocks. We utilize various numerical techniques to study these topics. In Chapter 2 we study the propagation of charged particles in turbulent magnetic fields similar to the propagation of solar energetic particles in the inner heliosphere. The trajectories of energetic charged particles in the turbulent magnetic field are numerically integrated. The turbulence model includes a Kolmogorov-like magnetic field power spectrum containing a broad range of scales from those that lead to large-scale field-line random walk to small scales leading to resonant pitch-angle scattering of energetic particles. We show that small-scale variations in particle intensities (the so-called "dropouts") and velocity dispersions observed by spacecraft can be reproduced using this method. Our study gives a new constraint on the error of "onset analysis", which is a technique commonly used to infer information about the initial release of energetic particles. We also find that the dropouts are rarely produced in the simulations using the so-called "two-component" magnetic turbulence model (Matthaeus et al., 1990). The result questions the validity of this model in studying particle transport. In the first part of Chapter 3 we study the acceleration of ions in the existence of turbulent magnetic fields. We use 3-D self-consistent hybrid simulations

Acceleration of monte Carlo solution by conjugate gradient method

International Nuclear Information System (INIS)

Toshihisa, Yamamoto

2005-01-01

The conjugate gradient method (CG) was applied to accelerate Monte Carlo solutions in fixed source problems. The equilibrium model based formulation enables to use CG scheme as well as initial guess to maximize computational performance. This method is available to arbitrary geometry provided that the neutron source distribution in each subregion can be regarded as flat. Even if it is not the case, the method can still be used as a powerful tool to provide an initial guess very close to the converged solution. The major difference of Monte Carlo CG to deterministic CG is that residual error is estimated using Monte Carlo sampling, thus statistical error exists in the residual. This leads to a flow diagram specific to Monte Carlo-CG. Three pre-conditioners were proposed for CG scheme and the performance was compared with a simple 1-D slab heterogeneous test problem. One of them, Sparse-M option, showed an excellent performance in convergence. The performance per unit cost was improved by four times in the test problem. Although direct estimation of efficiency of the method is impossible mainly because of the strong problem-dependence of the optimized pre-conditioner in CG, the method seems to have efficient potential as a fast solution algorithm for Monte Carlo calculations. (author)

Analytical and numerical investigation of nonlinear internal gravity waves

Directory of Open Access Journals (Sweden)

S. P. Kshevetskii

2001-01-01

Full Text Available The propagation of long, weakly nonlinear internal waves in a stratified gas is studied. Hydrodynamic equations for an ideal fluid with the perfect gas law describe the atmospheric gas behaviour. If we neglect the term Ͽ dw/dt (product of the density and vertical acceleration, we come to a so-called quasistatic model, while we name the full hydro-dynamic model as a nonquasistatic one. Both quasistatic and nonquasistatic models are used for wave simulation and the models are compared among themselves. It is shown that a smooth classical solution of a nonlinear quasistatic problem does not exist for all t because a gradient catastrophe of non-linear internal waves occurs. To overcome this difficulty, we search for the solution of the quasistatic problem in terms of a generalised function theory as a limit of special regularised equations containing some additional dissipation term when the dissipation factor vanishes. It is shown that such solutions of the quasistatic problem qualitatively differ from solutions of a nonquasistatic nature. It is explained by the fact that in a nonquasistatic model the vertical acceleration term plays the role of a regularizator with respect to a quasistatic model, while the solution qualitatively depends on the regularizator used. The numerical models are compared with some analytical results. Within the framework of the analytical model, any internal wave is described as a system of wave modes; each wave mode interacts with others due to equation non-linearity. In the principal order of a perturbation theory, each wave mode is described by some equation of a KdV type. The analytical model reveals that, in a nonquasistatic model, an internal wave should disintegrate into solitons. The time of wave disintegration into solitons, the scales and amount of solitons generated are important characteristics of the non-linear process; they are found with the help of analytical and numerical investigations. Satisfactory

An “Airy gun”: Self-accelerating solutions of the time-dependent Schrödinger equation in vacuum

International Nuclear Information System (INIS)

Mahalov, Alex; Suslov, Sergei K.

2012-01-01

We consider generalizations of the Berry and Balazs nonspreading and accelerating solution of the time-dependent Schrödinger equation in empty space, which has been experimentally demonstrated in paraxial optics. In particular, we show that the original nonspreading wave packet is unstable. An explicit variation of the initial Airy-state evolves into the self-accelerating and self-compressing solution presented here. Quasi-diffraction-free finite energy Airy beams that are more realistic for experimental study are obtained by analytic continuation and their Wigner function is evaluated. Nonlinear generalizations related to second Painlevé transcendents are briefly discussed.

The Numerical Solution of the Equilibrium Problem for a Stretchable Elastic Beam

Science.gov (United States)

Mehdiyeva, G. Y.; Aliyev, A. Y.

2017-08-01

The boundary value problem under consideration describes the equilibrium of an elastic beam that is stretched or contracted by specified forces. The left end of the beam is free of load, and the right end is rigidly lapped. To solve the problem numerically, an appropriate difference problem is constructed. Solving the difference problem, we obtain an approximate solution of the problem. We estimate the approximate solution of the stated problem.

Criteria for the reliability of numerical approximations to the solution of fluid flow problems

International Nuclear Information System (INIS)

Foias, C.

1986-01-01

The numerical approximation of the solutions of fluid flows models is a difficult problem in many cases of energy research. In all numerical methods implementable on digital computers, a basic question is if the number N of elements (Galerkin modes, finite-difference cells, finite-elements, etc.) is sufficient to describe the long time behavior of the exact solutions. It was shown using several approaches that some of the estimates based on physical intuition of N are rigorously valid under very general conditions and follow directly from the mathematical theory of the Navier-Stokes equations. Among the mathematical approaches to these estimates, the most promising (which can be and was already applied to many other dissipative partial differential systems) consists in giving upper estimates to the fractal dimension of the attractor associated to one (or all) solution(s) of the respective partial differential equations. 56 refs

Identifying generalized Fitzhugh-Nagumo equation from a numerical solution of Hodgkin-Huxley model

Directory of Open Access Journals (Sweden)

Nikola V. Georgiev

2003-01-01

Full Text Available An analytic time series in the form of numerical solution (in an appropriate finite time interval of the Hodgkin-Huxley current clamped (HHCC system of four differential equations, well known in the neurophysiology as an exact empirical model of excitation of a giant axon of Loligo, is presented. Then we search for a second-order differential equation of generalized Fitzhugh-Nagumo (GFN type, having as a solution the given single component (action potential of the numerical solution. The given time series is used as a basis for reconstructing orders, powers, and coefficients of the polynomial right-hand sides of GFN equation approximately governing the process of action potential. For this purpose, a new geometrical method for determining phase space dimension of the unknown dynamical system (GFN equation and a specific modification of least squares method for identifying unknown coefficients are developed and applied.

A numerical scheme using multi-shockpeakons to compute solutions of the Degasperis-Procesi equation

Directory of Open Access Journals (Sweden)

Hakon A. Hoel

2007-07-01

Full Text Available We consider a numerical scheme for entropy weak solutions of the DP (Degasperis-Procesi equation $u_t - u_{xxt} + 4uu_x = 3u_{x}u_{xx}+ uu_{xxx}$. Multi-shockpeakons, functions of the form $$ u(x,t =sum_{i=1}^n(m_i(t -hbox{sign}(x-x_i(ts_i(te^{-|x-x_i(t|}, $$ are solutions of the DP equation with a special property; their evolution in time is described by a dynamical system of ODEs. This property makes multi-shockpeakons relatively easy to simulate numerically. We prove that if we are given a non-negative initial function $u_0 in L^1(mathbb{R}cap BV(mathbb{R}$ such that $u_{0} - u_{0,x}$ is a positive Radon measure, then one can construct a sequence of multi-shockpeakons which converges to the unique entropy weak solution in $mathbb{R}imes[0,T$ for any $T>0$. From this convergence result, we construct a multi-shockpeakon based numerical scheme for solving the DP equation.

Mathematical modelling and numerical solution of swelling of cartilaginous tissues. Part II: Mixed hybrid finite element solution

NARCIS (Netherlands)

Malakpoor, K.; Kaasschieter, E.F.; Huyghe, J.M.R.J.

2007-01-01

The swelling and shrinkage of biological tissues are modelled by a four-component mixture theory [J.M. Huyghe and J.D. Janssen, Int. J. Engng. Sci. 35 (1997) 793-802; K. Malakpoor, E.F. Kaasschieter and J.M. Huyghe, Mathematical modelling and numerical solution of swelling of cartilaginous tissues.

Numerical solution for identification of feedback coefficients in nuclear reactors

International Nuclear Information System (INIS)

Ebizuka, Yoshie; Sakai, Hideo

1975-01-01

Quasilinearization technique was studied to determine the Kinetic parameters of nuclear reactors. The method of solution was generalized to the determination of the parameters contained in a nonlinear system with nonlinear boundary conditions. A computer program, SNR-3, was developed to solve the resulting nonlinear two-point boundary value equations with generalized boundary conditions. In this paper, the problem formulation and the method of solution are explained for a general type of time dependent problem. A flow chart shows the procedure of numerical solution. The method was then applied to the determination of the critical factor and the reactivity feedback coefficients of reactors to investigate the accuracy and the applicability of the present method. The results showed that the present method was considerably successful, but that the random observation error effected the results of the identification. (Aoki, K.)

Hall effects on MHD flow past an accelerated plate

International Nuclear Information System (INIS)

Soundalgekar, V.M.; Ravi, S.; Hiremath, S.B.

1980-01-01

An exact solution of the MHD flow of an incompressible, electrically conducting, viscous fluid past a uniformly accelerated plate is presented. The velocity profiles are shown graphically and the numerical values of axial and transverse components of skin friction are tabulated. At high values of the Hall parameter, ωtau, the velocity is found to be oscillatory near the plate. (author)

A numerical solution to the radial equation of the tidal wave propagation

International Nuclear Information System (INIS)

Makarious, S.H.

1981-08-01

The tidal wave function y(x) is a solution to an inhomogeneous, linear, second-order differential equation with variable coefficient. Numerical values for the height-dependence terms, in the observed tides, have been utilized in finding y(x) as a solution to an initial-value problem. Complex Fast Fourier Transform technique is also used to obtain the solution in a complex form. Based on a realistic temperature structure, the atmosphere - below 110 km - has been divided into layers with distinct characteristics, and thus the technique of propagation in stratified media has been applied. The reduced homogeneous equation assumes the form of Helmholtz equation and with initial conditions the general solution is obtained. (author)

Numerical evaluation of path-integral solutions to Fokker-Planck equations. II. Restricted stochastic processes

International Nuclear Information System (INIS)

Wehner, M.F.

1983-01-01

A path-integral solution is derived for processes described by nonlinear Fokker-Plank equations together with externally imposed boundary conditions. This path-integral solution is written in the form of a path sum for small time steps and contains, in addition to the conventional volume integral, a surface integral which incorporates the boundary conditions. A previously developed numerical method, based on a histogram representation of the probability distribution, is extended to a trapezoidal representation. This improved numerical approach is combined with the present path-integral formalism for restricted processes and is show t give accurate results. 35 refs., 5 figs

A hybrid numerical method for orbit correction

International Nuclear Information System (INIS)

White, G.; Himel, T.; Shoaee, H.

1997-09-01

The authors describe a simple hybrid numerical method for beam orbit correction in particle accelerators. The method overcomes both degeneracy in the linear system being solved and respects boundaries on the solution. It uses the Singular Value Decomposition (SVD) to find and remove the null-space in the system, followed by a bounded Linear Least Squares analysis of the remaining recast problem. It was developed for correcting orbit and dispersion in the B-factory rings

A numerical method for finding sign-changing solutions of superlinear Dirichlet problems

Energy Technology Data Exchange (ETDEWEB)

Neuberger, J.M.

1996-12-31

In a recent result it was shown via a variational argument that a class of superlinear elliptic boundary value problems has at least three nontrivial solutions, a pair of one sign and one which sign changes exactly once. These three and all other nontrivial solutions are saddle points of an action functional, and are characterized as local minima of that functional restricted to a codimension one submanifold of the Hilbert space H-0-1-2, or an appropriate higher codimension subset of that manifold. In this paper, we present a numerical Sobolev steepest descent algorithm for finding these three solutions.

Possibilities for Beam Stripping Solutions at a Rare Isotope Accelerator (RIA)

International Nuclear Information System (INIS)

Greife, Uwe

2006-01-01

As part of the DOE RIA R and D effort we investigated the possibilities and problems of beam strippers in the different heavy ion accelerator components of a possible Rare Isotope Accelerator (RIA) facility. We focused on two beam stripping positions in the RIA heavy ion driver where benchmark currents of up to 5 particle (micro)A 238-U were projected at energies of 10.5 MeV/u and 85 MeV/u respectively. In order to select feasible stripper materials, data from experiments with Uranium beams at Texas A and M and GSI were evaluated. Based on these results thermal estimates for a possible design were calculated and cooling simulations with commercially available software performed. Additionally, we performed simulations with the GEANT4 code on evaluating the radiation environment for our beam stripping solution at the 85 MeV/u position in the RIA driver

A New Method to Solve Numeric Solution of Nonlinear Dynamic System

Directory of Open Access Journals (Sweden)

Min Hu

2016-01-01

Full Text Available It is well known that the cubic spline function has advantages of simple forms, good convergence, approximation, and second-order smoothness. A particular class of cubic spline function is constructed and an effective method to solve the numerical solution of nonlinear dynamic system is proposed based on the cubic spline function. Compared with existing methods, this method not only has high approximation precision, but also avoids the Runge phenomenon. The error analysis of several methods is given via two numeric examples, which turned out that the proposed method is a much more feasible tool applied to the engineering practice.

Solution of combinatorial optimization problems by an accelerated hopfield neural network. Kobai kasokugata poppu firudo nyuraru netto ni yoru kumiawase saitekika mondai no kaiho

Energy Technology Data Exchange (ETDEWEB)

Ohori, T.; Yamamoto, H.; Setsu, Nenso; Watanabe, K. (Hokkaido Inst. of Technology, Hokkaido (Japan))

1994-04-20

The accelerated approximate solution of combinatorial optimization problems by symmetry integrating hopfield neural network (NN) has been applied to many combinatorial problems such as the traveling salesman problem, the network planning problem, etc. However, the hopfield NN converges to local minimum solutions very slowly. In this paper, a general inclination model composed by introducing an accelerated parameter to the hopfield model is proposed, and it has been shown that the acceleration parameter can make the model converge to the local minima more quickly. Moreover, simulation experiments for random quadratic combinatorial problems with two and twenty-five variables were carried out. The results show that the acceleration of convergence makes the attraction region of the local minimum change and the accuracy of solution worse. If an initial point is selected around the center of unit hyper cube, solutions with high accuracy not affected by the acceleration parameter can be obtained. 9 refs., 8 figs., 3 tabs.

Reusable Object-Oriented Solutions for Numerical Simulation of PDEs in a High Performance Environment

Directory of Open Access Journals (Sweden)

Andrea Lani

2006-01-01

Full Text Available Object-oriented platforms developed for the numerical solution of PDEs must combine flexibility and reusability, in order to ease the integration of new functionalities and algorithms. While designing similar frameworks, a built-in support for high performance should be provided and enforced transparently, especially in parallel simulations. The paper presents solutions developed to effectively tackle these and other more specific problems (data handling and storage, implementation of physical models and numerical methods that have arisen in the development of COOLFluiD, an environment for PDE solvers. Particular attention is devoted to describe a data storage facility, highly suitable for both serial and parallel computing, and to discuss the application of two design patterns, Perspective and Method-Command-Strategy, that support extensibility and run-time flexibility in the implementation of physical models and generic numerical algorithms respectively.

A Mass Conservative Numerical Solution for Two-Phase Flow in Porous Media With Application to Unsaturated Flow

DEFF Research Database (Denmark)

Celia, Michael A.; Binning, Philip John

1992-01-01

that the algorithm produces solutions that are essentially mass conservative and oscillation free, even in the presence of steep infiltrating fronts. When the algorithm is applied to the case of air and water flow in unsaturated soils, numerical results confirm the conditions under which Richards's equation is valid....... Numerical results also demonstrate the potential importance of air phase advection when considering contaminant transport in unsaturated soils. Comparison to several other numerical algorithms shows that the modified Picard approach offers robust, mass conservative solutions to the general equations...

Numerical simulation of solute trapping phenomena using phase-field solidification model for dilute binary alloys

Directory of Open Access Journals (Sweden)

Henrique Silva Furtado

2009-09-01

Full Text Available Numerical simulation of solute trapping during solidification, using two phase-field model for dilute binary alloys developed by Kim et al. [Phys. Rev. E, 60, 7186 (1999] and Ramirez et al. [Phys. Rev. E, 69, 05167 (2004] is presented here. The simulations on dilute Cu-Ni alloy are in good agreement with one dimensional analytic solution of sharp interface model. Simulation conducted under small solidification velocity using solid-liquid interface thickness (2λ of 8 nanometers reproduced the solute (Cu equilibrium partition coefficient. The spurious numerical solute trapping in solid phase, due to the interface thickness was negligible. A parameter used in analytical solute trapping model was determined by isothermal phase-field simulation of Ni-Cu alloy. Its application to Si-As and Si-Bi alloys reproduced results that agree reasonably well with experimental data. A comparison between the three models of solute trapping (Aziz, Sobolev and Galenko [Phys. Rev. E, 76, 031606 (2007] was performed. It resulted in large differences in predicting the solidification velocity for partition-less solidification, indicating the necessity for new and more acute experimental data.

Introduction of Parallel GPGPU Acceleration Algorithms for the Solution of Radiative Transfer

Science.gov (United States)

Godoy, William F.; Liu, Xu

2011-01-01

General-purpose computing on graphics processing units (GPGPU) is a recent technique that allows the parallel graphics processing unit (GPU) to accelerate calculations performed sequentially by the central processing unit (CPU). To introduce GPGPU to radiative transfer, the Gauss-Seidel solution of the well-known expressions for 1-D and 3-D homogeneous, isotropic media is selected as a test case. Different algorithms are introduced to balance memory and GPU-CPU communication, critical aspects of GPGPU. Results show that speed-ups of one to two orders of magnitude are obtained when compared to sequential solutions. The underlying value of GPGPU is its potential extension in radiative solvers (e.g., Monte Carlo, discrete ordinates) at a minimal learning curve.

Calculation of radiation effects in solids by direct numerical solution of the adjoint transport equation

International Nuclear Information System (INIS)

Matthes, W.K.

1998-01-01

The 'adjoint transport equation in its integro-differential form' is derived for the radiation damage produced by atoms injected into solids. We reduce it to the one-dimensional form and prepare it for a numerical solution by: --discretizing the continuous variables energy, space and direction, --replacing the partial differential quotients by finite differences and --evaluating the collision integral by a double sum. By a proper manipulation of this double sum the adjoint transport equation turns into a (very large) set of linear equations with tridiagonal matrix which can be solved by a special (simple and fast) algorithm. The solution of this set of linear equations contains complete information on a specified damage type (e.g. the energy deposited in a volume V) in terms of the function D(i,E,c,x) which gives the damage produced by all particles generated in a cascade initiated by a particle of type i starting at x with energy E in direction c. It is essential to remark that one calculation gives the damage function D for the complete ranges of the variables {i,E,c and x} (for numerical reasons of course on grid-points in the {E,c,x}-space). This is most useful to applications where a general source-distribution S(i,E,c,x) of particles is given by the experimental setup (e.g. beam-window and and target in proton accelerator work. The beam-protons along their path through the window--or target material generate recoil atoms by elastic collisions or nuclear reactions. These recoil atoms form the particle source S). The total damage produced then is eventually given by: D = (Σ)i ∫ ∫ ∫ S(i, E, c, x)*D(i, E, c, x)*dE*dc*dx A Fortran-77 program running on a PC-486 was written for the overall procedure and applied to some problems

Enriched Meshfree Method for an Accurate Numerical Solution of the Motz Problem

Directory of Open Access Journals (Sweden)

Won-Tak Hong

2016-01-01

Full Text Available We present an enriched meshfree solution of the Motz problem. The Motz problem has been known as a benchmark problem to verify the efficiency of numerical methods in the presence of a jump boundary data singularity at a point, where an abrupt change occurs for the boundary condition. We propose a singular basis function enrichment technique in the context of partition of unity based meshfree method. We take the leading terms of the local series expansion at the point singularity and use them as enrichment functions for the local approximation space. As a result, we obtain highly accurate leading coefficients of the Motz problem that are comparable to the most accurate numerical solution. The proposed singular enrichment technique is highly effective in the case of the local series expansion of the solution being known. The enrichment technique that is used in this study can be applied to monotone singularities (of type rα with α<1 as well as oscillating singularities (of type rαsin⁡(ϵlog⁡r. It is the first attempt to apply singular meshfree enrichment technique to the Motz problem.

Modeling of electron cyclotron resonance acceleration in a stationary inhomogeneous magnetic field

Directory of Open Access Journals (Sweden)

Valeri D. Dougar-Jabon

2008-04-01

Full Text Available In this paper, the cyclotron autoresonance acceleration of electrons in a stationary inhomogeneous magnetic field is studied. The trajectory and energy of electrons are found through a numerical solution of the relativistic Newton-Lorentz equation by a finite difference method. The electrons move along a TE_{112} cylinder cavity in a steady-state magnetic field whose axis coincides with the cavity axis. The magnetic field profile is such that it keeps the phase difference between the electric microwave field and the electron velocity vector within the acceleration phase band. The microwaves amplitude of 6  kV/cm is used for numerical calculations. It is shown that an electron with an initial longitudinal energy of 8 keV can be accelerated up to 260 keV by 2.45 GHz microwaves at a distance of 17 cm.

Accelerated numerical processing of electronically recorded holograms with reduced speckle noise.

Science.gov (United States)

Trujillo, Carlos; Garcia-Sucerquia, Jorge

2013-09-01

The numerical reconstruction of digitally recorded holograms suffers from speckle noise. An accelerated method that uses general-purpose computing in graphics processing units to reduce that noise is shown. The proposed methodology utilizes parallelized algorithms to record, reconstruct, and superimpose multiple uncorrelated holograms of a static scene. For the best tradeoff between reduction of the speckle noise and processing time, the method records, reconstructs, and superimposes six holograms of 1024 × 1024 pixels in 68 ms; for this case, the methodology reduces the speckle noise by 58% compared with that exhibited by a single hologram. The fully parallelized method running on a commodity graphics processing unit is one order of magnitude faster than the same technique implemented on a regular CPU using its multithreading capabilities. Experimental results are shown to validate the proposal.

Efficient Numerical Solution of Coupled Radial Differential Equations in Multichannel Scattering Problems

International Nuclear Information System (INIS)

Houfek, Karel

2008-01-01

Numerical solution of coupled radial differential equations which are encountered in multichannel scattering problems is presented. Numerical approach is based on the combination of the exterior complex scaling method and the finite-elements method with the discrete variable representation. This method can be used not only to solve multichannel scattering problem but also to find bound states and resonance positions and widths directly by diagonalization of the corresponding complex scaled Hamiltonian. Efficiency and accuracy of this method is demonstrated on an analytically solvable two-channel problem.

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)

Synthetic acceleration methods for linear transport problems with highly anisotropic scattering

International Nuclear Information System (INIS)

Khattab, K.M.; Larsen, E.W.

1992-01-01

The diffusion synthetic acceleration (DSA) algorithm effectively accelerates the iterative solution of transport problems with isotropic or mildly anisotropic scattering. However, DSA loses its effectiveness for transport problems that have strongly anisotropic scattering. Two generalizations of DSA are proposed, which, for highly anisotropic scattering problems, converge at least an order of magnitude (clock time) faster than the DSA method. These two methods are developed, the results of Fourier analysis that theoretically predict their efficiency are described, and numerical results that verify the theoretical predictions are presented. (author). 10 refs., 7 figs., 5 tabs

Synthetic acceleration methods for linear transport problems with highly anisotropic scattering

International Nuclear Information System (INIS)

Khattab, K.M.; Larsen, E.W.

1991-01-01

This paper reports on the diffusion synthetic acceleration (DSA) algorithm that effectively accelerates the iterative solution of transport problems with isotropic or mildly anisotropic scattering. However, DSA loses its effectiveness for transport problems that have strongly anisotropic scattering. Two generalizations of DSA are proposed, which, for highly anisotropic scattering problems, converge at least an order of magnitude (clock time) faster than the DSA method. These two methods are developed, the results of Fourier analyses that theoretically predict their efficiency are described, and numerical results that verify the theoretical predictions are presented

A Predictor-Corrector Approach for the Numerical Solution of Fractional Differential Equations

Science.gov (United States)

Diethelm, Kai; Ford, Neville J.; Freed, Alan D.; Gray, Hugh R. (Technical Monitor)

2002-01-01

We discuss an Adams-type predictor-corrector method for the numerical solution of fractional differential equations. The method may be used both for linear and for nonlinear problems, and it may be extended to multi-term equations (involving more than one differential operator) too.

Intuitional experiment and numerical analysis of flow characteristics affected by flow accelerated corrosion in elbow pipe system

Energy Technology Data Exchange (ETDEWEB)

Kim, Hyung Joon [School of Mechanical and Aerospace Engineering, Seoul National University, Gwanak-gu, Seoul 151-744 (Korea, Republic of); Kim, Kyung Hoon, E-mail: kimkh@khu.ac.kr [Department of Mechanical Engineering, Kyung Hee University, Seochun 1, Yongin, Gyeonggi 446-701 (Korea, Republic of)

2016-05-15

Highlights: • Wall-thinning erosion of pipelines in plants leads to fatal accidents unexpectedly. • Flow Acceleration Corrosion (FAC) is a main reason of wall-thinning. • For industrial safety, it is necessary to verify the tendency of FAC. • We focused on local wall thinning by FAC with intuitional visualization experiment and numerical analysis in elbow pipe.

Numerical treatment of elliptic BVP with several solutions and of MHD equilibrium problems

International Nuclear Information System (INIS)

Meyer-Spasche, R.

1975-12-01

It is found out empirically that Newton iteration and difference methods are very suitable for the numerical treatment of elliptic boundary value problems (Lu)(x) = f(x,u(x)) in D c R 2 , u/deltaD = g having several solutions. Some convergence theorems for these methods are presented. Some notable numerical examples are given, including bifurcation diagrams, which are interesting in themselves and show also the applicability of the methods developed. (orig./WB) [de

Numerical solution of inviscid and viscous laminar and turbulent flow around the airfoil

Directory of Open Access Journals (Sweden)

Slouka Martin

2016-01-01

Full Text Available This work deals with the 2D numerical solution of inviscid compressible flow and viscous compressible laminar and turbulent flow around the profile. In a case of turbulent flow algebraic Baldwin-Lomax model is used and compared with Wilcox k-omega model. Calculations are done for NACA 0012 and RAE 2822 airfoil profile for the different angles of upstream flow. Numerical results are compared and discussed with experimental data.

Numerical solutions of differential equations of an ionization chamber

International Nuclear Information System (INIS)

Novkovic, D.; Tomasevic, M.; Subotic, K.; Manic, S.

1998-01-01

A system of reduced differential equations generally valid for plane-parallel, cylindrical, and spherical ionization chambers filled with air, which is appropriate for numerical solution, has been derived. The system has been solved for all three geometries. The comparison of the calculated results of Armstrong and Tate, for plane-parallel ionization chambers, and Sprinkle and Tate, for spherical ionization chambers, with the present calculations has shown a good agreement. The calculated values for ionization chambers filled with CO 2 were also in good agreement with the experimental data of Moriuchi et al (author)

Electromagnetic projectile acceleration utilizing distributed energy sources

International Nuclear Information System (INIS)

Parker, J.V.

1982-01-01

Circuit equations are derived for an electromagnetic projectile accelerator (railgun) powered by a large number of capacitive discharge circuits distributed along its length. The circuit equations are put into dimensionless form and the parameters governing the solutions derived. After specializing the equations to constant spacing between circuits, the case of lossless rails and negligible drag is analyzed to show that the electrical to kinetic energy transfer efficiency is equal to sigma/2, where sigma = 2mS/Lq 2 0 and m is the projectile mass, S the distance between discharge circuit, Lthe rail inductance per unit length, and q 0 the charge on the first stage capacitor. For sigma = 2 complete transfer of electrical to kinetic energy is predicted while for sigma>2 the projective-discharge circuit system is unstable. Numerical solutions are presented for both lossless rails and for finite rail resistance. When rail resistance is included, >70% transfer is calculated for accelerators of arbitrary length. The problem of projectile startup is considered and a simple modification of the first two stages is described which provides proper startup. Finally, the results of the numerical solutions are applied to a practical railgun design. A research railgun designed for repeated operation at 50 km/sec is described. It would have an overall length of 77 m, an electrical efficiency of 81%, a stored energy per stage of 105 kJ, and a charge transfer of <50 C per stage. A railgun of this design appears to be practicable with current pulsed power technology

Numerical solution of plasma fluid equations using locally refined grids

International Nuclear Information System (INIS)

Colella, P.

1997-01-01

This paper describes a numerical method for the solution of plasma fluid equations on block-structured, locally refined grids. The plasma under consideration is typical of those used for the processing of semiconductors. The governing equations consist of a drift-diffusion model of the electrons and an isothermal model of the ions coupled by Poisson's equation. A discretization of the equations is given for a uniform spatial grid, and a time-split integration scheme is developed. The algorithm is then extended to accommodate locally refined grids. This extension involves the advancement of the discrete system on a hierarchy of levels, each of which represents a degree of refinement, together with synchronization steps to ensure consistency across levels. A brief discussion of a software implementation is followed by a presentation of numerical results

Transport synthetic acceleration scheme for multi-dimensional neutron transport problems

Energy Technology Data Exchange (ETDEWEB)

Modak, R S; Kumar, Vinod; Menon, S V.G. [Theoretical Physics Div., Bhabha Atomic Research Centre, Mumbai (India); Gupta, Anurag [Reactor Physics Design Div., Bhabha Atomic Research Centre, Mumbai (India)

2005-09-15

The numerical solution of linear multi-energy-group neutron transport equation is required in several analyses in nuclear reactor physics and allied areas. Computer codes based on the discrete ordinates (Sn) method are commonly used for this purpose. These codes solve external source problem and K-eigenvalue problem. The overall solution technique involves solution of source problem in each energy group as intermediate procedures. Such a single-group source problem is solved by the so-called Source Iteration (SI) method. As is well-known, the SI-method converges very slowly for optically thick and highly scattering regions, leading to large CPU times. Over last three decades, many schemes have been tried to accelerate the SI; the most prominent being the Diffusion Synthetic Acceleration (DSA) scheme. The DSA scheme, however, often fails and is also rather difficult to implement. In view of this, in 1997, Ramone and others have developed a new acceleration scheme called Transport Synthetic Acceleration (TSA) which is much more robust and easy to implement. This scheme has been recently incorporated in 2-D and 3-D in-house codes at BARC. This report presents studies on the utility of TSA scheme for fairly general test problems involving many energy groups and anisotropic scattering. The scheme is found to be useful for problems in Cartesian as well as Cylindrical geometry. (author)

Transport synthetic acceleration scheme for multi-dimensional neutron transport problems

International Nuclear Information System (INIS)

Modak, R.S.; Vinod Kumar; Menon, S.V.G.; Gupta, Anurag

2005-09-01

The numerical solution of linear multi-energy-group neutron transport equation is required in several analyses in nuclear reactor physics and allied areas. Computer codes based on the discrete ordinates (Sn) method are commonly used for this purpose. These codes solve external source problem and K-eigenvalue problem. The overall solution technique involves solution of source problem in each energy group as intermediate procedures. Such a single-group source problem is solved by the so-called Source Iteration (SI) method. As is well-known, the SI-method converges very slowly for optically thick and highly scattering regions, leading to large CPU times. Over last three decades, many schemes have been tried to accelerate the SI; the most prominent being the Diffusion Synthetic Acceleration (DSA) scheme. The DSA scheme, however, often fails and is also rather difficult to implement. In view of this, in 1997, Ramone and others have developed a new acceleration scheme called Transport Synthetic Acceleration (TSA) which is much more robust and easy to implement. This scheme has been recently incorporated in 2-D and 3-D in-house codes at BARC. This report presents studies on the utility of TSA scheme for fairly general test problems involving many energy groups and anisotropic scattering. The scheme is found to be useful for problems in Cartesian as well as Cylindrical geometry. (author)

Reduction of numerical diffusion in three-dimensional vortical flows using a coupled Eulerian/Lagrangian solution procedure

Science.gov (United States)

Felici, Helene M.; Drela, Mark

1993-01-01

A new approach based on the coupling of an Eulerian and a Lagrangian solver, aimed at reducing the numerical diffusion errors of standard Eulerian time-marching finite-volume solvers, is presented. The approach is applied to the computation of the secondary flow in two bent pipes and the flow around a 3D wing. Using convective point markers the Lagrangian approach provides a correction of the basic Eulerian solution. The Eulerian flow in turn integrates in time the Lagrangian state-vector. A comparison of coarse and fine grid Eulerian solutions makes it possible to identify numerical diffusion. It is shown that the Eulerian/Lagrangian approach is an effective method for reducing numerical diffusion errors.

A numerical method for osmotic water flow and solute diffusion with deformable membrane boundaries in two spatial dimension

Science.gov (United States)

Yao, Lingxing; Mori, Yoichiro

2017-12-01

Osmotic forces and solute diffusion are increasingly seen as playing a fundamental role in cell movement. Here, we present a numerical method that allows for studying the interplay between diffusive, osmotic and mechanical effects. An osmotically active solute obeys a advection-diffusion equation in a region demarcated by a deformable membrane. The interfacial membrane allows transmembrane water flow which is determined by osmotic and mechanical pressure differences across the membrane. The numerical method is based on an immersed boundary method for fluid-structure interaction and a Cartesian grid embedded boundary method for the solute. We demonstrate our numerical algorithm with the test case of an osmotic engine, a recently proposed mechanism for cell propulsion.

Continuous Analog of Accelerated OS-EM Algorithm for Computed Tomography

Directory of Open Access Journals (Sweden)

Kiyoko Tateishi

2017-01-01

Full Text Available The maximum-likelihood expectation-maximization (ML-EM algorithm is used for an iterative image reconstruction (IIR method and performs well with respect to the inverse problem as cross-entropy minimization in computed tomography. For accelerating the convergence rate of the ML-EM, the ordered-subsets expectation-maximization (OS-EM with a power factor is effective. In this paper, we propose a continuous analog to the power-based accelerated OS-EM algorithm. The continuous-time image reconstruction (CIR system is described by nonlinear differential equations with piecewise smooth vector fields by a cyclic switching process. A numerical discretization of the differential equation by using the geometric multiplicative first-order expansion of the nonlinear vector field leads to an exact equivalent iterative formula of the power-based OS-EM. The convergence of nonnegatively constrained solutions to a globally stable equilibrium is guaranteed by the Lyapunov theorem for consistent inverse problems. We illustrate through numerical experiments that the convergence characteristics of the continuous system have the highest quality compared with that of discretization methods. We clarify how important the discretization method approximates the solution of the CIR to design a better IIR method.

Comptonization in Ultra-Strong Magnetic Fields: Numerical Solution to the Radiative Transfer Problem

Science.gov (United States)

Ceccobello, C.; Farinelli, R.; Titarchuk, L.

2014-01-01

We consider the radiative transfer problem in a plane-parallel slab of thermal electrons in the presence of an ultra-strong magnetic field (B approximately greater than B(sub c) approx. = 4.4 x 10(exp 13) G). Under these conditions, the magnetic field behaves like a birefringent medium for the propagating photons, and the electromagnetic radiation is split into two polarization modes, ordinary and extraordinary, that have different cross-sections. When the optical depth of the slab is large, the ordinary-mode photons are strongly Comptonized and the photon field is dominated by an isotropic component. Aims. The radiative transfer problem in strong magnetic fields presents many mathematical issues and analytical or numerical solutions can be obtained only under some given approximations. We investigate this problem both from the analytical and numerical point of view, provide a test of the previous analytical estimates, and extend these results with numerical techniques. Methods. We consider here the case of low temperature black-body photons propagating in a sub-relativistic temperature plasma, which allows us to deal with a semi-Fokker-Planck approximation of the radiative transfer equation. The problem can then be treated with the variable separation method, and we use a numerical technique to find solutions to the eigenvalue problem in the case of a singular kernel of the space operator. The singularity of the space kernel is the result of the strong angular dependence of the electron cross-section in the presence of a strong magnetic field. Results. We provide the numerical solution obtained for eigenvalues and eigenfunctions of the space operator, and the emerging Comptonization spectrum of the ordinary-mode photons for any eigenvalue of the space equation and for energies significantly lesser than the cyclotron energy, which is on the order of MeV for the intensity of the magnetic field here considered. Conclusions. We derived the specific intensity of the

An analytic solution for numerical modeling validation in electromagnetics: the resistive sphere

Science.gov (United States)

Swidinsky, Andrei; Liu, Lifei

2017-11-01

We derive the electromagnetic response of a resistive sphere to an electric dipole source buried in a conductive whole space. The solution consists of an infinite series of spherical Bessel functions and associated Legendre polynomials, and follows the well-studied problem of a conductive sphere buried in a resistive whole space in the presence of a magnetic dipole. Our result is particularly useful for controlled-source electromagnetic problems using a grounded electric dipole transmitter and can be used to check numerical methods of calculating the response of resistive targets (such as finite difference, finite volume, finite element and integral equation). While we elect to focus on the resistive sphere in our examples, the expressions in this paper are completely general and allow for arbitrary source frequency, sphere radius, transmitter position, receiver position and sphere/host conductivity contrast so that conductive target responses can also be checked. Commonly used mesh validation techniques consist of comparisons against other numerical codes, but such solutions may not always be reliable or readily available. Alternatively, the response of simple 1-D models can be tested against well-known whole space, half-space and layered earth solutions, but such an approach is inadequate for validating models with curved surfaces. We demonstrate that our theoretical results can be used as a complementary validation tool by comparing analytic electric fields to those calculated through a finite-element analysis; the software implementation of this infinite series solution is made available for direct and immediate application.

New numerical solutions of three-dimensional compressible hydrodynamic convection. [in stars

Science.gov (United States)

Hossain, Murshed; Mullan, D. J.

1990-01-01

Numerical solutions of three-dimensional compressible hydrodynamics (including sound waves) in a stratified medium with open boundaries are presented. Convergent/divergent points play a controlling role in the flows, which are dominated by a single frequency related to the mean sound crossing time. Superposed on these rapid compressive flows, slower eddy-like flows eventually create convective transport. The solutions contain small structures stacked on top of larger ones, with vertical scales equal to the local pressure scale heights, H sub p. Although convective transport starts later in the evolution, vertical scales of H sub p are apparently selected at much earlier times by nonlinear compressive effects.

The Navier-Stokes-Fourier system: From weak solutions to numerical analysis

Czech Academy of Sciences Publication Activity Database

Feireisl, Eduard

2015-01-01

Roč. 35, č. 3 (2015), s. 185-193 ISSN 0174-4747 R&D Projects: GA ČR GA13-00522S Institutional support: RVO:67985840 Keywords : Navier-Stokes-Fourier system * weak solution * mixed finite-volume finite-element numerical scheme Subject RIV: BA - General Mathematics http://www.degruyter.com/view/j/anly.2015.35.issue-3/anly-2014-1300/anly-2014-1300. xml

Numerical solution of fluid-structure interaction represented by human vocal folds in airflow

Directory of Open Access Journals (Sweden)

Valášek J.

2016-01-01

Full Text Available The paper deals with the human vocal folds vibration excited by the fluid flow. The vocal fold is modelled as an elastic body assuming small displacements and therefore linear elasticity theory is used. The viscous incompressible fluid flow is considered. For purpose of numerical solution the arbitrary Lagrangian-Euler method (ALE is used. The whole problem is solved by the finite element method (FEM based solver. Results of numerical experiments with different boundary conditions are presented.

Numerical solution of fluid-structure interaction represented by human vocal folds in airflow

Science.gov (United States)

Valášek, J.; Sváček, P.; Horáček, J.

2016-03-01

The paper deals with the human vocal folds vibration excited by the fluid flow. The vocal fold is modelled as an elastic body assuming small displacements and therefore linear elasticity theory is used. The viscous incompressible fluid flow is considered. For purpose of numerical solution the arbitrary Lagrangian-Euler method (ALE) is used. The whole problem is solved by the finite element method (FEM) based solver. Results of numerical experiments with different boundary conditions are presented.

Numerical Modeling for the Solute Uptake from Groundwater by Plants-Plant Uptake Package

OpenAIRE

El-Sayed, Amr A.

2006-01-01

A numerical model is presented to describe solute transport in groundwater coupled to sorption by plant roots, translocation into plant stems, and finally evapotranspiration. The conceptual model takes into account both Root Concentration Factor, RCF, and Transpiration Stream Concentration Factor, TSCF for chemicals which are a function of Kow. A similar technique used to simulate the solute transport in groundwater to simulate sorption and plant uptake is used. The mathematical equation is s...

Nature Inspired Computational Technique for the Numerical Solution of Nonlinear Singular Boundary Value Problems Arising in Physiology

Directory of Open Access Journals (Sweden)

Suheel Abdullah Malik

2014-01-01

Full Text Available We present a hybrid heuristic computing method for the numerical solution of nonlinear singular boundary value problems arising in physiology. The approximate solution is deduced as a linear combination of some log sigmoid basis functions. A fitness function representing the sum of the mean square error of the given nonlinear ordinary differential equation (ODE and its boundary conditions is formulated. The optimization of the unknown adjustable parameters contained in the fitness function is performed by the hybrid heuristic computation algorithm based on genetic algorithm (GA, interior point algorithm (IPA, and active set algorithm (ASA. The efficiency and the viability of the proposed method are confirmed by solving three examples from physiology. The obtained approximate solutions are found in excellent agreement with the exact solutions as well as some conventional numerical solutions.

Numerical Modeling Tools for the Prediction of Solution Migration Applicable to Mining Site

International Nuclear Information System (INIS)

Martell, M.; Vaughn, P.

1999-01-01

Mining has always had an important influence on cultures and traditions of communities around the globe and throughout history. Today, because mining legislation places heavy emphasis on environmental protection, there is great interest in having a comprehensive understanding of ancient mining and mining sites. Multi-disciplinary approaches (i.e., Pb isotopes as tracers) are being used to explore the distribution of metals in natural environments. Another successful approach is to model solution migration numerically. A proven method to simulate solution migration in natural rock salt has been applied to project through time for 10,000 years the system performance and solution concentrations surrounding a proposed nuclear waste repository. This capability is readily adaptable to simulate solution migration around mining

A third-order KdV solution for internal solitary waves and its application in the numerical wave tank

Directory of Open Access Journals (Sweden)

Qicheng Meng

2016-04-01

Full Text Available A third-order KdV solution to the internal solitary wave is derived by a new method based on the weakly nonlinear assumptions in a rigid-lid two-layer system. The solution corrects an error by Mirie and Su (1984. A two-dimensional numerical wave tank has been established with the help of the open source CFD library OpenFOAM and the third-party software waves2Foam. Various analytical solutions, including the first-order to third-order KdV solutions, the eKdV solution and the MCC solution, have been used to initialise the flow fields in the CFD simulations of internal solitary waves. Two groups including 11 numerical cases have been carried out. In the same group, the initial wave amplitudes are the same but the implemented analytical solutions are different. The simulated wave profiles at different moments have been presented. The relative errors in terms of the wave amplitude between the last time step and the initial input have been analysed quantitatively. It is found that the third-order KdV solution results in the most stable internal solitary wave in the numerical wave tank for both small-amplitude and finite-amplitude cases. The finding is significant for the further simulations involving internal solitary waves.

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.

Almost Surely Asymptotic Stability of Numerical Solutions for Neutral Stochastic Delay Differential Equations

Directory of Open Access Journals (Sweden)

Zhanhua Yu

2011-01-01

convergence theorem. It is shown that the Euler method and the backward Euler method can reproduce the almost surely asymptotic stability of exact solutions to NSDDEs under additional conditions. Numerical examples are demonstrated to illustrate the effectiveness of our theoretical results.

Recursive algorithm for arrays of generalized Bessel functions: Numerical access to Dirac-Volkov solutions.

Science.gov (United States)

Lötstedt, Erik; Jentschura, Ulrich D

2009-02-01

In the relativistic and the nonrelativistic theoretical treatment of moderate and high-power laser-matter interaction, the generalized Bessel function occurs naturally when a Schrödinger-Volkov and Dirac-Volkov solution is expanded into plane waves. For the evaluation of cross sections of quantum electrodynamic processes in a linearly polarized laser field, it is often necessary to evaluate large arrays of generalized Bessel functions, of arbitrary index but with fixed arguments. We show that the generalized Bessel function can be evaluated, in a numerically stable way, by utilizing a recurrence relation and a normalization condition only, without having to compute any initial value. We demonstrate the utility of the method by illustrating the quantum-classical correspondence of the Dirac-Volkov solutions via numerical calculations.

Exploiting multi-scale parallelism for large scale numerical modelling of laser wakefield accelerators

International Nuclear Information System (INIS)

Fonseca, R A; Vieira, J; Silva, L O; Fiuza, F; Davidson, A; Tsung, F S; Mori, W B

2013-01-01

A new generation of laser wakefield accelerators (LWFA), supported by the extreme accelerating fields generated in the interaction of PW-Class lasers and underdense targets, promises the production of high quality electron beams in short distances for multiple applications. Achieving this goal will rely heavily on numerical modelling to further understand the underlying physics and identify optimal regimes, but large scale modelling of these scenarios is computationally heavy and requires the efficient use of state-of-the-art petascale supercomputing systems. We discuss the main difficulties involved in running these simulations and the new developments implemented in the OSIRIS framework to address these issues, ranging from multi-dimensional dynamic load balancing and hybrid distributed/shared memory parallelism to the vectorization of the PIC algorithm. We present the results of the OASCR Joule Metric program on the issue of large scale modelling of LWFA, demonstrating speedups of over 1 order of magnitude on the same hardware. Finally, scalability to over ∼10 6 cores and sustained performance over ∼2 P Flops is demonstrated, opening the way for large scale modelling of LWFA scenarios. (paper)

An Effective Numerical Method and Its Utilization to Solution of Fractional Models Used in Bioengineering Applications

Directory of Open Access Journals (Sweden)

Petráš Ivo

2011-01-01

Full Text Available This paper deals with the fractional-order linear and nonlinear models used in bioengineering applications and an effective method for their numerical solution. The proposed method is based on the power series expansion of a generating function. Numerical solution is in the form of the difference equation, which can be simply applied in the Matlab/Simulink to simulate the dynamics of system. Several illustrative examples are presented, which can be widely used in bioengineering as well as in the other disciplines, where the fractional calculus is often used.

Numerical solution of an inverse 2D Cauchy problem connected with the Helmholtz equation

International Nuclear Information System (INIS)

Wei, T; Qin, H H; Shi, R

2008-01-01

In this paper, the Cauchy problem for the Helmholtz equation is investigated. By Green's formulation, the problem can be transformed into a moment problem. Then we propose a numerical algorithm for obtaining an approximate solution to the Neumann data on the unspecified boundary. Error estimate and convergence analysis have also been given. Finally, we present numerical results for several examples and show the effectiveness of the proposed method

Temperature prediction in a coal fired boiler with a fixed bed by fuzzy logic based on numerical solution

International Nuclear Information System (INIS)

Biyikoglu, A.; Akcayol, M.A.; Oezdemir, V.; Sivrioglu, M.

2005-01-01

In this study, steady state combustion in boilers with a fixed bed has been investigated. Temperature distributions in the combustion chamber of a coal fired boiler with a fixed bed are predicted using fuzzy logic based on data obtained from the numerical solution method for various coal and air feeding rates. The numerical solution method and the discretization of the governing equations of two dimensional turbulent flow in the combustion chamber and one dimensional coal combustion in the fixed bed are explained. Control Volume and Finite Difference Methods are used in the discretization of the equations in the combustion chamber and in the fixed bed, respectively. Results are presented as contours within the solution domain and compared with numerical ones. Comparison of the results shows that the difference between the numerical solution and fuzzy logic prediction throughout the computational domain is less than 1.5%. The statistical coefficient of multiple determinations for the investigated cases is about 0.9993 to 0.9998. This accuracy degree is acceptable in predicting the temperature values. So, it can be concluded that fuzzy logic provides a feasible method for defining the system properties

Numerical Methods for Solution of the Extended Linear Quadratic Control Problem

DEFF Research Database (Denmark)

Jørgensen, John Bagterp; Frison, Gianluca; Gade-Nielsen, Nicolai Fog

2012-01-01

In this paper we present the extended linear quadratic control problem, its efficient solution, and a discussion of how it arises in the numerical solution of nonlinear model predictive control problems. The extended linear quadratic control problem is the optimal control problem corresponding...... to the Karush-Kuhn-Tucker system that constitute the majority of computational work in constrained nonlinear and linear model predictive control problems solved by efficient MPC-tailored interior-point and active-set algorithms. We state various methods of solving the extended linear quadratic control problem...... and discuss instances in which it arises. The methods discussed in the paper have been implemented in efficient C code for both CPUs and GPUs for a number of test examples....

Final report for CAFDA project entitled, Experimental and numerical investigation of accelerated fluid interface

Energy Technology Data Exchange (ETDEWEB)

Greenough, J.A.; Jacobs, J.W.; Marcus, D.L.

1997-03-26

The main thrust of this collaborative effort can be summarized as an attempt to use the strengths of physical experiments and numerical simulations in understanding the dynamics of accelerated interfaces. Laboratory experiments represent the true nature of the physical processes and the simulations represent a model of these processes. We have taken the first steps toward this goal through development and calibration of new experimental techniques as well as validation and direct, systematic, and quantitative comparison with computational results. This report summarizes accomplishments made towards these goals. More detailed information is provided in reprints appended to this document.

Solved problems in classical mechanics analytical and numerical solutions with comments

CERN Document Server

de Lange, O L

2010-01-01

Apart from an introductory chapter giving a brief summary of Newtonian and Lagrangian mechanics, this book consists entirely of questions and solutions on topics in classical mechanics that will be encountered in undergraduate and graduate courses. These include one-, two-, and three- dimensional motion; linear and nonlinear oscillations; energy, potentials, momentum, and angular momentum; spherically symmetric potentials; multi-particle systems; rigid bodies; translation androtation of the reference frame; the relativity principle and some of its consequences. The solutions are followed by a set of comments intended to stimulate inductive reasoning and provide additional information of interest. Both analytical and numerical (computer) techniques are used to obtain andanalyze solutions. The computer calculations use Mathematica (version 7), and the relevant code is given in the text. It includes use of the interactive Manipulate function which enables one to observe simulated motion on a computer screen, and...

Bifurcation and chaos of an axially accelerating viscoelastic beam

International Nuclear Information System (INIS)

Yang Xiaodong; Chen Liqun

2005-01-01

This paper investigates bifurcation and chaos of an axially accelerating viscoelastic beam. The Kelvin-Voigt model is adopted to constitute the material of the beam. Lagrangian strain is used to account for the beam's geometric nonlinearity. The nonlinear partial-differential equation governing transverse motion of the beam is derived from the Newton second law. The Galerkin method is applied to truncate the governing equation into a set of ordinary differential equations. By use of the Poincare map, the dynamical behavior is identified based on the numerical solutions of the ordinary differential equations. The bifurcation diagrams are presented in the case that the mean axial speed, the amplitude of speed fluctuation and the dynamic viscoelasticity is respectively varied while other parameters are fixed. The Lyapunov exponent is calculated to identify chaos. From numerical simulations, it is indicated that the periodic, quasi-periodic and chaotic motions occur in the transverse vibrations of the axially accelerating viscoelastic beam

Efficient numerical methods for the large-scale, parallel solution of elastoplastic contact problems

KAUST Repository

Frohne, Jö rg; Heister, Timo; Bangerth, Wolfgang

2015-01-01

© 2016 John Wiley & Sons, Ltd. Quasi-static elastoplastic contact problems are ubiquitous in many industrial processes and other contexts, and their numerical simulation is consequently of great interest in accurately describing and optimizing production processes. The key component in these simulations is the solution of a single load step of a time iteration. From a mathematical perspective, the problems to be solved in each time step are characterized by the difficulties of variational inequalities for both the plastic behavior and the contact problem. Computationally, they also often lead to very large problems. In this paper, we present and evaluate a complete set of methods that are (1) designed to work well together and (2) allow for the efficient solution of such problems. In particular, we use adaptive finite element meshes with linear and quadratic elements, a Newton linearization of the plasticity, active set methods for the contact problem, and multigrid-preconditioned linear solvers. Through a sequence of numerical experiments, we show the performance of these methods. This includes highly accurate solutions of a three-dimensional benchmark problem and scaling our methods in parallel to 1024 cores and more than a billion unknowns.

Efficient numerical methods for the large-scale, parallel solution of elastoplastic contact problems

KAUST Repository

Frohne, Jörg

2015-08-06

© 2016 John Wiley & Sons, Ltd. Quasi-static elastoplastic contact problems are ubiquitous in many industrial processes and other contexts, and their numerical simulation is consequently of great interest in accurately describing and optimizing production processes. The key component in these simulations is the solution of a single load step of a time iteration. From a mathematical perspective, the problems to be solved in each time step are characterized by the difficulties of variational inequalities for both the plastic behavior and the contact problem. Computationally, they also often lead to very large problems. In this paper, we present and evaluate a complete set of methods that are (1) designed to work well together and (2) allow for the efficient solution of such problems. In particular, we use adaptive finite element meshes with linear and quadratic elements, a Newton linearization of the plasticity, active set methods for the contact problem, and multigrid-preconditioned linear solvers. Through a sequence of numerical experiments, we show the performance of these methods. This includes highly accurate solutions of a three-dimensional benchmark problem and scaling our methods in parallel to 1024 cores and more than a billion unknowns.

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

Dynamic Beam Solutions for Real-Time Simulation and Control Development of Flexible Rockets

Science.gov (United States)

Su, Weihua; King, Cecilia K.; Clark, Scott R.; Griffin, Edwin D.; Suhey, Jeffrey D.; Wolf, Michael G.

2016-01-01

In this study, flexible rockets are structurally represented by linear beams. Both direct and indirect solutions of beam dynamic equations are sought to facilitate real-time simulation and control development for flexible rockets. The direct solution is completed by numerically integrate the beam structural dynamic equation using an explicit Newmark-based scheme, which allows for stable and fast transient solutions to the dynamics of flexile rockets. Furthermore, in the real-time operation, the bending strain of the beam is measured by fiber optical sensors (FOS) at intermittent locations along the span, while both angular velocity and translational acceleration are measured at a single point by the inertial measurement unit (IMU). Another study in this paper is to find the analytical and numerical solutions of the beam dynamics based on the limited measurement data to facilitate the real-time control development. Numerical studies demonstrate the accuracy of these real-time solutions to the beam dynamics. Such analytical and numerical solutions, when integrated with data processing and control algorithms and mechanisms, have the potential to increase launch availability by processing flight data into the flexible launch vehicle's control system.

Application of the reduction of scale range in a Lorentz boosted frame to the numerical simulation of particle acceleration devices

International Nuclear Information System (INIS)

Vay, J.; Fawley, W.M.; Geddes, C.G.; Cormier-Michel, E.; Grote, D.P.

2009-01-01

It has been shown that the ratio of longest to shortest space and time scales of a system of two or more components crossing at relativistic velocities is not invariant under Lorentz transformation. This implies the existence of a frame of reference minimizing an aggregate measure of the ratio of space and time scales. It was demonstrated that this translated into a reduction by orders of magnitude in computer simulation run times, using methods based on first principles (e.g., Particle-In-Cell), for particle acceleration devices and for problems such as: free electron laser, laser-plasma accelerator, and particle beams interacting with electron clouds. Since then, speed-ups ranging from 75 to more than four orders of magnitude have been reported for the simulation of either scaled or reduced models of the above-cited problems. In it was shown that to achieve full benefits of the calculation in a boosted frame, some of the standard numerical techniques needed to be revised. The theory behind the speed-up of numerical simulation in a boosted frame, latest developments of numerical methods, and example applications with new opportunities that they offer are all presented

Pseudospectral operational matrix for numerical solution of single and multiterm time fractional diffusion equation

OpenAIRE

GHOLAMI, SAEID; BABOLIAN, ESMAIL; JAVIDI, MOHAMMAD

2016-01-01

This paper presents a new numerical approach to solve single and multiterm time fractional diffusion equations. In this work, the space dimension is discretized to the Gauss$-$Lobatto points. We use the normalized Grunwald approximation for the time dimension and a pseudospectral successive integration matrix for the space dimension. This approach shows that with fewer numbers of points, we can approximate the solution with more accuracy. Some examples with numerical results in tables and fig...

Numerical Solutions for Nonlinear High Damping Rubber Bearing Isolators: Newmark's Method with Netwon-Raphson Iteration Revisited

Science.gov (United States)

Markou, A. A.; Manolis, G. D.

2018-03-01

Numerical methods for the solution of dynamical problems in engineering go back to 1950. The most famous and widely-used time stepping algorithm was developed by Newmark in 1959. In the present study, for the first time, the Newmark algorithm is developed for the case of the trilinear hysteretic model, a model that was used to describe the shear behaviour of high damping rubber bearings. This model is calibrated against free-vibration field tests implemented on a hybrid base isolated building, namely the Solarino project in Italy, as well as against laboratory experiments. A single-degree-of-freedom system is used to describe the behaviour of a low-rise building isolated with a hybrid system comprising high damping rubber bearings and low friction sliding bearings. The behaviour of the high damping rubber bearings is simulated by the trilinear hysteretic model, while the description of the behaviour of the low friction sliding bearings is modeled by a linear Coulomb friction model. In order to prove the effectiveness of the numerical method we compare the analytically solved trilinear hysteretic model calibrated from free-vibration field tests (Solarino project) against the same model solved with the Newmark method with Netwon-Raphson iteration. Almost perfect agreement is observed between the semi-analytical solution and the fully numerical solution with Newmark's time integration algorithm. This will allow for extension of the trilinear mechanical models to bidirectional horizontal motion, to time-varying vertical loads, to multi-degree-of-freedom-systems, as well to generalized models connected in parallel, where only numerical solutions are possible.

Glass-surface area to solution-volume ratio and its implications to accelerated leach testing

International Nuclear Information System (INIS)

Pederson, L.R.; Buckwalter, C.Q.; McVay, G.L.; Riddle, B.L.

1982-10-01

The value of glass surface area to solution volume ratio (SA/V) can strongly influence the leaching rate of PNL 76-68 glass. The leaching rate is largely governed by silicon solubility constraints. Silicic acid in solution reduced the elemental release of all glass components. No components are leached to depths greater than that of silicon. The presence of the reaction layer had no measurable effect on the rate of leaching. Accelerated leach testing is possible since PNL 76-68 glass leaching is solubility-controlled (except at very low SA/V values). A series of glasses leached with SA/V x time = constant will yield identical elemental release

assessment of concentration of air pollutants using analytical and numerical solution of the atmospheric diffusion equation

International Nuclear Information System (INIS)

Esmail, S.F.H.

2011-01-01

The mathematical formulation of numerous physical problems a results in differential equations actually partial or ordinary differential equations.In our study we are interested in solutions of partial differential equations.The aim of this work is to calculate the concentrations of the pollution, by solving the atmospheric diffusion equation(ADE) using different mathematical methods of solution. It is difficult to solve the general form of ADE analytically, so we use some assumptions to get its solution.The solutions of it depend on the eddy diffusivity profiles(k) and the wind speed u. We use some physical assumptions to simplify its formula and solve it. In the present work, we solve the ADE analytically in three dimensions using Green's function method, Laplace transform method, normal mode method and these separation of variables method. Also, we use ADM as a numerical method. Finally, comparisons are made with the results predicted by the previous methods and the observed data.

Analytical solutions of a fractional diffusion-advection equation for solar cosmic-ray transport

International Nuclear Information System (INIS)

Litvinenko, Yuri E.; Effenberger, Frederic

2014-01-01

Motivated by recent applications of superdiffusive transport models to shock-accelerated particle distributions in the heliosphere, we analytically solve a one-dimensional fractional diffusion-advection equation for the particle density. We derive an exact Fourier transform solution, simplify it in a weak diffusion approximation, and compare the new solution with previously available analytical results and with a semi-numerical solution based on a Fourier series expansion. We apply the results to the problem of describing the transport of energetic particles, accelerated at a traveling heliospheric shock. Our analysis shows that significant errors may result from assuming an infinite initial distance between the shock and the observer. We argue that the shock travel time should be a parameter of a realistic superdiffusive transport model.

Beam polarization at the ILC. The physics impact and the accelerator solutions

Energy Technology Data Exchange (ETDEWEB)

Aurand, B. [Bonn Univ. (Germany). Phys. Inst.; Bailey, I. [Liverpool Univ. (United Kingdom). Cockcroft Inst.; Bartels, C. [DESY, Hamburg (Germany); DESY, Zeuthen (DE)] (and others)

2009-03-15

In this contribution accelerator solutions for polarized beams and their impact on physics measurements are discussed. Focus are physics requirements for precision polarimetry near the interaction point and their realization with polarized sources. Based on the ILC baseline programme as described in the Reference Design Report (RDR), recent developments are discussed and evaluated taking into account physics runs at beam energies between 100 GeV and 250 GeV, as well as calibration runs on the Z-pole and options as the 1 TeV upgrade and GigaZ. (orig.)

Application of a space-time CE/SE (Conversation Element/Solution Element) method to the numerical solution of chromatographic separation processes

DEFF Research Database (Denmark)

including convection-difmsion-reaction PDEs are numerically solved using the two methods on the same spatial grid. Even though the CE/SE method uses a simple stencil structure and is developed on a simple mathematical basis (i.e., Gauss' divergence theorem), accurate and computationally-efficient solutions...

Numerical algorithm for rigid body position estimation using the quaternion approach

Science.gov (United States)

Zigic, Miodrag; Grahovac, Nenad

2017-11-01

This paper deals with rigid body attitude estimation on the basis of the data obtained from an inertial measurement unit mounted on the body. The aim of this work is to present the numerical algorithm, which can be easily applied to the wide class of problems concerning rigid body positioning, arising in aerospace and marine engineering, or in increasingly popular robotic systems and unmanned aerial vehicles. Following the considerations of kinematics of rigid bodies, the relations between accelerations of different points of the body are given. A rotation matrix is formed using the quaternion approach to avoid singularities. We present numerical procedures for determination of the absolute accelerations of the center of mass and of an arbitrary point of the body expressed in the inertial reference frame, as well as its attitude. An application of the algorithm to the example of a heavy symmetrical gyroscope is presented, where input data for the numerical procedure are obtained from the solution of differential equations of motion, instead of using sensor measurements.

A note on numerical solution to the problem of criticality

International Nuclear Information System (INIS)

Kyncl, J.

2002-01-01

The contribution deals with numerical solution to the problem of criticality for neutron transport equation by the external source iteration method. Especially, the speed of convergence is examined. It is shown that if neutron absorption in the medium considered is high and if the space region occupied by the medium is large then a slow convergence of the iterations can be expected. This expectation is confirmed by results to CB4 benchmark obtained by MCNP code. Besides the results presented some questions concerning applications of them to criticality calculations are pointed out (Author)

Use of Green's functions in the numerical solution of two-point boundary value problems

Science.gov (United States)

Gallaher, L. J.; Perlin, I. E.

1974-01-01

This study investigates the use of Green's functions in the numerical solution of the two-point boundary value problem. The first part deals with the role of the Green's function in solving both linear and nonlinear second order ordinary differential equations with boundary conditions and systems of such equations. The second part describes procedures for numerical construction of Green's functions and considers briefly the conditions for their existence. Finally, there is a description of some numerical experiments using nonlinear problems for which the known existence, uniqueness or convergence theorems do not apply. Examples here include some problems in finding rendezvous orbits of the restricted three body system.

Nuclear models, experiments and data libraries needed for numerical simulation of accelerator-driven system

International Nuclear Information System (INIS)

Bauge, E.; Bersillon, O.

2000-01-01

This paper presents the transparencies of the speech concerning the nuclear models, experiments and data libraries needed for numerical simulation of Accelerator-Driven Systems. The first part concerning the nuclear models defines the spallation process, the corresponding models (intra-nuclear cascade, statistical model, Fermi breakup, fission, transport, decay and macroscopic aspects) and the code systems. The second part devoted to the experiments presents the angular measurements, the integral measurements, the residual nuclei and the energy deposition. In the last part, dealing with the data libraries, the author details the fundamental quantities as the reaction cross-section, the low energy transport databases and the decay libraries. (A.L.B.)

Numerical methods for the simulation of particle generated electromagnetic fields in acclerator physics

International Nuclear Information System (INIS)

Lau, T.

2006-01-01

In this work modifications of the classical Particle-In-Cell method for the solution of the Maxwell-Vlasov equations are investigated with respect to their application in particle accelerator physics. The aim of the work is to find modifications of the method which minimize and under certain conditions even eliminate the numerical dispersion effect along the beam axis in the numerical solution of Maxwell's equations. This is achieved by the development of dedicated time-integration methods for the Finite Integration Technique and two Finite Volume Methods. The methods are theoretically investigated regarding the conservation of a discrete energy and the existence of a discrete continuity equation. Finally, some of the methods are applied to the simulation of a high frequency rf-gun. (orig.)

The generalized PN synthetic acceleration method for linear transport problems with highly anisotropic scattering

International Nuclear Information System (INIS)

Khattab, K.M.

1997-01-01

The diffusion synthetic acceleration (DSA) method has been known to be an effective tool for accelerating the iterative solution of transport equations with isotropic or mildly anisotropic scattering. However, the DSA method is not effective for transport equations that have strongly anisotropic scattering. A generalization of the modified DSA (MDSA) method is proposed that converges (clock time) faster than the MDSA method. This method is developed, the results of a Fourier analysis that theoretically predicts its efficiency are described, and numerical results that verify the theoretical prediction are presented

A student's guide to numerical methods

CERN Document Server

Hutchinson, Ian H

2015-01-01

This concise, plain-language guide for senior undergraduates and graduate students aims to develop intuition, practical skills and an understanding of the framework of numerical methods for the physical sciences and engineering. It provides accessible self-contained explanations of mathematical principles, avoiding intimidating formal proofs. Worked examples and targeted exercises enable the student to master the realities of using numerical techniques for common needs such as solution of ordinary and partial differential equations, fitting experimental data, and simulation using particle and Monte Carlo methods. Topics are carefully selected and structured to build understanding, and illustrate key principles such as: accuracy, stability, order of convergence, iterative refinement, and computational effort estimation. Enrichment sections and in-depth footnotes form a springboard to more advanced material and provide additional background. Whether used for self-study, or as the basis of an accelerated introdu...

An exact solution on unsteady MHD free convection chemically reacting silver nanofluid flow past an exponentially accelerated vertical plate through porous medium

Science.gov (United States)

Kumaresan, E.; Vijaya Kumar, A. G.; Rushi Kumar, B.

2017-11-01

This article studies, an exact solution of unsteady MHD free convection boundary-layer flow of a silver nanofluid past an exponentially accelerated moving vertical plate through aporous medium in the presence of thermal radiation, transverse applied amagnetic field, radiation absorption and Heat generation or absorption with chemical reaction are investigated theoretically. We consider nanofluids contain spherical shaped nanoparticle of silverwith a nanoparticle volume concentration range smaller than or equal to 0.04. This phenomenon is modeled in the form of partial differential equations with initial boundary conditions. Some suitable dimensional variables are introduced. The corresponding dimensionless equations with boundary conditions are solved by using Laplace transform technique. The exact solutions for velocity, energy, and species are obtained, also the corresponding numerical values of nanofluid velocity, temperature and concentration profiles are represented graphically. The expressions for skin friction coefficient, the rate of heat transfer and mass transfer are derived. The present study finds applications involving heat transfer, enhancement of thermal conductivity and other applications like transportation, industrial cooling applications, heating buildings and reducing pollution, energy applications and solar absorption. The effect of heat transfer is found to be more pronounced in a silver-water nanofluid than in the other nanofluids.

Numerical and experimental investigations of coupled electromagnetic and thermal fields in superconducting accelerator magnets

International Nuclear Information System (INIS)

Mierau, Anna

2013-01-01

and its individual components, which occur during acceleration cycles. The study and analysis of these physical characteristics of the superconducting magnets and the relation between thermal und magnetic fields are subject of this PhD thesis. The object of investigation was the first SIS100 full size fast ramped superconducting dipole magnet prototype. Due to the complex design of accelerator magnets numerical simulations as well as measurements on test models are commonly used methods to determine the characteristics of the electromagnetic and thermal fields of such magnets. In the frame of this work both methods have been used to study the properties of the static magnetic field in the aperture of the dipole magnet. The dynamic heat losses in the magnet and its vacuum chamber were measured using the calorimetrical method. The knowledge gained in this work has contributed to the development of superconducting dipole magnets which will satisfy the operational conditions of the SIS100 beam guiding magnets. Furthermore, the knowledge of the dynamic heat loads in individual dipole units is important for developing a reliable cooling system for the superconducting magnets in the accelerator ring and thus for the stable operation of the SIS100 heavy ion synchrotron.

Numerical solution to the hermitian Yang-Mills equation on the Fermat quintic

International Nuclear Information System (INIS)

Douglas, Michael R.; Karp, Robert L.; Lukic, Sergio; Reinbacher, Rene

2007-01-01

We develop an iterative method for finding solutions to the hermitian Yang-Mills equation on stable holomorphic vector bundles, following ideas recently developed by Donaldson. As illustrations, we construct numerically the hermitian Einstein metrics on the tangent bundle and a rank three vector bundle on P 2 . In addition, we find a hermitian Yang-Mills connection on a stable rank three vector bundle on the Fermat quintic

Mean-field learning for satisfactory solutions

KAUST Repository

Tembine, Hamidou

2013-12-01

One of the fundamental challenges in distributed interactive systems is to design efficient, accurate, and fair solutions. In such systems, a satisfactory solution is an innovative approach that aims to provide all players with a satisfactory payoff anytime and anywhere. In this paper we study fully distributed learning schemes for satisfactory solutions in games with continuous action space. Considering games where the payoff function depends only on own-action and an aggregate term, we show that the complexity of learning systems can be significantly reduced, leading to the so-called mean-field learning. We provide sufficient conditions for convergence to a satisfactory solution and we give explicit convergence time bounds. Then, several acceleration techniques are used in order to improve the convergence rate. We illustrate numerically the proposed mean-field learning schemes for quality-of-service management in communication networks. © 2013 IEEE.

Direct numerical solution of the Ornstein-Zernike integral equation and spatial distribution of water around hydrophobic molecules

Science.gov (United States)

Ikeguchi, Mitsunori; Doi, Junta

1995-09-01

The Ornstein-Zernike integral equation (OZ equation) has been used to evaluate the distribution function of solvents around solutes, but its numerical solution is difficult for molecules with a complicated shape. This paper proposes a numerical method to directly solve the OZ equation by introducing the 3D lattice. The method employs no approximation the reference interaction site model (RISM) equation employed. The method enables one to obtain the spatial distribution of spherical solvents around solutes with an arbitrary shape. Numerical accuracy is sufficient when the grid-spacing is less than 0.5 Å for solvent water. The spatial water distribution around a propane molecule is demonstrated as an example of a nonspherical hydrophobic molecule using iso-value surfaces. The water model proposed by Pratt and Chandler is used. The distribution agrees with the molecular dynamics simulation. The distribution increases offshore molecular concavities. The spatial distribution of water around 5α-cholest-2-ene (C27H46) is visualized using computer graphics techniques and a similar trend is observed.

Numerical solution of ordinary differential equations

CERN Document Server

Fox, L

1987-01-01

Nearly 20 years ago we produced a treatise (of about the same length as this book) entitled Computing methods for scientists and engineers. It was stated that most computation is performed by workers whose mathematical training stopped somewhere short of the 'professional' level, and that some books are therefore needed which use quite simple mathematics but which nevertheless communicate the essence of the 'numerical sense' which is exhibited by the real computing experts and which is surely needed, at least to some extent, by all who use modern computers and modern numerical software. In that book we treated, at no great length, a variety of computational problems in which the material on ordinary differential equations occupied about 50 pages. At that time it was quite common to find books on numerical analysis, with a little on each topic ofthat field, whereas today we are more likely to see similarly-sized books on each major topic: for example on numerical linear algebra, numerical approximation, numeri...

Analysis of the Multiple-Solution Response of a Flexible Rotor Supported on Non-Linear Squeeze Film Dampers

Science.gov (United States)

ZHU, C. S.; ROBB, D. A.; EWINS, D. J.

2002-05-01

The multiple-solution response of rotors supported on squeeze film dampers is a typical non-linear phenomenon. The behaviour of the multiple-solution response in a flexible rotor supported on two identical squeeze film dampers with centralizing springs is studied by three methods: synchronous circular centred-orbit motion solution, numerical integration method and slow acceleration method using the assumption of a short bearing and cavitated oil film; the differences of computational results obtained by the three different methods are compared in this paper. It is shown that there are three basic forms for the multiple-solution response in the flexible rotor system supported on the squeeze film dampers, which are the resonant, isolated bifurcation and swallowtail bifurcation multiple solutions. In the multiple-solution speed regions, the rotor motion may be subsynchronous, super-subsynchronous, almost-periodic and even chaotic, besides synchronous circular centred, even if the gravity effect is not considered. The assumption of synchronous circular centred-orbit motion for the journal and rotor around the static deflection line can be used only in some special cases; the steady state numerical integration method is very useful, but time consuming. Using the slow acceleration method, not only can the multiple-solution speed regions be detected, but also the non-synchronous response regions.

Numerical solution of the Schroedinger equation with a polynomial potential

International Nuclear Information System (INIS)

Campoy, G.; Palma, A.

1986-01-01

A numerical method for solving the Schroedinger equation for a potential expressed as a polynomial is proposed. The basic assumption relies on the asymptotic properties of the solution of this equation. It is possible to obtain the energies and the stationary state functions simultaneously. They analyze, in particular, the cases of the quartic anharmonic oscillator and a hydrogen atom perturbed by a quadratic term, obtaining its energy eigenvalues for some values of the perturbation parameter. Together with the Hellmann-Feynman theorem, they use their algorithm to calculate expectation values of x'' for arbitrary positive values of n. 4 tables

Long-time behavior in numerical solutions of certain dynamical systems

International Nuclear Information System (INIS)

Vazquez, L.

1987-01-01

A general discretization of the ordinary nonlinear differential equations d 2 v/dt 2 =f(v) and dv/dt=g(v) is studied. The discrete scheme conserves the discrete analogous of a quantity that is conserved by the corresponding equations. This method is applied to two cases and no ''ghost solutions'' were observed for the long range calculation. In these cases we analyze the stability of the corresponding numerical scheme as a dynamical system and in the sense studied by Kuo Pen-Yu and Stetter. In particular we find a correspondence between both kinds of stability. (author)

Exact and Numerical Solutions of a Spatially-Distributed Mathematical Model for Fluid and Solute Transport in Peritoneal Dialysis

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Roman Cherniha

2016-06-01

Full Text Available The nonlinear mathematical model for solute and fluid transport induced by the osmotic pressure of glucose and albumin with the dependence of several parameters on the hydrostatic pressure is described. In particular, the fractional space available for macromolecules (albumin was used as a typical example and fractional fluid void volume were assumed to be different functions of hydrostatic pressure. In order to find non-uniform steady-state solutions analytically, some mathematical restrictions on the model parameters were applied. Exact formulae (involving hypergeometric functions for the density of fluid flux from blood to tissue and the fluid flux across tissues were constructed. In order to justify the applicability of the analytical results obtained, a wide range of numerical simulations were performed. It was found that the analytical formulae can describe with good approximation the fluid and solute transport (especially the rate of ultrafiltration for a wide range of values of the model parameters.

Numerical Solutions for Nonlinear High Damping Rubber Bearing Isolators: Newmark’s Method with Netwon-Raphson Iteration Revisited

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Markou A.A.

2018-03-01

Full Text Available Numerical methods for the solution of dynamical problems in engineering go back to 1950. The most famous and widely-used time stepping algorithm was developed by Newmark in 1959. In the present study, for the first time, the Newmark algorithm is developed for the case of the trilinear hysteretic model, a model that was used to describe the shear behaviour of high damping rubber bearings. This model is calibrated against free-vibration field tests implemented on a hybrid base isolated building, namely the Solarino project in Italy, as well as against laboratory experiments. A single-degree-of-freedom system is used to describe the behaviour of a low-rise building isolated with a hybrid system comprising high damping rubber bearings and low friction sliding bearings. The behaviour of the high damping rubber bearings is simulated by the trilinear hysteretic model, while the description of the behaviour of the low friction sliding bearings is modeled by a linear Coulomb friction model. In order to prove the effectiveness of the numerical method we compare the analytically solved trilinear hysteretic model calibrated from free-vibration field tests (Solarino project against the same model solved with the Newmark method with Netwon-Raphson iteration. Almost perfect agreement is observed between the semi-analytical solution and the fully numerical solution with Newmark’s time integration algorithm. This will allow for extension of the trilinear mechanical models to bidirectional horizontal motion, to time-varying vertical loads, to multi-degree-of-freedom-systems, as well to generalized models connected in parallel, where only numerical solutions are possible.

WATSFAR: numerical simulation of soil WATer and Solute fluxes using a FAst and Robust method

Science.gov (United States)

Crevoisier, David; Voltz, Marc

2013-04-01

To simulate the evolution of hydro- and agro-systems, numerous spatialised models are based on a multi-local approach and improvement of simulation accuracy by data-assimilation techniques are now used in many application field. The latest acquisition techniques provide a large amount of experimental data, which increase the efficiency of parameters estimation and inverse modelling approaches. In turn simulations are often run on large temporal and spatial domains which requires a large number of model runs. Eventually, despite the regular increase in computing capacities, the development of fast and robust methods describing the evolution of saturated-unsaturated soil water and solute fluxes is still a challenge. Ross (2003, Agron J; 95:1352-1361) proposed a method, solving 1D Richards' and convection-diffusion equation, that fulfil these characteristics. The method is based on a non iterative approach which reduces the numerical divergence risks and allows the use of coarser spatial and temporal discretisations, while assuring a satisfying accuracy of the results. Crevoisier et al. (2009, Adv Wat Res; 32:936-947) proposed some technical improvements and validated this method on a wider range of agro- pedo- climatic situations. In this poster, we present the simulation code WATSFAR which generalises the Ross method to other mathematical representations of soil water retention curve (i.e. standard and modified van Genuchten model) and includes a dual permeability context (preferential fluxes) for both water and solute transfers. The situations tested are those known to be the less favourable when using standard numerical methods: fine textured and extremely dry soils, intense rainfall and solute fluxes, soils near saturation, ... The results of WATSFAR have been compared with the standard finite element model Hydrus. The analysis of these comparisons highlights two main advantages for WATSFAR, i) robustness: even on fine textured soil or high water and solute

Superconducting accelerator technology

International Nuclear Information System (INIS)

Grunder, H.A.; Hartline, B.K.

1986-01-01

Modern and future accelerators for high energy and nuclear physics rely increasingly on superconducting components to achieve the required magnetic fields and accelerating fields. This paper presents a practical overview of the phenomenon of superconductivity, and describes the design issues and solutions associated with superconducting magnets and superconducting rf acceleration structures. Further development and application of superconducting components promises increased accelerator performance at reduced electric power cost

Experimental and numerical investigation of reactive shock-accelerated flows

Energy Technology Data Exchange (ETDEWEB)

Bonazza, Riccardo [Univ. of Wisconsin, Madison, WI (United States). Dept. of Engineering Physics

2016-12-20

The main goal of this program was to establish a qualitative and quantitative connection, based on the appropriate dimensionless parameters and scaling laws, between shock-induced distortion of astrophysical plasma density clumps and their earthbound analog in a shock tube. These objectives were pursued by carrying out laboratory experiments and numerical simulations to study the evolution of two gas bubbles accelerated by planar shock waves and compare the results to available astrophysical observations. The experiments were carried out in an vertical, downward-firing shock tube, 9.2 m long, with square internal cross section (25×25 cm²). Specific goals were to quantify the effect of the shock strength (Mach number, M) and the density contrast between the bubble gas and its surroundings (usually quantified by the Atwood number, i.e. the dimensionless density difference between the two gases) upon some of the most important flow features (e.g. macroscopic properties; turbulence and mixing rates). The computational component of the work performed through this program was aimed at (a) studying the physics of multi-phase compressible flows in the context of astrophysics plasmas and (b) providing a computational connection between laboratory experiments and the astrophysical application of shock-bubble interactions. Throughout the study, we used the FLASH4.2 code to run hydrodynamical and magnetohydrodynamical simulations of shock bubble interactions on an adaptive mesh.

Experimental and numerical investigation of reactive shock-accelerated flows

International Nuclear Information System (INIS)

Bonazza, Riccardo

2016-01-01

The main goal of this program was to establish a qualitative and quantitative connection, based on the appropriate dimensionless parameters and scaling laws, between shock-induced distortion of astrophysical plasma density clumps and their earthbound analog in a shock tube. These objectives were pursued by carrying out laboratory experiments and numerical simulations to study the evolution of two gas bubbles accelerated by planar shock waves and compare the results to available astrophysical observations. The experiments were carried out in an vertical, downward-firing shock tube, 9.2 m long, with square internal cross section (25x25 cm"2). Specific goals were to quantify the effect of the shock strength (Mach number, M) and the density contrast between the bubble gas and its surroundings (usually quantified by the Atwood number, i.e. the dimensionless density difference between the two gases) upon some of the most important flow features (e.g. macroscopic properties; turbulence and mixing rates). The computational component of the work performed through this program was aimed at (a) studying the physics of multi-phase compressible flows in the context of astrophysics plasmas and (b) providing a computational connection between laboratory experiments and the astrophysical application of shock-bubble interactions. Throughout the study, we used the FLASH4.2 code to run hydrodynamical and magnetohydrodynamical simulations of shock bubble interactions on an adaptive mesh.

LIE GROUPS AND NUMERICAL SOLUTIONS OF DIFFERENTIAL EQUATIONS: INVARIANT DISCRETIZATION VERSUS DIFFERENTIAL APPROXIMATION

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Decio Levi

2013-10-01

Full Text Available We briefly review two different methods of applying Lie group theory in the numerical solution of ordinary differential equations. On specific examples we show how the symmetry preserving discretization provides difference schemes for which the “first differential approximation” is invariant under the same Lie group as the original ordinary differential equation.

Use of artificial bee colonies algorithm as numerical approximation of differential equations solution

Science.gov (United States)

Fikri, Fariz Fahmi; Nuraini, Nuning

2018-03-01

The differential equation is one of the branches in mathematics which is closely related to human life problems. Some problems that occur in our life can be modeled into differential equations as well as systems of differential equations such as the Lotka-Volterra model and SIR model. Therefore, solving a problem of differential equations is very important. Some differential equations are difficult to solve, so numerical methods are needed to solve that problems. Some numerical methods for solving differential equations that have been widely used are Euler Method, Heun Method, Runge-Kutta and others. However, some of these methods still have some restrictions that cause the method cannot be used to solve more complex problems such as an evaluation interval that we cannot change freely. New methods are needed to improve that problems. One of the method that can be used is the artificial bees colony algorithm. This algorithm is one of metaheuristic algorithm method, which can come out from local search space and do exploration in solution search space so that will get better solution than other method.

Aitken extrapolation and epsilon algorithm for an accelerated solution of weakly singular nonlinear Volterra integral equations

International Nuclear Information System (INIS)

Mesgarani, H; Parmour, P; Aghazadeh, N

2010-01-01

In this paper, we apply Aitken extrapolation and epsilon algorithm as acceleration technique for the solution of a weakly singular nonlinear Volterra integral equation of the second kind. In this paper, based on Tao and Yong (2006 J. Math. Anal. Appl. 324 225-37.) the integral equation is solved by Navot's quadrature formula. Also, Tao and Yong (2006) for the first time applied Richardson extrapolation to accelerating convergence for the weakly singular nonlinear Volterra integral equations of the second kind. To our knowledge, this paper may be the first attempt to apply Aitken extrapolation and epsilon algorithm for the weakly singular nonlinear Volterra integral equations of the second kind.

Numerical solution of newton´s cooling differential equation by the methods of euler and runge-kutta

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Andresa Pescador

2016-04-01

Full Text Available This article presents the first-order differential equations, which are a very important branch of mathematics as they have a wide applicability, in mathematics, as in physics, biology and economy. The objective of this study was to analyze the resolution of the equation that defines the cooling Newton's law. Verify its behavior using some applications that can be used in the classroom as an auxiliary instrument to the teacher in addressing these contents bringing answers to the questions of the students and motivating them to build their knowledge. It attempted to its resolution through two numerical methods, Euler method and Runge -Kutta method. Finally, there was a comparison of the approach of the solution given by the numerical solution with the analytical resolution whose solution is accurate.

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)

Different nonideality relationships, different databases and their effects on modeling precipitation from concentrated solutions using numerical speciation codes

Energy Technology Data Exchange (ETDEWEB)

Brown, L.F.; Ebinger, M.H.

1996-08-01

Four simple precipitation problems are solved to examine the use of numerical equilibrium codes. The study emphasizes concentrated solutions, assumes both ideal and nonideal solutions, and employs different databases and different activity-coefficient relationships. The study uses the EQ3/6 numerical speciation codes. The results show satisfactory material balances and agreement between solubility products calculated from free-energy relationships and those calculated from concentrations and activity coefficients. Precipitates show slightly higher solubilities when the solutions are regarded as nonideal than when considered ideal, agreeing with theory. When a substance may precipitate from a solution dilute in the precipitating substance, a code may or may not predict precipitation, depending on the database or activity-coefficient relationship used. In a problem involving a two-component precipitation, there are only small differences in the precipitate mass and composition between the ideal and nonideal solution calculations. Analysis of this result indicates that this may be a frequent occurrence. An analytical approach is derived for judging whether this phenomenon will occur in any real or postulated precipitation situation. The discussion looks at applications of this approach. In the solutes remaining after the precipitations, there seems to be little consistency in the calculated concentrations and activity coefficients. They do not appear to depend in any coherent manner on the database or activity-coefficient relationship used. These results reinforce warnings in the literature about perfunctory or mechanical use of numerical speciation codes.

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

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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. 

Comparative numerical solutions of stiff Ordinary differential equations using magnus series expansion method

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SURE KÖME

2014-12-01

Full Text Available In this paper, we investigated the effect of Magnus Series Expansion Method on homogeneous stiff ordinary differential equations with different stiffness ratios. A Magnus type integrator is used to obtain numerical solutions of two different examples of stiff problems and exact and approximate results are tabulated. Furthermore, absolute error graphics are demonstrated in detail.

Diffusion-synthetic acceleration methods for discrete-ordinates problems

International Nuclear Information System (INIS)

Larsen, E.W.

1984-01-01

The diffusion-synthetic acceleration (DSA) method is an iterative procedure for obtaining numerical solutions of discrete-ordinates problems. The DSA method is operationally more complicated than the standard source-iteration (SI) method, but if encoded properly it converges much more rapidly, especially for problems with diffusion-like regions. In this article we describe the basic ideas behind the DSA method and give a (roughly chronological) review of its long development. We conclude with a discussion which covers additional topics, including some remaining open problems an the status of current efforts aimed at solving these problems

Parameter estimation in IMEX-trigonometrically fitted methods for the numerical solution of reaction-diffusion problems

Science.gov (United States)

D'Ambrosio, Raffaele; Moccaldi, Martina; Paternoster, Beatrice

2018-05-01

In this paper, an adapted numerical scheme for reaction-diffusion problems generating periodic wavefronts is introduced. Adapted numerical methods for such evolutionary problems are specially tuned to follow prescribed qualitative behaviors of the solutions, making the numerical scheme more accurate and efficient as compared with traditional schemes already known in the literature. Adaptation through the so-called exponential fitting technique leads to methods whose coefficients depend on unknown parameters related to the dynamics and aimed to be numerically computed. Here we propose a strategy for a cheap and accurate estimation of such parameters, which consists essentially in minimizing the leading term of the local truncation error whose expression is provided in a rigorous accuracy analysis. In particular, the presented estimation technique has been applied to a numerical scheme based on combining an adapted finite difference discretization in space with an implicit-explicit time discretization. Numerical experiments confirming the effectiveness of the approach are also provided.

Multiresolution Modeling of Semidilute Polymer Solutions: Coarse-Graining Using Wavelet-Accelerated Monte Carlo

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Animesh Agarwal

2017-09-01

Full Text Available We present a hierarchical coarse-graining framework for modeling semidilute polymer solutions, based on the wavelet-accelerated Monte Carlo (WAMC method. This framework forms a hierarchy of resolutions to model polymers at length scales that cannot be reached via atomistic or even standard coarse-grained simulations. Previously, it was applied to simulations examining the structure of individual polymer chains in solution using up to four levels of coarse-graining (Ismail et al., J. Chem. Phys., 2005, 122, 234901 and Ismail et al., J. Chem. Phys., 2005, 122, 234902, recovering the correct scaling behavior in the coarse-grained representation. In the present work, we extend this method to the study of polymer solutions, deriving the bonded and non-bonded potentials between coarse-grained superatoms from the single chain statistics. A universal scaling function is obtained, which does not require recalculation of the potentials as the scale of the system is changed. To model semi-dilute polymer solutions, we assume the intermolecular potential between the coarse-grained beads to be equal to the non-bonded potential, which is a reasonable approximation in the case of semidilute systems. Thus, a minimal input of microscopic data is required for simulating the systems at the mesoscopic scale. We show that coarse-grained polymer solutions can reproduce results obtained from the more detailed atomistic system without a significant loss of accuracy.

Fourier analysis of Solar atmospheric numerical simulations accelerated with GPUs (CUDA).

Science.gov (United States)

Marur, A.

2015-12-01

Solar dynamics from the convection zone creates a variety of waves that may propagate through the solar atmosphere. These waves are important in facilitating the energy transfer between the sun's surface and the corona as well as propagating energy throughout the solar system. How and where these waves are dissipated remains an open question. Advanced 3D numerical simulations have furthered our understanding of the processes involved. Fourier transforms to understand the nature of the waves by finding the frequency and wavelength of these waves through the simulated atmosphere, as well as the nature of their propagation and where they get dissipated. In order to analyze the different waves produced by the aforementioned simulations and models, Fast Fourier Transform algorithms will be applied. Since the processing of the multitude of different layers of the simulations (of the order of several 100^3 grid points) would be time intensive and inefficient on a CPU, CUDA, a computing architecture that harnesses the power of the GPU, will be used to accelerate the calculations.

Multiresolution strategies for the numerical solution of optimal control problems

Science.gov (United States)

Jain, Sachin

There exist many numerical techniques for solving optimal control problems but less work has been done in the field of making these algorithms run faster and more robustly. The main motivation of this work is to solve optimal control problems accurately in a fast and efficient way. Optimal control problems are often characterized by discontinuities or switchings in the control variables. One way of accurately capturing the irregularities in the solution is to use a high resolution (dense) uniform grid. This requires a large amount of computational resources both in terms of CPU time and memory. Hence, in order to accurately capture any irregularities in the solution using a few computational resources, one can refine the mesh locally in the region close to an irregularity instead of refining the mesh uniformly over the whole domain. Therefore, a novel multiresolution scheme for data compression has been designed which is shown to outperform similar data compression schemes. Specifically, we have shown that the proposed approach results in fewer grid points in the grid compared to a common multiresolution data compression scheme. The validity of the proposed mesh refinement algorithm has been verified by solving several challenging initial-boundary value problems for evolution equations in 1D. The examples have demonstrated the stability and robustness of the proposed algorithm. The algorithm adapted dynamically to any existing or emerging irregularities in the solution by automatically allocating more grid points to the region where the solution exhibited sharp features and fewer points to the region where the solution was smooth. Thereby, the computational time and memory usage has been reduced significantly, while maintaining an accuracy equivalent to the one obtained using a fine uniform mesh. Next, a direct multiresolution-based approach for solving trajectory optimization problems is developed. The original optimal control problem is transcribed into a

Numerical analysis

CERN Document Server

Rao, G Shanker

2006-01-01

About the Book: This book provides an introduction to Numerical Analysis for the students of Mathematics and Engineering. The book is designed in accordance with the common core syllabus of Numerical Analysis of Universities of Andhra Pradesh and also the syllabus prescribed in most of the Indian Universities. Salient features: Approximate and Numerical Solutions of Algebraic and Transcendental Equation Interpolation of Functions Numerical Differentiation and Integration and Numerical Solution of Ordinary Differential Equations The last three chapters deal with Curve Fitting, Eigen Values and Eigen Vectors of a Matrix and Regression Analysis. Each chapter is supplemented with a number of worked-out examples as well as number of problems to be solved by the students. This would help in the better understanding of the subject. Contents: Errors Solution of Algebraic and Transcendental Equations Finite Differences Interpolation with Equal Intervals Interpolation with Unequal Int...

Spectrum Evolution of Accelerating or Slowing down Soliton at its Propagation in a Medium with Gold Nanorods

Science.gov (United States)

Trofimov, Vyacheslav A.; Lysak, Tatiana M.

2018-04-01

We investigate both numerically and analytically the spectrum evolution of a novel type soliton - nonlinear chirped accelerating or decelerating soliton - at a femtosecond pulse propagation in a medium containing noble nanoparticles. In our consideration, we take into account one- or two-photon absorption of laser radiation by nanorods, and time-dependent nanorod aspect ratio changing due to their melting or reshaping because of laser energy absorption. The chirped solitons are formed due to the trapping of laser radiation by the nanorods reshaping fronts, if a positive or negative phase-amplitude grating is induced by laser radiation. Accelerating or slowing down chirped soliton formation is accompanied by the soliton spectrum blue or red shift. To prove our numerical results, we derived the approximate analytical law for the spectrum maximum intensity evolution along the propagation coordinate, based on earlier developed approximate analytical solutions for accelerating and decelerating solitons.

Different Solutions for the Generator-accelerator Module

Science.gov (United States)

Savin, E. A.; Matsievskiy, S. V.; Sobenin, N. P.; Zavadtsev, A. A.; Zavadtsev, D. A.

The most important part of the particle accelerators [1] - is the power generator together with the whole feeding system [2]. All types of generators, such as klystrons, magnetrons, solid state generators cover their own field of power and pulse length values. For the last couple of year the Inductive Output Tubes (IOT) becomes very popular because of their comparative construction simplicity: it represents the klystron output cavity with the grid modulated electron beam injected in it. Now such IOTs are used with the superconductive particle accelerators at 700 MHz operating frequency with around 1MW output power. Higher frequencies problem - is the inability to apply high frequency modulated voltage to the grid. Thus we need to figure out some kind of RF gun. But this article is about the first steps of the geometry and beam dynamics simulation in the six beam S-band IOT, which will be used with the compact biperiodic accelerating structure.

Grad-Shafranov reconstruction: overview and improvement of the numerical solution used in space physics

Energy Technology Data Exchange (ETDEWEB)

Ojeda Gonzalez, A.; Domingues, M.O.; Mendes, O., E-mail: ojeda.gonzalez.a@gmail.com [Instituto Nacional de Pesquisas Espaciais (INPE), Sao Jose dos Campos, SP (Brazil); Kaibara, M.K. [Universidade Federal Fluminense (GMA/IME/UFF), Niteroi, RJ (Brazil); Prestes, A. [Universidade do Vale do Paraiba (IP and D/UNIVAP), Sao Jose dos Campos, SP (Brazil). Lab. de Fisica e Astronomia

2015-10-15

The Grad-Shafranov equation is a Poisson's equation, i.e., a partial differential equation of elliptic type. The problem is depending on the initial condition and can be treated as a Cauchy problem. Although it is ill-posed or ill-conditioned, it can be integrated numerically. In the integration of the GS equation, singularities with large values of the potential arise after a certain number of integration steps away from the original data line, and a filter should be used. The Grad-Shafranov reconstruction (GSR) technique was developed from 1996 to 2000 for recovering two-dimensional structures in the magnetopause in an ideal MHD formulation. Other works have used the GSR techniques to study magnetic flux ropes in the solar wind and in the magnetotail from a single spacecraft dataset; posteriorly, it was extended to treat measurements from multiple satellites. From Vlasov equation, it is possible to arrive at the GS-equation in function of the normalized vector potential. A general solution is obtained using complex variable theory. A specific solution was chosen as benchmark case to solve numerically the GS equation.We propose some changes in the resolution scheme of the GS equation to improve the solution. The result of each method is compared with the solution proposed by Hau and Sonnerup (J. Geophys. Res. 104(A4), 6899-6917 (1999)). The main improvement found in the GS resolution was the need to filter Bx values at each y value. (author)

Numerical Simulation of the Freeze-Thaw Behavior of Mortar Containing Deicing Salt Solution.

Science.gov (United States)

Esmaeeli, Hadi S; Farnam, Yaghoob; Bentz, Dale P; Zavattieri, Pablo D; Weiss, Jason

2017-02-01

This paper presents a one-dimensional finite difference model that is developed to describe the freeze-thaw behavior of an air-entrained mortar containing deicing salt solution. A phenomenological model is used to predict the temperature and the heat flow for mortar specimens during cooling and heating. Phase transformations associated with the freezing/melting of water/ice or transition of the eutectic solution from liquid to solid are included in this phenomenological model. The lever rule is used to calculate the quantity of solution that undergoes the phase transformation, thereby simulating the energy released/absorbed during phase transformation. Undercooling and pore size effects are considered in the numerical model. To investigate the effect of pore size distribution, this distribution is considered using the Gibbs-Thomson equation in a saturated mortar specimen. For an air-entrained mortar, the impact of considering pore size (and curvature) on freezing was relatively insignificant; however the impact of pore size is much more significant during melting. The fluid inside pores smaller than 5 nm (i.e., gel pores) has a relatively small contribution in the macroscopic freeze-thaw behavior of mortar specimens within the temperature range used in this study (i.e., +24 °C to -35 °C), and can therefore be neglected for the macroscopic freeze-thaw simulations. A heat sink term is utilized to simulate the heat dissipation during phase transformations. Data from experiments performed using a low-temperature longitudinal guarded comparative calorimeter (LGCC) on mortar specimens fully saturated with various concentration NaCl solutions or partially saturated with water is compared to the numerical results and a promising agreement is generally obtained.

ASAP - A symbolic algebra package for accelerator design

International Nuclear Information System (INIS)

Bozoki, E.; Friedman, A.; Ben-Zvi, I.

1991-01-01

The design of a modern accelerator is a complicated task that involves the integration of many devices. As a consequence many parameters must be optimized in order to achieve a satisfactory result. Even the design of a simple subsystem, such as a bending system, requires that the designer will pick a successful choice from a wide range of alternatives. Usually, the task is too large to allow an analytical design, and the designer has to use a computer code (such as MAD or TRANSPORT) to simulate the system and numerically find the desired conditions. The disadvantages of this numerical method are, that (1) the solutions, i.e. the choice of the parameters may or may not be optimal and (2) each change in a parameter requires to recalculate the whole system, thus a detailed design is lengthy and costly. The authors report the conceptual design and primary implementation steps of a symbolic algebra program based on MACSYMA for the design of accelerators, storage rings and transport lines. The motivation for using symbolic algebra is discussed and a design case is presented that shows the advantage of this approach

The generalized PN synthetic acceleration method for linear transport problems with highly anisotropic scattering

International Nuclear Information System (INIS)

Khattab, K.M.

1998-01-01

The diffusion synthetic acceleration (DSA) method has been known to be an effective tool for accelerating the iterative solution of transport equations with isotopic or mildly anisotropic scattering. However, the DSA method is not effective for transport equations that have strongly anisotropic scattering. A generalization of the modified DSA (MDSA) methods is proposed. This method converges (Clock time) faster than the MDSA method. It is developed, the results of a Fourier analysis that theoretically predicts its efficiency are described, and numerical results that verify the theoretical prediction are presented. (author). 9 refs., 2 tabs., 5 figs

Acceleration of polarized proton beams

International Nuclear Information System (INIS)

Roser, T.

1998-01-01

The acceleration of polarized beams in circular accelerators is complicated by the numerous depolarizing spin resonances. Using a partial Siberian snake and a rf dipole that ensure stable adiabatic spin motion during acceleration has made it possible to accelerate polarized protons to 25 GeV at the Brookhaven AGS. Full Siberian snakes are being developed for RHIC to make the acceleration of polarized protons to 250 GeV possible. A similar scheme is being studied for the 800 GeV HERA proton accelerator

Accelerated solution of non-linear flow problems using Chebyshev iteration polynomial based RK recursions

Energy Technology Data Exchange (ETDEWEB)

Lorber, A.A.; Carey, G.F.; Bova, S.W.; Harle, C.H. [Univ. of Texas, Austin, TX (United States)

1996-12-31

The connection between the solution of linear systems of equations by iterative methods and explicit time stepping techniques is used to accelerate to steady state the solution of ODE systems arising from discretized PDEs which may involve either physical or artificial transient terms. Specifically, a class of Runge-Kutta (RK) time integration schemes with extended stability domains has been used to develop recursion formulas which lead to accelerated iterative performance. The coefficients for the RK schemes are chosen based on the theory of Chebyshev iteration polynomials in conjunction with a local linear stability analysis. We refer to these schemes as Chebyshev Parameterized Runge Kutta (CPRK) methods. CPRK methods of one to four stages are derived as functions of the parameters which describe an ellipse {Epsilon} which the stability domain of the methods is known to contain. Of particular interest are two-stage, first-order CPRK and four-stage, first-order methods. It is found that the former method can be identified with any two-stage RK method through the correct choice of parameters. The latter method is found to have a wide range of stability domains, with a maximum extension of 32 along the real axis. Recursion performance results are presented below for a model linear convection-diffusion problem as well as non-linear fluid flow problems discretized by both finite-difference and finite-element methods.

Application of preconditioned GMRES to the numerical solution of the neutron transport equation

International Nuclear Information System (INIS)

Patton, B.W.; Holloway, J.P.

2002-01-01

The generalized minimal residual (GMRES) method with right preconditioning is examined as an alternative to both standard and accelerated transport sweeps for the iterative solution of the diamond differenced discrete ordinates neutron transport equation. Incomplete factorization (ILU) type preconditioners are used to determine their effectiveness in accelerating GMRES for this application. ILU(τ), which requires the specification of a dropping criteria τ, proves to be a good choice for the types of problems examined in this paper. The combination of ILU(τ) and GMRES is compared with both DSA and unaccelerated transport sweeps for several model problems. It is found that the computational workload of the ILU(τ)-GMRES combination scales nonlinearly with the number of energy groups and quadrature order, making this technique most effective for problems with a small number of groups and discrete ordinates. However, the cost of preconditioner construction can be amortized over several calculations with different source and/or boundary values. Preconditioners built upon standard transport sweep algorithms are also evaluated as to their effectiveness in accelerating the convergence of GMRES. These preconditioners show better scaling with such problem parameters as the scattering ratio, the number of discrete ordinates, and the number of spatial meshes. These sweeps based preconditioners can also be cast in a matrix free form that greatly reduces storage requirements

A Comparison of Numerical and Analytical Radiative-Transfer Solutions for Plane Albedo in Natural Waters

Science.gov (United States)

Several numerical and analytical solutions of the radiative transfer equation (RTE) for plane albedo were compared for solar light reflection by sea water. The study incorporated the simplest case, that being a semi-infinite one-dimensional plane-parallel absorbing and scattering...

Numerical solution of multi group-Two dimensional- Adjoint equation with finite element method

International Nuclear Information System (INIS)

Poursalehi, N.; Khalafi, H.; Shahriari, M.; Minoochehr

2008-01-01

Adjoint equation is used for perturbation theory in nuclear reactor design. For numerical solution of adjoint equation, usually two methods are applied. These are Finite Element and Finite Difference procedures. Usually Finite Element Procedure is chosen for solving of adjoint equation, because it is more use able in variety of geometries. In this article, Galerkin Finite Element method is discussed. This method is applied for numerical solving multi group, multi region and two dimensional (X, Y) adjoint equation. Typical reactor geometry is partitioned with triangular meshes and boundary condition for adjoint flux is considered zero. Finally, for a case of defined parameters, Finite Element Code was applied and results were compared with Citation Code

A numerical solution of a singular boundary value problem arising in boundary layer theory.

Science.gov (United States)

Hu, Jiancheng

2016-01-01

In this paper, a second-order nonlinear singular boundary value problem is presented, which is equivalent to the well-known Falkner-Skan equation. And the one-dimensional third-order boundary value problem on interval [Formula: see text] is equivalently transformed into a second-order boundary value problem on finite interval [Formula: see text]. The finite difference method is utilized to solve the singular boundary value problem, in which the amount of computational effort is significantly less than the other numerical methods. The numerical solutions obtained by the finite difference method are in agreement with those obtained by previous authors.

A numerical comparison between the multiple-scales and finite-element solution for sound propagation in lined flow ducts

NARCIS (Netherlands)

Rienstra, S.W.; Eversman, W.

2001-01-01

An explicit, analytical, multiple-scales solution for modal sound transmission through slowly varying ducts with mean flow and acoustic lining is tested against a numerical finite-element solution solving the same potential flow equations. The test geometry taken is representative of a high-bypass

Particle acceleration in solar flares: observations versus numerical simulations

International Nuclear Information System (INIS)

Benz, A O; Grigis, P C; Battaglia, M

2006-01-01

Solar flares are generally agreed to be impulsive releases of magnetic energy. Reconnection in dilute plasma is the suggested trigger for the coronal phenomenon. It releases up to 10 26 J, accelerates up to 10 38 electrons and ions and must involve a volume that greatly exceeds the current sheet dimension. The Ramaty High-Energy Solar Spectroscopic Imager satellite can image a source in the corona that appears to contain the acceleration region and can separate it from other x-ray emissions. The new observations constrain the acceleration process by a quantitative relation between spectral index and flux. We present recent observational results and compare them with theoretical modelling by a stochastic process assuming transit-time damping of fast-mode waves, escape and replenishment. The observations can only be fitted if additional assumptions on trapping by an electric potential and possibly other processes such as isotropization and magnetic trapping are made

Numerical solution of fully developed heat transfer problem with constant wall temperature and application to isosceles triangle and parabolic ducts

International Nuclear Information System (INIS)

Karabulut, Halit; Ipci, Duygu; Cinar, Can

2016-01-01

Highlights: • A numerical method has been developed for fully developed flows with constant wall temperature. • The governing equations were transformed to boundary fitted coordinates. • The Nusselt number of parabolic duct has been investigated. • Validation of the numerical method has been made by comparing published data. - Abstract: In motor-vehicles the use of more compact radiators have several advantages such as; improving the aerodynamic form of cars, reducing the weight and volume of the cars, reducing the material consumption and environmental pollutions, and enabling faster increase of the engine coolant temperature after starting to run and thereby improving the thermal efficiency. For the design of efficient and compact radiators, the robust determination of the heat transfer coefficient becomes imperative. In this study the external heat transfer coefficient of the radiator has been investigated for hydrodynamically and thermally fully developed flows in channels with constant wall temperature. In such situation the numerical treatment of the problem results in a trivial solution. To find a non-trivial solution the problem is treated either as an eigenvalue problem or as a thermally developing flow problem. In this study a numerical solution procedure has been developed and the heat transfer coefficients of the fully developed flow in triangular and parabolic air channels were investigated. The governing equations were transformed to boundary fitted coordinates and numerically solved. The non-trivial solution was obtained by means of guessing the temperature of any grid point within the solution domain. The correction of the guessed temperature was performed via smoothing the temperature profile on a line passing through the mentioned grid point. Results were compared with literature data and found to be consistent.

Longitudinal wake field for an electron beam accelerated through a ultra-high field gradient

Energy Technology Data Exchange (ETDEWEB)

Geloni, G.; Saldin, E.; Schneidmiller, E.; Yurkov, M.

2006-12-15

Electron accelerators with higher and higher longitudinal field gradients are desirable, as they allow for the production of high energy beams by means of compact and cheap setups. The new laser-plasma acceleration technique appears to constitute the more promising breakthrough in this direction, delivering unprecedent field gradients up to TV/m. In this article we give a quantitative description of the impact of longitudinal wake fields on the electron beam. Our paper is based on the solution of Maxwell's equations for the longitudinal field. Our conclusions are valid when the acceleration distance is much smaller than the the overtaking length, that is the length that electrons travel as a light signal from the tail of the bunch overtakes the head of the bunch. This condition is well verified for laser-plasma devices. We calculate a closed expression for the impedance and the wake function that may be evaluated numerically. It is shown that the rate of energy loss in the bunch due to radiative interaction is equal to the energy emitted through coherent radiation in the far-zone. Furthermore, an expression is found for the asymptotic limit of a large distance of the electron beam from the accelerator compared with the overtaking length. Such expression allows us to calculate analytical solutions for a Gaussian transverse and longitudinal bunch shape. Finally, we study the feasibility of Table-Top Free-Electron Lasers in the Vacuum Ultra-Violet (TT-VUV FEL) and X-ray range (TT-XFEL), respectively based on 100 MeV and 1 GeV laser-plasma accelerator drivers. Numerical estimations presented in this paper indicate that the effects of the time-dependent energy change induced by the longitudinal wake pose a serious threat to the operation of these devices. (orig.)

Numerical analysis of the asymptotic behavior of solutions of a boundary problem for a nonlinear parabolic equation

International Nuclear Information System (INIS)

Vasileva, D.P.

1993-01-01

Blow-up and global time self-similar solutions of a boundary problem for a nonlinear equation u t = Δ u σ+1 + u β are found in the case β = σ + 1. It is shown that they describe the asymptotic behavior of a wide class of initial perturbations. A numerical investigation of the solutions in the case β>σ + 1 is also made. A hypothesis is done that the behavior for large times of global time solutions is described by the self-similar solutions of the equation without source.(author). 20 refs.; 9 figs

Numerical Approximations to the Solution of Ray Tracing through the Crystalline Lens

International Nuclear Information System (INIS)

Yildirim, A.; Gökdoğan, A.; Merdan, M.; Lakshminarayanan, V.

2012-01-01

An approximate analytical solution in the form of a rapidly convergent series for tracing light rays through an inhomogeneous graded index medium is developed, using the multi-step differential transform method based on the classical differential transformation method. Numerical results are compared to those obtained by the fourth-order Runge—Kutta method to illustrate the precision and effectiveness of the proposed method. Results are given in explicit and graphical forms. (fundamental areas of phenomenology(including applications))

The numerical solution of thawing process in phase change slab using variable space grid technique

Directory of Open Access Journals (Sweden)

Serttikul, C.

2007-09-01

Full Text Available This paper focuses on the numerical analysis of melting process in phase change material which considers the moving boundary as the main parameter. In this study, pure ice slab and saturated porous packed bed are considered as the phase change material. The formulation of partial differential equations is performed consisting heat conduction equations in each phase and moving boundary equation (Stefan equation. The variable space grid method is then applied to these equations. The transient heat conduction equations and the Stefan condition are solved by using the finite difference method. A one-dimensional melting model is then validated against the available analytical solution. The effect of constant temperature heat source on melting rate and location of melting front at various times is studied in detail.It is found that the nonlinearity of melting rate occurs for a short time. The successful comparison with numerical solution and analytical solution should give confidence in the proposed mathematical treatment, and encourage the acceptance of this method as useful tool for exploring practical problems such as forming materials process, ice melting process, food preservation process and tissue preservation process.

Almost Surely Asymptotic Stability of Exact and Numerical Solutions for Neutral Stochastic Pantograph Equations

Directory of Open Access Journals (Sweden)

Zhanhua Yu

2011-01-01

Full Text Available We study the almost surely asymptotic stability of exact solutions to neutral stochastic pantograph equations (NSPEs, and sufficient conditions are obtained. Based on these sufficient conditions, we show that the backward Euler method (BEM with variable stepsize can preserve the almost surely asymptotic stability. Numerical examples are demonstrated for illustration.

Solving the quasi-static field model of the pulse-line accelerator; relationship to a circuit model

International Nuclear Information System (INIS)

Friedman, Alex

2005-01-01

The Pulse-Line Ion Accelerator (PLIA) is a promising approach to high-gradient acceleration of an ion beam at high line charge density. A recent note by R. J. Briggs suggests that a 'sheath helix' model of such a system can be solved numerically in the quasi-static limit. Such a model captures the correct macroscopic behavior from first principles without the need to time-advance the full Maxwell equations on a grid. This note describes numerical methods that may be used to effect such a solution, and their connection to the circuit model that was described in an earlier note by the author. Fine detail of the fields in the vicinity of the helix wires is not obtained by this approach, but for purposes of beam dynamics simulation such detail is not generally needed

Numerical solution of quadratic matrix equations for free vibration analysis of structures

Science.gov (United States)

Gupta, K. K.

1975-01-01

This paper is concerned with the efficient and accurate solution of the eigenvalue problem represented by quadratic matrix equations. Such matrix forms are obtained in connection with the free vibration analysis of structures, discretized by finite 'dynamic' elements, resulting in frequency-dependent stiffness and inertia matrices. The paper presents a new numerical solution procedure of the quadratic matrix equations, based on a combined Sturm sequence and inverse iteration technique enabling economical and accurate determination of a few required eigenvalues and associated vectors. An alternative procedure based on a simultaneous iteration procedure is also described when only the first few modes are the usual requirement. The employment of finite dynamic elements in conjunction with the presently developed eigenvalue routines results in a most significant economy in the dynamic analysis of structures.

A high-current racetrack induction accelerator

International Nuclear Information System (INIS)

Mondelli, A.; Roberson, C.W.

1983-01-01

In this paper, the energy and system scaling laws of the Racetrack Induction Accelerator are determined and its operating principles are discussed. This device is a cyclic accelerator that is capable of multi-kiloamp operation. Long pulse induction linac technology is used to obtain short acceleration times. The accelerator consists of a long-pulse linear induction module and a racetrack beam transport system. For detailed studies of the particle dynamics in a racetrack, a numerical model is required to integrate the fully-relativistic single-particle equations of motion in an externally applied magnetic field. The numerical model is a compromise between the need for a large rotational transform and the need for a reasonable volume within the separatrix

Diffusion-synthetic acceleration methods for the discrete-ordinates equations

International Nuclear Information System (INIS)

Larsen, E.W.

1983-01-01

The diffusion-synthetic acceleration (DSA) method is an iterative procedure for obtaining numerical solutions of discrete-ordinates problems. The DSA method is operationally more complicated than the standard source-iteration (SI) method, but if encoded properly it converges much more rapidly, especially for problems with diffusion-like regions. In this article we describe the basic ideas beind the DSA method and give a (roughly chronological) review of its long development. We conclude with a discussion which covers additional topics, including some remaining open problems and the status of current efforts aimed at solving these problems

Canonical harmonic tracking of charged particles in circular accelerators

International Nuclear Information System (INIS)

Kvardakov, V.; Levichev, E.

2006-01-01

Harmonic tracking is a method used to study non-linear particle dynamics in a circular accelerator. The tracking algorithm is based on numerical solution of the Hamilton equations of motion. An essential feature of the method is the approximation of Hamiltonian perturbation terms by a finite number of azimuthal harmonics, which provides an effective tool for optimization of non-linear particle motion. The equations of motion are solved canonically, with the first-order prediction made using the explicit Lie transformation. The major features of harmonic tracking are presented and examples of its application are discussed

Canonical harmonic tracking of charged particles in circular accelerators

Science.gov (United States)

Kvardakov, V.; Levichev, E.

2006-03-01

Harmonic tracking is a method used to study non-linear particle dynamics in a circular accelerator. The tracking algorithm is based on numerical solution of the Hamilton equations of motion. An essential feature of the method is the approximation of Hamiltonian perturbation terms by a finite number of azimuthal harmonics, which provides an effective tool for optimization of non-linear particle motion. The equations of motion are solved canonically, with the first-order prediction made using the explicit Lie transformation. The major features of harmonic tracking are presented and examples of its application are discussed.

Numerical modeling of the plasma ring acceleration experiment

International Nuclear Information System (INIS)

Eddleman, J.L.; Hammer, J.H.; Hartman, C.W.

1987-01-01

Modeling of the LLNL RACE experiment and its many applications has necessitated the development and use of a wide array of computational tools. The two-dimensional MHD code, HAM, has been used to model the formation of a compact torus plasma ring in a magnetized coaxial gun and its subsequent acceleration by an additional applied toroidal field. Features included in the 2-D calculations are self-consistent models for (1) the time-dependent poloidal field produced by a capacitor bank discharge through a solenoid field coil (located either inside the gun inner electrode or outside the outer gun electrode) and the associated diffusion of magnetic flux through neighboring conductors, (2) gas flow into the gun annular region from a simulated puffed gas valve plenum, (3) formation and motion of a current sheet produced by J x B forces resulting from discharge of the gun capacitor bank through the plasma load between the coaxial gun electrodes, (4) the subsequent stretching and reconnection of the poloidal field lines to form a compact torus plasma ring, and (5) finally the discharge of the accelerator capacitor bank producing an additional toroidal field for acceleration of the plasma ring. The code has been extended to include various models for gas breakdown, plasma anomalous resistivity, and mass entrainment from ablation of electrode material

Determination of Solution Accuracy of Numerical Schemes as Part of Code and Calculation Verification

Energy Technology Data Exchange (ETDEWEB)

Blottner, F.G.; Lopez, A.R.

1998-10-01

This investigation is concerned with the accuracy of numerical schemes for solving partial differential equations used in science and engineering simulation codes. Richardson extrapolation methods for steady and unsteady problems with structured meshes are presented as part of the verification procedure to determine code and calculation accuracy. The local truncation error de- termination of a numerical difference scheme is shown to be a significant component of the veri- fication procedure as it determines the consistency of the numerical scheme, the order of the numerical scheme, and the restrictions on the mesh variation with a non-uniform mesh. Genera- tion of a series of co-located, refined meshes with the appropriate variation of mesh cell size is in- vestigated and is another important component of the verification procedure. The importance of mesh refinement studies is shown to be more significant than just a procedure to determine solu- tion accuracy. It is suggested that mesh refinement techniques can be developed to determine con- sistency of numerical schemes and to determine if governing equations are well posed. The present investigation provides further insight into the conditions and procedures required to effec- tively use Richardson extrapolation with mesh refinement studies to achieve confidence that sim- ulation codes are producing accurate numerical solutions.

Acceleration of Lateral Equilibration in Mixed Lipid Bilayers Using Replica Exchange with Solute Tempering.

Science.gov (United States)

Huang, Kun; García, Angel E

2014-10-14

The lateral heterogeneity of cellular membranes plays an important role in many biological functions such as signaling and regulating membrane proteins. This heterogeneity can result from preferential interactions between membrane components or interactions with membrane proteins. One major difficulty in molecular dynamics simulations aimed at studying the membrane heterogeneity is that lipids diffuse slowly and collectively in bilayers, and therefore, it is difficult to reach equilibrium in lateral organization in bilayer mixtures. Here, we propose the use of the replica exchange with solute tempering (REST) approach to accelerate lateral relaxation in heterogeneous bilayers. REST is based on the replica exchange method but tempers only the solute, leaving the temperature of the solvent fixed. Since the number of replicas in REST scales approximately only with the degrees of freedom in the solute, REST enables us to enhance the configuration sampling of lipid bilayers with fewer replicas, in comparison with the temperature replica exchange molecular dynamics simulation (T-REMD) where the number of replicas scales with the degrees of freedom of the entire system. We apply the REST method to a cholesterol and 1,2-dipalmitoyl- sn -glycero-3-phosphocholine (DPPC) bilayer mixture and find that the lateral distribution functions of all molecular pair types converge much faster than in the standard MD simulation. The relative diffusion rate between molecules in REST is, on average, an order of magnitude faster than in the standard MD simulation. Although REST was initially proposed to study protein folding and its efficiency in protein folding is still under debate, we find a unique application of REST to accelerate lateral equilibration in mixed lipid membranes and suggest a promising way to probe membrane lateral heterogeneity through molecular dynamics simulation.

A variational numerical method based on finite elements for the nonlinear solution characteristics of the periodically forced Chen system

Science.gov (United States)

Khan, Sabeel M.; Sunny, D. A.; Aqeel, M.

2017-09-01

Nonlinear dynamical systems and their solutions are very sensitive to initial conditions and therefore need to be approximated carefully. In this article, we present and analyze nonlinear solution characteristics of the periodically forced Chen system with the application of a variational method based on the concept of finite time-elements. Our approach is based on the discretization of physical time space into finite elements where each time-element is mapped to a natural time space. The solution of the system is then determined in natural time space using a set of suitable basis functions. The numerical algorithm is presented and implemented to compute and analyze nonlinear behavior at different time-step sizes. The obtained results show an excellent agreement with the classical RK-4 and RK-5 methods. The accuracy and convergence of the method is shown by comparing numerically computed results with the exact solution for a test problem. The presented method has shown a great potential in dealing with the solutions of nonlinear dynamical systems and thus can be utilized in delineating different features and characteristics of their solutions.

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

Numerical Solutions for Supersonic Flow of an Ideal Gas Around Blunt Two-Dimensional Bodies

Science.gov (United States)

Fuller, Franklyn B.

1961-01-01

The method described is an inverse one; the shock shape is chosen and the solution proceeds downstream to a body. Bodies blunter than circular cylinders are readily accessible, and any adiabatic index can be chosen. The lower limit to the free-stream Mach number available in any case is determined by the extent of the subsonic field, which in turn depends upon the body shape. Some discussion of the stability of the numerical processes is given. A set of solutions for flows about circular cylinders at several Mach numbers and several values of the adiabatic index is included.

The development of high performance numerical simulation code for transient groundwater flow and reactive solute transport problems based on local discontinuous Galerkin method

International Nuclear Information System (INIS)

Suzuki, Shunichi; Motoshima, Takayuki; Naemura, Yumi; Kubo, Shin; Kanie, Shunji

2009-01-01

The authors develop a numerical code based on Local Discontinuous Galerkin Method for transient groundwater flow and reactive solute transport problems in order to make it possible to do three dimensional performance assessment on radioactive waste repositories at the earliest stage possible. Local discontinuous Galerkin Method is one of mixed finite element methods which are more accurate ones than standard finite element methods. In this paper, the developed numerical code is applied to several problems which are provided analytical solutions in order to examine its accuracy and flexibility. The results of the simulations show the new code gives highly accurate numeric solutions. (author)

Self-consistent model of the Rayleigh--Taylor instability in ablatively accelerated laser plasma

International Nuclear Information System (INIS)

Bychkov, V.V.; Golberg, S.M.; Liberman, M.A.

1994-01-01

A self-consistent approach to the problem of the growth rate of the Rayleigh--Taylor instability in laser accelerated targets is developed. The analytical solution of the problem is obtained by solving the complete system of the hydrodynamical equations which include both thermal conductivity and energy release due to absorption of the laser light. The developed theory provides a rigorous justification for the supplementary boundary condition in the limiting case of the discontinuity model. An analysis of the suppression of the Rayleigh--Taylor instability by the ablation flow is done and it is found that there is a good agreement between the obtained solution and the approximate formula σ = 0.9√gk - 3u 1 k, where g is the acceleration, u 1 is the ablation velocity. This paper discusses different regimes of the ablative stabilization and compares them with previous analytical and numerical works

A Lie-admissible method of integration of Fokker-Planck equations with non-linear coefficients (exact and numerical solutions)

International Nuclear Information System (INIS)

Fronteau, J.; Combis, P.

1984-08-01

A Lagrangian method is introduced for the integration of non-linear Fokker-Planck equations. Examples of exact solutions obtained in this way are given, and also the explicit scheme used for the computation of numerical solutions. The method is, in addition, shown to be of a Lie-admissible type

Numerical solution of large nonlinear boundary value problems by quadratic minimization techniques

International Nuclear Information System (INIS)

Glowinski, R.; Le Tallec, P.

1984-01-01

The objective of this paper is to describe the numerical treatment of large highly nonlinear two or three dimensional boundary value problems by quadratic minimization techniques. In all the different situations where these techniques were applied, the methodology remains the same and is organized as follows: 1) derive a variational formulation of the original boundary value problem, and approximate it by Galerkin methods; 2) transform this variational formulation into a quadratic minimization problem (least squares methods) or into a sequence of quadratic minimization problems (augmented lagrangian decomposition); 3) solve each quadratic minimization problem by a conjugate gradient method with preconditioning, the preconditioning matrix being sparse, positive definite, and fixed once for all in the iterative process. This paper will illustrate the methodology above on two different examples: the description of least squares solution methods and their application to the solution of the unsteady Navier-Stokes equations for incompressible viscous fluids; the description of augmented lagrangian decomposition techniques and their application to the solution of equilibrium problems in finite elasticity

Accelerated Stochastic Matrix Inversion: General Theory and Speeding up BFGS Rules for Faster Second-Order Optimization

KAUST Repository

Gower, Robert M.

2018-02-12

We present the first accelerated randomized algorithm for solving linear systems in Euclidean spaces. One essential problem of this type is the matrix inversion problem. In particular, our algorithm can be specialized to invert positive definite matrices in such a way that all iterates (approximate solutions) generated by the algorithm are positive definite matrices themselves. This opens the way for many applications in the field of optimization and machine learning. As an application of our general theory, we develop the {\\\\em first accelerated (deterministic and stochastic) quasi-Newton updates}. Our updates lead to provably more aggressive approximations of the inverse Hessian, and lead to speed-ups over classical non-accelerated rules in numerical experiments. Experiments with empirical risk minimization show that our rules can accelerate training of machine learning models.

Stochastic acceleration by hydromagnetic turbulence

International Nuclear Information System (INIS)

Kulsrud, R.M.

1979-03-01

A general theory for particle acceleration by weak hydromagnetic turbulence with a given spectrum of waves is described. Various limiting cases, corresponding to Fermi acceleration and magnetic pumping, are discussed and two numerical examples illustrating them are given. An attempt is made to show that the expression for the rate of Fermi acceleration is valid for finite amplitudes

Optimality conditions for the numerical solution of optimization problems with PDE constraints :

Energy Technology Data Exchange (ETDEWEB)

Aguilo Valentin, Miguel Alejandro; Ridzal, Denis

2014-03-01

A theoretical framework for the numerical solution of partial di erential equation (PDE) constrained optimization problems is presented in this report. This theoretical framework embodies the fundamental infrastructure required to e ciently implement and solve this class of problems. Detail derivations of the optimality conditions required to accurately solve several parameter identi cation and optimal control problems are also provided in this report. This will allow the reader to further understand how the theoretical abstraction presented in this report translates to the application.

Asia honours accelerator physicists

CERN Multimedia

2010-01-01

"Steve Meyers of Cern and Jie Wei of Beijing's Tsinghua University are the first recipients of a new prize for particle physics. The pair were honoured for their contributions to numerous particle-accelerator projects - including Cern's Large Hadron Collider - by the Asian Committee for Future Accelerators (ACFA)..." (1 paragraph)

Bäcklund transformation, analytic soliton solutions and numerical simulation for a (2+1)-dimensional complex Ginzburg-Landau equation in a nonlinear fiber

Science.gov (United States)

Yu, Ming-Xiao; Tian, Bo; Chai, Jun; Yin, Hui-Min; Du, Zhong

2017-10-01

In this paper, we investigate a nonlinear fiber described by a (2+1)-dimensional complex Ginzburg-Landau equation with the chromatic dispersion, optical filtering, nonlinear and linear gain. Bäcklund transformation in the bilinear form is constructed. With the modified bilinear method, analytic soliton solutions are obtained. For the soliton, the amplitude can decrease or increase when the absolute value of the nonlinear or linear gain is enlarged, and the width can be compressed or amplified when the absolute value of the chromatic dispersion or optical filtering is enhanced. We study the stability of the numerical solutions numerically by applying the increasing amplitude, embedding the white noise and adding the Gaussian pulse to the initial values based on the analytic solutions, which shows that the numerical solutions are stable, not influenced by the finite initial perturbations.

Collective acceleration investigations with the ionization front accelerator

International Nuclear Information System (INIS)

Olson, C.L.; Poukey, J.W.; VanDevender, J.P.; Owyoung, A.; Pearlman, J.S.

1977-01-01

Part I of a three part program to demonstrate feasibility of the Ionization Front Accelerator (IFA) has been completed and is successful. Experiments describing intense relativistic electron beam (IREB) propagation in Cs are reported. The threshold pressure for electron beam ionization of Cs is found to agree with earlier theoretical predictions. These results experimentally establish Cs as a feasible working gas for the IFA. Numerical simulation results are also reported which demonstrate controlled potential well motion and collective ion acceleration with the IFA

MLFMA-accelerated Nyström method for ultrasonic scattering - Numerical results and experimental validation

Science.gov (United States)

Gurrala, Praveen; Downs, Andrew; Chen, Kun; Song, Jiming; Roberts, Ron

2018-04-01

Full wave scattering models for ultrasonic waves are necessary for the accurate prediction of voltage signals received from complex defects/flaws in practical nondestructive evaluation (NDE) measurements. We propose the high-order Nyström method accelerated by the multilevel fast multipole algorithm (MLFMA) as an improvement to the state-of-the-art full-wave scattering models that are based on boundary integral equations. We present numerical results demonstrating improvements in simulation time and memory requirement. Particularly, we demonstrate the need for higher order geom-etry and field approximation in modeling NDE measurements. Also, we illustrate the importance of full-wave scattering models using experimental pulse-echo data from a spherical inclusion in a solid, which cannot be modeled accurately by approximation-based scattering models such as the Kirchhoff approximation.

Research Article. Geodesic equations and their numerical solutions in geodetic and Cartesian coordinates on an oblate spheroid

Directory of Open Access Journals (Sweden)

Panou G.

2017-02-01

Full Text Available The direct geodesic problem on an oblate spheroid is described as an initial value problem and is solved numerically using both geodetic and Cartesian coordinates. The geodesic equations are formulated by means of the theory of differential geometry. The initial value problem under consideration is reduced to a system of first-order ordinary differential equations, which is solved using a numerical method. The solution provides the coordinates and the azimuths at any point along the geodesic. The Clairaut constant is not used for the solution but it is computed, allowing to check the precision of the method. An extensive data set of geodesics is used, in order to evaluate the performance of the method in each coordinate system. The results for the direct geodesic problem are validated by comparison to Karney’s method. We conclude that a complete, stable, precise, accurate and fast solution of the problem in Cartesian coordinates is accomplished.

Numerical solution of kinetics equation for point defects accumulation in metals under irradiation

International Nuclear Information System (INIS)

Aldzhambekova, G.T.; Iskakov, B.M.

1999-01-01

In the report the mathematical model, describing processes of generation and accumulation of defects in solids under irradiation is considered. The equations of this model take into account the velocity of Frenkel pairs generation, the mutual recombination of vacancies and the interstitials, as well as velocity of defects absorption by discharge channeling of vacancies and interstitials. By Runge-Kutta method the numerical solution of the model was carried out

Numerical Solutions of Mechanical Turbulent Filtration Equation Used in Mechatronics and Micro Mechanic

OpenAIRE

Hassan Fathabadi

2013-01-01

In this study, several novel numerical solutions are presented to solve the turbulent filtration equation and its special case called “Non-Newtonian mechanical filtration equation”. The turbulent filtration equation in porous media is a very important equation which has many applications to solve the problems appearing especially in mechatronics, micro mechanic and fluid mechanic. Many applied mechanical problems can be solved using this equation. For example, non-Newtonian mechanical filtrat...

A coarse-mesh diffusion synthetic acceleration of the scattering source iteration scheme for one-speed slab-geometry discrete ordinates problems

International Nuclear Information System (INIS)

Santos, Frederico P.; Alves Filho, Hermes; Barros, Ricardo C.; Xavier, Vinicius S.

2011-01-01

The scattering source iterative (SI) scheme is traditionally applied to converge fine-mesh numerical solutions to fixed-source discrete ordinates (S N ) neutron transport problems. The SI scheme is very simple to implement under a computational viewpoint. However, the SI scheme may show very slow convergence rate, mainly for diffusive media (low absorption) with several mean free paths in extent. In this work we describe an acceleration technique based on an improved initial guess for the scattering source distribution within the slab. In other words, we use as initial guess for the fine-mesh scattering source, the coarse-mesh solution of the neutron diffusion equation with special boundary conditions to account for the classical S N prescribed boundary conditions, including vacuum boundary conditions. Therefore, we first implement a spectral nodal method that generates coarse-mesh diffusion solution that is completely free from spatial truncation errors, then we reconstruct this coarse-mesh solution within each spatial cell of the discretization grid, to further yield the initial guess for the fine-mesh scattering source in the first S N transport sweep (μm > 0 and μm < 0, m = 1:N) across the spatial grid. We consider a number of numerical experiments to illustrate the efficiency of the offered diffusion synthetic acceleration (DSA) technique. (author)

Multiconfiguration time-dependent self-consistent field approximations in the numerical solution of quantum dynamical problems

International Nuclear Information System (INIS)

Kotler, Z.; Neria, E.; Nitzan, A.

1991-01-01

The use of the time-dependent self-consistent field approximation (TDSCF) in the numerical solution of quantum curve crossing and tunneling dynamical problems is investigated. Particular emphasis is given to multiconfiguration TDSCF (MCTDSCF) approximations, which are shown to perform considerably better with only a small increase in computational effort. We investigate a number of simple models in which a 'system' characterized by two electronic potential surfaces evolves while interacting with a 'bath' mode described by an harmonic oscillator, and compare exact numerical solutions to one- and two-configuration TDSCF approximations. We also introduce and investigate a semiclassical approximation in which the 'bath' mode is described by semiclassical wavepackets (one for each electronic state) and show that for all models investigated this scheme works very well in comparison with the fully quantum MCTDSCF approximation. This provides a potentially very useful method to simulate strongly quantum systems coupled to an essentially classical environment. (orig.)

Multiconfiguration time-dependent self-consistent field approximations in the numerical solution of quantum dynamical problems

Energy Technology Data Exchange (ETDEWEB)

Kotler, Z.; Neria, E.; Nitzan, A. (Tel Aviv Univ. (Israel). School of Chemistry)

1991-02-01

The use of the time-dependent self-consistent field approximation (TDSCF) in the numerical solution of quantum curve crossing and tunneling dynamical problems is investigated. Particular emphasis is given to multiconfiguration TDSCF (MCTDSCF) approximations, which are shown to perform considerably better with only a small increase in computational effort. We investigate a number of simple models in which a 'system' characterized by two electronic potential surfaces evolves while interacting with a 'bath' mode described by an harmonic oscillator, and compare exact numerical solutions to one- and two-configuration TDSCF approximations. We also introduce and investigate a semiclassical approximation in which the 'bath' mode is described by semiclassical wavepackets (one for each electronic state) and show that for all models investigated this scheme works very well in comparison with the fully quantum MCTDSCF approximation. This provides a potentially very useful method to simulate strongly quantum systems coupled to an essentially classical environment. (orig.).

Recent advances in acceleration of source iterations for fixed-source slab-geometry S{sub N} calculations based on P{sub N} synthetic initial guess

Energy Technology Data Exchange (ETDEWEB)

Guida, Mateus Rodrigues; Alves Filho, Hermes; Barros, Ricardo C., E-mail: mguida@iprj.uerj.br, E-mail: halves@iprj.uerj.br, E-mail: rcbarros@pq.cnpq.br [Universidade do Estado do Rio de Janeiro (UERJ), Nova Friburgo, RJ (Brazil). Instituto Politecnico. Programa de Pos-Graduacao em Modelagem Computacional

2015-07-01

The scattering source iterative (SI) scheme is applied traditionally to converge fine-mesh numerical solutions to fixed-source discrete ordinates (S{sub N}) neutron transport problems with linearly anisotropic scattering. The SI scheme is very simple to implement under a computational viewpoint. However, the SI scheme may show very slow convergence rate, mainly for diffusive media (low absorption) with several mean free paths in extent. In this work we describe two acceleration techniques based on improved initial guesses for the SI scheme, wherein we initialize the scattering source distribution within the slab using the P{sub 1} and P{sub 3} approximations. In order to estimate these initial guesses, we use the coarse-mesh solution of the PN equations with special boundary conditions to account for the classical S{sub N} prescribed boundary conditions, including vacuum boundary conditions. To apply this coarse-mesh P{sub N} solution for the accelerated scheme, we first perform within-node spatial reconstruction, and then we determine the fine-mesh average scalar flux and total current for initializing the linearly anisotropic scattering source terms for the SI scheme. We consider a number of numerical experiments to illustrate the efficiency of the offered P{sub N} synthetic acceleration (P{sub N}SA) technique based on initial guess. (author)

Classical and modern numerical analysis theory, methods and practice

CERN Document Server

Ackleh, Azmy S; Kearfott, R Baker; Seshaiyer, Padmanabhan

2009-01-01

Mathematical Review and Computer Arithmetic Mathematical Review Computer Arithmetic Interval ComputationsNumerical Solution of Nonlinear Equations of One Variable Introduction Bisection Method The Fixed Point Method Newton's Method (Newton-Raphson Method) The Univariate Interval Newton MethodSecant Method and Müller's Method Aitken Acceleration and Steffensen's Method Roots of Polynomials Additional Notes and SummaryNumerical Linear Algebra Basic Results from Linear Algebra Normed Linear Spaces Direct Methods for Solving Linear SystemsIterative Methods for Solving Linear SystemsThe Singular Value DecompositionApproximation TheoryIntroduction Norms, Projections, Inner Product Spaces, and Orthogonalization in Function SpacesPolynomial ApproximationPiecewise Polynomial ApproximationTrigonometric ApproximationRational ApproximationWavelet BasesLeast Squares Approximation on a Finite Point SetEigenvalue-Eigenvector Computation Basic Results from Linear Algebra The Power Method The Inverse Power Method Deflation T...

Department of Accelerator Physics and Technology: Overview

International Nuclear Information System (INIS)

Pachan, M.

2000-01-01

selection of solution for accelerating structure operating in broad energy range 6 to 15 MeV; - advance in technique and metrology of narrow photon beams for stereotactic radiosurgery. Collaboration with DESY was concentrated on problems in design and modelling of accelerating structure for TESLA collider. Successive series of numerical calculations was effectuated for evaluation of conditions for excitation and suppressing of higher order field modes. The complete copper model of ''superstructure'' section has been built and measured in Swierk and Hamburg. In effect of positive results, a first series of niobium resonators for superconducting structure is in preparation. In the frame of Italian-Polish collaboration a new proposal has been prepared for design and construction of a 10-12 MeV bunching section in the injector of Trieste electron synchrotron. (author)

Boundary integral equation methods and numerical solutions thin plates on an elastic foundation

CERN Document Server

Constanda, Christian; Hamill, William

2016-01-01

This book presents and explains a general, efficient, and elegant method for solving the Dirichlet, Neumann, and Robin boundary value problems for the extensional deformation of a thin plate on an elastic foundation. The solutions of these problems are obtained both analytically—by means of direct and indirect boundary integral equation methods (BIEMs)—and numerically, through the application of a boundary element technique. The text discusses the methodology for constructing a BIEM, deriving all the attending mathematical properties with full rigor. The model investigated in the book can serve as a template for the study of any linear elliptic two-dimensional problem with constant coefficients. The representation of the solution in terms of single-layer and double-layer potentials is pivotal in the development of a BIEM, which, in turn, forms the basis for the second part of the book, where approximate solutions are computed with a high degree of accuracy. The book is intended for graduate students and r...

Numerical doubly-periodic solution of the (2+1)-dimensional Boussinesq equation with initial conditions by the variational iteration method

International Nuclear Information System (INIS)

Inc, Mustafa

2007-01-01

In this Letter, a scheme is developed to study numerical doubly-periodic solutions of the (2+1)-dimensional Boussinesq equation with initial condition by the variational iteration method. As a result, the approximate and exact doubly-periodic solutions are obtained. For different modulus m, comparison between the approximate solution and the exact solution is made graphically, revealing that the variational iteration method is a powerful and effective tool to non-linear problems

Salpeter equation in position space: Numerical solution for arbitrary confining potentials

International Nuclear Information System (INIS)

Nickisch, L.J.; Durand, L.; Durand, B.

1984-01-01

We present and test two new methods for the numerical solution of the relativistic wave equation [(-del 2 +m 1 2 )/sup 1/2/+(-del 2 +m 2 2 )/sup 1/2/+V(r)-M]psi( r ) = 0, which appears in the theory of relativistic quark-antiquark bound states. Our methods work directly in position space, and hence have the desirable features that we can vary the potential V(r) locally in fitting the qq-bar mass spectrum, and can easily build in the expected behavior of V for r→0,infinity. Our first method converts the nonlocal square-root operators to mildly singular integral operators involving hyperbolic Bessel functions. The resulting integral equation can be solved numerically by matrix techniques. Our second method approximates the square-root operators directly by finite matrices. Both methods converge rapidly with increasing matrix size (the square-root matrix method more rapidly) and can be used in fast-fitting routines. We present some tests for oscillator and Coulomb interactions, and for the realistic Coulomb-plus-linear potential used in qq-bar phenomenology

Accelerator development

International Nuclear Information System (INIS)

Anon.

1975-01-01

Because the use of accelerated heavy ions would provide many opportunities for new and important studies in nuclear physics and nuclear chemistry, as well as other disciplines, both the Chemistry and Physics Divisions are supporting the development of a heavy-ion accelerator. The design of greatest current interest includes a tandem accelerator with a terminal voltage of approximately 25 MV injecting into a linear accelerator with rf superconducting resonators. This combined accelerator facility would be capable of accelerating ions of masses ranging over the entire periodic table to an energy corresponding to approximately 10 MeV/nucleon. This approach, as compared to other concepts, has the advantages of lower construction costs, lower operating power, 100 percent duty factor, and high beam quality (good energy resolution, good timing resolution, small beam size, and small beam divergence). The included sections describe the concept of the proposed heavy-ion accelerator, and the development program aiming at: (1) investigation of the individual questions concerning the superconducting accelerating resonators; (2) construction and testing of prototype accelerator systems; and (3) search for economical solutions to engineering problems. (U.S.)

Requirements and solutions for accelerator control systems

International Nuclear Information System (INIS)

Anicic, D.; Blumer, T.; Jirousek, I.; Lutz, H.; Mezger, A.

2001-01-01

Throughout the life cycle of control systems, we are faced with the question of what fabulous new piece of hardware or software should be used and how to integrate this into a viable system. Accelerators cover a wide range, from simple cyclotrons for isotope production, to cascades of cyclotrons for variable energy and multiple particles, this precludes a standard answer for all cases. The system requirements according to the purpose and nature of the accelerator are analyzed and we try to extract some guidelines for implementation, development and maintenance of the appropriate control systems. We then try to analyze present trends in a selection of fields like operating systems, commercial systems, software sharing, field busses, etc

US DOE Grand Challenge in Computational Accelerator Physics

International Nuclear Information System (INIS)

Ryne, R.; Habib, S.; Qiang, J.; Ko, K.; Li, Z.; McCandless, B.; Mi, W.; Ng, C.; Saparov, M.; Srinivas, V.; Sun, Y.; Zhan, X.; Decyk, V.; Golub, G.

1998-01-01

Particle accelerators are playing an increasingly important role in basic and applied science, and are enabling new accelerator-driven technologies. But the design of next-generation accelerators, such as linear colliders and high intensity linacs, will require a major advance in numerical modeling capability due to extremely stringent beam control and beam loss requirements, and the presence of highly complex three-dimensional accelerator components. To address this situation, the U.S. Department of Energy has approved a ''Grand Challenge'' in Computational Accelerator Physics, whose primary goal is to develop a parallel modeling capability that will enable high performance, large scale simulations for the design, optimization, and numerical validation of next-generation accelerators. In this paper we report on the status of the Grand Challenge

Accelerated and decelerated expansion in a causal dissipative cosmology

Science.gov (United States)

Cruz, Miguel; Cruz, Norman; Lepe, Samuel

2017-12-01

In this work we explore a new cosmological solution for an universe filled with one dissipative fluid, described by a barotropic equation of state (EoS) p =ω ρ , in the framework of the full Israel-Stewart theory. The form of the bulk viscosity has been assumed of the form ξ =ξ0ρ1 /2. The relaxation time is taken to be a function of the EoS, the bulk viscosity and the speed of bulk viscous perturbations, cb. The solution presents an initial singularity, where the curvature scalar diverges as the scale factor goes to zero. Depending on the values for ω , ξ0, cb accelerated and decelerated cosmic expansion can be obtained. In the case of accelerated expansion, the viscosity drives the effective EoS to be of quintessence type, for the single fluid with positive pressure. Nevertheless, we show that only the solution with decelerated expansion satisfies the thermodynamics conditions d S /d t >0 (growth of the entropy) and d2S /d t2<0 (convexity condition). We show that an exact stiff matter EoS is not allowed in the framework of the full causal thermodynamic approach; and in the case of a EoS very close to the stiff matter regime, we found that dissipative effects becomes negligible so the entropy remains constant. Finally, we show numerically that the solution is stable under small perturbations.

Numerical model for the solution of two-dimensional natural convection problems in arbitrary cavities

International Nuclear Information System (INIS)

Milioli, F.E.

1985-01-01

In this research work a numerical model for the solution of two-dimensional natural convection problems in arbitrary cavities of a Boussinesq fluid is presented. The conservation equations are written in a general curvilinear coordinate system which matches the irregular boundaries of the domain. The nonorthogonal system is generated by a suitable system of elliptic equations. The momentum and continuity equations are transformed from the Cartesian system to the general curvilinear system keeping the Cartesian velocity components as the dependent variables in the transformed domain. Finite difference equations are obtained for the contravariant velocity components in the transformed domain. The numerical calculations are performed in a fixed rectangular domain and both the Cartesian and the contravariant velocity components take part in the solutiomn procedure. The dependent variables are arranged on the grid in a staggered manner. The numerical model is tested by solving the driven flow in a square cavity with a moving side using a nonorthogoanl grid. The natural convenction in a square cavity, using an orthogonal and a nonorthogonal grid, is also solved for the model test. Also, the solution for the buoyancy flow between a square cylinder placed inside a circular cylinder is presented. The results of the test problems are compared with those available in the specialized literature. Finally, in order to show the generality of the model, the natural convection problem inside a very irregular cavity is presented. (Author) [pt

Numerical Uncertainty Analysis for Computational Fluid Dynamics using Student T Distribution -- Application of CFD Uncertainty Analysis Compared to Exact Analytical Solution

Science.gov (United States)

Groves, Curtis E.; Ilie, marcel; Shallhorn, Paul A.

2014-01-01

Computational Fluid Dynamics (CFD) is the standard numerical tool used by Fluid Dynamists to estimate solutions to many problems in academia, government, and industry. CFD is known to have errors and uncertainties and there is no universally adopted method to estimate such quantities. This paper describes an approach to estimate CFD uncertainties strictly numerically using inputs and the Student-T distribution. The approach is compared to an exact analytical solution of fully developed, laminar flow between infinite, stationary plates. It is shown that treating all CFD input parameters as oscillatory uncertainty terms coupled with the Student-T distribution can encompass the exact solution.

Accelerated lattice Boltzmann model for colloidal suspensions rheology and interface morphology

CERN Document Server

Farhat, Hassan; Kondaraju, Sasidhar

2014-01-01

Colloids are ubiquitous in the food, medical, cosmetics, polymers, water purification, and pharmaceutical industries. The thermal, mechanical, and storage properties of colloids are highly dependent on their interface morphology and their rheological behavior. Numerical methods provide a convenient and reliable tool for the study of colloids. Accelerated Lattice Boltzmann Model for Colloidal Suspensions introduce the main building-blocks for an improved lattice Boltzmann–based numerical tool designed for the study of colloidal rheology and interface morphology. This book also covers the migrating multi-block used to simulate single component, multi-component, multiphase, and single component multiphase flows and their validation by experimental, numerical, and analytical solutions.   Among other topics discussed are the hybrid lattice Boltzmann method (LBM) for surfactant-covered droplets; biological suspensions such as blood; used in conjunction with the suppression of coalescence for investigating the...

Fast and high-order numerical algorithms for the solution of multidimensional nonlinear fractional Ginzburg-Landau equation

Science.gov (United States)

Mohebbi, Akbar

2018-02-01

In this paper we propose two fast and accurate numerical methods for the solution of multidimensional space fractional Ginzburg-Landau equation (FGLE). In the presented methods, to avoid solving a nonlinear system of algebraic equations and to increase the accuracy and efficiency of method, we split the complex problem into simpler sub-problems using the split-step idea. For a homogeneous FGLE, we propose a method which has fourth-order of accuracy in time component and spectral accuracy in space variable and for nonhomogeneous one, we introduce another scheme based on the Crank-Nicolson approach which has second-order of accuracy in time variable. Due to using the Fourier spectral method for fractional Laplacian operator, the resulting schemes are fully diagonal and easy to code. Numerical results are reported in terms of accuracy, computational order and CPU time to demonstrate the accuracy and efficiency of the proposed methods and to compare the results with the analytical solutions. The results show that the present methods are accurate and require low CPU time. It is illustrated that the numerical results are in good agreement with the theoretical ones.

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.

BOKASUN: a fast and precise numerical program to calculate the Master Integrals of the two-loop sunrise diagrams

OpenAIRE

Caffo, Michele; Czyz, Henryk; Gunia, Michal; Remiddi, Ettore

2008-01-01

We present the program BOKASUN for fast and precise evaluation of the Master Integrals of the two-loop self-mass sunrise diagram for arbitrary values of the internal masses and the external four-momentum. We use a combination of two methods: a Bernoulli accelerated series expansion and a Runge-Kutta numerical solution of a system of linear differential equations.

Reactor fuel element heat conduction via numerical Laplace transform inversion

International Nuclear Information System (INIS)

Ganapol, Barry D.; Furfaro, Roberto

2001-01-01

A newly developed numerical Laplace transform inversion (NLTI) will be presented to determine the transient temperature distribution within a nuclear reactor fuel element. The NLTI considered in this presentation has evolved to its present state over the past 10 years of application. The methodology adopted is one that relies on acceleration of the convergence of an infinite series towards its limit. The inversion will be applied to the prediction of the transient temperature distribution within an MTR type nuclear fuel element through a novel formulation of the solution to the transformed heat conduction equation. (author)

Reactor fuel element heat conduction via numerical Laplace transform inversion

Energy Technology Data Exchange (ETDEWEB)

Ganapol, Barry D.; Furfaro, Roberto [University of Arizona, Tucson, AZ (United States). Dept. of Aerospace and Mechanical Engineering], e-mail: ganapol@cowboy.ame.arizona.edu

2001-07-01

A newly developed numerical Laplace transform inversion (NLTI) will be presented to determine the transient temperature distribution within a nuclear reactor fuel element. The NLTI considered in this presentation has evolved to its present state over the past 10 years of application. The methodology adopted is one that relies on acceleration of the convergence of an infinite series towards its limit. The inversion will be applied to the prediction of the transient temperature distribution within an MTR type nuclear fuel element through a novel formulation of the solution to the transformed heat conduction equation. (author)

A coarse-mesh diffusion synthetic acceleration of the source iteration scheme for one-speed discrete ordinates transport calculations in Slab geometry

International Nuclear Information System (INIS)

Santos, Frederico P.; Xavier, Vinicius S.; Alves Filho, Hermes; Barros, Ricardo C.

2011-01-01

The scattering source iterative (SI) scheme is traditionally applied to converge fine-mesh numerical solutions to fixed-source discrete ordinates (S N ) neutron transport problems. The SI scheme is very simple to implement under a computational viewpoint. However, the SI scheme may show very slow convergence rate, mainly for diffusive media (low absorption) with several mean free paths in extent. In this work we describe an acceleration technique based on an improved initial guess for the scattering source distribution within the slab. In other words, we use as initial guess for the fine-mesh scattering source, the coarse-mesh solution of the neutron diffusion equation with special boundary conditions to account for the classical S N prescribed boundary conditions, including vacuum boundary conditions. Therefore, we first implement a spectral nodal method that generates coarse-mesh diffusion solution that is completely free from spatial truncation errors, then we reconstruct this coarse-mesh solution within each spatial cell of the discretization grid, to further yield the initial guess for the fine-mesh scattering source in the first S N transport sweep (μm > 0 and μm < 0, m = 1:N) across the spatial grid. We consider a number of numerical experiments to illustrate the efficiency of the offered diffusion synthetic acceleration (DSA) technique. (author)

Numerical solution of the unsteady diffusion-convection-reaction equation based on improved spectral Galerkin method

Science.gov (United States)

Zhong, Jiaqi; Zeng, Cheng; Yuan, Yupeng; Zhang, Yuzhe; Zhang, Ye

2018-04-01

The aim of this paper is to present an explicit numerical algorithm based on improved spectral Galerkin method for solving the unsteady diffusion-convection-reaction equation. The principal characteristics of this approach give the explicit eigenvalues and eigenvectors based on the time-space separation method and boundary condition analysis. With the help of Fourier series and Galerkin truncation, we can obtain the finite-dimensional ordinary differential equations which facilitate the system analysis and controller design. By comparing with the finite element method, the numerical solutions are demonstrated via two examples. It is shown that the proposed method is effective.

Analytical solution and numerical simulation of the liquid nitrogen freezing-temperature field of a single pipe

Science.gov (United States)

Cai, Haibing; Xu, Liuxun; Yang, Yugui; Li, Longqi

2018-05-01

Artificial liquid nitrogen freezing technology is widely used in urban underground engineering due to its technical advantages, such as simple freezing system, high freezing speed, low freezing temperature, high strength of frozen soil, and absence of pollution. However, technical difficulties such as undefined range of liquid nitrogen freezing and thickness of frozen wall gradually emerge during the application process. Thus, the analytical solution of the freezing-temperature field of a single pipe is established considering the freezing temperature of soil and the constant temperature of freezing pipe wall. This solution is then applied in a liquid nitrogen freezing project. Calculation results show that the radius of freezing front of liquid nitrogen is proportional to the square root of freezing time. The radius of the freezing front also decreases with decreased the freezing temperature, and the temperature gradient of soil decreases with increased distance from the freezing pipe. The radius of cooling zone in the unfrozen area is approximately four times the radius of the freezing front. Meanwhile, the numerical simulation of the liquid nitrogen freezing-temperature field of a single pipe is conducted using the Abaqus finite-element program. Results show that the numerical simulation of soil temperature distribution law well agrees with the analytical solution, further verifies the reliability of the established analytical solution of the liquid nitrogen freezing-temperature field of a single pipe.

Human-computer interfaces applied to numerical solution of the Plateau problem

Science.gov (United States)

Elias Fabris, Antonio; Soares Bandeira, Ivana; Ramos Batista, Valério

2015-09-01

In this work we present a code in Matlab to solve the Problem of Plateau numerically, and the code will include human-computer interface. The Problem of Plateau has applications in areas of knowledge like, for instance, Computer Graphics. The solution method will be the same one of the Surface Evolver, but the difference will be a complete graphical interface with the user. This will enable us to implement other kinds of interface like ocular mouse, voice, touch, etc. To date, Evolver does not include any graphical interface, which restricts its use by the scientific community. Specially, its use is practically impossible for most of the Physically Challenged People.

An Explicit Finite Difference scheme for numerical solution of fractional neutron point kinetic equation

International Nuclear Information System (INIS)

Saha Ray, S.; Patra, A.

2012-01-01

Highlights: ► In this paper fractional neutron point kinetic equation has been analyzed. ► The numerical solution for fractional neutron point kinetic equation is obtained. ► Explicit Finite Difference Method has been applied. ► Supercritical reactivity, critical reactivity and subcritical reactivity analyzed. ► Comparison between fractional and classical neutron density is presented. - Abstract: In the present article, a numerical procedure to efficiently calculate the solution for fractional point kinetics equation in nuclear reactor dynamics is investigated. The Explicit Finite Difference Method is applied to solve the fractional neutron point kinetic equation with the Grunwald–Letnikov (GL) definition (). Fractional Neutron Point Kinetic Model has been analyzed for the dynamic behavior of the neutron motion in which the relaxation time associated with a variation in the neutron flux involves a fractional order acting as exponent of the relaxation time, to obtain the best operation of a nuclear reactor dynamics. Results for neutron dynamic behavior for subcritical reactivity, supercritical reactivity and critical reactivity and also for different values of fractional order have been presented and compared with the classical neutron point kinetic (NPK) equation as well as the results obtained by the learned researchers .

Numerical and analytical solutions for problems relevant for quantum computers

International Nuclear Information System (INIS)

Spoerl, Andreas

2008-01-01

Quantum computers are one of the next technological steps in modern computer science. Some of the relevant questions that arise when it comes to the implementation of quantum operations (as building blocks in a quantum algorithm) or the simulation of quantum systems are studied. Numerical results are gathered for variety of systems, e.g. NMR systems, Josephson junctions and others. To study quantum operations (e.g. the quantum fourier transform, swap operations or multiply-controlled NOT operations) on systems containing many qubits, a parallel C++ code was developed and optimised. In addition to performing high quality operations, a closer look was given to the minimal times required to implement certain quantum operations. These times represent an interesting quantity for the experimenter as well as for the mathematician. The former tries to fight dissipative effects with fast implementations, while the latter draws conclusions in the form of analytical solutions. Dissipative effects can even be included in the optimisation. The resulting solutions are relaxation and time optimised. For systems containing 3 linearly coupled spin (1)/(2) qubits, analytical solutions are known for several problems, e.g. indirect Ising couplings and trilinear operations. A further study was made to investigate whether there exists a sufficient set of criteria to identify systems with dynamics which are invertible under local operations. Finally, a full quantum algorithm to distinguish between two knots was implemented on a spin(1)/(2) system. All operations for this experiment were calculated analytically. The experimental results coincide with the theoretical expectations. (orig.)

Theoretical and numerical study of the expansion of a laser-produced plasma: high energy ion acceleration; Etude theorique et numerique de l'expansion d'un plasma cree par laser: acceleration d'ions a haute energie

Energy Technology Data Exchange (ETDEWEB)

Grismayer, T

2006-12-15

This work is a theoretical and numerical study on the high energy ion acceleration in laser created plasma expansion. The ion beams produced on the rear side of an irradiated foil reveal some characteristics (low divergence, wide spectra) which distinguish them from the ones coming from the front side. The discovery of these beams has renewed speculation for applications such as proton-therapy or proton radiography. The ion acceleration is performed via a self-consistent electrostatic field due to the charge separation between ions and hot electrons. In the first part of this dissertation, we present the fluid theoretical model and the hybrid code which simulates the plasma expansion. The numerical simulation of a recent experience on the dynamic of the electric field by proton radiography validates the theoretical model. The second part deals with the influence of an initial ion density gradient on the acceleration efficiency. We establish a model which relates the plasma dynamic and more precisely the wave breaking of the ion flow. The numerical results which predict a strong decrease of the ion maximum energy for large gradient length are in agreement with the experimental data. The Boltzmann equilibrium for the electron assumed in the first part has been thrown back into doubt in the third part. We adopt a kinetic description for the electron. The new version of the code can measure the Boltzmann law deviation which does not strongly modify the maximum energy that can reach the ions. (author)

Numerical solution of chemically reactive non-Newtonian fluid flow: Dual stratification

Science.gov (United States)

Rehman, Khalil Ur; Malik, M. Y.; Khan, Abid Ali; Zehra, Iffat; Zahri, Mostafa; Tahir, M.

2017-12-01

We have found that only a few attempts are available in the literature relatively to the tangent hyperbolic fluid flow induced by stretching cylindrical surfaces. In particular, temperature and concentration stratification effects have not been investigated until now with respect to the tangent hyperbolic fluid model. Therefore, we have considered the tangent hyperbolic fluid flow induced by an acutely inclined cylindrical surface in the presence of both temperature and concentration stratification effects. To be more specific, the fluid flow is attained with the no slip condition, which implies that the bulk motion of the fluid particles is the same as the stretching velocity of a cylindrical surface. Additionally, the flow field situation is manifested with heat generation, mixed convection and chemical reaction effects. The flow partial differential equations give a complete description of the present problem. Therefore, to trace out the solution, a set of suitable transformations is introduced to convert these equations into ordinary differential equations. In addition, a self-coded computational algorithm is executed to inspect the numerical solution of these reduced equations. The effect logs of the involved parameters are provided graphically. Furthermore, the variations of the physical quantities are examined and given with the aid of tables. It is observed that the fluid temperature is a decreasing function of the thermal stratification parameter and a similar trend is noticed for the concentration via the solutal stratification parameter.

Acceleration ion focusing (IFR) and transport experiments with the recirculating linear accelerator (RLA)

International Nuclear Information System (INIS)

Mazarakis, M.G.; Smith, D.L.; Puokey, J.W.; Bennett, L.F.; Wagner, J.S.; Olson, W.R.; George, M.; Turman, B.N.; Prestwich, K.R.; Struve, K.W.

1992-01-01

The focusing and transport of intense relativistic electron beams in the Sandia Laboratories Recirculating Linear Accelerator (RLA) is accomplished with the aid of an ion focusing channel (IFR). We report here experiments evaluating the beam generation in the injector and its subsequent acceleration and transport through the first post-accelerating cavity. Two injectors and one type of post-accelerating cavity were studied. Beams of 6-20 kA current were injected and successfully transported and accelerated through the cavity. The transport efficiencies were 90% - 100%, and the beam Gaussian profile (4 MeV injector) and radius (5 mm) remained the same through acceleration. We describe the RLA, present the experimental results and compare them with numerical simulations. (Author) 3 refs., 7 figs

An efficient approach to the numerical solution of rate-independent problems with nonconvex energies

Czech Academy of Sciences Publication Activity Database

Bartels, S.; Kružík, Martin

2011-01-01

Roč. 9, č. 3 (2011), s. 1275-1300 ISSN 1540-3459 R&D Projects: GA AV ČR IAA100750802 Grant - others:GA ČR(CZ) GAP201/10/0357 Institutional research plan: CEZ:AV0Z10750506 Keywords : numerical solution * nonconvexity Subject RIV: BA - General Mathematics Impact factor: 2.009, year: 2011 http://library.utia.cas.cz/separaty/2011/MTR/kruzik-0364707.pdf

Particle acceleration in modified shocks

Energy Technology Data Exchange (ETDEWEB)

Drury, L.O' C. (Max-Planck-Institut fuer Kernphysik, Heidelberg (Germany, F.R.)); Axford, W.I. (Max-Planck-Institut fuer Aeronomie, Katlenburg-Lindau (Germany, F.R.)); Summers, D. (Memorial Univ. of Newfoundland, St. John' s (Canada))

1982-03-01

Efficient particle acceleration in shocks must modify the shock structure with consequent changes in the particle acceleration. This effect is studied and analytic solutions are found describing the diffusive acceleration of particles with momentum independent diffusion coefficients in hyperbolic tangent type velocity transitions. If the input particle spectrum is a delta function, the shock smoothing replaces the truncated power-law downstream particle spectrum by a more complicated form, but one which has a power-law tail at high momenta. For a cold plasma this solution can be made completely self-consistent. Some problems associated with momentum dependent diffusion coefficients are discussed.

Particle acceleration in modified shocks

International Nuclear Information System (INIS)

Drury, L.O'C.; Axford, W.I.; Summers, D.

1982-01-01

Efficient particle acceleration in shocks must modify the shock structure with consequent changes in the particle acceleration. This effect is studied and analytic solutions are found describing the diffusive acceleration of particles with momentum independent diffusion coefficients in hyperbolic tangent type velocity transitions. If the input particle spectrum is a delta function, the shock smoothing replaces the truncated power-law downstream particle spectrum by a more complicated form, but one which has a power-law tail at high momenta. For a cold plasma this solution can be made completely self-consistent. Some problems associated with momentum dependent diffusion coefficients are discussed. (author)

A numerical study of shock-acceleration of a diffuse helium cylinder

International Nuclear Information System (INIS)

Greenough, J.A.; Bell, J.; Colella, P.

1995-08-01

The development of a shock-accelerated diffuse Helium cylindrical inhomogeneity is investigated using a new numerical method. The new algorithm is a higher-order Godunov implementation of the so-called multi-fluid equations. This system correctly models multiple component mixtures by accounting for differential compressibility effects. This base integrator is embedded in an implementation of adaptive mesh refinement (AMR) that allows efficient increase in resolution where the computational effort is concentrated where high accuracy, or increased resolution, are required. Qualitative and quantitative comparison with previous experimental data is excellent. The simulations show that counter-sign vortex blobs are deposited in the jet core by baroclinic generation of the curved shock wave as it traverses the jet. This vorticity deposition occurs over timescales that scale with the shock passage time (∼ 10μsec). Three phases of development are identified and characterized. The first is the weak deformation (WD) phase, where there is weak distortion of the Helium jet due to weak vorticity induced velocity effects. The second phase is the strong deformation (SD) phase where there is large distortion for the jet and the vortex blobs due to large induced velocity effects. The last is a relaxation/reorganization (RR) phase where the vorticity field reorganizes into point-like vortex pair

Numerical simulation of particle jet formation induced by shock wave acceleration in a Hele-Shaw cell

Science.gov (United States)

Osnes, A. N.; Vartdal, M.; Pettersson Reif, B. A.

2018-05-01

The formation of jets from a shock-accelerated cylindrical shell of particles, confined in a Hele-Shaw cell, is studied by means of numerical simulation. A number of simulations have been performed, systematically varying the coupling between the gas and solid phases in an effort to identify the primary mechanism(s) responsible for jet formation. We find that coupling through drag is sufficient for the formation of jets. Including the effect of particle volume fraction and particle collisions did not alter the general behaviour, but had some influence on the length, spacing and number of jets. Furthermore, we find that the jet selection process starts early in the dispersal process, during the initial expansion of the particle layer.

Numerical solution of viscous and viscoelastic fluids flow through the branching channel by finite volume scheme

Science.gov (United States)

Keslerová, Radka; Trdlička, David

2015-09-01

This work deals with the numerical modelling of steady flows of incompressible viscous and viscoelastic fluids through the three dimensional channel with T-junction. The fundamental system of equations is the system of generalized Navier-Stokes equations for incompressible fluids. This system is based on the system of balance laws of mass and momentum for incompressible fluids. Two different mathematical models for the stress tensor are used for simulation of Newtonian and Oldroyd-B fluids flow. Numerical solution of the described models is based on cetral finite volume method using explicit Runge-Kutta time integration.

Paraxial light distribution in the focal region of a lens: a comparison of several analytical solutions and a numerical result

Science.gov (United States)

Wu, Yang; Kelly, Damien P.

2014-12-01

The distribution of the complex field in the focal region of a lens is a classical optical diffraction problem. Today, it remains of significant theoretical importance for understanding the properties of imaging systems. In the paraxial regime, it is possible to find analytical solutions in the neighborhood of the focus, when a plane wave is incident on a focusing lens whose finite extent is limited by a circular aperture. For example, in Born and Wolf's treatment of this problem, two different, but mathematically equivalent analytical solutions, are presented that describe the 3D field distribution using infinite sums of ? and ? type Lommel functions. An alternative solution expresses the distribution in terms of Zernike polynomials, and was presented by Nijboer in 1947. More recently, Cao derived an alternative analytical solution by expanding the Fresnel kernel using a Taylor series expansion. In practical calculations, however, only a finite number of terms from these infinite series expansions is actually used to calculate the distribution in the focal region. In this manuscript, we compare and contrast each of these different solutions to a numerically calculated result, paying particular attention to how quickly each solution converges for a range of different spatial locations behind the focusing lens. We also examine the time taken to calculate each of the analytical solutions. The numerical solution is calculated in a polar coordinate system and is semi-analytic. The integration over the angle is solved analytically, while the radial coordinate is sampled with a sampling interval of ? and then numerically integrated. This produces an infinite set of replicas in the diffraction plane, that are located in circular rings centered at the optical axis and each with radii given by ?, where ? is the replica order. These circular replicas are shown to be fundamentally different from the replicas that arise in a Cartesian coordinate system.

Numerical Solution of the Kzk Equation for Pulsed Finite Amplitude Sound Beams in Thermoviscous Fluids

Science.gov (United States)

Lee, Yang-Sub

A time-domain numerical algorithm for solving the KZK (Khokhlov-Zabolotskaya-Kuznetsov) nonlinear parabolic wave equation is developed for pulsed, axisymmetric, finite amplitude sound beams in thermoviscous fluids. The KZK equation accounts for the combined effects of diffraction, absorption, and nonlinearity at the same order of approximation. The accuracy of the algorithm is established via comparison with analytical solutions for several limiting cases, and with numerical results obtained from a widely used algorithm for solving the KZK equation in the frequency domain. The time domain algorithm is used to investigate waveform distortion and shock formation in directive sound beams radiated by pulsed circular piston sources. New results include predictions for the entire process of self-demodulation, and for the effect of frequency modulation on pulse envelope distortion. Numerical results are compared with measurements, and focused sources are investigated briefly.

Numerical solution of the helmholtz equation for the superellipsoid via the galerkin method

Directory of Open Access Journals (Sweden)

Hy Dinh

2013-01-01

Full Text Available The objective of this work was to find the numerical solution of the Dirichlet problem for the Helmholtz equation for a smooth superellipsoid. The superellipsoid is a shape that is controlled by two parameters. There are some numerical issues in this type of an analysis; any integration method is affected by the wave number k, because of the oscillatory behavior of the fundamental solution. In this case we could only obtain good numerical results for super ellipsoids that were more shaped like super cones, which is a narrow range of super ellipsoids. The formula for these shapes was: $x=cos(xsin(y^{n},y=sin(xsin(y^{n},z=cos(y$ where $n$ varied from 0.5 to 4. The Helmholtz equation, which is the modified wave equation, is used in many scattering problems. This project was funded by NASA RI Space Grant for testing of the Dirichlet boundary condition for the shape of the superellipsoid. One practical value of all these computations can be getting a shape for the engine nacelles in a ray tracing the space shuttle. We are researching the feasibility of obtaining good convergence results for the superellipsoid surface. It was our view that smaller and lighter wave numbers would reduce computational costs associated with obtaining Galerkin coefficients. In addition, we hoped to significantly reduce the number of terms in the infinite series needed to modify the original integral equation, all of which were achieved in the analysis of the superellipsoid in a finite range. We used the Green's theorem to solve the integral equation for the boundary of the surface. Previously, multiple surfaces were used to test this method, such as the sphere, ellipsoid, and perturbation of the sphere, pseudosphere and the oval of Cassini Lin and Warnapala , Warnapala and Morgan .

Underestimation of nuclear fuel burnup – theory, demonstration and solution in numerical models

Directory of Open Access Journals (Sweden)

Gajda Paweł

2016-01-01

Full Text Available Monte Carlo methodology provides reference statistical solution of neutron transport criticality problems of nuclear systems. Estimated reaction rates can be applied as an input to Bateman equations that govern isotopic evolution of reactor materials. Because statistical solution of Boltzmann equation is computationally expensive, it is in practice applied to time steps of limited length. In this paper we show that simple staircase step model leads to underprediction of numerical fuel burnup (Fissions per Initial Metal Atom – FIMA. Theoretical considerations indicates that this error is inversely proportional to the length of the time step and origins from the variation of heating per source neutron. The bias can be diminished by application of predictor-corrector step model. A set of burnup simulations with various step length and coupling schemes has been performed. SERPENT code version 1.17 has been applied to the model of a typical fuel assembly from Pressurized Water Reactor. In reference case FIMA reaches 6.24% that is equivalent to about 60 GWD/tHM of industrial burnup. The discrepancies up to 1% have been observed depending on time step model and theoretical predictions are consistent with numerical results. Conclusions presented in this paper are important for research and development concerning nuclear fuel cycle also in the context of Gen4 systems.

Numerical solutions of the N-body problem

International Nuclear Information System (INIS)

Marciniak, A.

1985-01-01

Devoted to the study of numerical methods for solving the general N-body problem and related problems, this volume starts with an overview of the conventional numerical methods for solving the initial value problem. The major part of the book contains original work and features a presentation of special numerical methods conserving the constants of motion in the general N-body problem and methods conserving the Jacobi constant in the problem of motion of N bodies in a rotating frame, as well as an analysis of the applications of both (conventional and special) kinds of methods for solving these problems. For all the methods considered, the author presents algorithms which are easily programmable in any computer language. Moreover, the author compares various methods and presents adequate numerical results. The appendix contains PL/I procedures for all the special methods conserving the constants of motion. 91 refs.; 35 figs.; 41 tabs

Numerical relativity

International Nuclear Information System (INIS)

Piran, T.

1982-01-01

There are many recent developments in numerical relativity, but there remain important unsolved theoretical and practical problems. The author reviews existing numerical approaches to solution of the exact Einstein equations. A framework for classification and comparison of different numerical schemes is presented. Recent numerical codes are compared using this framework. The discussion focuses on new developments and on currently open questions, excluding a review of numerical techniques. (Auth.)

Application of Four-Point Newton-EGSOR iteration for the numerical solution of 2D Porous Medium Equations

Science.gov (United States)

Chew, J. V. L.; Sulaiman, J.

2017-09-01

Partial differential equations that are used in describing the nonlinear heat and mass transfer phenomena are difficult to be solved. For the case where the exact solution is difficult to be obtained, it is necessary to use a numerical procedure such as the finite difference method to solve a particular partial differential equation. In term of numerical procedure, a particular method can be considered as an efficient method if the method can give an approximate solution within the specified error with the least computational complexity. Throughout this paper, the two-dimensional Porous Medium Equation (2D PME) is discretized by using the implicit finite difference scheme to construct the corresponding approximation equation. Then this approximation equation yields a large-sized and sparse nonlinear system. By using the Newton method to linearize the nonlinear system, this paper deals with the application of the Four-Point Newton-EGSOR (4NEGSOR) iterative method for solving the 2D PMEs. In addition to that, the efficiency of the 4NEGSOR iterative method is studied by solving three examples of the problems. Based on the comparative analysis, the Newton-Gauss-Seidel (NGS) and the Newton-SOR (NSOR) iterative methods are also considered. The numerical findings show that the 4NEGSOR method is superior to the NGS and the NSOR methods in terms of the number of iterations to get the converged solutions, the time of computation and the maximum absolute errors produced by the methods.

Numerical solution of the Schrodinger equation for stationary bound states using nodel theorem

International Nuclear Information System (INIS)

Chen Zhijiang; Kong Fanmei; Din Yibin

1987-01-01

An iterative procedure for getting the numerical solution of Schrodinger equation on stationary bound states is introduced. The theoretical foundtion, the practical steps and the method are presented. An example is added at the end. Comparing with other methods, the present one requires less storage, less running time but posesses higher accuracy. It can be run on the personal computer or microcomputer with 256 K memory and 16 bit word length such as IBM/PC, MC68000/83/20, PDP11/23 etc

On the numerical solution of the neutron fractional diffusion equation

International Nuclear Information System (INIS)

Maleki Moghaddam, Nader; Afarideh, Hossein; Espinosa-Paredes, Gilberto

2014-01-01

Highlights: • The new version of neutron diffusion equation which established on the fractional derivatives is presented. • The Neutron Fractional Diffusion Equation (NFDE) is solved in the finite differences frame. • NFDE is solved using shifted Grünwald-Letnikov definition of fractional operators. • The results show that “K eff ” strongly depends on the order of fractional derivative. - Abstract: In order to core calculation in the nuclear reactors there is a new version of neutron diffusion equation which is established on the fractional partial derivatives, named Neutron Fractional Diffusion Equation (NFDE). In the NFDE model, neutron flux in each zone depends directly on the all previous zones (not only on the nearest neighbors). Under this circumstance, it can be said that the NFDE has the space history. We have developed a one-dimension code, NFDE-1D, which can simulate the reactor core using arbitrary exponent of differential operators. In this work a numerical solution of the NFDE is presented using shifted Grünwald-Letnikov definition of fractional derivative in finite differences frame. The model is validated with some numerical experiments where different orders of fractional derivative are considered (e.g. 0.999, 0.98, 0.96, and 0.94). The results show that the effective multiplication factor (K eff ) depends strongly on the order of fractional derivative

Expert system for accelerator single-freedom nonlinear components

International Nuclear Information System (INIS)

Wang Sheng; Xie Xi; Liu Chunliang

1995-01-01

An expert system by Arity Prolog is developed for accelerator single-freedom nonlinear components. It automatically yields any order approximate analytical solutions for various accelerator single-freedom nonlinear components. As an example, the eighth order approximate analytical solution is derived by this expert system for a general accelerator single-freedom nonlinear component, showing that the design of the expert system is successful

Applications of Operator-Splitting Methods to the Direct Numerical Simulation of Particulate and Free-Surface Flows and to the Numerical Solution of the Two-Dimensional Elliptic Monge--Ampère Equation

OpenAIRE

Glowinski, R.; Dean, E.J.; Guidoboni, G.; Juárez, L.H.; Pan, T.-W.

2008-01-01

The main goal of this article is to review some recent applications of operator-splitting methods. We will show that these methods are well-suited to the numerical solution of outstanding problems from various areas in Mechanics, Physics and Differential Geometry, such as the direct numerical simulation of particulate flow, free boundary problems with surface tension for incompressible viscous fluids, and the elliptic real Monge--Ampère equation. The results of numerical ...

Numerical solution to generalized Burgers'-Fisher equation using Exp-function method hybridized with heuristic computation.

Science.gov (United States)

Malik, Suheel Abdullah; Qureshi, Ijaz Mansoor; Amir, Muhammad; Malik, Aqdas Naveed; Haq, Ihsanul

2015-01-01

In this paper, a new heuristic scheme for the approximate solution of the generalized Burgers'-Fisher equation is proposed. The scheme is based on the hybridization of Exp-function method with nature inspired algorithm. The given nonlinear partial differential equation (NPDE) through substitution is converted into a nonlinear ordinary differential equation (NODE). The travelling wave solution is approximated by the Exp-function method with unknown parameters. The unknown parameters are estimated by transforming the NODE into an equivalent global error minimization problem by using a fitness function. The popular genetic algorithm (GA) is used to solve the minimization problem, and to achieve the unknown parameters. The proposed scheme is successfully implemented to solve the generalized Burgers'-Fisher equation. The comparison of numerical results with the exact solutions, and the solutions obtained using some traditional methods, including adomian decomposition method (ADM), homotopy perturbation method (HPM), and optimal homotopy asymptotic method (OHAM), show that the suggested scheme is fairly accurate and viable for solving such problems.

Numerical solution to generalized Burgers'-Fisher equation using Exp-function method hybridized with heuristic computation.

Directory of Open Access Journals (Sweden)

Suheel Abdullah Malik

Full Text Available In this paper, a new heuristic scheme for the approximate solution of the generalized Burgers'-Fisher equation is proposed. The scheme is based on the hybridization of Exp-function method with nature inspired algorithm. The given nonlinear partial differential equation (NPDE through substitution is converted into a nonlinear ordinary differential equation (NODE. The travelling wave solution is approximated by the Exp-function method with unknown parameters. The unknown parameters are estimated by transforming the NODE into an equivalent global error minimization problem by using a fitness function. The popular genetic algorithm (GA is used to solve the minimization problem, and to achieve the unknown parameters. The proposed scheme is successfully implemented to solve the generalized Burgers'-Fisher equation. The comparison of numerical results with the exact solutions, and the solutions obtained using some traditional methods, including adomian decomposition method (ADM, homotopy perturbation method (HPM, and optimal homotopy asymptotic method (OHAM, show that the suggested scheme is fairly accurate and viable for solving such problems.

The numerical analysis of eigenvalue problem solutions in multigroup neutron diffusion theory

International Nuclear Information System (INIS)

Woznicki, Z.I.

1995-01-01

The main goal of this paper is to present a general iteration strategy for solving the discrete form of multidimensional neutron diffusion equations equivalent mathematically to an eigenvalue problem. Usually a solution method is based on different levels of iterations. The presented matrix formalism allows us to visualize explicitly how the used matrix splitting influences the matrix structure in an eigenvalue problem to be solved as well as the interdependence between inner and outer iterations within global iterations. Particular iterative strategies are illustrated by numerical results obtained for several reactor problems. (author). 21 refs, 35 figs, 16 tabs

Numerical Solution of Stokes Flow in a Circular Cavity Using Mesh-free Local RBF-DQ

DEFF Research Database (Denmark)

Kutanaai, S Soleimani; Roshan, Naeem; Vosoughi, A

2012-01-01

This work reports the results of a numerical investigation of Stokes flow problem in a circular cavity as an irregular geometry using mesh-free local radial basis function-based differential quadrature (RBF-DQ) method. This method is the combination of differential quadrature approximation of der...... in solution of partial differential equations (PDEs).......This work reports the results of a numerical investigation of Stokes flow problem in a circular cavity as an irregular geometry using mesh-free local radial basis function-based differential quadrature (RBF-DQ) method. This method is the combination of differential quadrature approximation...... is applied on a two-dimensional geometry. The obtained results from the numerical simulations are compared with those gained by previous works. Outcomes prove that the current technique is in very good agreement with previous investigations and this fact that RBF-DQ method is an accurate and flexible method...

CAS CERN Accelerator School. Third advanced accelerator physics course

International Nuclear Information System (INIS)

Turner, S.

1990-01-01

The third version of the CERN Accelerator School's (CAS) advanced course on General Accelerator Physics was given at Uppsala University from 18-29 September, 1989. Its syllabus was based on the previous courses held in Oxford, 1985 and Berlin, 1987 whose proceedings were published as CERN Yellow Reports 87-03 and 89-01 respectively. However, the opportunity was taken to emphasize the physics of small accelerators and storage rings, to present some topics in new ways, and to introduce new seminars. Thus the lectures contained in the present volume include chromaticity, dynamic aperture, kinetic theory, Landau damping, ion-trapping, Schottky noise, laser cooling and small ring lattice problems while the seminars include interpretation of numerical tracking, internal targets and living with radiation. (orig.)

The Numerical Solution of the Navier-Stokes Equations for Laminar, Incompressible Flow past a Parabolic Cylinder

NARCIS (Netherlands)

Botta, E.F.F.; Dijkstra, D.; Veldman, A.E.P.

1972-01-01

The numerical method of solution for the semi-infinite flat plate has been extended to the case of the parabolic cylinder. Results are presented for the skin friction, the friction drag, the pressure and the pressure drag. The drag coefficients have been checked by means of an application of the

Numerical simulations of subcritical reactor kinetics in thermal hydraulic transient phases

Energy Technology Data Exchange (ETDEWEB)

Yoo, J; Park, W S [Korea Atomic Energy Research Institute, Taejon (Korea, Republic of)

1999-12-31

A subcritical reactor driven by a linear proton accelerator has been considered as a nuclear waste incinerator at Korea Atomic Energy Research Institute (KAERI). Since the multiplication factor of a subcritical reactor is less than unity, to compensate exponentially decreasing fission neutrons, external neutrons form spallation reactions are essentially required for operating the reactor in its steady state. Furthermore, the profile of accelerator beam currents is very important in controlling a subcritical reactor, because the reactor power varies in accordance to the profile of external neutrons. We have developed a code system to find numerical solutions of reactor kinetics equations, which are the simplest dynamic model for controlling reactors. In a due course of our previous numerical study of point kinetics equations for critical reactors, however, we learned that the same code system can be used in studying dynamic behavior of the subcritical reactor. Our major motivation of this paper is to investigate responses of subcritical reactors for small changes in thermal hydraulic parameters. Building a thermal hydraulic model for the subcritical reactor dynamics, we performed numerical simulations for dynamic responses of the reactor based on point kinetics equations with a source term. Linearizing a set of coupled differential equations for reactor responses, we focus our research interest on dynamic responses of the reactor to variations of the thermal hydraulic parameters in transient phases. 5 refs., 8 figs. (Author)

Numerical simulations of subcritical reactor kinetics in thermal hydraulic transient phases

Energy Technology Data Exchange (ETDEWEB)

Yoo, J.; Park, W. S. [Korea Atomic Energy Research Institute, Taejon (Korea, Republic of)

1998-12-31

A subcritical reactor driven by a linear proton accelerator has been considered as a nuclear waste incinerator at Korea Atomic Energy Research Institute (KAERI). Since the multiplication factor of a subcritical reactor is less than unity, to compensate exponentially decreasing fission neutrons, external neutrons form spallation reactions are essentially required for operating the reactor in its steady state. Furthermore, the profile of accelerator beam currents is very important in controlling a subcritical reactor, because the reactor power varies in accordance to the profile of external neutrons. We have developed a code system to find numerical solutions of reactor kinetics equations, which are the simplest dynamic model for controlling reactors. In a due course of our previous numerical study of point kinetics equations for critical reactors, however, we learned that the same code system can be used in studying dynamic behavior of the subcritical reactor. Our major motivation of this paper is to investigate responses of subcritical reactors for small changes in thermal hydraulic parameters. Building a thermal hydraulic model for the subcritical reactor dynamics, we performed numerical simulations for dynamic responses of the reactor based on point kinetics equations with a source term. Linearizing a set of coupled differential equations for reactor responses, we focus our research interest on dynamic responses of the reactor to variations of the thermal hydraulic parameters in transient phases. 5 refs., 8 figs. (Author)

Elliptic solutions of generalized Brans-Dicke gravity with a non-universal coupling

Energy Technology Data Exchange (ETDEWEB)

Alimi, J.M.; Reverdy, V. [Observatoire de Paris, Laboratoire Univers et Theories (LUTh), Meudon (France); Golubtsova, A.A. [Observatoire de Paris, Laboratoire Univers et Theories (LUTh), Meudon (France); Peoples' Friendship University of Russia, Institute of Gravitation and Cosmology, Moscow (Russian Federation)

2014-10-15

We study a model of the generalized Brans-Dicke gravity presented in both the Jordan and in the Einstein frames, which are conformally related. We show that the scalar field equations in the Einstein frame are reduced to the geodesics equations on the target space of the nonlinear sigma model. The analytical solutions in elliptical functions are obtained when the conformal couplings are given by reciprocal exponential functions. The behavior of the scale factor in the Jordan frame is studied using numerical computations. For certain parameters the solutions can describe an accelerated expansion. We also derive an analytical approximation in exponential functions. (orig.)

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)

Some properties of band matrix and its application to the numerical solution one-dimensional Bratu's problem

Directory of Open Access Journals (Sweden)

Reza Jalilian

2014-07-01

Full Text Available ‎A Class of new methods based on a septic non-polynomial spline‎‎function for the numerical solution one-dimensional Bratu's problem‎are presented‎. ‎The local truncation errors and the methods of order‎‎2th‎, ‎4th‎, ‎6th‎, ‎8th‎, ‎10th‎, ‎and 12th‎, ‎are obtained‎. ‎The inverse of‎some band matrixes are obtained which are required in provingthe‎ convergence analysis of the presented method‎. ‎Associatedboundary‎ formulas are developed‎. ‎Convergence analysis of thesemethods is‎ discussed‎. ‎Numerical results are given to illustrate theefficiency‎ of methods‎.

PONDEROMOTIVE ACCELERATION IN CORONAL LOOPS

International Nuclear Information System (INIS)

Dahlburg, R. B.; Obenschain, K.; Laming, J. M.; Taylor, B. D.

2016-01-01

Ponderomotive acceleration has been asserted to be a cause of the first ionization potential (FIP) effect, the well-known enhancement in abundance by a factor of 3–4 over photospheric values of elements in the solar corona with FIP less than about 10 eV. It is shown here by means of numerical simulations that ponderomotive acceleration occurs in solar coronal loops, with the appropriate magnitude and direction, as a “by-product” of coronal heating. The numerical simulations are performed with the HYPERION code, which solves the fully compressible three-dimensional magnetohydrodynamic equations including nonlinear thermal conduction and optically thin radiation. Numerical simulations of coronal loops with an axial magnetic field from 0.005 to 0.02 T and lengths from 25,000 to 75,000 km are presented. In the simulations the footpoints of the axial loop magnetic field are convected by random, large-scale motions. There is a continuous formation and dissipation of field-aligned current sheets, which act to heat the loop. As a consequence of coronal magnetic reconnection, small-scale, high-speed jets form. The familiar vortex quadrupoles form at reconnection sites. Between the magnetic footpoints and the corona the reconnection flow merges with the boundary flow. It is in this region that the ponderomotive acceleration occurs. Mirroring the character of the coronal reconnection, the ponderomotive acceleration is also found to be intermittent.

PONDEROMOTIVE ACCELERATION IN CORONAL LOOPS

Energy Technology Data Exchange (ETDEWEB)

Dahlburg, R. B.; Obenschain, K. [LCP and FD, Naval Research Laboratory, Washington, DC 20375 (United States); Laming, J. M. [Space Science Division, Naval Research Laboratory, Washington, DC 20375 (United States); Taylor, B. D. [AFRL Eglin AFB, Pensacola, FL 32542 (United States)

2016-11-10

Ponderomotive acceleration has been asserted to be a cause of the first ionization potential (FIP) effect, the well-known enhancement in abundance by a factor of 3–4 over photospheric values of elements in the solar corona with FIP less than about 10 eV. It is shown here by means of numerical simulations that ponderomotive acceleration occurs in solar coronal loops, with the appropriate magnitude and direction, as a “by-product” of coronal heating. The numerical simulations are performed with the HYPERION code, which solves the fully compressible three-dimensional magnetohydrodynamic equations including nonlinear thermal conduction and optically thin radiation. Numerical simulations of coronal loops with an axial magnetic field from 0.005 to 0.02 T and lengths from 25,000 to 75,000 km are presented. In the simulations the footpoints of the axial loop magnetic field are convected by random, large-scale motions. There is a continuous formation and dissipation of field-aligned current sheets, which act to heat the loop. As a consequence of coronal magnetic reconnection, small-scale, high-speed jets form. The familiar vortex quadrupoles form at reconnection sites. Between the magnetic footpoints and the corona the reconnection flow merges with the boundary flow. It is in this region that the ponderomotive acceleration occurs. Mirroring the character of the coronal reconnection, the ponderomotive acceleration is also found to be intermittent.

Coaxial two-channel high-gradient dielectric wakefield accelerator

Directory of Open Access Journals (Sweden)

G. V. Sotnikov

2009-06-01

Full Text Available A new scheme for a dielectric wakefield accelerator is proposed that employs a cylindrical multizone dielectric structure configured as two concentric dielectric tubes with outer and inner vacuum channels for drive and accelerated bunches. Analytical and numerical studies have been carried out for such coaxial dielectric-loaded structures (CDS for high-gradient acceleration. An analytical theory of wakefield excitation by particle bunches in a multizone CDS has been formulated. Numerical calculations are presented for an example of a CDS using dielectric tubes with dielectric permittivity 5.7, having external diameters of 2.121 and 0.179 mm with inner diameters of 2.095 and 0.1 mm. An annular 5 GeV, 6 nC electron bunch with rms length of 0.035 mm energizes a wakefield on the structure axis having an accelerating gradient of ∼600  MeV/m with a transformer ratio ∼8∶1. The period of the accelerating field is ∼0.33  mm. If the width of the drive bunch channel is decreased, it is possible to obtain an accelerating gradient of >1  GeV/m while keeping the transformer ratio approximately the same. Full numerical simulations using a particle-in-cell code have confirmed results of the linear theory and furthermore have shown the important influence of the quenching wave that restricts the region of the wakefield to within several periods following the drive bunch. Numerical simulations for another example have shown nearly stable transport of drive and accelerated bunches through the CDS, using a short train of drive bunches.

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

A general solution strategy of modified power method for higher mode solutions

International Nuclear Information System (INIS)

Zhang, Peng; Lee, Hyunsuk; Lee, Deokjung

2016-01-01

A general solution strategy of the modified power iteration method for calculating higher eigenmodes has been developed and applied in continuous energy Monte Carlo simulation. The new approach adopts four features: 1) the eigen decomposition of transfer matrix, 2) weight cancellation for higher modes, 3) population control with higher mode weights, and 4) stabilization technique of statistical fluctuations using multi-cycle accumulations. The numerical tests of neutron transport eigenvalue problems successfully demonstrate that the new strategy can significantly accelerate the fission source convergence with stable convergence behavior while obtaining multiple higher eigenmodes at the same time. The advantages of the new strategy can be summarized as 1) the replacement of the cumbersome solution step of high order polynomial equations required by Booth's original method with the simple matrix eigen decomposition, 2) faster fission source convergence in inactive cycles, 3) more stable behaviors in both inactive and active cycles, and 4) smaller variances in active cycles. Advantages 3 and 4 can be attributed to the lower sensitivity of the new strategy to statistical fluctuations due to the multi-cycle accumulations. The application of the modified power method to continuous energy Monte Carlo simulation and the higher eigenmodes up to 4th order are reported for the first time in this paper. -- Graphical abstract: -- Highlights: •Modified power method is applied to continuous energy Monte Carlo simulation. •Transfer matrix is introduced to generalize the modified power method. •All mode based population control is applied to get the higher eigenmodes. •Statistic fluctuation can be greatly reduced using accumulated tally results. •Fission source convergence is accelerated with higher mode solutions.

Topical 5% potassium permanganate solution accelerates the healing process in chronic diabetic foot ulcers.

Science.gov (United States)

Delgado-Enciso, Iván; Madrigal-Perez, Violeta M; Lara-Esqueda, Agustin; Diaz-Sanchez, Martha G; Guzman-Esquivel, Jose; Rosas-Vizcaino, Luis E; Virgen-Jimenez, Oscar O; Kleiman-Trujillo, Juleny; Lagarda-Canales, Maria R; Ceja-Espiritu, Gabriel; Rangel-Salgado, Viridiana; Lopez-Lemus, Uriel A; Delgado-Enciso, Josuel; Lara-Basulto, Agustin D; Soriano Hernández, Alejandro D

2018-02-01

Potassium permanganate has been reported to be an effective treatment for certain types of wounds. The aim of the present study was to evaluate the use of potassium permanganate in the treatment of diabetic foot ulcers. A single-blind, randomized, controlled clinical trial was conducted on patients with type 2 diabetes mellitus that presented with a foot ulcer persisting for >3 months. The control group (n=10) was treated with the current standard treatment, which comprises of measures for reducing pressure in the ulcerated area, daily cleansing of the ulcer with potable water and antiseptic wash solution, and the application of a disinfectant solution on the entire surface area of the ulcer; while the intervention group (n=15) received the standard treatment plus 5% topical potassium permanganate solution applied once a day for 21 days. In the intervention group, 1 patient did not tolerate the treatment and was eliminated from the study on the first day. The remaining patients tolerated the interventions well. At the end of the treatment period, ulcers in the control group had decreased by 38% whereas those in the intervention group decreased by 73% (Ppermanganate is well tolerated and significantly accelerates the healing process of diabetic foot ulcers.

Homogenized blocked arcs for multicriteria optimization of radiotherapy: Analytical and numerical solutions

International Nuclear Information System (INIS)

Fenwick, John D.; Pardo-Montero, Juan

2010-01-01

Purpose: Homogenized blocked arcs are intuitively appealing as basis functions for multicriteria optimization of rotational radiotherapy. Such arcs avoid an organ-at-risk (OAR), spread dose out well over the rest-of-body (ROB), and deliver homogeneous doses to a planning target volume (PTV) using intensity modulated fluence profiles, obtainable either from closed-form solutions or iterative numerical calculations. Here, the analytic and iterative arcs are compared. Methods: Dose-distributions have been calculated for nondivergent beams, both including and excluding scatter, beam penumbra, and attenuation effects, which are left out of the derivation of the analytic arcs. The most straightforward analytic arc is created by truncating the well-known Brahme, Roos, and Lax (BRL) solution, cutting its uniform dose region down from an annulus to a smaller nonconcave region lying beyond the OAR. However, the truncation leaves behind high dose hot-spots immediately on either side of the OAR, generated by very high BRL fluence levels just beyond the OAR. These hot-spots can be eliminated using alternative analytical solutions ''C'' and ''L,'' which, respectively, deliver constant and linearly rising fluences in the gap region between the OAR and PTV (before truncation). Results: Measured in terms of PTV dose homogeneity, ROB dose-spread, and OAR avoidance, C solutions generate better arc dose-distributions than L when scatter, penumbra, and attenuation are left out of the dose modeling. Including these factors, L becomes the best analytical solution. However, the iterative approach generates better dose-distributions than any of the analytical solutions because it can account and compensate for penumbra and scatter effects. Using the analytical solutions as starting points for the iterative methodology, dose-distributions almost as good as those obtained using the conventional iterative approach can be calculated very rapidly. Conclusions: The iterative methodology is

Analytical solution and numerical study on water hammer in a pipeline closed with an elastically attached valve

Science.gov (United States)

Henclik, Sławomir

2018-03-01

The influence of dynamic fluid-structure interaction (FSI) onto the course of water hammer (WH) can be significant in non-rigid pipeline systems. The essence of this effect is the dynamic transfer of liquid energy to the pipeline structure and back, which is important for elastic structures and can be negligible for rigid ones. In the paper a special model of such behavior is analyzed. A straight pipeline with a steady flow, fixed to the floor with several rigid supports is assumed. The transient is generated by a quickly closed valve installed at the end of the pipeline. FSI effects are assumed to be present mainly at the valve which is fixed with a spring dash-pot attachment. Analysis of WH runs, especially transient pressure changes, for various stiffness and damping parameters of the spring dash-pot valve attachment is presented in the paper. The solutions are found analytically and numerically. Numerical results have been computed with the use of an own computer program developed on the basis of the four equation model of WH-FSI and the specific boundary conditions formulated at the valve. Analytical solutions have been found with the separation of variables method for slightly simplified assumptions. Damping at the dash-pot is taken into account within the numerical study. The influence of valve attachment parameters onto the WH courses was discovered and it was found the transient amplitudes can be reduced. Such a system, elastically attached shut-off valve in a pipeline or other, equivalent design can be a real solution applicable in practice.

Acceleration of compact torus plasma rings in a coaxial rail-gun

International Nuclear Information System (INIS)

Hartman, C.W.; Hammer, J.H.; Eddleman, J.

1986-01-01

They discuss here theoretical studies of magnetic acceleration of Compact Torus plasma rings in a coaxial, rail-gun accelerator. The rings are formed using a magnetized coaxial plasma gun and are accelerated by injection of B/sub Theta/ flux from an accelerator bank. After acceleration, the rings enter a focusing cone where the ring is decelerated and reduced in radius. As the ring radius decreases, the ring magnetic energy increases until it equals the entering kinetic energy and the ring stagnates. Scaling laws and numerical calculations of acceleration using a O-D numerical code are presented. 2-D, MHD simulations are shown which demonstrate ring formation, acceleration, and focusing. Finally, 3-D calculations are discussed which determine the ideal MHD stability of the accelerated ring

Acceleration of compact torus plasma rings in a coaxial rail-gun

International Nuclear Information System (INIS)

Hartman, C.W.; Hammer, J.H.; Eddleman, J.

1985-01-01

We discuss here theoretical studies of magnetic acceleration of Compact Torus plasma rings in a coaxial, rail-gun accelerator. The rings are formed using a magnetized coaxial plasma gun and are accelerated by injection of B/sub theta/ flux from an accelerator bank. After acceleration, the rings enter a focusing cone where the ring is decelerated and reduced in radius. As the ring radius decreases, the ring magnetic energy increases until it equals the entering kinetic energy and the ring stagnates. Scaling laws and numerical calculations of acceleration using a O-D numerical code are presented. 2-D, MHD simulations are shown which demonstrate ring formation, acceleration, and focusing. Finally, 3-D calculations are discussed which determine the ideal MHD stability of the accelerated ring

The numerical solution of linear multi-term fractional differential equations: systems of equations

Science.gov (United States)

Edwards, John T.; Ford, Neville J.; Simpson, A. Charles

2002-11-01

In this paper, we show how the numerical approximation of the solution of a linear multi-term fractional differential equation can be calculated by reduction of the problem to a system of ordinary and fractional differential equations each of order at most unity. We begin by showing how our method applies to a simple class of problems and we give a convergence result. We solve the Bagley Torvik equation as an example. We show how the method can be applied to a general linear multi-term equation and give two further examples.

Numerical analysis

CERN Document Server

Brezinski, C

2012-01-01

Numerical analysis has witnessed many significant developments in the 20th century. This book brings together 16 papers dealing with historical developments, survey papers and papers on recent trends in selected areas of numerical analysis, such as: approximation and interpolation, solution of linear systems and eigenvalue problems, iterative methods, quadrature rules, solution of ordinary-, partial- and integral equations. The papers are reprinted from the 7-volume project of the Journal of Computational and Applied Mathematics on '/homepage/sac/cam/na2000/index.html<

Development of an accelerated test for Internal Sulfate Attack study

Directory of Open Access Journals (Sweden)

Khelil Nacim

2014-04-01

Full Text Available Internal Sulfate Attack (ISA is a pathology that occurs under certain conditions in concrete having undergone heating above 70 °C at early age (through heating in pre-casting industry or due to hydration in large concrete parts. This reaction deemed very slow, numerous methods to speed up reactions leading to delayed ettringite formation have been developed. These methods are all based on the material damage. Another type of test is currently under development. It is based on rehabilitation techniques such as electrochemical chloride extraction (ECE in order to accelerate the leaching of alkalis that could be one of the triggers of the pathology. The study presented in this paper focused on concrete specimens prepared from cement (CEM I 52.5 N enriched with Na2SO4. These concretes have undergone a heat treatment typical of those used in precast plants (up to 24 hours with a maximum temperature of 80 °C. Various paths were explored for the development of the accelerated test. The first results showed that it was necessary to use a removable titanium anode ruthenium anode instead of stainless steel embedded in the concrete. Then tests with de-ionized water as the solute to the cathode did not accelerate the onset of expansions. The experiment has been modified and potassium carbonate was added to the solution. This modification didn’t show any significant improvement, and other experiments are being carried out to explain this result.

Paraxial light distribution in the focal region of a lens: a comparison of several analytical solutions and a numerical result.

Science.gov (United States)

Wu, Yang; Kelly, Damien P

2014-12-12

The distribution of the complex field in the focal region of a lens is a classical optical diffraction problem. Today, it remains of significant theoretical importance for understanding the properties of imaging systems. In the paraxial regime, it is possible to find analytical solutions in the neighborhood of the focus, when a plane wave is incident on a focusing lens whose finite extent is limited by a circular aperture. For example, in Born and Wolf's treatment of this problem, two different, but mathematically equivalent analytical solutions, are presented that describe the 3D field distribution using infinite sums of [Formula: see text] and [Formula: see text] type Lommel functions. An alternative solution expresses the distribution in terms of Zernike polynomials, and was presented by Nijboer in 1947. More recently, Cao derived an alternative analytical solution by expanding the Fresnel kernel using a Taylor series expansion. In practical calculations, however, only a finite number of terms from these infinite series expansions is actually used to calculate the distribution in the focal region. In this manuscript, we compare and contrast each of these different solutions to a numerically calculated result, paying particular attention to how quickly each solution converges for a range of different spatial locations behind the focusing lens. We also examine the time taken to calculate each of the analytical solutions. The numerical solution is calculated in a polar coordinate system and is semi-analytic. The integration over the angle is solved analytically, while the radial coordinate is sampled with a sampling interval of [Formula: see text] and then numerically integrated. This produces an infinite set of replicas in the diffraction plane, that are located in circular rings centered at the optical axis and each with radii given by [Formula: see text], where [Formula: see text] is the replica order. These circular replicas are shown to be fundamentally

The preparation of accelerator targets by the evaporation of acetate-organic solutions in the presence of NH3 gas

International Nuclear Information System (INIS)

Cai, S.Y.; Ghiorso, A.; Hoffman, D.C.

1987-03-01

The chemical methods described in this paper have been developed for preparation of isotopic targets for bombardment by accelerator-produced ions. Three systems are compared: nitrate-, chloride-, and acetate-organic solutions. The best method was found to be the metallic acetate-organic solution system, evaporated onto the substrate in the presence of ammonia gas. A detailed procedure is given for this method. The targets obtained by the acetate-organic solution system are uniform and adherent. The hydroxide forms fine crystals of good quality for target thicknesses from a few μg/cm 2 to several mg/cm 2 . Thicknesses up to 5 mg/cm 2 of Eu as the oxide were obtained by this method. The process is simple and fast. 18 refs., 1 tab

Numerical Solution of the Fractional Partial Differential Equations by the Two-Dimensional Fractional-Order Legendre Functions

Directory of Open Access Journals (Sweden)

Fukang Yin

2013-01-01

Full Text Available A numerical method is presented to obtain the approximate solutions of the fractional partial differential equations (FPDEs. The basic idea of this method is to achieve the approximate solutions in a generalized expansion form of two-dimensional fractional-order Legendre functions (2D-FLFs. The operational matrices of integration and derivative for 2D-FLFs are first derived. Then, by these matrices, a system of algebraic equations is obtained from FPDEs. Hence, by solving this system, the unknown 2D-FLFs coefficients can be computed. Three examples are discussed to demonstrate the validity and applicability of the proposed method.

A Family of Symmetric Linear Multistep Methods for the Numerical Solution of the Schroedinger Equation and Related Problems

International Nuclear Information System (INIS)

Anastassi, Z. A.; Simos, T. E.

2010-01-01

We develop a new family of explicit symmetric linear multistep methods for the efficient numerical solution of the Schroedinger equation and related problems with oscillatory solution. The new methods are trigonometrically fitted and have improved intervals of periodicity as compared to the corresponding classical method with constant coefficients and other methods from the literature. We also apply the methods along with other known methods to real periodic problems, in order to measure their efficiency.

Two numerical methods for the solution of two-dimensional eddy current problems

International Nuclear Information System (INIS)

Biddlecombe, C.S.

1978-07-01

A general method for the solution of eddy current problems in two dimensions - one component of current density and two of magnetic field, is reported. After examining analytical methods two numerical methods are presented. Both solve the two dimensional, low frequency limit of Maxwell's equations for transient eddy currents in conducting material, which may be permeable, in the presence of other non-conducting permeable material. Both solutions are expressed in terms of the magnetic vector potential. The first is an integral equation method, using zero order elements in the discretisation of the unknown source regions. The other is a differential equation method, using a first order finite element mesh, and the Galerkin weighted residual procedure. The resulting equations are solved as initial-value problems. Results from programs based on each method are presented showing the power and limitations of the methods and the range of problems solvable. The methods are compared and recommendations are made for choosing between them. Suggestions are made for improving both methods, involving boundary integral techniques. (author)

Particle acceleration by inverse-Weibel instability

International Nuclear Information System (INIS)

Kawata, S.

1996-01-01

A high demagnetization rate delta B/delta t can be obtained through fast decoupling of a magnetic field from an electric circuit which generates the magnetic field. Nowadays fast decoupling is possible by present switching technologies. A high particle-acceleration gradient can be obtained in an inductive acceleration system compared with that in a conventional induction accelerator. Based on this new proposal, inductive ion and electron accelerations were investigated numerically. The mechanism presented can be considered as pseudo-inverse Weibel instability. (author). 3 figs., 7 refs

Particle acceleration by inverse-Weibel instability

Energy Technology Data Exchange (ETDEWEB)

Kawata, S [Nagaoka Univ. of Technology (Japan). Dept. of Electrical Engineering

1997-12-31

A high demagnetization rate delta B/delta t can be obtained through fast decoupling of a magnetic field from an electric circuit which generates the magnetic field. Nowadays fast decoupling is possible by present switching technologies. A high particle-acceleration gradient can be obtained in an inductive acceleration system compared with that in a conventional induction accelerator. Based on this new proposal, inductive ion and electron accelerations were investigated numerically. The mechanism presented can be considered as pseudo-inverse Weibel instability. (author). 3 figs., 7 refs.

The numerical solution of the Navier-Stokes equations for laminar incompressible flow past a paraboloid of revolution

NARCIS (Netherlands)

Veldman, A.E.P.

1973-01-01

A numerical method is presented for the solution of the Navier-Stokes equations for flow past a paraboloid of revolution. The flow field has been computed for a large range of Reynolds numbers. Results are presented for the skinfriction and the pressure together with their respective drag

Numerical solutions of multi-dimensional solidification/melting problems by the dual reciprocity boundary element method

International Nuclear Information System (INIS)

Jo, Jong Chull; Shin, Won Ky

1997-01-01

This paper presents an effective and simple procedure for the simulation of the motion of the solid-liquid interfacial boundary and the transient temperature field during phase change process. To accomplish this purpose, an iterative implicit solution algorithm has been developed by employing the dual reciprocity boundary element method. The dual reciprocity boundary element approach provided in this paper is much simpler than the usual boundary element method applying a reciprocity principle and an available technique for dealing with domain integral of boundary element formulation simultaneously. The effectiveness of the present analysis method have been illustrated through comparisons of the calculation results of an example with its semi-analytical or other numerical solutions where available

Third-order-accurate numerical methods for efficient, large time-step solutions of mixed linear and nonlinear problems

Energy Technology Data Exchange (ETDEWEB)

Cobb, J.W.

1995-02-01

There is an increasing need for more accurate numerical methods for large-scale nonlinear magneto-fluid turbulence calculations. These methods should not only increase the current state of the art in terms of accuracy, but should also continue to optimize other desired properties such as simplicity, minimized computation, minimized memory requirements, and robust stability. This includes the ability to stably solve stiff problems with long time-steps. This work discusses a general methodology for deriving higher-order numerical methods. It also discusses how the selection of various choices can affect the desired properties. The explicit discussion focuses on third-order Runge-Kutta methods, including general solutions and five examples. The study investigates the linear numerical analysis of these methods, including their accuracy, general stability, and stiff stability. Additional appendices discuss linear multistep methods, discuss directions for further work, and exhibit numerical analysis results for some other commonly used lower-order methods.

A relativistic model of the topological acceleration effect

International Nuclear Information System (INIS)

Ostrowski, Jan J; Roukema, Boudewijn F; Buliński, Zbigniew P

2012-01-01

It has previously been shown heuristically that the topology of the Universe affects gravity, in the sense that a test particle near a massive object in a multiply connected universe is subject to a topologically induced acceleration that opposes the local attraction to the massive object. It is necessary to check if this effect occurs in a fully relativistic solution of the Einstein equations that has a multiply connected spatial section. A Schwarzschild-like exact solution that is multiply connected in one spatial direction is checked for analytical and numerical consistency with the heuristic result. The T 1 (slab-space) heuristic result is found to be relativistically correct. For a fundamental domain size of L, a slow-moving, negligible-mass test particle lying at distance x along the axis from the object of mass M to its nearest multiple image, where GM/c 2 3 )x, where ζ(3) is Apery's constant. For M ∼ 10 14 M sun and L ∼ 10-20h -1 Gpc, this linear expression is accurate to ±10% over h -1 Mpc/h -1 Gpc. Thus, at least in a simple example of a multiply connected universe, the topological acceleration effect is not an artefact of Newtonian-like reasoning, and its linear derivation is accurate over about three orders of magnitude in x. (paper)

Solution of relativistic quantum optics problems using clusters of graphical processing units

Energy Technology Data Exchange (ETDEWEB)

Gordon, D.F., E-mail: daviel.gordon@nrl.navy.mil; Hafizi, B.; Helle, M.H.

2014-06-15

Numerical solution of relativistic quantum optics problems requires high performance computing due to the rapid oscillations in a relativistic wavefunction. Clusters of graphical processing units are used to accelerate the computation of a time dependent relativistic wavefunction in an arbitrary external potential. The stationary states in a Coulomb potential and uniform magnetic field are determined analytically and numerically, so that they can used as initial conditions in fully time dependent calculations. Relativistic energy levels in extreme magnetic fields are recovered as a means of validation. The relativistic ionization rate is computed for an ion illuminated by a laser field near the usual barrier suppression threshold, and the ionizing wavefunction is displayed.

Numerical solution to a multi-dimensional linear inverse heat conduction problem by a splitting-based conjugate gradient method

International Nuclear Information System (INIS)

Dinh Nho Hao; Nguyen Trung Thanh; Sahli, Hichem

2008-01-01

In this paper we consider a multi-dimensional inverse heat conduction problem with time-dependent coefficients in a box, which is well-known to be severely ill-posed, by a variational method. The gradient of the functional to be minimized is obtained by aids of an adjoint problem and the conjugate gradient method with a stopping rule is then applied to this ill-posed optimization problem. To enhance the stability and the accuracy of the numerical solution to the problem we apply this scheme to the discretized inverse problem rather than to the continuous one. The difficulties with large dimensions of discretized problems are overcome by a splitting method which only requires the solution of easy-to-solve one-dimensional problems. The numerical results provided by our method are very good and the techniques seem to be very promising.

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

Numerical relativity

CERN Document Server

Shibata, Masaru

2016-01-01

This book is composed of two parts: First part describes basics in numerical relativity, that is, the formulations and methods for a solution of Einstein's equation and general relativistic matter field equations. This part will be helpful for beginners of numerical relativity who would like to understand the content of numerical relativity and its background. The second part focuses on the application of numerical relativity. A wide variety of scientific numerical results are introduced focusing in particular on the merger of binary neutron stars and black holes.

Numerical analysis

CERN Document Server

Khabaza, I M

1960-01-01

Numerical Analysis is an elementary introduction to numerical analysis, its applications, limitations, and pitfalls. Methods suitable for digital computers are emphasized, but some desk computations are also described. Topics covered range from the use of digital computers in numerical work to errors in computations using desk machines, finite difference methods, and numerical solution of ordinary differential equations. This book is comprised of eight chapters and begins with an overview of the importance of digital computers in numerical analysis, followed by a discussion on errors in comput

ANALYTIC SOLUTION FOR SELF-REGULATED COLLECTIVE ESCAPE OF COSMIC RAYS FROM THEIR ACCELERATION SITES

International Nuclear Information System (INIS)

Malkov, M. A.; Diamond, P. H.; Sagdeev, R. Z.; Aharonian, F. A.; Moskalenko, I. V.

2013-01-01

Supernova remnants (SNRs), as the major contributors to the galactic cosmic rays (CRs), are believed to maintain an average CR spectrum by diffusive shock acceleration regardless of the way they release CRs into the interstellar medium (ISM). However, the interaction of the CRs with nearby gas clouds crucially depends on the release mechanism. We call into question two aspects of a popular paradigm of the CR injection into the ISM, according to which they passively and isotropically diffuse in the prescribed magnetic fluctuations as test particles. First, we treat the escaping CR and the Alfvén waves excited by them on an equal footing. Second, we adopt field-aligned CR escape outside the source, where the waves become weak. An exact analytic self-similar solution for a CR ''cloud'' released by a dimmed accelerator strongly deviates from the test-particle result. The normalized CR partial pressure may be approximated as P(p,z,t)=2[|z| 5/3 +z dif 5/3 (p,t)] -3/5 exp[-z 2 /4D ISM (p)t], where p is the momentum of CR particle, and z is directed along the field. The core of the cloud expands as z dif ∝√(D NL (p)t) and decays in time as p∝2z -1 dif (t). The diffusion coefficient D NL is strongly suppressed compared to its background ISM value D ISM : D NL ∼ D ISM exp (– Π) ISM for sufficiently high field-line-integrated CR partial pressure, Π. When Π >> 1, the CRs drive Alfvén waves efficiently enough to build a transport barrier (p≈2/∣z∣— p edestal ) that strongly reduces the leakage. The solution has a spectral break at p = p br , where p br satisfies the equation D NL (p br ) ≅ z 2 /t.

Numerical study of partitions effect on multiplicity of solutions in an infinite channel periodically heated from below

International Nuclear Information System (INIS)

Abourida, B.; Hasnaoui, M.

2005-01-01

Laminar natural convection in an infinite horizontal channel heated periodically from below and provided with thin adiabatic partitions on its lower wall, is investigated numerically. The effect of these partitions on the multiplicity of solutions and heat transfer characteristics in the computational domain is studied. The parameters of the study are the Rayleigh number (10 2 Ra 4.9 x 10 6 ) and the height of the partitions (0 B = h'/H' 1/2). The results obtained in the case of air (Pr = 0.72) as working fluid show that depending on the governing parameters, the existence of multiple solutions is possible. Important differences in terms of heat transfer are observed between two different solutions

Numeric algorithms for parallel processors computer architectures with applications to the few-groups neutron diffusion equations

International Nuclear Information System (INIS)

Zee, S.K.

1987-01-01

A numeric algorithm and an associated computer code were developed for the rapid solution of the finite-difference method representation of the few-group neutron-diffusion equations on parallel computers. Applications of the numeric algorithm on both SIMD (vector pipeline) and MIMD/SIMD (multi-CUP/vector pipeline) architectures were explored. The algorithm was successfully implemented in the two-group, 3-D neutron diffusion computer code named DIFPAR3D (DIFfusion PARallel 3-Dimension). Numerical-solution techniques used in the code include the Chebyshev polynomial acceleration technique in conjunction with the power method of outer iteration. For inner iterations, a parallel form of red-black (cyclic) line SOR with automated determination of group dependent relaxation factors and iteration numbers required to achieve specified inner iteration error tolerance is incorporated. The code employs a macroscopic depletion model with trace capability for selected fission products' transients and critical boron. In addition to this, moderator and fuel temperature feedback models are also incorporated into the DIFPAR3D code, for realistic simulation of power reactor cores. The physics models used were proven acceptable in separate benchmarking studies

FEM Techniques for High Stress Detection in Accelerated Fatigue Simulation

Science.gov (United States)

Veltri, M.

2016-09-01

This work presents the theory and a numerical validation study in support to a novel method for a priori identification of fatigue critical regions, with the aim to accelerate durability design in large FEM problems. The investigation is placed in the context of modern full-body structural durability analysis, where a computationally intensive dynamic solution could be required to identify areas with potential for fatigue damage initiation. The early detection of fatigue critical areas can drive a simplification of the problem size, leading to sensible improvement in solution time and model handling while allowing processing of the critical areas in higher detail. The proposed technique is applied to a real life industrial case in a comparative assessment with established practices. Synthetic damage prediction quantification and visualization techniques allow for a quick and efficient comparison between methods, outlining potential application benefits and boundaries.

Breakdowns and solutions in 15 UD pelletron ion accelerator facility at Inter-University Accelerator Centre, New Delhi

International Nuclear Information System (INIS)

Joshi, R.; Singh, P.; Suraj; Nishal, S.M.; Panwar, N.S.; Singh, M.P.; Kumar, R.; Prasad, J.; Sota, M.; Patel, V.P.; Sharma, R.P.; Kumar, Pankaj; Devi, K.D.; Ojha, S.; Gargari, S.; Chopra, S.; Kanjilal, D.

2013-01-01

15UD Pelletron accelerator, installed in Inter-University Accelerator Centre (IUAC), New Delhi, is a tandem ion accelerator and is performing well since its commissioning. Constant efforts have been put to keep high uptime and better performance of the accelerator for more than two decades. In recent years, the facility was improved by many modifications and up gradations. It has also gone through a few major breakdowns related to charging system and fiber optic cables. Out of two charging systems, one system failed and devices housed in tank stopped working due to the damage of fiber optic cables. The reasons for both of these breakdowns were studied thoroughly. The entire charging system and fiber optic cable network have been rebuilt and tested. The diagnostic techniques and maintenance methods for these two breakdowns will be discussed in this paper. (author)

Superconducting linac at Inter-University Accelerator Centre: Operational challenges and solutions

Directory of Open Access Journals (Sweden)

S. Ghosh

2009-04-01

Full Text Available A superconducting linear accelerator based on niobium quarter wave resonators has recently become operational to boost the energy of the heavy ion beams available from the existing 15 UD (unit doubled Pelletron accelerator. The niobium resonators typically performed at an accelerating field of 3–6  MV/m at 6 watts of input power in the test cryostat. When they were tested in the linac cryostat, the accelerating fields were drastically reduced and a number of other problems were also encountered. At present, all the problems have been diagnosed and solved. Many design modifications, e.g., in power coupler, mechanical tuner, helium cooling system, etc. were incorporated to solve the problems. A novel method of vibration damping was also implemented to reduce the effect of microphonics on the resonators. Finally, the accelerated beam through linac was delivered to conduct experiments.

Distribution of the Discretization and Algebraic Error in Numerical Solution of Partial Differential Equations

Czech Academy of Sciences Publication Activity Database

Papež, Jan; Liesen, J.; Strakoš, Z.

2014-01-01

Roč. 449, 15 May (2014), s. 89-114 ISSN 0024-3795 R&D Projects: GA AV ČR IAA100300802; GA ČR GA201/09/0917 Grant - others:GA MŠk(CZ) LL1202; GA UK(CZ) 695612 Institutional support: RVO:67985807 Keywords : numerical solution of partial differential equations * finite element method * adaptivity * a posteriori error analysis * discretization error * algebra ic error * spatial distribution of the error Subject RIV: BA - General Mathematics Impact factor: 0.939, year: 2014

Iteration and accelerator dynamics

International Nuclear Information System (INIS)

Peggs, S.

1987-10-01

Four examples of iteration in accelerator dynamics are studied in this paper. The first three show how iterations of the simplest maps reproduce most of the significant nonlinear behavior in real accelerators. Each of these examples can be easily reproduced by the reader, at the minimal cost of writing only 20 or 40 lines of code. The fourth example outlines a general way to iteratively solve nonlinear difference equations, analytically or numerically

The numerical analysis of eigenvalue problem solutions in the multigroup neutron diffusion theory

International Nuclear Information System (INIS)

Woznicki, Z.I.

1994-01-01

The main goal of this paper is to present a general iteration strategy for solving the discrete form of multidimensional neutron diffusion equations equivalent mathematically to an eigenvalue problem. Usually a solution method is based on different levels of iterations. The presented matrix formalism allows us to visualize explicitly how the used matrix splitting influences the matrix structure in an eigenvalue problem to be solved as well as the interdependence between inner and outer iteration within global iterations. Particular interactive strategies are illustrated by numerical results obtained for several reactor problems. (author). 21 refs, 32 figs, 15 tabs

The numerical analysis of eigenvalue problem solutions in the multigroup neutron diffusion theory

Energy Technology Data Exchange (ETDEWEB)

Woznicki, Z I [Institute of Atomic Energy, Otwock-Swierk (Poland)

1994-12-31

The main goal of this paper is to present a general iteration strategy for solving the discrete form of multidimensional neutron diffusion equations equivalent mathematically to an eigenvalue problem. Usually a solution method is based on different levels of iterations. The presented matrix formalism allows us to visualize explicitly how the used matrix splitting influences the matrix structure in an eigenvalue problem to be solved as well as the interdependence between inner and outer iteration within global iterations. Particular interactive strategies are illustrated by numerical results obtained for several reactor problems. (author). 21 refs, 32 figs, 15 tabs.

A numerical technique for enhanced efficiency and stability for the solution of the nuclear reactor equation

International Nuclear Information System (INIS)

Khotylev, V.A.; Hoogenboom, J.E.

1996-01-01

The paper presents new techniques for the solution of the nuclear reactor equation in diffusion approximation, that has enhanced efficiency and stability. The code system based on the new technique solves a number of steady-state and/or transient problems with coupled thermal hydraulics in one-, two-, or three dimensional geometry with reduced CPU time as compared to similar code systems of previous generations if well-posed neutronics problems are considered. Automated detection of ill-posed problem and selection of the appropriate numerical method makes the new code system capable of yielding a correct solution for wider range of problems without user intervention. (author)

A numerical technique for enhanced efficiency and stability for the solution of the nuclear reactor equation

Energy Technology Data Exchange (ETDEWEB)

Khotylev, V.A.; Hoogenboom, J.E. [Delft Univ. of Technology, Interfaculty Reactor Inst., Delft (Netherlands)

1996-07-01

The paper presents new techniques for the solution of the nuclear reactor equation in diffusion approximation, that has enhanced efficiency and stability. The code system based on the new technique solves a number of steady-state and/or transient problems with coupled thermal hydraulics in one-, two-, or three dimensional geometry with reduced CPU time as compared to similar code systems of previous generations if well-posed neutronics problems are considered. Automated detection of ill-posed problem and selection of the appropriate numerical method makes the new code system capable of yielding a correct solution for wider range of problems without user intervention. (author)

Cosmic-ray acceleration and the radio evolution of Cassiopeia A

International Nuclear Information System (INIS)

Chevalier, R.A.; Robertson, J.W.; Scott, J.S.

1976-01-01

A more detailed analysis of the Scott and Chevalier model for production of galactic cosmic rays in supernova remnants is presented. Particles are accelerated by second-order Fermi acceleration with turbulent vortices (produced by the motions of the supernova ejecta through the remnant) acting as moving scattering centers. The time-dependent equation of continuity in particle energy space is solved numerically. The results of the calculations are in substantial agreement with all time-dependent observations of the radio emission from Cas A. This mechanism implies an dependent solution yields a cosmic ray spectrum with the same slope as galactic cosmic rays. The results of our calculations and new work on γ-rays by, e.g., Stecker and by Lingenfelter and Higdon and cosmic ray composition by, e.g., Hainebach, Norman, and Schramm support our hypothesis that galactic cosmic rays are produced in supernova remnants by the mechanism proposed by Scott and Chevalier

'Diffraction-free' optical beams in inverse free electron laser accelerators

International Nuclear Information System (INIS)

Cai, S.Y.; Bhattacharjee, A.; Marshall, T.C.

1988-01-01

'Diffraction-free' optical beams correspond to exact solutions of the wave equation in free space with the remarkable property that they propagate with negligible transverse spreading for distances much larger than the Rayleigh range. The requirement for this to occur is a large aperture. Using a 2D computer code, we find that these optical beams will also propagate with negligible diffraction even when perturbed by the electron beam in an IFEL; indeed they match well the FEL requirement for the accelerator. The numerical simulations are performed for the proposed facility at Brookhaven in which λ s =10 μm, B=1.5 T (linearly tapered l w =1.31-6.28 cm) and the optical beam power is either 8x10 11 W or 2.3x10 10 W. Approximately 70% of the electrons constituting a beam of current 5 mA or 15 A, radius 0.14 mm and initial energy of 50 MeV is accelerated at 50 MeV/m. (orig.)

Numerical solutions of multi-dimensional solidification/melting problems by the dual reciprocity boundary element method

Energy Technology Data Exchange (ETDEWEB)

Jo, Jong Chull; Shin, Won Ky [Korea Institute of Nuclear Safety, Taejon (Korea, Republic of)

1998-12-31

This paper presents an effective and simple procedure for the simulation of the motion of the solid-liquid interfacial boundary and the transient temperature field during phase change process. To accomplish this purpose, an iterative implicit solution algorithm has been developed by employing the dual reciprocity boundary element method. The dual reciprocity boundary element approach provided in this paper is much simpler than the usual boundary element method applying a reciprocity principle and an available technique for dealing with domain integral of boundary element formulation simultaneously. The effectiveness of the present analysis method have been illustrated through comparisons of the calculation results of an example with its semi-analytical or other numerical solutions where available. 22 refs., 3 figs. (Author)

Numerical solutions of multi-dimensional solidification/melting problems by the dual reciprocity boundary element method

Energy Technology Data Exchange (ETDEWEB)

Jo, Jong Chull; Shin, Won Ky [Korea Institute of Nuclear Safety, Taejon (Korea, Republic of)

1997-12-31

This paper presents an effective and simple procedure for the simulation of the motion of the solid-liquid interfacial boundary and the transient temperature field during phase change process. To accomplish this purpose, an iterative implicit solution algorithm has been developed by employing the dual reciprocity boundary element method. The dual reciprocity boundary element approach provided in this paper is much simpler than the usual boundary element method applying a reciprocity principle and an available technique for dealing with domain integral of boundary element formulation simultaneously. The effectiveness of the present analysis method have been illustrated through comparisons of the calculation results of an example with its semi-analytical or other numerical solutions where available. 22 refs., 3 figs. (Author)

Numerical simulation on range of high-energy electron moving in accelerator target

International Nuclear Information System (INIS)

Shao Wencheng; Sun Punan; Dai Wenjiang

2008-01-01

In order to determine the range of high-energy electron moving in accelerator target, the range of electron with the energy range of 1 to 100 MeV moving in common target material of accelerator was calculated by Monte-Carlo method. Comparison between the calculated result and the published data were performed. The results of Monte-Carlo calculation are in good agreement with the published data. Empirical formulas were obtained for the range of high-energy electron with the energy range of 1 to 100 MeV in common target material by curve fitting, offering a series of referenced data for the design of targets in electron accelerator. (authors)

Solving radiative transfer problems in highly heterogeneous media via domain decomposition and convergence acceleration techniques

International Nuclear Information System (INIS)

Previti, Alberto; Furfaro, Roberto; Picca, Paolo; Ganapol, Barry D.; Mostacci, Domiziano

2011-01-01

This paper deals with finding accurate solutions for photon transport problems in highly heterogeneous media fastly, efficiently and with modest memory resources. We propose an extended version of the analytical discrete ordinates method, coupled with domain decomposition-derived algorithms and non-linear convergence acceleration techniques. Numerical performances are evaluated using a challenging case study available in the literature. A study of accuracy versus computational time and memory requirements is reported for transport calculations that are relevant for remote sensing applications.

Large-Scale Experimental and Numerical Study of Blast Acceleration Created by Close-In Buried Explosion on Underground Tunnel Lining

Directory of Open Access Journals (Sweden)

Mohamad Reza Soheyli

2016-01-01

Full Text Available Despite growing demands for structures in water transportation tunnels, underground installations, subsurface dams, and subterranean channels, there is limited field knowledge about the dynamic behavior of these structures in the face of near-fault earthquakes or impulse excitations. This study conducted a large-scale test on underground tunnel excited by two close-in subsurface explosions. The horizontal and vertical acceleration were recorded on the vertical wall of the tunnel and the free field data including the acceleration on the ground surface at 11-meter distance from the tunnel. The frequency domain analysis of recorded results determined the frequency 961 Hz and 968 Hz for 1.69 kg and 2.76 kg equivalent T.N.T., respectively. Then, finite element analysis results were compared with the test data. The comparisons demonstrated a good correlation and satisfied the field data. Finally, based on numerical modeling, a parametric study was applied to determine the effects of shear wave velocity distance of the crater with respect to the tunnel on impulse response of the tunnel.

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

International Nuclear Information System (INIS)

Serrano Pedraza, F.

1985-01-01

in developing of this work are presented. In Appendix B a general list of computer program is given, in Appendix C analytical solutions for two simple problems are presented and finally in appendix D some concepts and definitions about numerical stability are given. It can also be mentioned that computer code has no limitation with to number of regions and number of energy groups. Furnishing cross sections, the computer program gives the following results. 1) Angular flux when a problem with independent source without fissions are considered, 2) number of secondary neutrons for collition or 3) effective multiplication factor (Author)

Dynamical Solution to the Problem of a Small Cosmological Constant and Late-Time Cosmic Acceleration

International Nuclear Information System (INIS)

Armendariz-Picon, C.; Mukhanov, V.; Steinhardt, Paul J.

2000-01-01

Increasing evidence suggests that most of the energy density of the universe consists of a dark energy component with negative pressure that causes the cosmic expansion to accelerate. We address why this component comes to dominate the universe only recently. We present a class of theories based on an evolving scalar field where the explanation is based entirely on internal dynamical properties of the solutions. In the theories we consider, the dynamics causes the scalar field to lock automatically into a negative pressure state at the onset of matter domination such that the present epoch is the earliest possible time consistent with nucleosynthesis restrictions when it can start to dominate

Numerical solution of a flow inside a labyrinth seal

Directory of Open Access Journals (Sweden)

Šimák Jan

2012-04-01

Full Text Available The aim of this study is a behaviour of a flow inside a labyrinth seal on a rotating shaft. The labyrinth seal is a type of a non-contact seal where a leakage of a fluid is prevented by a rather complicated path, which the fluid has to overcome. In the presented case the sealed medium is the air and the seal is made by a system of 20 teeth on a rotating shaft situated against a smooth static surface. Centrifugal forces present due to the rotation of the shaft create vortices in each chamber and thus dissipate the axial velocity of the escaping air.The structure of the flow field inside the seal is studied through the use of numerical methods. Three-dimensional solution of the Navier-Stokes equations for turbulent flow is very time consuming. In order to reduce the computational time we can simplify our problem and solve it as an axisymmetric problem in a two-dimensional meridian plane. For this case we use a transformation of the Navier-Stokes equations and of the standard k-omega turbulence model into a cylindrical coordinate system. A finite volume method is used for the solution of the resulting problem. A one-side modification of the Riemann problem for boundary conditions is used at the inlet and at the outlet of the axisymmetric channel. The total pressure and total density (temperature are to be used preferably at the inlet whereas the static pressure is used at the outlet for the compatibility. This idea yields physically relevant boundary conditions. The important characteristics such as a mass flow rate and a power loss, depending on a pressure ratio (1.1 - 4 and an angular velocity (1000 - 15000 rpm are evaluated.

Feasibility of using laser ion accelerators in proton therapy

CERN Document Server

Bulanov, S V

2002-01-01

The feasibility of using the laser plasma as a source of the high-energy ions for the proton radiation therapy is discussed. The proposal is based on the recent inventions of the effective ions acceleration in the experiments and through numerical modeling of the powerful laser radiation interaction with the gaseous and solid state targets. The principal peculiarity of the dependence of the protons energy losses in the tissues (the Bragg peak of losses) facilities the solution of one of the most important problems of the radiation therapy, which consists in realizing the tumor irradiation by sufficiently high and homogeneous dose with simultaneous minimization of the irradiation level, relative to the healthy and neighbouring tissues and organs

Numerical path integral solution to strong Coulomb correlation in one dimensional Hooke's atom

Science.gov (United States)

Ruokosenmäki, Ilkka; Gholizade, Hossein; Kylänpää, Ilkka; Rantala, Tapio T.

2017-01-01

We present a new approach based on real time domain Feynman path integrals (RTPI) for electronic structure calculations and quantum dynamics, which includes correlations between particles exactly but within the numerical accuracy. We demonstrate that incoherent propagation by keeping the wave function real is a novel method for finding and simulation of the ground state, similar to Diffusion Monte Carlo (DMC) method, but introducing new useful tools lacking in DMC. We use 1D Hooke's atom, a two-electron system with very strong correlation, as our test case, which we solve with incoherent RTPI (iRTPI) and compare against DMC. This system provides an excellent test case due to exact solutions for some confinements and because in 1D the Coulomb singularity is stronger than in two or three dimensional space. The use of Monte Carlo grid is shown to be efficient for which we determine useful numerical parameters. Furthermore, we discuss another novel approach achieved by combining the strengths of iRTPI and DMC. We also show usefulness of the perturbation theory for analytical approximates in case of strong confinements.

A Novel Machine Learning Strategy Based on Two-Dimensional Numerical Models in Financial Engineering

Directory of Open Access Journals (Sweden)

Qingzhen Xu

2013-01-01

Full Text Available Machine learning is the most commonly used technique to address larger and more complex tasks by analyzing the most relevant information already present in databases. In order to better predict the future trend of the index, this paper proposes a two-dimensional numerical model for machine learning to simulate major U.S. stock market index and uses a nonlinear implicit finite-difference method to find numerical solutions of the two-dimensional simulation model. The proposed machine learning method uses partial differential equations to predict the stock market and can be extensively used to accelerate large-scale data processing on the history database. The experimental results show that the proposed algorithm reduces the prediction error and improves forecasting precision.

Numerical studies and measurements on the side-coupled drift tube linac (SCDTL) accelerating structure

International Nuclear Information System (INIS)

Picardi, L.; Ronsivalle, C.; Spataro, B.

2000-01-01

The 3 GHz linac section designed for the low energy (7-65 MeV) part of TOP (therapy oncological protons) linac (Picardi et al., 1997, 1996), operating at 3 GHz frequency and in π/2 mode, consists of eight modules of the structure SCDTL (side-coupled drift tube linac). The first module is designed to accelerate 7 MeV protons up to 13.4 MeV, and a prototype is presently under construction. Electromagnetic field calculations of the non-axisymmetric cavities carried out by using MAFIA 3D code (Weiland, 1986) gave the RF wall losses and the full mode spectrum. Two prototypes, an aluminium model of the first quintuplet and a copper model of the last triplet of the module, were built in order to check the complex 3D properties of the structure, and to refine the tuning procedure. This paper reports the results of the 3D numerical simulations about the RF properties of the first module and of some RF measurements on the prototypes. The beam dynamics study results in the SCDTL section are discussed as well

New numerical methods for open-loop and feedback solutions to dynamic optimization problems

Science.gov (United States)

Ghosh, Pradipto

The topic of the first part of this research is trajectory optimization of dynamical systems via computational swarm intelligence. Particle swarm optimization is a nature-inspired heuristic search method that relies on a group of potential solutions to explore the fitness landscape. Conceptually, each particle in the swarm uses its own memory as well as the knowledge accumulated by the entire swarm to iteratively converge on an optimal or near-optimal solution. It is relatively straightforward to implement and unlike gradient-based solvers, does not require an initial guess or continuity in the problem definition. Although particle swarm optimization has been successfully employed in solving static optimization problems, its application in dynamic optimization, as posed in optimal control theory, is still relatively new. In the first half of this thesis particle swarm optimization is used to generate near-optimal solutions to several nontrivial trajectory optimization problems including thrust programming for minimum fuel, multi-burn spacecraft orbit transfer, and computing minimum-time rest-to-rest trajectories for a robotic manipulator. A distinct feature of the particle swarm optimization implementation in this work is the runtime selection of the optimal solution structure. Optimal trajectories are generated by solving instances of constrained nonlinear mixed-integer programming problems with the swarming technique. For each solved optimal programming problem, the particle swarm optimization result is compared with a nearly exact solution found via a direct method using nonlinear programming. Numerical experiments indicate that swarm search can locate solutions to very great accuracy. The second half of this research develops a new extremal-field approach for synthesizing nearly optimal feedback controllers for optimal control and two-player pursuit-evasion games described by general nonlinear differential equations. A notable revelation from this development

Multi-beam linear accelerator EVT

Energy Technology Data Exchange (ETDEWEB)

Teryaev, Vladimir E., E-mail: vladimir_teryaev@mail.ru [Omega-P, Inc., New Haven, CT 06510 (United States); Kazakov, Sergey Yu. [Fermilab, Batavia, IL 60510 (United States); Hirshfield, Jay L. [Omega-P, Inc., New Haven, CT 06510 (United States); Yale University, New Haven, CT 06511 (United States)

2016-09-01

A novel electron multi-beam accelerator is presented. The accelerator, short-named EVT (Electron Voltage Transformer) belongs to the class of two-beam accelerators. It combines an RF generator and essentially an accelerator within the same vacuum envelope. Drive beam-lets and an accelerated beam are modulated in RF modulators and then bunches pass into an accelerating structure, comprising uncoupled with each other and inductive tuned cavities, where the energy transfer from the drive beams to the accelerated beam occurs. A phasing of bunches is solved by choice correspond distances between gaps of the adjacent cavities. Preliminary results of numerical simulations and the initial specification of EVT operating in S-band, with a 60 kV gun and generating a 2.7 A, 1.1 MV beam at its output is presented. A relatively high efficiency of 67% and high design average power suggest that EVT can find its use in industrial applications.

Discrete convolution-operators and radioactive disintegration. [Numerical solution

Energy Technology Data Exchange (ETDEWEB)

Kalla, S L; VALENTINUZZI, M E [UNIVERSIDAD NACIONAL DE TUCUMAN (ARGENTINA). FACULTAD DE CIENCIAS EXACTAS Y TECNOLOGIA

1975-08-01

The basic concepts of discrete convolution and discrete convolution-operators are briefly described. Then, using the discrete convolution - operators, the differential equations associated with the process of radioactive disintegration are numerically solved. The importance of the method is emphasized to solve numerically, differential and integral equations.

A cyclotron resonance laser accelerator

International Nuclear Information System (INIS)

Sprangle, P.; Tang, C.M.; Vlahos, L.

1983-01-01

A laser acceleration mechanism which utilizes a strong static, almost uniform, magnetic field together with an intense laser pulse is analyzed. The interaction and acceleration mechanism relies on a self resonance effect. Since the laser field is assumed to be diffraction limited, the magnetic field must be spatially varied to maintain resonance. The effective accelerating gradient is shown to scale like 1/√E /SUB b/ , where E /SUB b/ is the electron energy. For a numerical illustration the authors consider a 1 x 10 13 W/cm 2 , CO 2 laser and show that electrons can be accelerated to more than 500 MeV in a distance of 15 m (approximately two Rayleigh lengths)

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)

Multi-level nonlinear diffusion acceleration method for multigroup transport k-Eigenvalue problems

International Nuclear Information System (INIS)

Anistratov, Dmitriy Y.

2011-01-01

The nonlinear diffusion acceleration (NDA) method is an efficient and flexible transport iterative scheme for solving reactor-physics problems. This paper presents a fast iterative algorithm for solving multigroup neutron transport eigenvalue problems in 1D slab geometry. The proposed method is defined by a multi-level system of equations that includes multigroup and effective one-group low-order NDA equations. The Eigenvalue is evaluated in the exact projected solution space of smallest dimensionality, namely, by solving the effective one- group eigenvalue transport problem. Numerical results that illustrate performance of the new algorithm are demonstrated. (author)

Methods of numerical relativity

International Nuclear Information System (INIS)

Piran, T.

1983-01-01

Numerical Relativity is an alternative to analytical methods for obtaining solutions for Einstein equations. Numerical methods are particularly useful for studying generation of gravitational radiation by potential strong sources. The author reviews the analytical background, the numerical analysis aspects and techniques and some of the difficulties involved in numerical relativity. (Auth.)

Mathematical and numerical methods for Vlasov-Maxwell equations: the contributions of data mining

International Nuclear Information System (INIS)

Assous, F.; Chaskalovic, J.

2014-01-01

There exist a lot of formulations that can model plasma physics or particle accelerators problems as the Vlasov- Maxwell equations. This paper deals with the applications of data mining techniques in the evaluation of numerical solutions of Vlasov-Maxwell models. This is part of the topic of characterizing the model and approximation errors via learning techniques. We give two examples of application. The first one aims at comparing two Vlasov-Maxwell approximate models. In the second one, a scheme based on data mining techniques is proposed to characterize the errors between a P1 and a P2 finite element Particle-In-Cell approach. Beyond these examples, this original approach should operate in all cases where intricate numerical simulations like for the Vlasov-Maxwell equations take a central part. (authors)

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

An automated approach for solution based mesh adaptation to enhance numerical accuracy for a given number of grid cells

NARCIS (Netherlands)

Lucas, P.; Van Zuijlen, A.H.; Bijl, H.

2009-01-01

Mesh adaptation is a fairly established tool to obtain numerically accurate solutions for flow problems. Computational efficiency is, however, not always guaranteed for the adaptation strategies found in literature. Typically excessive mesh growth diminishes the potential efficiency gain. This

Survey of a numerical procedure for the solution of hyperbolic systems of three dimensional fluid flow

International Nuclear Information System (INIS)

Graf, U.

1986-01-01

A combination of several numerical methods is used to construct a procedure for effective calculation of complex three-dimensional fluid flow problems. The split coefficient matrix (SCM) method is used so that the differenced equations of the hyperbolic system do not disturb correct signal propagation. The semi-discretisation of the equations of the SCM method is done with the asymmetric, separated region, weighted residual (ASWR) method to give accurate solutions on a relatively coarse mesh. For the resulting system of ordinary differential equations, a general-purpose ordinary differential equation solver is used in conjunction with a method of fractional steps for an economic solution of the large system of linear equations. (orig.) [de

Final Report for 'Modeling Electron Cloud Diagnostics for High-Intensity Proton Accelerators'

International Nuclear Information System (INIS)

Veitzer, Seth A.

2009-01-01

Electron clouds in accelerators such as the ILC degrade beam quality and limit operating efficiency. The need to mitigate electron clouds has a direct impact on the design and operation of these accelerators, translating into increased cost and reduced performance. Diagnostic techniques for measuring electron clouds in accelerating cavities are needed to provide an assessment of electron cloud evolution and mitigation. Accurate numerical modeling of these diagnostics is needed to validate the experimental techniques. In this Phase I, we developed detailed numerical models of microwave propagation through electron clouds in accelerating cavities with geometries relevant to existing and future high-intensity proton accelerators such as Project X and the ILC. Our numerical techniques and simulation results from the Phase I showed that there was a high probability of success in measuring both the evolution of electron clouds and the effects of non-uniform electron density distributions in Phase II.

A numerical model for the determination of periodic solutions of pipes subjected to non-conservative loads

International Nuclear Information System (INIS)

Velloso, P.A.; Galeao, A.C.

1989-05-01

This paper deals with nonlinear vibrations of pipes subjected to non-conservative loads. Periodic solutions of these problems are determined using a variational approach based on Hamilton's Principle combined with a Fourier series expansion to describe the displacement field time dependence. A finite element model which utilizes Hemite's cubic interpolation for both axial and transversal displacement amplitudes is used. This model is applied to the problem of a pipe subjected to a tangential and a normal follower force. The numerical results obtained with this model are compared with the corespondent solutions determined using a total lagrangian description for the Principle of Virtual Work, coupled with Newmark's step-by-step integration procedure. It is shown that for small to moderate displacement amplitudes the one-term Fourier series approximation compares fairly well with the predicted solution. For large displacements as least a two-term approximation should be utilized [pt

On randomized algorithms for numerical solution of applied Fredholm integral equations of the second kind

Science.gov (United States)

Voytishek, Anton V.; Shipilov, Nikolay M.

2017-11-01

In this paper, the systematization of numerical (implemented on a computer) randomized functional algorithms for approximation of a solution of Fredholm integral equation of the second kind is carried out. Wherein, three types of such algorithms are distinguished: the projection, the mesh and the projection-mesh methods. The possibilities for usage of these algorithms for solution of practically important problems is investigated in detail. The disadvantages of the mesh algorithms, related to the necessity of calculation values of the kernels of integral equations in fixed points, are identified. On practice, these kernels have integrated singularities, and calculation of their values is impossible. Thus, for applied problems, related to solving Fredholm integral equation of the second kind, it is expedient to use not mesh, but the projection and the projection-mesh randomized algorithms.

Time domain numerical calculations of the short electron bunch wakefields in resistive structures

Energy Technology Data Exchange (ETDEWEB)

Tsakanian, Andranik

2010-10-15

The acceleration of electron bunches with very small longitudinal and transverse phase space volume is one of the most actual challenges for the future International Linear Collider and high brightness X-Ray Free Electron Lasers. The exact knowledge on the wake fields generated by the ultra-short electron bunches during its interaction with surrounding structures is a very important issue to prevent the beam quality degradation and to optimize the facility performance. The high accuracy time domain numerical calculations play the decisive role in correct evaluation of the wake fields in advanced accelerators. The thesis is devoted to the development of a new longitudinally dispersion-free 3D hybrid numerical scheme in time domain for wake field calculation of ultra short bunches in structures with walls of finite conductivity. The basic approaches used in the thesis to solve the problem are the following. For materials with high but finite conductivity the model of the plane wave reflection from a conducting half-space is used. It is shown that in the conductive half-space the field components perpendicular to the interface can be neglected. The electric tangential component on the surface contributes to the tangential magnetic field in the lossless area just before the boundary layer. For high conducting media, the task is reduced to 1D electromagnetic problem in metal and the so-called 1D conducting line model can be applied instead of a full 3D space description. Further, a TE/TM (''transverse electric - transverse magnetic'') splitting implicit numerical scheme along with 1D conducting line model is applied to develop a new longitudinally dispersion-free hybrid numerical scheme in the time domain. The stability of the new hybrid numerical scheme in vacuum, conductor and bound cell is studied. The convergence of the new scheme is analyzed by comparison with the well-known analytical solutions. The wakefield calculations for a number of

Laser-driven acceleration with Bessel beam

International Nuclear Information System (INIS)

Imasaki, Kazuo; Li, Dazhi

2005-01-01

A new approach of laser-driven acceleration with Bessel beam is described. Bessel beam, in contrast to the Gaussian beam, shows diffraction-free'' characteristics in its propagation, which implies potential in laser-driven acceleration. But a normal laser, even if the Bessel beam, laser can not accelerate charged particle efficiently because the difference of velocity between the particle and photon makes cyclic acceleration and deceleration phase. We proposed a Bessel beam truncated by a set of annular slits those makes several special regions in its travelling path, where the laser field becomes very weak and the accelerated particles are possible to receive no deceleration as they undergo decelerating phase. Thus, multistage acceleration is realizable with high gradient. In a numerical computation, we have shown the potential of multistage acceleration based on a three-stage model. (author)

Flame acceleration in the early stages of burning in tubes

Energy Technology Data Exchange (ETDEWEB)

Bychkov, Vitaly; Fru, Gordon; Petchenko, Arkady [Institute of Physics, Umeaa University, S-901 87 Umeaa (Sweden); Akkerman, V' yacheslav [Institute of Physics, Umeaa University, S-901 87 Umeaa (Sweden); Nuclear Safety Institute (IBRAE) of Russian Academy of Sciences, B. Tulskaya 52, 115191 Moscow (Russian Federation); Eriksson, Lars-Erik [Department of Applied Mechanics, Chalmers University of Technology, 412 96 Goeteborg (Sweden)

2007-09-15

Acceleration of premixed laminar flames in the early stages of burning in long tubes is considered. The acceleration mechanism was suggested earlier by Clanet and Searby [Combust. Flame 105 (1996) 225]. Acceleration happens due to the initial ignition geometry at the tube axis when a flame develops to a finger-shaped front, with surface area growing exponentially in time. Flame surface area grows quite fast but only for a short time. The analytical theory of flame acceleration is developed, which determines the growth rate, the total acceleration time, and the maximal increase of the flame surface area. Direct numerical simulations of the process are performed for the complete set of combustion equations. The simulations results and the theory are in good agreement with the previous experiments. The numerical simulations also demonstrate flame deceleration, which follows acceleration, and the so-called ''tulip flames''. (author)

Solutions for acceleration measurement in vehicle crash tests

Science.gov (United States)

Dima, D. S.; Covaciu, D.

2017-10-01

Crash tests are useful for validating computer simulations of road traffic accidents. One of the most important parameters measured is the acceleration. The evolution of acceleration versus time, during a crash test, form a crash pulse. The correctness of the crash pulse determination depends on the data acquisition system used. Recommendations regarding the instrumentation for impact tests are given in standards, which are focused on the use of accelerometers as impact sensors. The goal of this paper is to present the device and software developed by authors for data acquisition and processing. The system includes two accelerometers with different input ranges, a processing unit based on a 32-bit microcontroller and a data logging unit with SD card. Data collected on card, as text files, is processed with a dedicated software running on personal computers. The processing is based on diagrams and includes the digital filters recommended in standards.

Numerical Solution of a Fractional Order Model of HIV Infection of CD4+T Cells Using Müntz-Legendre Polynomials

Directory of Open Access Journals (Sweden)

Mojtaba Rasouli Gandomani

2016-06-01

Full Text Available In this paper, the model of HIV infection of CD4+ T cells is considered as a system of fractional differential equations. Then, a numerical method by using collocation method based on the Müntz-Legendre polynomials to approximate solution of the model is presented. The application of the proposed numerical method causes fractional differential equations system to convert into the algebraic equations system. The new system can be solved by one of the existing methods. Finally, we compare the result of this numerical method with the result of the methods have already been presented in the literature.

Numerical Algorithm for Delta of Asian Option

Directory of Open Access Journals (Sweden)

Boxiang Zhang

2015-01-01

Full Text Available We study the numerical solution of the Greeks of Asian options. In particular, we derive a close form solution of Δ of Asian geometric option and use this analytical form as a control to numerically calculate Δ of Asian arithmetic option, which is known to have no explicit close form solution. We implement our proposed numerical method and compare the standard error with other classical variance reduction methods. Our method provides an efficient solution to the hedging strategy with Asian options.

FPGA Acceleration of Information Management Services

National Research Council Canada - National Science Library

Linderman, Richard W; Linderman, Mark H; Lin, Chun-Shin

2005-01-01

.... However, this paper reports on the ability of FPGAs to greatly accelerate non-numerical applications, particularly fundamental operations supporting publish subscribe information management environments...

Overview of SSC accelerator requirements

International Nuclear Information System (INIS)

Dugan, G.

1992-03-01

This paper will present a general overview of the requirements of the Superconducting Super Collider (SSC) accelerators. Each accelerator in the injector chain will be discussed separately, followed by a discussion of the collider itself. In conclusion, the top level requirements of the overall accelerator system will be presented. For each accelerator, the primary operating parameters will be presented in tabular form. A brief narrative discussion of the principal technical features of each machine will be given. Finally, the principal technical design challenges for the machine will be noted, together with the currently planned solution to these challenges

An Exact and Grid-free Numerical Scheme for the Hybrid Two Phase Traffic Flow Model Based on the Lighthill-Whitham-Richards Model with Bounded Acceleration

KAUST Repository

Qiu, Shanwen

2012-07-01

In this article, we propose a new grid-free and exact solution method for computing solutions associated with an hybrid traffic flow model based on the Lighthill- Whitham-Richards (LWR) partial differential equation. In this hybrid flow model, the vehicles satisfy the LWR equation whenever possible, and have a fixed acceleration otherwise. We first present a grid-free solution method for the LWR equation based on the minimization of component functions. We then show that this solution method can be extended to compute the solutions to the hybrid model by proper modification of the component functions, for any concave fundamental diagram. We derive these functions analytically for the specific case of a triangular fundamental diagram. We also show that the proposed computational method can handle fixed or moving bottlenecks.

A study of reflex tandem accelerator

Energy Technology Data Exchange (ETDEWEB)

Nakajima, Takao; Morinobu, Shunpei; Gono, Yasuyuki; Sagara, Kenji; Sugimitsu, Tsuyoshi; Mitarai, Shiro; Nakamura, Hiroyuki; Ikeda, Nobuo; Morikawa, Tsuneyasu [Kyushu Univ., Fukuoka (Japan). Faculty of Science

1996-12-01

An investigation on `developing research theme and its realizing experimental apparatus` based on the tandem accelerator facility is executed. At a standpoint of recognition on essentiality of preparation, improvement or novel technical development capable of extreme increase in capacity of the tandem accelerator facility to form COE with high uniqueness, proposal of numerous ideas and their investigations and searches were conducted. In this paper, consideration results of `beam reacceleration using tandem accelerator` were shown as follows: (1) Short life unstable nuclei formed by nuclear reaction using tandem acceleration primary beam is ionized to negative and to reaccelerate by using the same tandem accelerator. And (2) by combination of plural electrons with the tandem primary accelerated beam, numbers of charge is reduced to reaccelerate by the tandem. (G.K.)

Spacetime transformations from a uniformly accelerated frame

International Nuclear Information System (INIS)

Friedman, Yaakov; Scarr, Tzvi

2013-01-01

We use the generalized Fermi–Walker transport to construct a one-parameter family of inertial frames which are instantaneously comoving to a uniformly accelerated observer. We explain the connection between our approach and that of Mashhoon. We show that our solutions of uniformly accelerated motion have constant acceleration in the comoving frame. Assuming the weak hypothesis of locality, we obtain local spacetime transformations from a uniformly accelerated frame K′ to an inertial frame K. The spacetime transformations between two uniformly accelerated frames with the same acceleration are Lorentz. We compute the metric at an arbitrary point of a uniformly accelerated frame. (paper)

Numerical investigation of the possibility of ions acceleration by virtual cathode

International Nuclear Information System (INIS)

Lymar', A.G.; Bondarenko, L.A.; Egorov, A.M.

2012-01-01

The first results of studies of the behavior of the virtual cathode formed in the ribbon electron beam, which moves in a strong longitudinal magnetic field in the space between two parallel conducting plates: the dependence of the perveance of the electron beam, in which there is a virtual cathode, the thickness of the beam; the possibility of implementing an accelerated movement of the potential well formed by the virtual cathode, the time variation of the perveance of the injected electron beam. The results obtained suggest that in the test device can be implemented to accelerate the ions.

Connecting the dots: Semi-analytical and random walk numerical solutions of the diffusion–reaction equation with stochastic initial conditions

Energy Technology Data Exchange (ETDEWEB)

Paster, Amir, E-mail: paster@tau.ac.il [Environmental Fluid Mechanics Laboratories, Dept. of Civil and Environmental Engineering and Earth Sciences, University of Notre Dame, Notre Dame, IN (United States); School of Mechanical Engineering, Tel Aviv University, Tel Aviv, 69978 (Israel); Bolster, Diogo [Environmental Fluid Mechanics Laboratories, Dept. of Civil and Environmental Engineering and Earth Sciences, University of Notre Dame, Notre Dame, IN (United States); Benson, David A. [Hydrologic Science and Engineering, Colorado School of Mines, Golden, CO, 80401 (United States)

2014-04-15

We study a system with bimolecular irreversible kinetic reaction A+B→∅ where the underlying transport of reactants is governed by diffusion, and the local reaction term is given by the law of mass action. We consider the case where the initial concentrations are given in terms of an average and a white noise perturbation. Our goal is to solve the diffusion–reaction equation which governs the system, and we tackle it with both analytical and numerical approaches. To obtain an analytical solution, we develop the equations of moments and solve them approximately. To obtain a numerical solution, we develop a grid-less Monte Carlo particle tracking approach, where diffusion is modeled by a random walk of the particles, and reaction is modeled by annihilation of particles. The probability of annihilation is derived analytically from the particles' co-location probability. We rigorously derive the relationship between the initial number of particles in the system and the amplitude of white noise represented by that number. This enables us to compare the particle simulations and the approximate analytical solution and offer an explanation of the late time discrepancies. - Graphical abstract:.