CPDES2: A preconditioned conjugate gradient solver for linear asymmetric matrix equations arising from coupled partial differential equations in two dimensions

Science.gov (United States)

Anderson, D. V.; Koniges, A. E.; Shumaker, D. E.

1988-11-01

Many physical problems require the solution of coupled partial differential equations on two-dimensional domains. When the time scales of interest dictate an implicit discretization of the equations a rather complicated global matrix system needs solution. The exact form of the matrix depends on the choice of spatial grids and on the finite element or finite difference approximations employed. CPDES2 allows each spatial operator to have 5 or 9 point stencils and allows for general couplings between all of the component PDE's and it automatically generates the matrix structures needed to perform the algorithm. The resulting sparse matrix equation is solved by either the preconditioned conjugate gradient (CG) method or by the preconditioned biconjugate gradient (BCG) algorithm. An arbitrary number of component equations are permitted only limited by available memory. In the sub-band representation used, we generate an algorithm that is written compactly in terms of indirect indices which is vectorizable on some of the newer scientific computers.

CPDES3: A preconditioned conjugate gradient solver for linear asymmetric matrix equations arising from coupled partial differential equations in three dimensions

Science.gov (United States)

Anderson, D. V.; Koniges, A. E.; Shumaker, D. E.

1988-11-01

Many physical problems require the solution of coupled partial differential equations on three-dimensional domains. When the time scales of interest dictate an implicit discretization of the equations a rather complicated global matrix system needs solution. The exact form of the matrix depends on the choice of spatial grids and on the finite element or finite difference approximations employed. CPDES3 allows each spatial operator to have 7, 15, 19, or 27 point stencils and allows for general couplings between all of the component PDE's and it automatically generates the matrix structures needed to perform the algorithm. The resulting sparse matrix equation is solved by either the preconditioned conjugate gradient (CG) method or by the preconditioned biconjugate gradient (BCG) algorithm. An arbitrary number of component equations are permitted only limited by available memory. In the sub-band representation used, we generate an algorithm that is written compactly in terms of indirect induces which is vectorizable on some of the newer scientific computers.

Numerical resolution of Navier-Stokes equations coupled to the heat equation

International Nuclear Information System (INIS)

Zenouda, Jean-Claude

1970-08-01

The author proves a uniqueness theorem for the time dependent Navier-Stokes equations coupled with heat flow in the two-dimensional case. He studies stability and convergence of several finite - difference schemes to solve these equations. Numerical experiments are done in the case of a square domain. (author) [fr

Similarity-transformed equation-of-motion vibrational coupled-cluster theory

Science.gov (United States)

Faucheaux, Jacob A.; Nooijen, Marcel; Hirata, So

2018-02-01

A similarity-transformed equation-of-motion vibrational coupled-cluster (STEOM-XVCC) method is introduced as a one-mode theory with an effective vibrational Hamiltonian, which is similarity transformed twice so that its lower-order operators are dressed with higher-order anharmonic effects. The first transformation uses an exponential excitation operator, defining the equation-of-motion vibrational coupled-cluster (EOM-XVCC) method, and the second uses an exponential excitation-deexcitation operator. From diagonalization of this doubly similarity-transformed Hamiltonian in the small one-mode excitation space, the method simultaneously computes accurate anharmonic vibrational frequencies of all fundamentals, which have unique significance in vibrational analyses. We establish a diagrammatic method of deriving the working equations of STEOM-XVCC and prove their connectedness and thus size-consistency as well as the exact equality of its frequencies with the corresponding roots of EOM-XVCC. We furthermore elucidate the similarities and differences between electronic and vibrational STEOM methods and between STEOM-XVCC and vibrational many-body Green's function theory based on the Dyson equation, which is also an anharmonic one-mode theory. The latter comparison inspires three approximate STEOM-XVCC methods utilizing the common approximations made in the Dyson equation: the diagonal approximation, a perturbative expansion of the Dyson self-energy, and the frequency-independent approximation. The STEOM-XVCC method including up to the simultaneous four-mode excitation operator in a quartic force field and its three approximate variants are formulated and implemented in computer codes with the aid of computer algebra, and they are applied to small test cases with varied degrees of anharmonicity.

The strong running coupling from an approximate gluon Dyson-Schwinger equation

International Nuclear Information System (INIS)

Alkofer, R.; Hauck, A.

1996-01-01

Using Mandelstam's approximation to the gluon Dyson-Schwinger equation we calculate the gluon self-energy in a renormalisation group invariant fashion. We obtain a non-perturbative Β function. The scaling behavior near the ultraviolet stable fixed point is in good agreement with perturbative QCD. No further fixed point for positive values of the coupling is found: α S increases without bound in the infrared

Soliton solutions of coupled nonlinear Klein-Gordon equations

International Nuclear Information System (INIS)

Alagesan, T.; Chung, Y.; Nakkeeran, K.

2004-01-01

The coupled nonlinear Klein-Gordon equations are analyzed for their integrability properties in a systematic manner through Painleve test. From the Painleve test, by truncating the Laurent series at the constant level term, the Hirota bilinear form is identified, from which one-soliton solutions are derived. Then, the results are generalized to the two, three and N-coupled Klein-Gordon equations

A CPT-even and Lorentz-Violating nonminimal coupling in the Dirac equation

Energy Technology Data Exchange (ETDEWEB)

Ferreira Junior, Manoel; Casana, M.R.; Santos, Frederico E.P. dos; Silva, E.O. [UFMA, Sao Luis (Brazil); Passos, E. [UFCG, Campina Grande, PB (Brazil)

2013-07-01

Full text: The Standard Model Extension (SME) has been the usual framework for investigating signals of Lorentz violation in physical systems. It is the natural framework for studying properties of physical systems with Lorentz-violation since it includes Lorentz-violating terms in all sectors of the minimal standard model. The Lorentz-violating (LV) terms are generated as vacuum expectation values of tensors defined in a high energy scale. This framework has inspired a great deal of investigation in recent years. Such works encompass several distinct aspects involving fermion systems and radiative corrections, CPT- probing experiments, the electromagnetic CPT- and Lorentz-odd term, the 19 electromagnetic CPT-even coefficients. Recently, some studies involving higher dimensional operators have also been reported with great interest, including nonminimal interactions. These many contributions have elucidated the effects induced by Lorentz violation and served to set up stringent upper bounds on the LV coefficients. In the present work, we propose a new CPT-even, dimension-five, nonminimal coupling linking the fermionic and gauge fields in the context of the Dirac equation, involving the CPT-even tensor of the gauge term of the SME. By considering the nonrelativistic limit of the modified Dirac equation, we explicitly evaluate the new contributions to the nonrelativistic Hamiltonian. These new terms imply a direct correction on the anomalous magnetic moment, a kind of electrical Zeeman-like effect on the atomic spectrum, and a Rashba-like coupling term. These effects are then used to impose upper bounds on the magnitude of the non minimally coupled LV coefficients at the level of 1 part in 10{sub 16}. (author)

A CPT-even and Lorentz-Violating nonminimal coupling in the Dirac equation

International Nuclear Information System (INIS)

Ferreira Junior, Manoel; Casana, M.R.; Santos, Frederico E.P. dos; Silva, E.O.; Passos, E.

2013-01-01

Full text: The Standard Model Extension (SME) has been the usual framework for investigating signals of Lorentz violation in physical systems. It is the natural framework for studying properties of physical systems with Lorentz-violation since it includes Lorentz-violating terms in all sectors of the minimal standard model. The Lorentz-violating (LV) terms are generated as vacuum expectation values of tensors defined in a high energy scale. This framework has inspired a great deal of investigation in recent years. Such works encompass several distinct aspects involving fermion systems and radiative corrections, CPT- probing experiments, the electromagnetic CPT- and Lorentz-odd term, the 19 electromagnetic CPT-even coefficients. Recently, some studies involving higher dimensional operators have also been reported with great interest, including nonminimal interactions. These many contributions have elucidated the effects induced by Lorentz violation and served to set up stringent upper bounds on the LV coefficients. In the present work, we propose a new CPT-even, dimension-five, nonminimal coupling linking the fermionic and gauge fields in the context of the Dirac equation, involving the CPT-even tensor of the gauge term of the SME. By considering the nonrelativistic limit of the modified Dirac equation, we explicitly evaluate the new contributions to the nonrelativistic Hamiltonian. These new terms imply a direct correction on the anomalous magnetic moment, a kind of electrical Zeeman-like effect on the atomic spectrum, and a Rashba-like coupling term. These effects are then used to impose upper bounds on the magnitude of the non minimally coupled LV coefficients at the level of 1 part in 10 16 . (author)

Analytical solutions of coupled-mode equations for microring ...

Indian Academy of Sciences (India)

equivalent to waveguide and single microring coupled system. The 3 × 3 coupled system is equivalent to waveguide and double microring coupled system. In this paper, we adopt a novel approach for obtaining coupled-mode equations for linearly distributed and circularly distributed multiwaveguide systems with different ...

Local control of globally competing patterns in coupled Swift-Hohenberg equations

Science.gov (United States)

Becker, Maximilian; Frenzel, Thomas; Niedermayer, Thomas; Reichelt, Sina; Mielke, Alexander; Bär, Markus

2018-04-01

We present analytical and numerical investigations of two anti-symmetrically coupled 1D Swift-Hohenberg equations (SHEs) with cubic nonlinearities. The SHE provides a generic formulation for pattern formation at a characteristic length scale. A linear stability analysis of the homogeneous state reveals a wave instability in addition to the usual Turing instability of uncoupled SHEs. We performed weakly nonlinear analysis in the vicinity of the codimension-two point of the Turing-wave instability, resulting in a set of coupled amplitude equations for the Turing pattern as well as left- and right-traveling waves. In particular, these complex Ginzburg-Landau-type equations predict two major things: there exists a parameter regime where multiple different patterns are stable with respect to each other and that the amplitudes of different patterns interact by local mutual suppression. In consequence, different patterns can coexist in distinct spatial regions, separated by localized interfaces. We identified specific mechanisms for controlling the position of these interfaces, which distinguish what kinds of patterns the interface connects and thus allow for global pattern selection. Extensive simulations of the original SHEs confirm our results.

Toward enabling large-scale open-shell equation-of-motion coupled cluster calculations: triplet states of β-carotene

Energy Technology Data Exchange (ETDEWEB)

Hu, Hanshi; Bhaskaran-Nair, Kiran; Apra, Edoardo; Govind, Niranjan; Kowalski, Karol

2014-10-02

In this paper we discuss the application of novel parallel implementation of the coupled cluster (CC) and equation-of-motion coupled cluster methods (EOMCC) in calculations of excitation energies of triplet states in beta-carotene. Calculated excitation energies are compared with experimental data, where available. We also provide a detailed description of the new parallel algorithms for iterative CC and EOMCC models involving single and doubles excitations.

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.

Exact Solution of Space-Time Fractional Coupled EW and Coupled MEW Equations Using Modified Kudryashov Method

International Nuclear Information System (INIS)

Raslan, K. R.; Ali, Khalid K.; EL-Danaf, Talaat S.

2017-01-01

In the present paper, we established a traveling wave solution by using modified Kudryashov method for the space-time fractional nonlinear partial differential equations. The method is used to obtain the exact solutions for different types of the space-time fractional nonlinear partial differential equations such as, the space-time fractional coupled equal width wave equation (CEWE) and the space-time fractional coupled modified equal width wave equation (CMEW), which are the important soliton equations. Both equations are reduced to ordinary differential equations by the use of fractional complex transform and properties of modified Riemann–Liouville derivative. We plot the exact solutions for these equations at different time levels. (paper)

Probing the desert by the two-loop renormalization-group equations

International Nuclear Information System (INIS)

Tanimoto, M.; Suetake, Y.; Senba, K.

1987-01-01

We have reexamined the study of probing the desert with fermion masses, presented by Bagger, Dimopoulos, and Masso, by using the two-loop renormalization-group equations in the framework of the SU(3) x SU(2) x U(1) model with three generations and one Higgs doublet. The blow-up energy scale of the Yukawa coupling is found to be dependent on the Higgs quartic coupling λ. If the Yukawa coupling blows up between the electroweak scale M/sub W/ and the grand unified scale M/sub X/, the Higgs potential is destabilized for small values of λ at the electroweak scale M/sub W/, and becomes strongly coupled for large values of λ at M/sub W/. It is found that the Higgs-scalar mass as well as the fermion masses are important to probe the desert

Solving large sets of coupled equations iteratively by vector processing on the CYBER 205 computer

International Nuclear Information System (INIS)

Tolsma, L.D.

1985-01-01

The set of coupled linear second-order differential equations which has to be solved for the quantum-mechanical description of inelastic scattering of atomic and nuclear particles can be rewritten as an equivalent set of coupled integral equations. When some type of functions is used as piecewise analytic reference solutions, the integrals that arise in this set can be evaluated analytically. The set of integral equations can be solved iteratively. For the results mentioned an inward-outward iteration scheme has been applied. A concept of vectorization of coupled-channel Fortran programs, based on this integral method, is presented for the use on the Cyber 205 computer. It turns out that, for two heavy ion nuclear scattering test cases, this vector algorithm gives an overall speed-up of about a factor of 2 to 3 compared to a highly optimized scalar algorithm for a one vector pipeline computer

Evaluation of Tsunami Run-Up on Coastal Areas at Regional Scale

Science.gov (United States)

González, M.; Aniel-Quiroga, Í.; Gutiérrez, O.

2017-12-01

Tsunami hazard assessment is tackled by means of numerical simulations, giving as a result, the areas flooded by tsunami wave inland. To get this, some input data is required, i.e., the high resolution topobathymetry of the study area, the earthquake focal mechanism parameters, etc. The computational cost of these kinds of simulations are still excessive. An important restriction for the elaboration of large scale maps at National or regional scale is the reconstruction of high resolution topobathymetry on the coastal zone. An alternative and traditional method consists of the application of empirical-analytical formulations to calculate run-up at several coastal profiles (i.e. Synolakis, 1987), combined with numerical simulations offshore without including coastal inundation. In this case, the numerical simulations are faster but some limitations are added as the coastal bathymetric profiles are very simply idealized. In this work, we present a complementary methodology based on a hybrid numerical model, formed by 2 models that were coupled ad hoc for this work: a non-linear shallow water equations model (NLSWE) for the offshore part of the propagation and a Volume of Fluid model (VOF) for the areas near the coast and inland, applying each numerical scheme where they better reproduce the tsunami wave. The run-up of a tsunami scenario is obtained by applying the coupled model to an ad-hoc numerical flume. To design this methodology, hundreds of worldwide topobathymetric profiles have been parameterized, using 5 parameters (2 depths and 3 slopes). In addition, tsunami waves have been also parameterized by their height and period. As an application of the numerical flume methodology, the coastal parameterized profiles and tsunami waves have been combined to build a populated database of run-up calculations. The combination was tackled by means of numerical simulations in the numerical flume The result is a tsunami run-up database that considers real profiles shape

Lax pair and exact solutions of a discrete coupled system related to coupled KdV and coupled mKdV equations

International Nuclear Information System (INIS)

Liu Ping; Jia Man; Lou Senyue

2007-01-01

A modified Korteweg-de Vries (mKdV) lattice is also found to be a discrete Korteweg-de Vries (KdV) equation in this paper. The Lax pair for the discrete equation is found with the help of the Lax pair for a similar discrete equation. A Lax-integrable coupled extension of the lattice is posed, which is a common discrete version of both the coupled KdV and coupled mKdV systems. Some rational expansions of the Jacobian elliptic, trigonometric and hyperbolic functions are used to construct cnoidal waves, negaton and positon solutions of the discrete coupled system

Coupling 2D Finite Element Models and Circuit Equations Using a Bottom-Up Methodology

Science.gov (United States)

2002-11-01

EQUATIONS USING A BOTTOM-UP METHODOLOGY E. G6mezl, J. Roger-Folch2 , A. Gabald6nt and A. Molina’ ’Dpto. de Ingenieria Eldctrica. Universidad Polit...de Ingenieria Elictrica. ETSII. Universidad Politdcnica de Valencia. PO Box 22012, 46071. Valencia, Spain. E-mail: iroger adie.upv.es ABSTRACT The

Coupled-channel equations and off-shell transformations in many-body scattering

International Nuclear Information System (INIS)

Cattapan, G.; Vanzani, V.

1977-01-01

The general structure and the basic features of several many-body coupled-channel integral equations, obtained by means of the channel coupling array device, are studied in a systematic way. Particular attention is paid to the employment of symmetric transition operators. The connection between different formulations has been clarified and the role played by some off-shell transformations for many-body transition operators has been discussed. Specific choices of the coupling scheme are considered and the corresponding coupled equations are compared with similar equations previously derived. Several sets of linear relations between transition operators have also been presented and used in a three-body context to derive uncoupled integral equations with connected kernel

Coupled numerical approach combining finite volume and lattice Boltzmann methods for multi-scale multi-physicochemical processes

Energy Technology Data Exchange (ETDEWEB)

Chen, Li; He, Ya-Ling [Key Laboratory of Thermo-Fluid Science and Engineering of MOE, School of Energy and Power Engineering, Xi' an Jiaotong University, Xi' an, Shaanxi 710049 (China); Kang, Qinjun [Computational Earth Science Group (EES-16), Los Alamos National Laboratory, Los Alamos, NM (United States); Tao, Wen-Quan, E-mail: wqtao@mail.xjtu.edu.cn [Key Laboratory of Thermo-Fluid Science and Engineering of MOE, School of Energy and Power Engineering, Xi' an Jiaotong University, Xi' an, Shaanxi 710049 (China)

2013-12-15

A coupled (hybrid) simulation strategy spatially combining the finite volume method (FVM) and the lattice Boltzmann method (LBM), called CFVLBM, is developed to simulate coupled multi-scale multi-physicochemical processes. In the CFVLBM, computational domain of multi-scale problems is divided into two sub-domains, i.e., an open, free fluid region and a region filled with porous materials. The FVM and LBM are used for these two regions, respectively, with information exchanged at the interface between the two sub-domains. A general reconstruction operator (RO) is proposed to derive the distribution functions in the LBM from the corresponding macro scalar, the governing equation of which obeys the convection–diffusion equation. The CFVLBM and the RO are validated in several typical physicochemical problems and then are applied to simulate complex multi-scale coupled fluid flow, heat transfer, mass transport, and chemical reaction in a wall-coated micro reactor. The maximum ratio of the grid size between the FVM and LBM regions is explored and discussed. -- Highlights: •A coupled simulation strategy for simulating multi-scale phenomena is developed. •Finite volume method and lattice Boltzmann method are coupled. •A reconstruction operator is derived to transfer information at the sub-domains interface. •Coupled multi-scale multiple physicochemical processes in micro reactor are simulated. •Techniques to save computational resources and improve the efficiency are discussed.

Coupling and reduction of the HAWC equations

DEFF Research Database (Denmark)

Nim, E.

2001-01-01

This report contains a description of a general method for coupling and reduction of the so-called HAWC equations, which constitute the basis equations of motion of the aeroelastic model HAWC used widely by research institutes and industrial companies formore than the ten years. The principal aim....... In addition, the method enables the reduction of the number of degrees of freedom of the structure in order to increase the calculation efficiency and improve thecondition of the system.......This report contains a description of a general method for coupling and reduction of the so-called HAWC equations, which constitute the basis equations of motion of the aeroelastic model HAWC used widely by research institutes and industrial companies formore than the ten years. The principal aim...... of the work has been to enable the modelling wind turbines with large displacements of the blades in order to predict phenomena caused by geometric non-linear effects. However, the method can also be applied tomodel the nacelle/shaft structure of a turbine more detailed than the present HAWC model...

Analytical solutions for coupling fractional partial differential equations with Dirichlet boundary conditions

Science.gov (United States)

Ding, Xiao-Li; Nieto, Juan J.

2017-11-01

In this paper, we consider the analytical solutions of coupling fractional partial differential equations (FPDEs) with Dirichlet boundary conditions on a finite domain. Firstly, the method of successive approximations is used to obtain the analytical solutions of coupling multi-term time fractional ordinary differential equations. Then, the technique of spectral representation of the fractional Laplacian operator is used to convert the coupling FPDEs to the coupling multi-term time fractional ordinary differential equations. By applying the obtained analytical solutions to the resulting multi-term time fractional ordinary differential equations, the desired analytical solutions of the coupling FPDEs are given. Our results are applied to derive the analytical solutions of some special cases to demonstrate their applicability.

Renormalization group equations with multiple coupling constants

International Nuclear Information System (INIS)

Ghika, G.; Visinescu, M.

1975-01-01

The main purpose of this paper is to study the renormalization group equations of a renormalizable field theory with multiple coupling constants. A method for the investigation of the asymptotic stability is presented. This method is applied to a gauge theory with Yukawa and self-quartic couplings of scalar mesons in order to find the domains of asymptotic freedom. An asymptotic expansion for the solutions which tend to the origin of the coupling constants is given

Tensor-decomposed vibrational coupled-cluster theory: Enabling large-scale, highly accurate vibrational-structure calculations

Science.gov (United States)

Madsen, Niels Kristian; Godtliebsen, Ian H.; Losilla, Sergio A.; Christiansen, Ove

2018-01-01

A new implementation of vibrational coupled-cluster (VCC) theory is presented, where all amplitude tensors are represented in the canonical polyadic (CP) format. The CP-VCC algorithm solves the non-linear VCC equations without ever constructing the amplitudes or error vectors in full dimension but still formally includes the full parameter space of the VCC[n] model in question resulting in the same vibrational energies as the conventional method. In a previous publication, we have described the non-linear-equation solver for CP-VCC calculations. In this work, we discuss the general algorithm for evaluating VCC error vectors in CP format including the rank-reduction methods used during the summation of the many terms in the VCC amplitude equations. Benchmark calculations for studying the computational scaling and memory usage of the CP-VCC algorithm are performed on a set of molecules including thiadiazole and an array of polycyclic aromatic hydrocarbons. The results show that the reduced scaling and memory requirements of the CP-VCC algorithm allows for performing high-order VCC calculations on systems with up to 66 vibrational modes (anthracene), which indeed are not possible using the conventional VCC method. This paves the way for obtaining highly accurate vibrational spectra and properties of larger molecules.

Elliptic and solitary wave solutions for Bogoyavlenskii equations system, couple Boiti-Leon-Pempinelli equations system and Time-fractional Cahn-Allen equation

Directory of Open Access Journals (Sweden)

Mostafa M.A. Khater

Full Text Available In this article and for the first time, we introduce and describe Khater method which is a new technique for solving nonlinear partial differential equations (PDEs.. We apply this method for each of the following models Bogoyavlenskii equation, couple Boiti-Leon-Pempinelli system and Time-fractional Cahn-Allen equation. Khater method is very powerful, Effective, felicitous and fabulous method to get exact and solitary wave solution of (PDEs.. Not only just like that but it considers too one of the general methods for solving that kind of equations since it involves some methods as we will see in our discuss of the results. We make a comparison between the results of this new method and another method. Keywords: Bogoyavlenskii equations system, Couple Boiti-Leon-Pempinelli equations system, Time-fractional Cahn-Allen equation, Khater method, Traveling wave solutions, Solitary wave solutions

arXiv GeV-scale hot sterile neutrino oscillations: a derivation of evolution equations

CERN Document Server

Ghiglieri, J.

2017-05-23

Starting from operator equations of motion and making arguments based on a separation of time scales, a set of equations is derived which govern the non-equilibrium time evolution of a GeV-scale sterile neutrino density matrix and active lepton number densities at temperatures T > 130 GeV. The density matrix possesses generation and helicity indices; we demonstrate how helicity permits for a classification of various sources for leptogenesis. The coefficients parametrizing the equations are determined to leading order in Standard Model couplings, accounting for the LPM resummation of 1+n 2+n scatterings and for all 2 2 scatterings. The regime in which sphaleron processes gradually decouple so that baryon plus lepton number becomes a separate non-equilibrium variable is also considered.

MOOSE: A parallel computational framework for coupled systems of nonlinear equations

International Nuclear Information System (INIS)

Gaston, Derek; Newman, Chris; Hansen, Glen; Lebrun-Grandie, Damien

2009-01-01

Systems of coupled, nonlinear partial differential equations (PDEs) often arise in simulation of nuclear processes. MOOSE: Multiphysics Object Oriented Simulation Environment, a parallel computational framework targeted at the solution of such systems, is presented. As opposed to traditional data-flow oriented computational frameworks, MOOSE is instead founded on the mathematical principle of Jacobian-free Newton-Krylov (JFNK). Utilizing the mathematical structure present in JFNK, physics expressions are modularized into 'Kernels,' allowing for rapid production of new simulation tools. In addition, systems are solved implicitly and fully coupled, employing physics-based preconditioning, which provides great flexibility even with large variance in time scales. A summary of the mathematics, an overview of the structure of MOOSE, and several representative solutions from applications built on the framework are presented.

Alternative integral equations and perturbation expansions for self-coupled scalar fields

International Nuclear Information System (INIS)

Ford, L.H.

1985-01-01

It is shown that the theory of a self-coupled scalar field may be expressed in terms of a class of integral equations which include the Yang-Feldman equation as a particular case. Other integral equations in this class could be used to generate alternative perturbation expansions which contain a nonanalytic dependence upon the coupling constant and are less ultraviolet divergent than the conventional perturbation expansion. (orig.)

Positive Solutions for Coupled Nonlinear Fractional Differential Equations

Directory of Open Access Journals (Sweden)

Wenning Liu

2014-01-01

Full Text Available We consider the existence of positive solutions for a coupled system of nonlinear fractional differential equations with integral boundary values. Assume the nonlinear term is superlinear in one equation and sublinear in the other equation. By constructing two cones K1, K2 and computing the fixed point index in product cone K1×K2, we obtain that the system has a pair of positive solutions. It is remarkable that it is established on the Cartesian product of two cones, in which the feature of two equations can be opposite.

Multiscale functions, scale dynamics, and applications to partial differential equations

Science.gov (United States)

Cresson, Jacky; Pierret, Frédéric

2016-05-01

Modeling phenomena from experimental data always begins with a choice of hypothesis on the observed dynamics such as determinism, randomness, and differentiability. Depending on these choices, different behaviors can be observed. The natural question associated to the modeling problem is the following: "With a finite set of data concerning a phenomenon, can we recover its underlying nature? From this problem, we introduce in this paper the definition of multi-scale functions, scale calculus, and scale dynamics based on the time scale calculus [see Bohner, M. and Peterson, A., Dynamic Equations on Time Scales: An Introduction with Applications (Springer Science & Business Media, 2001)] which is used to introduce the notion of scale equations. These definitions will be illustrated on the multi-scale Okamoto's functions. Scale equations are analysed using scale regimes and the notion of asymptotic model for a scale equation under a particular scale regime. The introduced formalism explains why a single scale equation can produce distinct continuous models even if the equation is scale invariant. Typical examples of such equations are given by the scale Euler-Lagrange equation. We illustrate our results using the scale Newton's equation which gives rise to a non-linear diffusion equation or a non-linear Schrödinger equation as asymptotic continuous models depending on the particular fractional scale regime which is considered.

Asymptotic densities from the modified Montroll-Weiss equation for coupled CTRWs

Science.gov (United States)

Aghion, Erez; Kessler, David A.; Barkai, Eli

2018-01-01

We examine the bi-scaling behavior of Lévy walks with nonlinear coupling, where χ, the particle displacement during each step, is coupled to the duration of the step, τ, by χ τβ. An example of such a process is regular Lévy walks, where β = 1. In recent years such processes were shown to be highly useful for analysis of a class of Langevin dynamics, in particular a system of Sisyphus laser-cooled atoms in an optical lattice, where β = 3/2. We discuss the well-known decoupling approximation used to describe the central part of the particles' position distribution, and use the recently introduced infinite-covariant density approach to study the large fluctuations. Since the density of the step displacements is fat-tailed, the last travel event must be treated with care for the latter. This effect requires a modification of the Montroll-Weiss equation, an equation which has proved important for the analysis of many microscopic models. Contribution to the Topical Issue "Continuous Time Random Walk Still Trendy: Fifty-year History, Current State and Outlook", edited by Ryszard Kutner and Jaume Masoliver.

Parallel Algorithm Solves Coupled Differential Equations

Science.gov (United States)

Hayashi, A.

1987-01-01

Numerical methods adapted to concurrent processing. Algorithm solves set of coupled partial differential equations by numerical integration. Adapted to run on hypercube computer, algorithm separates problem into smaller problems solved concurrently. Increase in computing speed with concurrent processing over that achievable with conventional sequential processing appreciable, especially for large problems.

Solutions of system of P1 equations without use of auxiliary differential equations coupled

International Nuclear Information System (INIS)

Martinez, Aquilino Senra; Silva, Fernando Carvalho da; Cardoso, Carlos Eduardo Santos

2000-01-01

The system of P1 equations is composed by two equations coupled itself one for the neutron flux and other for the current. Usually this system is solved by definitions of two integrals parameters, which are named slowing down densities of the flux and the current. Hence, the system P1 can be change from integral to only two differential equations. However, there are two new differentials equations that may be solved with the initial system. The present work analyzes this procedure and studies a method, which solve the P1 equations directly, without definitions of slowing down densities. (author)

The Fokker-Planck equation for coupled Brown-Néel-rotation.

Science.gov (United States)

Weizenecker, Jürgen

2018-01-22

Calculating the dynamic properties of magnetization of single-domain particles is of great importance for the tomographic imaging modality known as magnetic particle imaging (MPI). Although the assumption of instantaneous thermodynamic equilibrium (Langevin function) after application of time-dependent magnetic fields is sufficient for understanding the fundamental behavior, it is essential to consider the finite response times of magnetic particles for optimizing or analyzing various aspects, e.g. interpreting spectra, optimizing MPI sequences, developing new contrasts, and evaluating simplified models. The change in magnetization following the application of the fields is caused by two different movements: the geometric rotation of the particle and the rotation of magnetization with respect to the fixed particle axes. These individual rotations can be well described using the Langevin equations or the Fokker-Planck equation. However, because the two rotations generally exhibit interdependence, it is necessary to consider coupling between the two equations. This article shows how a coupled Fokker-Planck equation can be derived on the basis of coupled Langevin equations. Two physically equivalent Fokker-Planck equations are derived and transformed by means of an appropriate series expansion into a system of ordinary differential equations, which can be solved numerically. Finally, this system is also used to specify a system of differential equations for various limiting cases (Néel, Brown, uniaxial symmetry). Generally, the system exhibits a sparsely populated matrix and can therefore be handled well numerically.

The Fokker-Planck equation for coupled Brown-Néel-rotation

Science.gov (United States)

Weizenecker, Jürgen

2018-02-01

Calculating the dynamic properties of magnetization of single-domain particles is of great importance for the tomographic imaging modality known as magnetic particle imaging (MPI). Although the assumption of instantaneous thermodynamic equilibrium (Langevin function) after application of time-dependent magnetic fields is sufficient for understanding the fundamental behavior, it is essential to consider the finite response times of magnetic particles for optimizing or analyzing various aspects, e.g. interpreting spectra, optimizing MPI sequences, developing new contrasts, and evaluating simplified models. The change in magnetization following the application of the fields is caused by two different movements: the geometric rotation of the particle and the rotation of magnetization with respect to the fixed particle axes. These individual rotations can be well described using the Langevin equations or the Fokker-Planck equation. However, because the two rotations generally exhibit interdependence, it is necessary to consider coupling between the two equations. This article shows how a coupled Fokker-Planck equation can be derived on the basis of coupled Langevin equations. Two physically equivalent Fokker-Planck equations are derived and transformed by means of an appropriate series expansion into a system of ordinary differential equations, which can be solved numerically. Finally, this system is also used to specify a system of differential equations for various limiting cases (Néel, Brown, uniaxial symmetry). Generally, the system exhibits a sparsely populated matrix and can therefore be handled well numerically.

Travelling wave solutions of generalized coupled Zakharov–Kuznetsov and dispersive long wave equations

Directory of Open Access Journals (Sweden)

M. Arshad

Full Text Available In this manuscript, we constructed different form of new exact solutions of generalized coupled Zakharov–Kuznetsov and dispersive long wave equations by utilizing the modified extended direct algebraic method. New exact traveling wave solutions for both equations are obtained in the form of soliton, periodic, bright, and dark solitary wave solutions. There are many applications of the present traveling wave solutions in physics and furthermore, a wide class of coupled nonlinear evolution equations can be solved by this method. Keywords: Traveling wave solutions, Elliptic solutions, Generalized coupled Zakharov–Kuznetsov equation, Dispersive long wave equation, Modified extended direct algebraic method

Some results on the neutron transport and the coupling of equations

International Nuclear Information System (INIS)

Bal, G.

1997-01-01

Neutron transport in nuclear reactors is well modeled by the linear Boltzmann transport equation. Its resolution is relatively easy but very expensive. To achieve whole core calculations, one has to consider simpler models, such as diffusion or homogeneous transport equations. However, the solutions may become inaccurate in particular situations (as accidents for instance). That is the reason why we wish to solve the equations on small area accurately and more coarsely on the remaining part of the core. It is than necessary to introduce some links between different discretizations or modelizations. In this note, we give some results on the coupling of different discretizations of all degrees of freedom of the integral-differential neutron transport equation (two degrees for the angular variable, on for the energy component, and two or three degrees for spatial position respectively in 2D (cylindrical symmetry) and 3D). Two chapters are devoted to the coupling of discrete ordinates methods (for angular discretization). The first one is theoretical and shows the well posing of the coupled problem, whereas the second one deals with numerical applications of practical interest (the results have been obtained from the neutron transport code developed at the R and D, which has been modified for introducing the coupling). Next, we present the nodal scheme RTN0, used for the spatial discretization. We show well posing results for the non-coupled and the coupled problems. At the end, we deal with the coupling of energy discretizations for the multigroup equations obtained by homogenization. Some theoretical results of the discretization of the velocity variable (well-posing of problems), which do not deal directly with the purposes of coupling, are presented in the annexes. (author)

Constraints of the variation of fundamental couplings and sensitivity of the equation of state of dense matter

Energy Technology Data Exchange (ETDEWEB)

Perez-Garcia, M. Angeles, E-mail: mperezga@usal.es [Departamento de Fisica Fundamental and IUFFyM, Universidad de Salamanca, E-37008 Salamanca (Spain); Martins, C.J.A.P., E-mail: Carlos.Martins@astro.up.pt [Centro de Astrofisica da Universidade do Porto, Rua das Estrelas, 4150-762 Porto (Portugal)

2012-12-05

We discuss the coupled variations of the gravitational, strong and electroweak coupling constants and the current knowledge of the nuclear equation of state based on heavy ion collision experiments and neutron star mass-radius relationship. In particular we focus in our description on phenomenological parameters, R, relating variations in the quantum chromodynamics scale {Lambda}{sub QCD} and the fine structure constant {alpha}, and S, relating variations of v, the Higgs vacuum expectation value and the Yukawa couplings, h, in the quark sector. This parametrization is valid for any model where gauge coupling unification occurs at some (unspecified) high energy scale. From a physically motivated set of equations of state for dense matter we obtain the constrained parameter phase space (R,S) in high density nuclear environments. This procedure is complementary to (although currently less powerful than) those used in low-density conditions. For variations of {Delta}{alpha}/{alpha}=0.005 we find that the obtained constrained parameter lies on a strip region in the (R,S) plane that partially overlaps some of the allowed values of parameters derived from primordial abundances. This may be of interest in the context of unification scenarios where a dense phase of the universe may have existed at early times.

Discrete coupled derivative nonlinear Schroedinger equations and their quasi-periodic solutions

International Nuclear Information System (INIS)

Geng Xianguo; Su Ting

2007-01-01

A hierarchy of nonlinear differential-difference equations associated with a discrete isospectral problem is proposed, in which a typical differential-difference equation is a discrete coupled derivative nonlinear Schroedinger equation. With the help of the nonlinearization of the Lax pairs, the hierarchy of nonlinear differential-difference equations is decomposed into a new integrable symplectic map and a class of finite-dimensional integrable Hamiltonian systems. Based on the theory of algebraic curve, the Abel-Jacobi coordinates are introduced to straighten out the corresponding flows, from which quasi-periodic solutions for these differential-difference equations are obtained resorting to the Riemann-theta functions. Moreover, a (2+1)-dimensional discrete coupled derivative nonlinear Schroedinger equation is proposed and its quasi-periodic solutions are derived

Rate equation analysis and non-Hermiticity in coupled semiconductor laser arrays

Science.gov (United States)

Gao, Zihe; Johnson, Matthew T.; Choquette, Kent D.

2018-05-01

Optically coupled semiconductor laser arrays are described by coupled rate equations. The coupled mode equations and carrier densities are included in the analysis, which inherently incorporate the carrier-induced nonlinearities including gain saturation and amplitude-phase coupling. We solve the steady-state coupled rate equations and consider the cavity frequency detuning and the individual laser pump rates as the experimentally controlled variables. We show that the carrier-induced nonlinearities play a critical role in the mode control, and we identify gain contrast induced by cavity frequency detuning as a unique mechanism for mode control. Photon-mediated energy transfer between cavities is also discussed. Parity-time symmetry and exceptional points in this system are studied. Unbroken parity-time symmetry can be achieved by judiciously combining cavity detuning and unequal pump rates, while broken symmetry lies on the boundary of the optical locking region. Exceptional points are identified at the intersection between broken symmetry and unbroken parity-time symmetry.

Iteratively-coupled propagating exterior complex scaling method for electron-hydrogen collisions

International Nuclear Information System (INIS)

Bartlett, Philip L; Stelbovics, Andris T; Bray, Igor

2004-01-01

A newly-derived iterative coupling procedure for the propagating exterior complex scaling (PECS) method is used to efficiently calculate the electron-impact wavefunctions for atomic hydrogen. An overview of this method is given along with methods for extracting scattering cross sections. Differential scattering cross sections at 30 eV are presented for the electron-impact excitation to the n = 1, 2, 3 and 4 final states, for both PECS and convergent close coupling (CCC), which are in excellent agreement with each other and with experiment. PECS results are presented at 27.2 eV and 30 eV for symmetric and asymmetric energy-sharing triple differential cross sections, which are in excellent agreement with CCC and exterior complex scaling calculations, and with experimental data. At these intermediate energies, the efficiency of the PECS method with iterative coupling has allowed highly accurate partial-wave solutions of the full Schroedinger equation, for L ≤ 50 and a large number of coupled angular momentum states, to be obtained with minimal computing resources. (letter to the editor)

Novel method for solution of coupled radial Schrödinger equations

International Nuclear Information System (INIS)

Ershov, S. N.; Vaagen, J. S.; Zhukov, M. V.

2011-01-01

One of the major problems in numerical solution of coupled differential equations is the maintenance of linear independence for different sets of solution vectors. A novel method for solution of radial Schrödinger equations is suggested. It consists of rearrangement of coupled equations in a way that is appropriate to avoid usual numerical instabilities associated with components of the wave function in their classically forbidden regions. Applications of the new method for nuclear structure calculations within the hyperspherical harmonics approach are given.

Scale calculus and the Schroedinger equation

International Nuclear Information System (INIS)

Cresson, Jacky

2003-01-01

This paper is twofold. In a first part, we extend the classical differential calculus to continuous nondifferentiable functions by developing the notion of scale calculus. The scale calculus is based on a new approach of continuous nondifferentiable functions by constructing a one parameter family of differentiable functions f(t,ε) such that f(t,ε)→f(t) when ε goes to zero. This led to several new notions as representations: fractal functions and ε-differentiability. The basic objects of the scale calculus are left and right quantum operators and the scale operator which generalizes the classical derivative. We then discuss some algebraic properties of these operators. We define a natural bialgebra, called quantum bialgebra, associated with them. Finally, we discuss a convenient geometric object associated with our study. In a second part, we define a first quantization procedure of classical mechanics following the scale relativity theory developed by Nottale. We obtain a nonlinear Schroedinger equation via the classical Newton's equation of dynamics using the scale operator. Under special assumptions we recover the classical Schroedinger equation and we discuss the relevance of these assumptions

Nonlinear coupled equations for electrochemical cells as developed by the general equation for nonequilibrium reversible-irreversible coupling.

Science.gov (United States)

Bedeaux, Dick; Kjelstrup, Signe; Öttinger, Hans Christian

2014-09-28

We show how the Butler-Volmer and Nernst equations, as well as Peltier effects, are contained in the general equation for nonequilibrium reversible and irreversible coupling, GENERIC, with a unique definition of the overpotential. Linear flux-force relations are used to describe the transport in the homogeneous parts of the electrochemical system. For the electrode interface, we choose nonlinear flux-force relationships. We give the general thermodynamic basis for an example cell with oxygen electrodes and electrolyte from the solid oxide fuel cell. In the example cell, there are two activated chemical steps coupled also to thermal driving forces at the surface. The equilibrium exchange current density obtains contributions from both rate-limiting steps. The measured overpotential is identified at constant temperature and stationary states, in terms of the difference in electrochemical potential of products and reactants. Away from these conditions, new terms appear. The accompanying energy flux out of the surface, as well as the heat generation at the surface are formulated, adding to the general thermodynamic basis.

Nonlinear coupled equations for electrochemical cells as developed by the general equation for nonequilibrium reversible-irreversible coupling

Science.gov (United States)

Bedeaux, Dick; Kjelstrup, Signe; Öttinger, Hans Christian

2014-09-01

We show how the Butler-Volmer and Nernst equations, as well as Peltier effects, are contained in the general equation for nonequilibrium reversible and irreversible coupling, GENERIC, with a unique definition of the overpotential. Linear flux-force relations are used to describe the transport in the homogeneous parts of the electrochemical system. For the electrode interface, we choose nonlinear flux-force relationships. We give the general thermodynamic basis for an example cell with oxygen electrodes and electrolyte from the solid oxide fuel cell. In the example cell, there are two activated chemical steps coupled also to thermal driving forces at the surface. The equilibrium exchange current density obtains contributions from both rate-limiting steps. The measured overpotential is identified at constant temperature and stationary states, in terms of the difference in electrochemical potential of products and reactants. Away from these conditions, new terms appear. The accompanying energy flux out of the surface, as well as the heat generation at the surface are formulated, adding to the general thermodynamic basis.

New analytic solutions of stochastic coupled KdV equations

International Nuclear Information System (INIS)

Dai Chaoqing; Chen Junlang

2009-01-01

In this paper, firstly, we use the exp-function method to seek new exact solutions of the Riccati equation. Then, with the help of Hermit transformation, we employ the Riccati equation and its new exact solutions to find new analytic solutions of the stochastic coupled KdV equation in the white noise environment. As some special examples, some analytic solutions can degenerate into these solutions reported in open literatures.

Multiple spatial scaling and the weak-coupling approximation. I. General formulation and equilibrium theory

Energy Technology Data Exchange (ETDEWEB)

Kleinsmith, P E [Carnegie-Mellon Univ., Pittsburgh, Pa. (USA)

1976-04-01

Multiple spatial scaling is incorporated in a modified form of the Bogoliubov plasma cluster expansion; then this proposed reformulation of the plasma weak-coupling approximation is used to derive, from the BBGKY Hierarchy, a decoupled set of equations for the one-and two-particle distribution functions in the limit as the plasma parameter goes to zero. Because the reformulated cluster expansion permits retention of essential two-particle collisional information in the limiting equations, while simultaneously retaining the well-established Debye-scale relative ordering of the correlation functions, decoupling of the Hierarchy is accomplished without introduction of the divergence problems encountered in the Bogoliubov theory, as is indicated by an exact solution of the limiting equations for the equilibrium case. To establish additional links with existing plasma equilibrium theories, the two-particle equilibrium correlation function is used to calculate the interaction energy and the equation of state. The limiting equation for the equilibrium three-particle correlation function is then developed, and a formal solution is obtained.

Blowing-up Semilinear Wave Equation with Exponential ...

Indian Academy of Sciences (India)

Blowing-up Semilinear Wave Equation with Exponential Nonlinearity in Two Space ... We investigate the initial value problem for some semi-linear wave equation in two space dimensions with exponential nonlinearity growth. ... Current Issue

Continuum level density of a coupled-channel system in the complex scaling method

International Nuclear Information System (INIS)

Suzuki, Ryusuke; Kato, Kiyoshi; Kruppa, Andras; Giraud, Bertrand G.

2008-01-01

We study the continuum level density (CLD) in the formalism of the complex scaling method (CSM) for coupled-channel systems. We apply the formalism to the 4 He=[ 3 H+p]+[ 3 He+n] coupled-channel cluster model where there are resonances at low energy. Numerical calculations of the CLD in the CSM with a finite number of L 2 basis functions are consistent with the exact result calculated from the S-matrix by solving coupled-channel equations. We also study channel densities. In this framework, the extended completeness relation (ECR) plays an important role. (author)

Transition behaviours in two coupled Josephson junction equations

International Nuclear Information System (INIS)

Wang Jiazeng; Zhang Xuejuan; You Gongqiang; Zhou Fengyan

2007-01-01

The dynamics of two coupled Josephson junction equations are investigated via mathematical reasoning and numerical simulations. We show that for a fixed coupling K, the whole parameter space can be comparted into three regions: a quenching region, a synchronized running periodic region and a region where these two states coexist. It is further shown that with the increase of the coupling K, the system may transit from a synchronizing state to a quenching state. The characteristic of the critical line K*(b) which separates these two states is mathematically analysed

On non-linear dynamics of coupled 1+1DOF versus 1+1/2DOF Electro-Mechanical System

DEFF Research Database (Denmark)

Darula, Radoslav; Sorokin, Sergey

2014-01-01

The electro-mechanical systems (EMS) are used from nano-/micro-scale (NEMS/MEMS) up to macro-scale applications. From mathematical view point, they are modelled with the second order differential equation (or a set of equations) for mechanical system, which is nonlinearly coupled with the second...... or the first order differential equation (or a set of equations) for electrical system, depending on properties of the electrical circuit. For the sake of brevity, we assume a 1DOF mechanical system, coupled to 1 or 1/2DOF electrical system (depending whether the capacitance is, or is not considered......). In the paper, authors perform a parametric study to identify operation regimes, where the capacitance term contributes to the non-linear behaviour of the coupled system. To accomplish this task, the classical method of multiple scales is used. The parametric study allows us to assess for which applications...

CPDS3, Coupled 3-D Partial Differential Equation Solution

International Nuclear Information System (INIS)

Anderson, D.V.; Koniges, A.E.; Shumaker, D.E.

1992-01-01

1 - Description of program or function: CPDES3 solves the linear asymmetric matrix equations arising from coupled partial differential equations in three dimensions. The exact form of the matrix depends on the choice of spatial grids and on the finite element or finite difference approximation employed. CPDES3 allows each spatial operator to have 7, 15, 19, or 27 point stencils, permits general couplings between all of the component PDE's, and automatically generates the matrix structures needed to perform the algorithm. 2 - Method of solution: The resulting sparse matrix equation with a complicated sub-band structure and generally asymmetric is solved by either the preconditioned conjugate gradient (CG) method or the preconditioned bi-conjugate gradient (BCG) algorithm. BCG enjoys faster convergence in most cases but in rare instances diverges. Then, CG iterations must be used. 3 - Restrictions on the complexity of the problem: The discretization of the coupled three-dimensional PDE's and their boundary conditions must result in an operator stencil which fits in the Cray2 memory. In addition, the matrix must possess a reasonable amount of diagonal dominance for the preconditioning technique to be effective

CPDES2, Coupled 2-D Partial Differential Equation Solution

International Nuclear Information System (INIS)

Anderson, D.V.; Koniges, A.E.; Shumaker, D.E.

1992-01-01

1 - Description of program or function: CPDES2 solves the linear asymmetric equations arising from coupled partial differential equations in two dimensions. The exact form of the matrix depends on the choice of spatial grids and on the finite element or finite difference approximation employed. CPDES2 allows each spatial operator to have 5 or 9 point stencils, permits general coupling between all of the component PDE's, and automatically generates the matrix structures needed to perform the algorithm. 2 - Method of solution: The resulting sparse matrix equation with a complicated sub-band structure and generally asymmetric is solved by either the preconditioned conjugate gradient (CG) method or the preconditioned bi-conjugate gradient (BCG) algorithm. BCG enjoys faster convergence in most cases but in rare instances diverges. Then, CG iterations must be used. 3 - Restrictions on the complexity of the problem: The discretization of the coupled two-dimensional PDE's and their boundary conditions must result in an operator stencil which fits in the Cray2 memory. In addition, the matrix must possess a reasonable amount of diagonal dominance for the preconditioning technique to be effective

Constructing New Discrete Integrable Coupling System for Soliton Equation by Kronecker Product

International Nuclear Information System (INIS)

Yu Fajun; Zhang Hongqing

2008-01-01

It is shown that the Kronecker product can be applied to constructing new discrete integrable coupling system of soliton equation hierarchy in this paper. A direct application to the fractional cubic Volterra lattice spectral problem leads to a novel integrable coupling system of soliton equation hierarchy. It is also indicated that the study of discrete integrable couplings by using the Kronecker product is an efficient and straightforward method. This method can be used generally

A semi-analytical solution to accelerate spin-up of a coupled carbon and nitrogen land model to steady state

Directory of Open Access Journals (Sweden)

J. Y. Xia

2012-10-01

Full Text Available The spin-up of land models to steady state of coupled carbon–nitrogen processes is computationally so costly that it becomes a bottleneck issue for global analysis. In this study, we introduced a semi-analytical solution (SAS for the spin-up issue. SAS is fundamentally based on the analytic solution to a set of equations that describe carbon transfers within ecosystems over time. SAS is implemented by three steps: (1 having an initial spin-up with prior pool-size values until net primary productivity (NPP reaches stabilization, (2 calculating quasi-steady-state pool sizes by letting fluxes of the equations equal zero, and (3 having a final spin-up to meet the criterion of steady state. Step 2 is enabled by averaged time-varying variables over one period of repeated driving forcings. SAS was applied to both site-level and global scale spin-up of the Australian Community Atmosphere Biosphere Land Exchange (CABLE model. For the carbon-cycle-only simulations, SAS saved 95.7% and 92.4% of computational time for site-level and global spin-up, respectively, in comparison with the traditional method (a long-term iterative simulation to achieve the steady states of variables. For the carbon–nitrogen coupled simulations, SAS reduced computational cost by 84.5% and 86.6% for site-level and global spin-up, respectively. The estimated steady-state pool sizes represent the ecosystem carbon storage capacity, which was 12.1 kg C m⁻² with the coupled carbon–nitrogen global model, 14.6% lower than that with the carbon-only model. The nitrogen down-regulation in modeled carbon storage is partly due to the 4.6% decrease in carbon influx (i.e., net primary productivity and partly due to the 10.5% reduction in residence times. This steady-state analysis accelerated by the SAS method can facilitate comparative studies of structural differences in determining the ecosystem carbon storage capacity among biogeochemical models. Overall, the

Combined solitary-wave solution for coupled higher-order nonlinear Schroedinger equations

International Nuclear Information System (INIS)

Tian Jinping; Tian Huiping; Li Zhonghao; Zhou Guosheng

2004-01-01

Coupled nonlinear Schroedinger equations model several interesting physical phenomena. We used a trigonometric function transform method based on a homogeneous balance to solve the coupled higher-order nonlinear Schroedinger equations. We obtained four pairs of exact solitary-wave solutions including a dark and a bright-soliton pair, a bright- and a dark-soliton pair, a bright- and a bright-soliton pair, and the last pair, a combined bright-dark-soliton pair

Coupling of neutron transport equations. First results; Couplage d`equations en transport neutronique. premiere approche 1D monocinetique

Energy Technology Data Exchange (ETDEWEB)

Bal, G.

1995-07-01

To achieve whole core calculations of the neutron transport equation, we have to follow this 2 step method: space and energy homogenization of the assemblies; resolution of the homogenized equation on the whole core. However, this is no more valid when accidents occur (for instance depressurization causing locally strong heterogeneous media). One solution consists then in coupling two kinds of resolutions: a fine computation on the damaged cell (fine mesh, high number of energy groups) coupled with a coarse one everywhere else. We only deal here with steady state solutions (which already live in 6D spaces). We present here two such methods: The coupling by transmission of homogenized sections and the coupling by transmission of boundary conditions. To understand what this coupling is, we first restrict ourselves to 1D with respect to space in one energy group. The first two chapters deal with a recall of basic properties of the neutron transport equation. We give at chapter 3 some indications of the behaviour of the flux with respect to the cross sections. We present at chapter 4 some couplings and give some properties. Chapter 5 is devoted to a presentation of some numerical applications. (author). 9 refs., 7 figs.

Molecular-state close-coupling theory including continuum states. I. Derivation of close-coupled equations

International Nuclear Information System (INIS)

Thorson, W.R.; Bandarage, G.

1988-01-01

We formulate a close-coupling theory of slow ion-atom collisions based on molecular (adiabatic) electronic states, and including the electronic continuum. The continuum is represented by packet states spanning it locally and constructed explicitly from exact continuum states. Particular attention is given to two fundamental questions: (1) Unbound electrons can escape from the local region spanned by the packet states. We derive close-coupled integral equations correctly including the escape effects; the ''propagator'' generated by these integral equations does not conserve probability within the close-coupled basis. Previous molecular-state formulations including the continuum give no account of escape effects. (2) Nonadiabatic couplings of adiabatic continuum states with the same energy are singular, reflecting the fact that an adiabatic description of continuum behavior is not valid outside a local region. We treat these singularities explicitly and show that an accurate representation of nonadiabatic couplings within the local region spanned by a set of packet states is well behaved. Hence an adiabatic basis-set description can be used to describe close coupling to the continuum in a local ''interaction region,'' provided the effects of escape are included. In principle, the formulation developed here can be extended to a large class of model problems involving many-electron systems and including models for Penning ionization and collisional detachment processes

Singular solitons and other solutions to a couple of nonlinear wave equations

International Nuclear Information System (INIS)

Inc Mustafa; Ulutaş Esma; Biswas Anjan

2013-01-01

This paper addresses the extended (G'/G)-expansion method and applies it to a couple of nonlinear wave equations. These equations are modified the Benjamin—Bona—Mahoney equation and the Boussinesq equation. This extended method reveals several solutions to these equations. Additionally, the singular soliton solutions are revealed, for these two equations, with the aid of the ansatz method

Scale solutions and coupling constant in electrodynamics of vector particles

International Nuclear Information System (INIS)

Arbuzov, B.A.; Boos, E.E.; Kurennoy, S.S.

1980-01-01

A new approach in nonrenormalizable gauge theories is studied, the electrodynamics of vector particles being taken as an example. One and two-loop approximations in Schwinger-Dyson set of equations are considered with account for conditions imposed by gauge invariance. It is shown, that solutions with scale asymptotics can occur in this case but only for a particular value of coupling constant. This value in solutions obtained is close to the value of the fine structure constant α=1/137

Numerical Simulation on Hydromechanical Coupling in Porous Media Adopting Three-Dimensional Pore-Scale Model

Science.gov (United States)

Liu, Jianjun; Song, Rui; Cui, Mengmeng

2014-01-01

A novel approach of simulating hydromechanical coupling in pore-scale models of porous media is presented in this paper. Parameters of the sandstone samples, such as the stress-strain curve, Poisson's ratio, and permeability under different pore pressure and confining pressure, are tested in laboratory scale. The micro-CT scanner is employed to scan the samples for three-dimensional images, as input to construct the model. Accordingly, four physical models possessing the same pore and rock matrix characteristics as the natural sandstones are developed. Based on the micro-CT images, the three-dimensional finite element models of both rock matrix and pore space are established by MIMICS and ICEM software platform. Navier-Stokes equation and elastic constitutive equation are used as the mathematical model for simulation. A hydromechanical coupling analysis in pore-scale finite element model of porous media is simulated by ANSYS and CFX software. Hereby, permeability of sandstone samples under different pore pressure and confining pressure has been predicted. The simulation results agree well with the benchmark data. Through reproducing its stress state underground, the prediction accuracy of the porous rock permeability in pore-scale simulation is promoted. Consequently, the effects of pore pressure and confining pressure on permeability are revealed from the microscopic view. PMID:24955384

Muscle activation described with a differential equation model for large ensembles of locally coupled molecular motors.

Science.gov (United States)

Walcott, Sam

2014-10-01

Molecular motors, by turning chemical energy into mechanical work, are responsible for active cellular processes. Often groups of these motors work together to perform their biological role. Motors in an ensemble are coupled and exhibit complex emergent behavior. Although large motor ensembles can be modeled with partial differential equations (PDEs) by assuming that molecules function independently of their neighbors, this assumption is violated when motors are coupled locally. It is therefore unclear how to describe the ensemble behavior of the locally coupled motors responsible for biological processes such as calcium-dependent skeletal muscle activation. Here we develop a theory to describe locally coupled motor ensembles and apply the theory to skeletal muscle activation. The central idea is that a muscle filament can be divided into two phases: an active and an inactive phase. Dynamic changes in the relative size of these phases are described by a set of linear ordinary differential equations (ODEs). As the dynamics of the active phase are described by PDEs, muscle activation is governed by a set of coupled ODEs and PDEs, building on previous PDE models. With comparison to Monte Carlo simulations, we demonstrate that the theory captures the behavior of locally coupled ensembles. The theory also plausibly describes and predicts muscle experiments from molecular to whole muscle scales, suggesting that a micro- to macroscale muscle model is within reach.

New exact solutions of coupled Boussinesq–Burgers equations by Exp-function method

Directory of Open Access Journals (Sweden)

L.K. Ravi

2017-03-01

Full Text Available In the present paper, we build the new analytical exact solutions of a nonlinear differential equation, specifically, coupled Boussinesq–Burgers equations by means of Exp-function method. Then, we analyze the results by plotting the three dimensional soliton graphs for each case, which exhibit the simplicity and effectiveness of the proposed method. The primary purpose of this paper is to employ a new approach, which allows us victorious and efficient derivation of the new analytical exact solutions for the coupled Boussinesq–Burgers equations.

Hamiltonian structures and integrability for a discrete coupled KdV-type equation hierarchy

International Nuclear Information System (INIS)

Zhao Haiqiong; Zhu Zuonong; Zhang Jingli

2011-01-01

Coupled Korteweg-de Vries (KdV) systems have many important physical applications. By considering a 4 × 4 spectral problem, we derive a discrete coupled KdV-type equation hierarchy. Our hierarchy includes the coupled Volterra system proposed by Lou et al. (e-print arXiv: 0711.0420) as the first member which is a discrete version of the coupled KdV equation. We also investigate the integrability in the Liouville sense and the multi-Hamiltonian structures for the obtained hierarchy. (authors)

Effect of algae pigmentation on photobioreactor productivity and scale-up: A light transfer perspective

International Nuclear Information System (INIS)

Murphy, Thomas E.; Berberoglu, Halil

2011-01-01

This paper reports a numerical study coupling light transfer with photosynthetic rate models to determine the size and microorganism concentration of photobioreactors based on the pigmentation of algae to achieve maximum productivity. The wild strain Chlamydomonas reinhardtii and its transformant tla1 with 63% lower pigmentation are used as exemplary algae. First, empirical models of the specific photosynthetic rates were obtained from experimental data as a function of local irradiance using inverse methods. Then, these models were coupled with the radiative transfer equation (RTE) to predict both the local and total photosynthetic rates in a planar photobioreactor (PBR). The optical thickness was identified as the proper scaling parameter. The results indicated that under full sunlight corresponding to about 400 W/m 2 photosynthetically active irradiation, enhancement of PBR productivity up to 30% was possible with tla1. Moreover, under similar irradiation, optical thicknesses above 169 and 275 for the wild strain and tla1, respectively, did not further enhance PBR productivity. Based on these results guidelines are provided for maximizing PBR productivity from a light transport perspective.

Coupled equations for Kähler metrics and Yang-Mills connections

DEFF Research Database (Denmark)

Garcia Fernandez, Mario; Alvarez-Consul, Luis; Garcia-Prada, Oscar

2012-01-01

We study equations on a principal bundle over a compact complex manifold coupling connections on the bundle with K¨ahler structures in the base. These equations generalize the conditions of constant scalar curvature for a K¨ahler metric and Hermite– Yang–Mills for a connection. We provide a moment...

XMDS2: Fast, scalable simulation of coupled stochastic partial differential equations

Science.gov (United States)

Dennis, Graham R.; Hope, Joseph J.; Johnsson, Mattias T.

2013-01-01

XMDS2 is a cross-platform, GPL-licensed, open source package for numerically integrating initial value problems that range from a single ordinary differential equation up to systems of coupled stochastic partial differential equations. The equations are described in a high-level XML-based script, and the package generates low-level optionally parallelised C++ code for the efficient solution of those equations. It combines the advantages of high-level simulations, namely fast and low-error development, with the speed, portability and scalability of hand-written code. XMDS2 is a complete redesign of the XMDS package, and features support for a much wider problem space while also producing faster code. Program summaryProgram title: XMDS2 Catalogue identifier: AENK_v1_0 Program summary URL:http://cpc.cs.qub.ac.uk/summaries/AENK_v1_0.html Program obtainable from: CPC Program Library, Queen's University, Belfast, N. Ireland Licensing provisions: GNU General Public License, version 2 No. of lines in distributed program, including test data, etc.: 872490 No. of bytes in distributed program, including test data, etc.: 45522370 Distribution format: tar.gz Programming language: Python and C++. Computer: Any computer with a Unix-like system, a C++ compiler and Python. Operating system: Any Unix-like system; developed under Mac OS X and GNU/Linux. RAM: Problem dependent (roughly 50 bytes per grid point) Classification: 4.3, 6.5. External routines: The external libraries required are problem-dependent. Uses FFTW3 Fourier transforms (used only for FFT-based spectral methods), dSFMT random number generation (used only for stochastic problems), MPI message-passing interface (used only for distributed problems), HDF5, GNU Scientific Library (used only for Bessel-based spectral methods) and a BLAS implementation (used only for non-FFT-based spectral methods). Nature of problem: General coupled initial-value stochastic partial differential equations. Solution method: Spectral method

Simulation of Plasmonics Nanodevices with Coupled Maxwell and Schrödinger Equations using the FDTD Method

Directory of Open Access Journals (Sweden)

I. Ahmed

2012-09-01

Full Text Available Maxwell and Schrödinger equations are coupled to incorporate quantum effects for the simulation of plasmonics nanodevices. Maxwell equations with Lorentz-Drude (LD dispersive model are applied to large size plasmonics components, whereas coupled Maxwell and Schrödinger equations are applied to components where quantum effects are needed. The finite difference time domain method (FDTD is applied to simulate these coupled equations.

Scaling of differential equations

CERN Document Server

Langtangen, Hans Petter

2016-01-01

The book serves both as a reference for various scaled models with corresponding dimensionless numbers, and as a resource for learning the art of scaling. A special feature of the book is the emphasis on how to create software for scaled models, based on existing software for unscaled models. Scaling (or non-dimensionalization) is a mathematical technique that greatly simplifies the setting of input parameters in numerical simulations. Moreover, scaling enhances the understanding of how different physical processes interact in a differential equation model. Compared to the existing literature, where the topic of scaling is frequently encountered, but very often in only a brief and shallow setting, the present book gives much more thorough explanations of how to reason about finding the right scales. This process is highly problem dependent, and therefore the book features a lot of worked examples, from very simple ODEs to systems of PDEs, especially from fluid mechanics. The text is easily accessible and exam...

Asymptotic properties of blow-up solutions in reaction-diffusion equations with nonlocal boundary flux

Science.gov (United States)

Liu, Bingchen; Dong, Mengzhen; Li, Fengjie

2018-04-01

This paper deals with a reaction-diffusion problem with coupled nonlinear inner sources and nonlocal boundary flux. Firstly, we propose the critical exponents on nonsimultaneous blow-up under some conditions on the initial data. Secondly, we combine the scaling technique and the Green's identity method to determine four kinds of simultaneous blow-up rates. Thirdly, the lower and the upper bounds of blow-up time are derived by using Sobolev-type differential inequalities.

Mathematical and numerical study of nonlinear hyperbolic equations: model coupling and nonclassical shocks

International Nuclear Information System (INIS)

Boutin, B.

2009-11-01

This thesis concerns the mathematical and numerical study of nonlinear hyperbolic partial differential equations. A first part deals with an emergent problematic: the coupling of hyperbolic equations. The pursued applications are linked with the mathematical coupling of computing platforms, dedicated to an adaptative simulation of multi-scale phenomena. We propose and analyze a new coupling formalism based on extended PDE systems avoiding the geometric treatment of the interfaces. In addition, it allows to formulate the problem in a multidimensional setting, with possible covering of the coupled models. This formalism allows in particular to equip the coupling procedure with viscous regularization mechanisms, useful in the selection of natural discontinuous solutions. We analyze existence and uniqueness in the framework of a parabolic regularization a la Dafermos. Existence of a solution holds true under very general conditions but failure of uniqueness may naturally arise as soon as resonance occurs at the interfaces. Next, we highlight that our extended PDE framework gives rise to another regularization strategy based on thick interfaces. In this setting, we prove existence and uniqueness of the solutions of the Cauchy problem for initial data in L ∞ . The main tool consists in the derivation of a flexible and robust finite volume method for general triangulation which is analyzed in the setting of entropy measure-valued solutions by DiPerna. The second part is devoted to the definition of a finite volume scheme for the computing of nonclassical solutions of a scalar conservation law based on a kinetic relation. This scheme offers the feature to be stricto sensu conservative, in opposition to a Glimm approach that is only statistically conservative. The validity of our approach is illustrated through numerical examples. (author)

Global Solutions to the Coupled Chemotaxis-Fluid Equations

KAUST Repository

Duan, Renjun

2010-08-10

In this paper, we are concerned with a model arising from biology, which is a coupled system of the chemotaxis equations and the viscous incompressible fluid equations through transport and external forcing. The global existence of solutions to the Cauchy problem is investigated under certain conditions. Precisely, for the Chemotaxis-Navier-Stokes system over three space dimensions, we obtain global existence and rates of convergence on classical solutions near constant states. When the fluid motion is described by the simpler Stokes equations, we prove global existence of weak solutions in two space dimensions for cell density with finite mass, first-order spatial moment and entropy provided that the external forcing is weak or the substrate concentration is small. © Taylor & Francis Group, LLC.

Application of the fractional neutron point kinetic equation: Start-up of a nuclear reactor

International Nuclear Information System (INIS)

Polo-Labarrios, M.-A.; Espinosa-Paredes, G.

2012-01-01

Highlights: ► Neutron density behavior at reactor start up with fractional neutron point kinetics. ► There is a relaxation time associated with a rapid variation in the neutron flux. ► Physical interpretation of the fractional order is related with non-Fickian effects. ► Effect of the anomalous diffusion coefficient and the relaxation time is analyzed. ► Neutron density is related with speed and duration of the control rods lifting. - Abstract: In this paper we present the behavior of the variation of neutron density when the nuclear reactor power is increased using the fractional neutron point kinetic (FNPK) equation with a single-group of delayed neutron precursor. It is considered that there is a relaxation time associated with a rapid variation in the neutron flux and its physical interpretation of the fractional order is related with non-Fickian effects from the neutron diffusion equation point of view. We analyzed the case of increase the nuclear reactor power when reactor is cold start-up which is a process of inserting reactivity by lifting control rods discontinuously. The results show that for short time scales of the start-up the neutronic density behavior with FNPK shows sub-diffusive effects whose absorption are government by control rods velocity. For large times scale, the results shows that the classical equation of the neutron point kinetics over predicted the neutron density regarding to FNPK.

Scaling Relations and Self-Similarity of 3-Dimensional Reynolds-Averaged Navier-Stokes Equations.

Science.gov (United States)

Ercan, Ali; Kavvas, M Levent

2017-07-25

Scaling conditions to achieve self-similar solutions of 3-Dimensional (3D) Reynolds-Averaged Navier-Stokes Equations, as an initial and boundary value problem, are obtained by utilizing Lie Group of Point Scaling Transformations. By means of an open-source Navier-Stokes solver and the derived self-similarity conditions, we demonstrated self-similarity within the time variation of flow dynamics for a rigid-lid cavity problem under both up-scaled and down-scaled domains. The strength of the proposed approach lies in its ability to consider the underlying flow dynamics through not only from the governing equations under consideration but also from the initial and boundary conditions, hence allowing to obtain perfect self-similarity in different time and space scales. The proposed methodology can be a valuable tool in obtaining self-similar flow dynamics under preferred level of detail, which can be represented by initial and boundary value problems under specific assumptions.

Improved coupling of the conduction and flow equations in TRAC

International Nuclear Information System (INIS)

Addessio, F.L.

1981-01-01

Recent nuclear-reactor-systems modeling efforts have been directed toward the development of computer codes capable of simulating transients in short computational times. For this reason, a stability enhancing two-stem method (SETS) has been applied to the two-phase flow equations in the Transient Reactor Analysis Code (TRAC) allowing the Courant limit to be violated. Unfortunately, the coupling between the wall conduction equation and the fluid-dynamics equations is performed semi-implicitly, that is, the wall-heat transfer term, is evaluated using old-time heat-transfer coefficients and wall temperatures and new-time coolant temperatures. This coupling may lead to numerical instabilities at large time steps because of large variations in the heat-transfer coefficient in certain regimes of the boiling curve. Consequently, simply using new-time wall temperatures is not sufficient. A technique that also incorporates new-time heat-transfer coefficients must be used

Equation-of-motion coupled cluster perturbation theory revisited

DEFF Research Database (Denmark)

Eriksen, Janus Juul; Jørgensen, Poul; Olsen, Jeppe

2014-01-01

The equation-of-motion coupled cluster (EOM-CC) framework has been used for deriving a novel series of perturbative corrections to the coupled cluster singles and doubles energy that formally con- verges towards the full configuration interaction energy limit. The series is based on a Møller-Ples......-Plesset partitioning of the Hamiltonian and thus size extensive at any order in the perturbation, thereby rem- edying the major deficiency inherent to previous perturbation series based on the EOM-CC ansatz. © 2014 AIP Publishing LLC. [http://dx.doi.org/10.1063/1.4873138]...

The Neumann Type Systems and Algebro-Geometric Solutions of a System of Coupled Integrable Equations

International Nuclear Information System (INIS)

Chen Jinbing; Qiao Zhijun

2011-01-01

A system of (1+1)-dimensional coupled integrable equations is decomposed into a pair of new Neumann type systems that separate the spatial and temporal variables for this system over a symplectic submanifold. Then, the Neumann type flows associated with the coupled integrable equations are integrated on the complex tour of a Riemann surface. Finally, the algebro-geometric solutions expressed by Riemann theta functions of the system of coupled integrable equations are obtained by means of the Jacobi inversion.

Dynamics of wide and snake-like pulses in coupled Schrödinger equations with full-modulated nonlinearities

Energy Technology Data Exchange (ETDEWEB)

Yomba, Emmanuel, E-mail: emmanuel.yomba@csun.edu; Zakeri, Gholam-Ali, E-mail: ali.zakeri@csun.edu

2016-02-05

We investigate the existence of various solitary wave solutions in coupled Schrödinger equations with specific cubic and quintic nonlinearities. This system arises in wave propagation in fiber optics with focusing and defocusing with modulated nonlinearities. We obtain front–front, bright–bright, dark–dark, and dark–bright like solitons using a direct approach, and then, by reducing the system of equations to a single auxiliary equation of a Duffing-type ordinary differential equation, we provide a large class of Jacobi-elliptic solutions. These solutions are presented in the exact form and analyzed. We find a class of wide localized and snake-like (in both space and time) vector solitons. One of the novel aspects of this study is that we have shown that the qualitative behavior of the solutions is independent of the choice of similarity variables. Numerical results show that the solutions of the above system are stable with up to 10% white noises. - Highlights: • Dynamics of wide and snake-like pulses is analyzed for coupled Schrödinger equations. • Qualitative appearance of solutions is analyzed using various similarity variables. • Effect of change in parameter-values on dynamics of the solutions is investigated. • Vectors front–front, bright–bright, dark–dark and dark–bright solitons are obtained.

The thermal coupling constant and the gap equation in the λ φ 4D model

International Nuclear Information System (INIS)

Ananos, G.N.J.; Malbouisson, A.P.C.; Svaiter, N.F.

1998-05-01

By the concurrent use of two different resummation methods, the composite operator formalism and the Dyson-Schwinger equation, we re-examine the behaviour at finite temperature of the O(N)-symmetric λψ 4 model in a generic D-dimensional Euclidean space. In the cases D = 3 and D = 4, an analysis of the thermal behaviour of the renormalized squared mass and coupling constant are done for all temperatures. It results that the thermal renormalized squared mass is positive and increases monotonically with the temperature. The behavior of the thermal coupling constant is quite different in odd or even dimensional space. In D = 3, the thermal coupling constant decreases up to a minimum value different from zero and ten grows up monotonically as the temperature increases. In the case D = 4, it is found that the thermal renormalized coupling constant tends in the high temperature limit to a constant asymptotic value. Also for general D-dimensional Euclidean space, we are able to obtain a formula for the critical temperature of the second order phase transition. This formula agrees with previous known values at D = 3 and D 4. (author)

Preparation and scale up of extended-release tablets of bromopride

Directory of Open Access Journals (Sweden)

Guilherme Neves Ferreira

2014-04-01

Full Text Available Reproducibility of the tablet manufacturing process and control of its pharmaceutics properties depends on the optimization of formulation aspects and process parameters. Computer simulation such as Design of Experiments (DOE can be used to scale up the production of this formulation, in particular for obtaining sustained-release tablets. Bromopride formulations are marketed in the form of extended-release pellets, which makes the product more expensive and difficult to manufacture. The aim of this study was to formulate new bromopride sustained release formulations as tablets, and to develop mathematical models to standardize the scale up of this formulation, controlling weight and hardness of the tablets during manufacture according to the USP 34th edition. DOE studies were conducted using Minitab(tm software. Different excipient combinations were evaluated in order to produce bromopride sustained-release matrix tablets. In the scale-up study, data were collected and variations in tableting machine parameters were measured. Data were processed by Minitab(tm software, generating mathematical equations used for prediction of powder compaction behavior, according to the settings of the tableting machine suitable for scale-up purposes. Bromopride matrix tablets with appropriate characteristics for sustained release were developed. The scale-up of the formulation with the most suitable sustained release profile was established by using mathematical models, indicating that the formulation can be a substitute for the pellets currently marketed.

Coupled double-distribution-function lattice Boltzmann method for the compressible Navier-Stokes equations.

Science.gov (United States)

Li, Q; He, Y L; Wang, Y; Tao, W Q

2007-11-01

A coupled double-distribution-function lattice Boltzmann method is developed for the compressible Navier-Stokes equations. Different from existing thermal lattice Boltzmann methods, this method can recover the compressible Navier-Stokes equations with a flexible specific-heat ratio and Prandtl number. In the method, a density distribution function based on a multispeed lattice is used to recover the compressible continuity and momentum equations, while the compressible energy equation is recovered by an energy distribution function. The energy distribution function is then coupled to the density distribution function via the thermal equation of state. In order to obtain an adjustable specific-heat ratio, a constant related to the specific-heat ratio is introduced into the equilibrium energy distribution function. Two different coupled double-distribution-function lattice Boltzmann models are also proposed in the paper. Numerical simulations are performed for the Riemann problem, the double-Mach-reflection problem, and the Couette flow with a range of specific-heat ratios and Prandtl numbers. The numerical results are found to be in excellent agreement with analytical and/or other solutions.

Equations of motion for massive spin 2 field coupled to gravity

International Nuclear Information System (INIS)

Buchbinder, I.L.; Gitman, D.M.; Krykhtin, V.A.; Pershin, V.D.

2000-01-01

We investigate the problems of consistency and causality for the equations of motion describing massive spin two field in external gravitational and massless scalar dilaton fields in arbitrary spacetime dimension. From the field theoretical point of view we consider a general classical action with non-minimal couplings and find gravitational and dilaton background on which this action describes a theory consistent with the flat space limit. In the case of pure gravitational background all field components propagate causally. We show also that the massive spin two field can be consistently described in arbitrary background by means of the lagrangian representing an infinite series in the inverse mass. Within string theory we obtain equations of motion for the massive spin two field coupled to gravity from the requirement of quantum Weyl invariance of the corresponding two-dimensional sigma-model. In the lowest order in α' we demonstrate that these effective equations of motion coincide with consistent equations derived in field theory

Equations of motion for massive spin 2 field coupled to gravity

Energy Technology Data Exchange (ETDEWEB)

Buchbinder, I.L. E-mail: ilb@mail.tomsknet.ru; Gitman, D.M. E-mail: gitman@fma.if.usp.br; Krykhtin, V.A. E-mail: krykhtin@phys.dfe.tpu.edu.ru; Pershin, V.D. E-mail: pershin@ic.tsu.ru

2000-09-18

We investigate the problems of consistency and causality for the equations of motion describing massive spin two field in external gravitational and massless scalar dilaton fields in arbitrary spacetime dimension. From the field theoretical point of view we consider a general classical action with non-minimal couplings and find gravitational and dilaton background on which this action describes a theory consistent with the flat space limit. In the case of pure gravitational background all field components propagate causally. We show also that the massive spin two field can be consistently described in arbitrary background by means of the lagrangian representing an infinite series in the inverse mass. Within string theory we obtain equations of motion for the massive spin two field coupled to gravity from the requirement of quantum Weyl invariance of the corresponding two-dimensional sigma-model. In the lowest order in {alpha}' we demonstrate that these effective equations of motion coincide with consistent equations derived in field theory.

Discrete integrable couplings associated with Toda-type lattice and two hierarchies of discrete soliton equations

International Nuclear Information System (INIS)

Zhang Yufeng; Fan Engui; Zhang Yongqing

2006-01-01

With the help of two semi-direct sum Lie algebras, an efficient way to construct discrete integrable couplings is proposed. As its applications, the discrete integrable couplings of the Toda-type lattice equations are obtained. The approach can be devoted to establishing other discrete integrable couplings of the discrete lattice integrable hierarchies of evolution equations

Some results on the neutron transport and the coupling of equations; Quelques resultats sur le transport neutronique et le couplage d`equations

Energy Technology Data Exchange (ETDEWEB)

Bal, G. [Electricite de France (EDF), Direction des Etudes et Recherches, 92 - Clamart (France)

1997-12-31

Neutron transport in nuclear reactors is well modeled by the linear Boltzmann transport equation. Its resolution is relatively easy but very expensive. To achieve whole core calculations, one has to consider simpler models, such as diffusion or homogeneous transport equations. However, the solutions may become inaccurate in particular situations (as accidents for instance). That is the reason why we wish to solve the equations on small area accurately and more coarsely on the remaining part of the core. It is than necessary to introduce some links between different discretizations or modelizations. In this note, we give some results on the coupling of different discretizations of all degrees of freedom of the integral-differential neutron transport equation (two degrees for the angular variable, on for the energy component, and two or three degrees for spatial position respectively in 2D (cylindrical symmetry) and 3D). Two chapters are devoted to the coupling of discrete ordinates methods (for angular discretization). The first one is theoretical and shows the well posing of the coupled problem, whereas the second one deals with numerical applications of practical interest (the results have been obtained from the neutron transport code developed at the R and D, which has been modified for introducing the coupling). Next, we present the nodal scheme RTN0, used for the spatial discretization. We show well posing results for the non-coupled and the coupled problems. At the end, we deal with the coupling of energy discretizations for the multigroup equations obtained by homogenization. Some theoretical results of the discretization of the velocity variable (well-posing of problems), which do not deal directly with the purposes of coupling, are presented in the annexes. (author). 34 refs.

Continuous limits for an integrable coupling system of Toda equation hierarchy

International Nuclear Information System (INIS)

Li Li; Yu Fajun

2009-01-01

In this Letter, we present an integrable coupling system of lattice hierarchy and its continuous limits by using of Lie algebra sl(4). By introducing a complex discrete spectral problem, the integrable coupling system of Toda lattice hierarchy is derived. It is shown that a new complex lattice spectral problem converges to the integrable couplings of discrete soliton equation hierarchy, which has the integrable coupling system of C-KdV hierarchy as a new kind of continuous limit.

Continuous limits for an integrable coupling system of Toda equation hierarchy

Energy Technology Data Exchange (ETDEWEB)

Li Li [College of Maths and Systematic Science, Shenyang Normal University, Shenyang 110034 (China); Yu Fajun, E-mail: yfajun@163.co [College of Maths and Systematic Science, Shenyang Normal University, Shenyang 110034 (China)

2009-09-21

In this Letter, we present an integrable coupling system of lattice hierarchy and its continuous limits by using of Lie algebra sl(4). By introducing a complex discrete spectral problem, the integrable coupling system of Toda lattice hierarchy is derived. It is shown that a new complex lattice spectral problem converges to the integrable couplings of discrete soliton equation hierarchy, which has the integrable coupling system of C-KdV hierarchy as a new kind of continuous limit.

Coupled latent differential equation with moderators: simulation and application.

Science.gov (United States)

Hu, Yueqin; Boker, Steve; Neale, Michael; Klump, Kelly L

2014-03-01

Latent differential equations (LDE) use differential equations to analyze time series data. Because of the recent development of this technique, some issues critical to running an LDE model remain. In this article, the authors provide solutions to some of these issues and recommend a step-by-step procedure demonstrated on a set of empirical data, which models the interaction between ovarian hormone cycles and emotional eating. Results indicated that emotional eating is self-regulated. For instance, when people do more emotional eating than normal, they will subsequently tend to decrease their emotional eating behavior. In addition, a sudden increase will produce a stronger tendency to decrease than will a slow increase. We also found that emotional eating is coupled with the cycle of the ovarian hormone estradiol, and the peak of emotional eating occurs after the peak of estradiol. The self-reported average level of negative affect moderates the frequency of eating regulation and the coupling strength between eating and estradiol. Thus, people with a higher average level of negative affect tend to fluctuate faster in emotional eating, and their eating behavior is more strongly coupled with the hormone estradiol. Permutation tests on these empirical data supported the reliability of using LDE models to detect self-regulation and a coupling effect between two regulatory behaviors. (c) 2014 APA, all rights reserved.

Test equating, scaling, and linking methods and practices

CERN Document Server

Kolen, Michael J

2014-01-01

This book provides an introduction to test equating, scaling, and linking, including those concepts and practical issues that are critical for developers and all other testing professionals.  In addition to statistical procedures, successful equating, scaling, and linking involves many aspects of testing, including procedures to develop tests, to administer and score tests, and to interpret scores earned on tests. Test equating methods are used with many standardized tests in education and psychology to ensure that scores from multiple test forms can be used interchangeably.  Test scaling is the process of developing score scales that are used when scores on standardized tests are reported. In test linking, scores from two or more tests are related to one another. Linking has received much recent attention, due largely to investigations of linking similarly named tests from different test publishers or tests constructed for different purposes. In recent years, researchers from the education, psychology, and...

Fractional dynamic calculus and fractional dynamic equations on time scales

CERN Document Server

Georgiev, Svetlin G

2018-01-01

Pedagogically organized, this monograph introduces fractional calculus and fractional dynamic equations on time scales in relation to mathematical physics applications and problems. Beginning with the definitions of forward and backward jump operators, the book builds from Stefan Hilger’s basic theories on time scales and examines recent developments within the field of fractional calculus and fractional equations. Useful tools are provided for solving differential and integral equations as well as various problems involving special functions of mathematical physics and their extensions and generalizations in one and more variables. Much discussion is devoted to Riemann-Liouville fractional dynamic equations and Caputo fractional dynamic equations.  Intended for use in the field and designed for students without an extensive mathematical background, this book is suitable for graduate courses and researchers looking for an introduction to fractional dynamic calculus and equations on time scales. .

Innovation diffusion equations on correlated scale-free networks

Energy Technology Data Exchange (ETDEWEB)

Bertotti, M.L., E-mail: marialetizia.bertotti@unibz.it [Free University of Bozen–Bolzano, Faculty of Science and Technology, Bolzano (Italy); Brunner, J., E-mail: johannes.brunner@tis.bz.it [TIS Innovation Park, Bolzano (Italy); Modanese, G., E-mail: giovanni.modanese@unibz.it [Free University of Bozen–Bolzano, Faculty of Science and Technology, Bolzano (Italy)

2016-07-29

Highlights: • The Bass diffusion model can be formulated on scale-free networks. • In the trickle-down version, the hubs adopt earlier and act as monitors. • We improve the equations in order to describe trickle-up diffusion. • Innovation is generated at the network periphery, and hubs can act as stiflers. • We compare diffusion times, in dependence on the scale-free exponent. - Abstract: We introduce a heterogeneous network structure into the Bass diffusion model, in order to study the diffusion times of innovation or information in networks with a scale-free structure, typical of regions where diffusion is sensitive to geographic and logistic influences (like for instance Alpine regions). We consider both the diffusion peak times of the total population and of the link classes. In the familiar trickle-down processes the adoption curve of the hubs is found to anticipate the total adoption in a predictable way. In a major departure from the standard model, we model a trickle-up process by introducing heterogeneous publicity coefficients (which can also be negative for the hubs, thus turning them into stiflers) and a stochastic term which represents the erratic generation of innovation at the periphery of the network. The results confirm the robustness of the Bass model and expand considerably its range of applicability.

Innovation diffusion equations on correlated scale-free networks

International Nuclear Information System (INIS)

Bertotti, M.L.; Brunner, J.; Modanese, G.

2016-01-01

Highlights: • The Bass diffusion model can be formulated on scale-free networks. • In the trickle-down version, the hubs adopt earlier and act as monitors. • We improve the equations in order to describe trickle-up diffusion. • Innovation is generated at the network periphery, and hubs can act as stiflers. • We compare diffusion times, in dependence on the scale-free exponent. - Abstract: We introduce a heterogeneous network structure into the Bass diffusion model, in order to study the diffusion times of innovation or information in networks with a scale-free structure, typical of regions where diffusion is sensitive to geographic and logistic influences (like for instance Alpine regions). We consider both the diffusion peak times of the total population and of the link classes. In the familiar trickle-down processes the adoption curve of the hubs is found to anticipate the total adoption in a predictable way. In a major departure from the standard model, we model a trickle-up process by introducing heterogeneous publicity coefficients (which can also be negative for the hubs, thus turning them into stiflers) and a stochastic term which represents the erratic generation of innovation at the periphery of the network. The results confirm the robustness of the Bass model and expand considerably its range of applicability.

Nonlinear tunneling of optical soliton in 3 coupled NLS equation with symbolic computation

Energy Technology Data Exchange (ETDEWEB)

Mani Rajan, M.S., E-mail: senthilmanirajanofc@gmail.com [Department of Physics, Anna University, Madurai Region, Ramanathapuram (India); Mahalingam, A. [Department of Physics, Anna University, Chennai - 600 025 (India); Uthayakumar, A. [Department of Physics, Presidency College, Chennai - 600 005 (India)

2014-07-15

We investigated the soliton solution for N coupled nonlinear Schrödinger (CNLS) equations. These equations are coupled due to the cross-phase-modulation (CPM). Lax pair of this system is obtained via the Ablowitz–Kaup–Newell–Segur (AKNS) scheme and the corresponding Darboux transformation is constructed to derive the soliton solution. One and two soliton solutions are generated. Using two soliton solutions of 3 CNLS equation, nonlinear tunneling of soliton for both with and without exponential background has been discussed. Finally cascade compression of optical soliton through multi-nonlinear barrier has been discussed. The obtained results may have promising applications in all-optical devices based on optical solitons, study of soliton propagation in birefringence fiber systems and optical soliton with distributed dispersion and nonlinearity management. -- Highlights: •We consider the nonlinear tunneling of soliton in birefringence fiber. •3-coupled NLS (CNLS) equation with variable coefficients is considered. •Two soliton solutions are obtained via Darboux transformation using constructed Lax pair. •Soliton tunneling through dispersion barrier and well are investigated. •Finally, cascade compression of soliton has been achieved.

Multiple positive solutions to a coupled systems of nonlinear fractional differential equations.

Science.gov (United States)

Shah, Kamal; Khan, Rahmat Ali

2016-01-01

In this article, we study existence, uniqueness and nonexistence of positive solution to a highly nonlinear coupled system of fractional order differential equations. Necessary and sufficient conditions for the existence and uniqueness of positive solution are developed by using Perov's fixed point theorem for the considered problem. Further, we also established sufficient conditions for existence of multiplicity results for positive solutions. Also, we developed some conditions under which the considered coupled system of fractional order differential equations has no positive solution. Appropriate examples are also provided which demonstrate our results.

On Coupled System of Navier-Stokes Equations and Temperature

African Journals Online (AJOL)

Dr. Anthony Peter

ABSTRACT. This paper deals with the coupled system of Navier-Stokes equations and temperature (Thermohydraulics) in a strip in the class of spatially non-decaying (infinite-energy) solutions belonging to the properly chosen uniformly local Sobolev spaces. The global well-posedness and dissipativity of the Navier- ...

Similarity transformed equation of motion coupled-cluster theory based on an unrestricted Hartree-Fock reference for applications to high-spin open-shell systems.

Science.gov (United States)

Huntington, Lee M J; Krupička, Martin; Neese, Frank; Izsák, Róbert

2017-11-07

The similarity transformed equation of motion coupled-cluster approach is extended for applications to high-spin open-shell systems, within the unrestricted Hartree-Fock (UHF) formalism. An automatic active space selection scheme has also been implemented such that calculations can be performed in a black-box fashion. It is observed that both the canonical and automatic active space selecting similarity transformed equation of motion (STEOM) approaches perform about as well as the more expensive equation of motion coupled-cluster singles doubles (EOM-CCSD) method for the calculation of the excitation energies of doublet radicals. The automatic active space selecting UHF STEOM approach can therefore be employed as a viable, lower scaling alternative to UHF EOM-CCSD for the calculation of excited states in high-spin open-shell systems.

Similarity transformed equation of motion coupled-cluster theory based on an unrestricted Hartree-Fock reference for applications to high-spin open-shell systems

Science.gov (United States)

Huntington, Lee M. J.; Krupička, Martin; Neese, Frank; Izsák, Róbert

2017-11-01

The similarity transformed equation of motion coupled-cluster approach is extended for applications to high-spin open-shell systems, within the unrestricted Hartree-Fock (UHF) formalism. An automatic active space selection scheme has also been implemented such that calculations can be performed in a black-box fashion. It is observed that both the canonical and automatic active space selecting similarity transformed equation of motion (STEOM) approaches perform about as well as the more expensive equation of motion coupled-cluster singles doubles (EOM-CCSD) method for the calculation of the excitation energies of doublet radicals. The automatic active space selecting UHF STEOM approach can therefore be employed as a viable, lower scaling alternative to UHF EOM-CCSD for the calculation of excited states in high-spin open-shell systems.

New Iterative Method for Fractional Gas Dynamics and Coupled Burger’s Equations

Directory of Open Access Journals (Sweden)

Mohamed S. Al-luhaibi

2015-01-01

Full Text Available This paper presents the approximate analytical solutions to solve the nonlinear gas dynamics and coupled Burger’s equations with fractional time derivative. By using initial values, the explicit solutions of the equations are solved by using a reliable algorithm. Numerical results show that the new iterative method is easy to implement and accurate when applied to time-fractional partial differential equations.

Method of constructing a fundamental equation of state based on a scaling hypothesis

Science.gov (United States)

Rykov, V. A.; Rykov, S. V.; Kudryavtseva, I. V.; Sverdlov, A. V.

2017-11-01

The work studies the issues associated with the construction of the equation of state (EOS) taking due account of substance behavior in the critical region and associated with the scaling theory of critical phenomena (ST). The authors have developed a new version of the scaling hypothesis; this approach uses the following: a) substance equation of state having a form of a Schofield-Litster-Ho linear model (LM) and b) the Benedek hypothesis. The Benedek hypothesis has found a similar behavior character for a number of properties (isochoric and isobaric heat capacities, isothermal compressibility coefficient) at critical and near-critical isochors in the vicinity of the critical point. A method is proposed to build the fundamental equation of state (FEOS) which satisfies the ST power laws. The FEOS building method is verified by building the equation of state for argon within the state parameters range: up to 1000 MPa in terms of pressure, and from 83.056 К to 13000 К in terms of temperature. The executed comparison with the fundamental equations of state of Stewart-Jacobsen (1989), of Kozlov at al (1996), of Tegeler-Span-Wagner (1999), of has shown that the FEOS describes the known experimental data with an essentially lower error.

Formulation and application of optimal homotopty asymptotic method to coupled differential-difference equations.

Science.gov (United States)

Ullah, Hakeem; Islam, Saeed; Khan, Ilyas; Shafie, Sharidan; Fiza, Mehreen

2015-01-01

In this paper we applied a new analytic approximate technique Optimal Homotopy Asymptotic Method (OHAM) for treatment of coupled differential-difference equations (DDEs). To see the efficiency and reliability of the method, we consider Relativistic Toda coupled nonlinear differential-difference equation. It provides us a convenient way to control the convergence of approximate solutions when it is compared with other methods of solution found in the literature. The obtained solutions show that OHAM is effective, simpler, easier and explicit.

Multiple spatial scaling and the weak coupling approximation. II. Homogeneous kinetic equation

Energy Technology Data Exchange (ETDEWEB)

Kleinsmith, P E [Carnegie-Mellon Univ., Pittsburgh, Pa. (USA)

1977-08-01

A modified form of the Bogoliubov plasma cluster expansion is applied to the derivation of a divergence-free kinetic equation from the BBGKY hierarchy. Special attention is given to the conditions under which the Landau kinetic equation may be derived from this more general formulation.

Two-scale approach to oscillatory singularly perturbed transport equations

CERN Document Server

Frénod, Emmanuel

2017-01-01

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

Novel algorithm of large-scale simultaneous linear equations

International Nuclear Information System (INIS)

Fujiwara, T; Hoshi, T; Yamamoto, S; Sogabe, T; Zhang, S-L

2010-01-01

We review our recently developed methods of solving large-scale simultaneous linear equations and applications to electronic structure calculations both in one-electron theory and many-electron theory. This is the shifted COCG (conjugate orthogonal conjugate gradient) method based on the Krylov subspace, and the most important issue for applications is the shift equation and the seed switching method, which greatly reduce the computational cost. The applications to nano-scale Si crystals and the double orbital extended Hubbard model are presented.

An inexact Newton method for fully-coupled solution of the Navier-Stokes equations with heat and mass transport

Energy Technology Data Exchange (ETDEWEB)

Shadid, J.N.; Tuminaro, R.S. [Sandia National Labs., Albuquerque, NM (United States); Walker, H.F. [Utah State Univ., Logan, UT (United States). Dept. of Mathematics and Statistics

1997-02-01

The solution of the governing steady transport equations for momentum, heat and mass transfer in flowing fluids can be very difficult. These difficulties arise from the nonlinear, coupled, nonsymmetric nature of the system of algebraic equations that results from spatial discretization of the PDEs. In this manuscript the authors focus on evaluating a proposed nonlinear solution method based on an inexact Newton method with backtracking. In this context they use a particular spatial discretization based on a pressure stabilized Petrov-Galerkin finite element formulation of the low Mach number Navier-Stokes equations with heat and mass transport. The discussion considers computational efficiency, robustness and some implementation issues related to the proposed nonlinear solution scheme. Computational results are presented for several challenging CFD benchmark problems as well as two large scale 3D flow simulations.

Modified cable equation incorporating transverse polarization of neuronal membranes for accurate coupling of electric fields.

Science.gov (United States)

Wang, Boshuo; Aberra, Aman S; Grill, Warren M; Peterchev, Angel V

2018-04-01

We present a theory and computational methods to incorporate transverse polarization of neuronal membranes into the cable equation to account for the secondary electric field generated by the membrane in response to transverse electric fields. The effect of transverse polarization on nonlinear neuronal activation thresholds is quantified and discussed in the context of previous studies using linear membrane models. The response of neuronal membranes to applied electric fields is derived under two time scales and a unified solution of transverse polarization is given for spherical and cylindrical cell geometries. The solution is incorporated into the cable equation re-derived using an asymptotic model that separates the longitudinal and transverse dimensions. Two numerical methods are proposed to implement the modified cable equation. Several common neural stimulation scenarios are tested using two nonlinear membrane models to compare thresholds of the conventional and modified cable equations. The implementations of the modified cable equation incorporating transverse polarization are validated against previous results in the literature. The test cases show that transverse polarization has limited effect on activation thresholds. The transverse field only affects thresholds of unmyelinated axons for short pulses and in low-gradient field distributions, whereas myelinated axons are mostly unaffected. The modified cable equation captures the membrane's behavior on different time scales and models more accurately the coupling between electric fields and neurons. It addresses the limitations of the conventional cable equation and allows sound theoretical interpretations. The implementation provides simple methods that are compatible with current simulation approaches to study the effect of transverse polarization on nonlinear membranes. The minimal influence by transverse polarization on axonal activation thresholds for the nonlinear membrane models indicates that

Systematic analysis of scaling properties in deep inelastic scattering

International Nuclear Information System (INIS)

Beuf, Guillaume; Peschanski, Robi; Royon, Christophe; Salek, David

2008-01-01

Using the 'quality factor' method, we analyze the scaling properties of deep inelastic processes at the accelerator HERA and fixed target experiments for x≤10 -2 . We look for scaling formulas of the form σ γ * p (τ), where τ(L=logQ 2 ,Y) is a scaling variable suggested by the asymptotic properties of QCD evolution equations with rapidity Y. We consider four cases: 'fixed coupling', corresponding to the original geometric scaling proposal and motivated by the asymptotic properties of the Balitsky-Kovchegov equation with fixed QCD coupling constant; two versions, 'running coupling I, II,' of the scaling suggested by the Balitsky-Kovchegov equation with running coupling; and 'diffusive scaling' suggested by the QCD evolution equation with Pomeron loops. The quality factors, quantifying the phenomenological validity of the candidate scaling variables, are fitted on the total and deeply virtual Compton scattering cross-section data from HERA and predictions are made for the elastic vector meson and for the diffractive cross sections at fixed small x P or β. The first three scaling formulas have comparably good quality factors while the fourth one is disfavored. Adjusting initial conditions gives a significant improvement of the running coupling II scaling.

Formulation and Application of Optimal Homotopty Asymptotic Method to Coupled Differential - Difference Equations

Science.gov (United States)

Ullah, Hakeem; Islam, Saeed; Khan, Ilyas; Shafie, Sharidan; Fiza, Mehreen

2015-01-01

In this paper we applied a new analytic approximate technique Optimal Homotopy Asymptotic Method (OHAM) for treatment of coupled differential- difference equations (DDEs). To see the efficiency and reliability of the method, we consider Relativistic Toda coupled nonlinear differential-difference equation. It provides us a convenient way to control the convergence of approximate solutions when it is compared with other methods of solution found in the literature. The obtained solutions show that OHAM is effective, simpler, easier and explicit. PMID:25874457

Improvement of the symbolic Monte-Carlo method for the transport equation: P1 extension and coupling with diffusion

International Nuclear Information System (INIS)

Clouet, J.F.; Samba, G.

2005-01-01

We use asymptotic analysis to study the diffusion limit of the Symbolic Implicit Monte-Carlo (SIMC) method for the transport equation. For standard SIMC with piecewise constant basis functions, we demonstrate mathematically that the solution converges to the solution of a wrong diffusion equation. Nevertheless a simple extension to piecewise linear basis functions enables to obtain the correct solution. This improvement allows the calculation in opaque medium on a mesh resolving the diffusion scale much larger than the transport scale. Anyway, the huge number of particles which is necessary to get a correct answer makes this computation time consuming. Thus, we have derived from this asymptotic study an hybrid method coupling deterministic calculation in the opaque medium and Monte-Carlo calculation in the transparent medium. This method gives exactly the same results as the previous one but at a much lower price. We present numerical examples which illustrate the analysis. (authors)

Bright solitons in coupled defocusing NLS equation supported by coupling: Application to Bose-Einstein condensation

International Nuclear Information System (INIS)

Adhikari, Sadhan K.

2005-01-01

We demonstrate the formation of bright solitons in coupled self-defocusing nonlinear Schroedinger (NLS) equation supported by attractive coupling. As an application we use a time-dependent dynamical mean-field model to study the formation of stable bright solitons in two-component repulsive Bose-Einstein condensates (BECs) supported by interspecies attraction in a quasi one-dimensional geometry. When all interactions are repulsive, there cannot be bright solitons. However, bright solitons can be formed in two-component repulsive BECs for a sufficiently attractive interspecies interaction, which induces an attractive effective interaction among bosons of same type

BSDES IN GAMES, COUPLED WITH THE VALUE FUNCTIONS.ASSOCIATED NONLOCAL BELLMAN-ISAACS EQUATIONS

Institute of Scientific and Technical Information of China (English)

Tao HAO; Juan LI

2017-01-01

We establish a new type of backward stochastic differential equations (BSDEs) connected with stochastic differential games (SDGs),namely,BSDEs strongly coupled with the lower and the upper value functions of SDGs,where the lower and the upper value functions are defined through this BSDE.The existence and the uniqueness theorem and comparison theorem are proved for such equations with the help of an iteration method.We also show that the lower and the upper value functions satisfy the dynamic programming principle.Moreover,we study the associated Hamilton-Jacobi-Bellman-Isaacs (HJB-Isaacs) equations,which are nonlocal,and strongly coupled with the lower and the upper value functions.Using a new method,we characterize the pair (W,U) consisting of the lower and the upper value functions as the unique viscosity solution of our nonlocal HJB-Isaacs equation.Furthermore,the game has a value under the Isaacs' condition.

Solution of the Helmholtz-Poincare Wave Equation using the coupled boundary integral equations and optimal surface eigenfunctions

International Nuclear Information System (INIS)

Werby, M.F.; Broadhead, M.K.; Strayer, M.R.; Bottcher, C.

1992-01-01

The Helmholtz-Poincarf Wave Equation (H-PWE) arises in many areas of classical wave scattering theory. In particular it can be found for the cases of acoustical scattering from submerged bounded objects and electromagnetic scattering from objects. The extended boundary integral equations (EBIE) method is derived from considering both the exterior and interior solutions of the H-PWECs. This coupled set of expressions has the advantage of not only offering a prescription for obtaining a solution for the exterior scattering problem, but it also obviates the problem of irregular values corresponding to fictitious interior eigenvalues. Once the coupled equations are derived, they can be obtained in matrix form by expanding all relevant terms in partial wave expansions, including a bi-orthogonal expansion of the Green's function. However some freedom in the choice of the surface expansion is available since the unknown surface quantities may be expanded in a variety of ways so long as closure is obtained. Out of many possible choices, we develop an optimal method to obtain such expansions which is based on the optimum eigenfunctions related to the surface of the object. In effect, we convert part of the problem (that associated with the Fredholms integral equation of the first kind) an eigenvalue problem of a related Hermitian operator. The methodology will be explained in detail and examples will be presented

A polynomial expansion method and its application in the coupled Zakharov-Kuznetsov equations

International Nuclear Information System (INIS)

Huang Wenhua

2006-01-01

A polynomial expansion method is presented to solve nonlinear evolution equations. Applying this method, the coupled Zakharov-Kuznetsov equations in fluid system are studied and many exact travelling wave solutions are obtained. These solutions include solitary wave solutions, periodic solutions and rational type solutions

A Multi-Scale Method for Dynamics Simulation in Continuum Solvent Models I: Finite-Difference Algorithm for Navier-Stokes Equation.

Science.gov (United States)

Xiao, Li; Cai, Qin; Li, Zhilin; Zhao, Hongkai; Luo, Ray

2014-11-25

A multi-scale framework is proposed for more realistic molecular dynamics simulations in continuum solvent models by coupling a molecular mechanics treatment of solute with a fluid mechanics treatment of solvent. This article reports our initial efforts to formulate the physical concepts necessary for coupling the two mechanics and develop a 3D numerical algorithm to simulate the solvent fluid via the Navier-Stokes equation. The numerical algorithm was validated with multiple test cases. The validation shows that the algorithm is effective and stable, with observed accuracy consistent with our design.

Length scales for the Navier-Stokes equations on a rotating sphere

International Nuclear Information System (INIS)

Kyrychko, Yuliya N.; Bartuccelli, Michele V.

2004-01-01

In this Letter we obtain the dissipative length scale for the Navier-Stokes equations on a two-dimensional rotating sphere S 2 . This system is a fundamental model of the large scale atmospheric dynamics. Using the equations of motion in their vorticity form, we construct the ladder inequalities from which a set of time-averaged length scales is obtained

Scale-up of precipitation processes

OpenAIRE

Zauner, R.

1999-01-01

This thesis concerns the scale-up of precipitation processes aimed at predicting product particle characteristics. Although precipitation is widely used in the chemical and pharmaceutical industry, successful scale-up is difficult due to the absence of a validated methodology. It is found that none of the conventional scale-up criteria reported in the literature (equal power input per unit mass, equal tip speed, equal stirring rate) is capable of predicting the experimentally o...

Renormalization group analysis of the temperature dependent coupling constant in massless theory

International Nuclear Information System (INIS)

Yamada, Hirofumi.

1987-06-01

A general analysis of finite temperature renormalization group equations for massless theories is presented. It is found that in a direction where momenta and temperature are scaled up with their ratio fixed the coupling constant behaves in the same manner as in zero temperature and that asymptotic freedom at short distances is also maintained at finite temperature. (author)

The fractional coupled KdV equations: Exact solutions and white noise functional approach

International Nuclear Information System (INIS)

Ghany, Hossam A.; El Bab, A. S. Okb; Zabel, A. M.; Hyder, Abd-Allah

2013-01-01

Variable coefficients and Wick-type stochastic fractional coupled KdV equations are investigated. By using the modified fractional sub-equation method, Hermite transform, and white noise theory the exact travelling wave solutions and white noise functional solutions are obtained, including the generalized exponential, hyperbolic, and trigonometric types. (general)

Equation of state of strongly coupled plasma mixtures

International Nuclear Information System (INIS)

DeWitt, H.E.

1984-01-01

Thermodynamic properties of strongly coupled (high density) plasmas of mixtures of light elements have been obtained by Monte Carlo simulations. For an assumed uniform charge background the equation of state of ionic mixtures is a simple extension of the one-component plasma EOS. More realistic electron screening effects are treated in linear response theory and with an appropriate electron dielectric function. Results have been obtained for the ionic pair distribution functions, and for the electric microfield distribution

Modeling erosion and sedimentation coupled with hydrological and overland flow processes at the watershed scale

Science.gov (United States)

Kim, Jongho; Ivanov, Valeriy Y.; Katopodes, Nikolaos D.

2013-09-01

A novel two-dimensional, physically based model of soil erosion and sediment transport coupled to models of hydrological and overland flow processes has been developed. The Hairsine-Rose formulation of erosion and deposition processes is used to account for size-selective sediment transport and differentiate bed material into original and deposited soil layers. The formulation is integrated within the framework of the hydrologic and hydrodynamic model tRIBS-OFM, Triangulated irregular network-based, Real-time Integrated Basin Simulator-Overland Flow Model. The integrated model explicitly couples the hydrodynamic formulation with the advection-dominated transport equations for sediment of multiple particle sizes. To solve the system of equations including both the Saint-Venant and the Hairsine-Rose equations, the finite volume method is employed based on Roe's approximate Riemann solver on an unstructured grid. The formulation yields space-time dynamics of flow, erosion, and sediment transport at fine scale. The integrated model has been successfully verified with analytical solutions and empirical data for two benchmark cases. Sensitivity tests to grid resolution and the number of used particle sizes have been carried out. The model has been validated at the catchment scale for the Lucky Hills watershed located in southeastern Arizona, USA, using 10 events for which catchment-scale streamflow and sediment yield data were available. Since the model is based on physical laws and explicitly uses multiple types of watershed information, satisfactory results were obtained. The spatial output has been analyzed and the driving role of topography in erosion processes has been discussed. It is expected that the integrated formulation of the model has the promise to reduce uncertainties associated with typical parameterizations of flow and erosion processes. A potential for more credible modeling of earth-surface processes is thus anticipated.

Dark and composite rogue waves in the coupled Hirota equations

International Nuclear Information System (INIS)

Chen, Shihua

2014-01-01

The intriguing dark and composite rogue wave dynamics in a coupled Hirota system are unveiled, based on the exact explicit rational solutions obtained under the assumption of equal background height. It is found that a dark rogue wave state would occur as a result of the strong coupling between two field components with large wavenumber difference, and there would appear plenty of composite structures that are attributed to the specific wavenumber difference and the free choice of three independent structural parameters. The coexistence of different fundamental rogue waves in such a coupled system is also demonstrated. - Highlights: • Exact rational rogue wave solutions under different parameter conditions are presented for the coupled Hirota equations. • The basic rogue wave features and hence the intriguing dark structures are unveiled. • We attributed the diversity of composite rogue wave dynamics to the free choice of three independent structural parameters. • The remarkable coexisting rogue wave behaviors in such a coupled system are demonstrated

Self-consistent calculation of the coupling constant in the Gross-Pitaevskii equation

International Nuclear Information System (INIS)

Cherny, A.Yu.; Brand, J.

2004-01-01

A method is proposed for a self-consistent evaluation of the coupling constant in the Gross-Pitaevskii equation without involving a pseudopotential replacement. A renormalization of the coupling constant occurs due to medium effects and the trapping potential, e.g., in quasi-1D or quasi-2D systems. It is shown that a simplified version of the Hartree-Fock-Bogoliubov approximation leads to a variational problem for both the condensate and a two-body wave function describing the behavior of a pair of bosons in the Bose-Einstein condensate. The resulting coupled equations are free of unphysical divergences. Particular cases of this scheme that admit analytical estimations are considered and compared to the literature. In addition to the well-known cases of low-dimensional trapping, crossover regimes can be studied. The values of the kinetic, interaction, external, and release energies in low dimensions are also evaluated and contributions due to short-range correlations are found to be substantial

Exact master equation for a noncommutative Brownian particle

International Nuclear Information System (INIS)

Costa Dias, Nuno; Nuno Prata, Joao

2009-01-01

We derive the Hu-Paz-Zhang master equation for a Brownian particle linearly coupled to a bath of harmonic oscillators on the plane with spatial noncommutativity. The results obtained are exact to all orders in the noncommutative parameter. As a by-product we derive some miscellaneous results such as the equilibrium Wigner distribution for the reservoir of noncommutative oscillators, the weak coupling limit of the master equation and a set of sufficient conditions for strict purity decrease of the Brownian particle. Finally, we consider a high-temperature Ohmic model and obtain an estimate for the time scale of the transition from noncommutative to ordinary quantum mechanics. This scale is considerably smaller than the decoherence scale

Dressed skeleton expansion and the coupling scale ambiguity problem

International Nuclear Information System (INIS)

Lu, Hung Jung.

1992-09-01

Perturbative expansions in quantum field theories are usually expressed in powers of a coupling constant. In principle, the infinite sum of the expansion series is independent of the renormalization scale of the coupling constant. In practice, there is a remnant dependence of the truncated series on the renormalization scale. This scale ambiguity can severely restrict the predictive power of theoretical calculations. The dressed skeleton expansion is developed as a calculational method which avoids the coupling scale ambiguity problem. In this method, physical quantities are expressed as functional expansions in terms of a coupling vertex function. The arguments of the vertex function are given by the physical momenta of each process. These physical momenta effectively replace the unspecified renormalization scale and eliminate the ambiguity problem. This method is applied to various field theoretical models and its main features and limitations are explored. For quantum chromodynamics, an expression for the running coupling constant of the three-gluon vertex is obtained. The effective coupling scale of this vertex is shown to be essentially given by μ 2 ∼ Q min 2 Q med 2 /Q max 2 where Q min 2 Q med 2 /Q max 2 are respectively the smallest, the next-to-smallest and the largest scale among the three gluon virtualities. This functional form suggests that the three-gluon vertex becomes non-perturbative at asymmetric momentum configurations. Implications for four-jet physics is discussed

Reallocating risks and returns to scale up adoption of distributed electricity resources

International Nuclear Information System (INIS)

Kulatilaka, Nalin; Santiago, Leonardo; Vakili, Pirooz

2014-01-01

Deployment of distributed electricity resources requires bringing together assets that belong to diverse and geographically diffuse owners. Using the example of distributed solar PV, we analyze the schemes used to encourage/induce owners of distributed assets to make them available for electricity generation. The dominant model in the U.S. is long term power purchase agreements (PPA) offered to owners/consumers by solar developers. We show that these agreements (mis)allocate the electricity price risk to owners/consumers and impose limitations on the scale up of distributed solar. By proper use of financial markets it is possible to shift the electricity price risk from owners/consumers to parties that are better positioned to manage it. The proposed contracts simplify the adoption decision for owners/consumers and can lead to a wider adoption. Removing barriers to scale up requires (i) eliminating the tight coupling between consumers and owners and (ii) rewarding the owners unambiguously for the assets they provide. These necessitate the transformation of the current intermediary firms into full-fledged distributed generators. We discuss the implications of such a transformation and argue that the broad outline of our analysis can be used to assess scale up schemes in other domains of distributed electricity resources as well. - Highlights: • We analyze schemes used to induce owners of distributed assets to make them available for electricity generation. • We show that power purchase agreements used in solar PV “misallocate” electricity price risk to owners/consumers. • We propose new contracts forms that shift price risk from consumers to parties that are better able to manage it. • Full-fledged distributed generators are created by unambiguously rewarding owners and de-coupling consumption/ownership. • We argue that our analysis can be used to assess scale up schemes in other domains of distributed electricity resources

Scaled equation of state parameters for gases in the critical region

Science.gov (United States)

Sengers, J. M. H. L.; Greer, W. L.; Sengers, J. V.

1976-01-01

In the light of recent theoretical developments, the paper presents an accurate characterization of anomalous thermodynamic behavior of xenon, helium 4, helium 3, carbon dioxide, steam and oxygen in the critical region. This behavior is associated with long range fluctuations in the system and the physical properties depend primarily on a single variable, namely, the correlation length. A description of the thermodynamic behavior of fluids in terms of scaling laws is formulated, and the two successfully used scaled equations of state (NBS equation and Linear Model parametric equation) are compared. Methods for fitting both equations to experimental equation of state data are developed and formulated, and the optimum fit for each of the two scaled equations of the above gases are presented and the results are compared. By extending the experimental data for the above one-component fluids to partially miscible binary liquids, superfluid liquid helium, ferromagnets and solids exhibiting order-disorder transitions, the principle of universality is concluded. Finally by using this principle, the critical regions for nine additional fluids are described.

Problem on primary radiation filtration effect on form of coupling equations during X-ray fluorescence analysis

International Nuclear Information System (INIS)

Lavrent'ev, Yu.G.; Kuznetsova, A.I.

1976-01-01

A simplified method for x-ray fluorescence analysis is given. It is shown that the system of coupling equations with constant coefficients and with the number of equations equal to the number of unknown elements allows to obtain the same accuracy of the analysis as with the considerably more complex equations with variable coefficients which take into account the filtration of the primary radiation in a direct way. The system can even be more simplified by using linear equations with constant coefficients. In order to test these systems and to compare them with known coupling equations experimental data for the determination of zirconium and niobium from 16 artificial preparations with fillers of variable composition are presented. The calculation of the absorption of the secondary as well as the primary radiation by means of the proposed equations with constant coefficients is sufficiently good

Some blow-up problems for a semilinear parabolic equation with a potential

Science.gov (United States)

Cheng, Ting; Zheng, Gao-Feng

The blow-up rate estimate for the solution to a semilinear parabolic equation u=Δu+V(x)|u in Ω×(0,T) with 0-Dirichlet boundary condition is obtained. As an application, it is shown that the asymptotic behavior of blow-up time and blow-up set of the problem with nonnegative initial data u(x,0)=Mφ(x) as M goes to infinity, which have been found in [C. Cortazar, M. Elgueta, J.D. Rossi, The blow-up problem for a semilinear parabolic equation with a potential, preprint, arXiv: math.AP/0607055, July 2006], is improved under some reasonable and weaker conditions compared with [C. Cortazar, M. Elgueta, J.D. Rossi, The blow-up problem for a semilinear parabolic equation with a potential, preprint, arXiv: math.AP/0607055, July 2006].

Blow up of solutions to ordinary differential equations arising in nonlinear dispersive problems

Directory of Open Access Journals (Sweden)

Milena Dimova

2018-03-01

Full Text Available We study a new class of ordinary differential equations with blow up solutions. Necessary and sufficient conditions for finite blow up time are proved. Based on the new differential equation, a revised version of the concavity method of Levine is proposed. As an application we investigate the non-existence of global solutions to the Cauchy problem of Klein-Gordon, and to the double dispersive equations. We obtain necessary and sufficient condition for finite time blow up with arbitrary positive energy. A very general sufficient condition for blow up is also given.

Formal derivation of a 6 equation macro scale model for two-phase flows - link with the 4 equation macro scale model implemented in Flica 4; Etablissement formel d'un modele diphasique macroscopique a 6 equations - lien avec le modele macroscopique a 4 equations flica 4

Energy Technology Data Exchange (ETDEWEB)

Gregoire, O

2008-07-01

In order to simulate nuclear reactor cores, we presently use the 4 equation model implemented within FLICA4 code. This model is complemented with 2 algebraic closures for thermal disequilibrium and relative velocity between phases. Using such closures, means an 'a priori' knowledge of flows calculated in order to ensure that modelling assumptions apply. In order to improve the degree of universality to our macroscopic modelling, we propose in the report to derive a more general 6 equation model (balance equations for mass, momentum and enthalpy for each phase) for 2-phase flows. We apply the up-scaling procedure (Whitaker, 1999) classically used in porous media analysis to the statistically averaged equations (Aniel-Buchheit et al., 2003). By doing this, we apply the double-averaging procedure (Pedras and De Lemos, 2001 and Pinson et al. 2006): statistical and spatial averages. Then, using weighted averages (analogous to Favre's average) we extend the spatial averaging concept to variable density and 2-phase flows. This approach allows the global recovering of the structure of the systems of equations implemented in industrial codes. Supplementary contributions, such as dispersion, are also highlighted. Mechanical and thermal exchanges between solids and fluid are formally derived. Then, thanks to realistic simplifying assumptions, we show how it is possible to derive the original 4 equation model from the full 6 equation model. (author)

ScaleUp America Communities

Data.gov (United States)

Small Business Administration — SBA’s new ScaleUp America Initiative is designed to help small firms with high potential “scale up” and grow their businesses so that they will provide more jobs and...

Blow-Up Time for Nonlinear Heat Equations with Transcendental Nonlinearity

Directory of Open Access Journals (Sweden)

Hee Chul Pak

2012-01-01

Full Text Available A blow-up time for nonlinear heat equations with transcendental nonlinearity is investigated. An upper bound of the first blow-up time is presented. It is pointed out that the upper bound of the first blow-up time depends on the support of the initial datum.

Existence of a coupled system of fractional differential equations

International Nuclear Information System (INIS)

Ibrahim, Rabha W.; Siri, Zailan

2015-01-01

We manage the existence and uniqueness of a fractional coupled system containing Schrödinger equations. Such a system appears in quantum mechanics. We confirm that the fractional system under consideration admits a global solution in appropriate functional spaces. The solution is shown to be unique. The method is based on analytic technique of the fixed point theory. The fractional differential operator is considered from the virtue of the Riemann-Liouville differential operator

Existence of a coupled system of fractional differential equations

Energy Technology Data Exchange (ETDEWEB)

Ibrahim, Rabha W. [Multimedia unit, Department of Computer System and Technology Faculty of Computer Science & IT, University of Malaya, 50603 Kuala Lumpur (Malaysia); Siri, Zailan [Institute of Mathematical Sciences, University of Malaya, 50603 Kuala Lumpur (Malaysia)

2015-10-22

We manage the existence and uniqueness of a fractional coupled system containing Schrödinger equations. Such a system appears in quantum mechanics. We confirm that the fractional system under consideration admits a global solution in appropriate functional spaces. The solution is shown to be unique. The method is based on analytic technique of the fixed point theory. The fractional differential operator is considered from the virtue of the Riemann-Liouville differential operator.

Self-Adjoint Angular Flux Equation for Coupled Electron-Photon Transport

International Nuclear Information System (INIS)

Liscum-Powell, J.L.; Lorence, L.J. Jr.; Morel, J.E.; Prinja, A.K.

1999-01-01

Recently, Morel and McGhee described an alternate second-order form of the transport equation called the self adjoint angular flux (SAAF) equation that has the angular flux as its unknown. The SAAF formulation has all the advantages of the traditional even- and odd-parity self-adjoint equations, with the added advantages that it yields the full angular flux when it is numerically solved, it is significantly easier to implement reflective and reflective-like boundary conditions, and in the appropriate form it can be solved in void regions. The SAAF equation has the disadvantage that the angular domain is the full unit sphere and, like the even- and odd- parity form, S n source iteration cannot be implemented using the standard sweeping algorithm. Also, problems arise in pure scattering media. Morel and McGhee demonstrated the efficacy of the SAAF formulation for neutral particle transport. Here we apply the SAAF formulation to coupled electron-photon transport problems using multigroup cross-sections from the CEPXS code and S n discretization

Self-adjoint angular flux equation for coupled electron-photon transport

International Nuclear Information System (INIS)

Liscum-Powell, J.L.; Prinja, A.K.; Morel, J.E.; Lorence, L.J. Jr.

1999-01-01

Recently, Morel and McGhee described an alternate second-order form of the transport equation called the self-adjoint angular flux (SAAF) equation that has the angular flux as its unknown. The SAAF formulation has all the advantages of the traditional even- and odd-parity self-adjoint equations, with the added advantages that it yields the full angular flux when it is numerically solved, it is significantly easier to implement reflective and reflective-like boundary conditions, and in the appropriate form it can be solved in void regions. The SAAF equation has the disadvantage that the angular domain is the full unit sphere, and, like the even- and odd-parity form, S n source iteration cannot be implemented using the standard sweeping algorithm. Also, problems arise in pure scattering media. Morel and McGhee demonstrated the efficacy of the SAAF formulation for neutral particle transport. Here, the authors apply the SAAF formulation to coupled electron-photon transport problems using multigroup cross sections from the CEPXS code and S n discretization

Properties of coupled-cluster equations originating in excitation sub-algebras

Science.gov (United States)

Kowalski, Karol

2018-03-01

In this paper, we discuss properties of single-reference coupled cluster (CC) equations associated with the existence of sub-algebras of excitations that allow one to represent CC equations in a hybrid fashion where the cluster amplitudes associated with these sub-algebras can be obtained by solving the corresponding eigenvalue problem. For closed-shell formulations analyzed in this paper, the hybrid representation of CC equations provides a natural way for extending active-space and seniority number concepts to provide an accurate description of electron correlation effects. Moreover, a new representation can be utilized to re-define iterative algorithms used to solve CC equations, especially for tough cases defined by the presence of strong static and dynamical correlation effects. We will also explore invariance properties associated with excitation sub-algebras to define a new class of CC approximations referred to in this paper as the sub-algebra-flow-based CC methods. We illustrate the performance of these methods on the example of ground- and excited-state calculations for commonly used small benchmark systems.

Simulation on the start-up of MED seawater desalination system coupled with nuclear heating reactor

International Nuclear Information System (INIS)

Ge Zhihua; Du Xiaoze; Yang Lijun; Yang Yongping; Wu Shaorong

2008-01-01

The mathematical control model for dynamic start-up process of the VTE-MED seawater desalination system was established employing the previous developed non-linear differential equations for system design and performance analysis. The influences on the start-up process of the operating parameters, such as the initial feed brine flow rate and the top brine temperature were analyzed. The relationships among the feed brine flow rate, the gained output ratio (GOR) and the start-up time were also investigated, which can be evidence to determine the optimal initial feed brine flow rate. The results also indicate that the system can consume the total heat rating generated by the low temperature nuclear heating reactor (LT-NHR) even at the most initial start-up stage, implying the present desalination system has excellent coupling characteristics with the LT-NHR. With necessary experiments verifications, the start-up control model developed in this paper can be the theoretical base for the analysis of dynamic performances of the seawater desalination system

Optimizing basin-scale coupled water quantity and water quality management with stochastic dynamic programming

DEFF Research Database (Denmark)

Davidsen, Claus; Liu, Suxia; Mo, Xingguo

2015-01-01

Few studies address water quality in hydro-economic models, which often focus primarily on optimal allocation of water quantities. Water quality and water quantity are closely coupled, and optimal management with focus solely on either quantity or quality may cause large costs in terms of the oth......-er component. In this study, we couple water quality and water quantity in a joint hydro-economic catchment-scale optimization problem. Stochastic dynamic programming (SDP) is used to minimize the basin-wide total costs arising from water allocation, water curtailment and water treatment. The simple water...... quality module can handle conservative pollutants, first order depletion and non-linear reactions. For demonstration purposes, we model pollutant releases as biochemical oxygen demand (BOD) and use the Streeter-Phelps equation for oxygen deficit to compute the resulting min-imum dissolved oxygen...

Integrable discretizations and self-adaptive moving mesh method for a coupled short pulse equation

International Nuclear Information System (INIS)

Feng, Bao-Feng; Chen, Junchao; Chen, Yong; Maruno, Ken-ichi; Ohta, Yasuhiro

2015-01-01

In the present paper, integrable semi-discrete and fully discrete analogues of a coupled short pulse (CSP) equation are constructed. The key to the construction are the bilinear forms and determinant structure of the solutions of the CSP equation. We also construct N-soliton solutions for the semi-discrete and fully discrete analogues of the CSP equations in the form of Casorati determinants. In the continuous limit, we show that the fully discrete CSP equation converges to the semi-discrete CSP equation, then further to the continuous CSP equation. Moreover, the integrable semi-discretization of the CSP equation is used as a self-adaptive moving mesh method for numerical simulations. The numerical results agree with the analytical results very well. (paper)

Optimization of mixed quantum-classical dynamics: Time-derivative coupling terms and selected couplings

International Nuclear Information System (INIS)

Pittner, Jiri; Lischka, Hans; Barbatti, Mario

2009-01-01

The usage of time-derivative non-adiabatic coupling terms and partially coupled time-dependent equations are investigated to accelerate non-adiabatic dynamics simulations at multireference configuration interaction (MRCI) level. The quality of the results and computational costs are compared against non-adiabatic benchmark dynamics calculations using non-adiabatic coupling vectors. In the comparison between the time-derivative couplings and coupling vectors, deviations in the adiabatic population of individual trajectories were observed in regions of rapid variation of the coupling terms. They, however, affected the average adiabatic population to only about 5%. For small multiconfiguration spaces, dynamics with time-derivative couplings are significantly faster than those with coupling vectors. This relation inverts for larger configuration spaces. The use of the partially coupled equations approach speeds up the simulations significantly while keeping the deviations in the population below few percent. Imidazole and the methaniminium cation are used as test examples

N-fold Darboux Transformation for Integrable Couplings of AKNS Equations

Science.gov (United States)

Yu, Jing; Chen, Shou-Ting; Han, Jing-Wei; Ma, Wen-Xiu

2018-04-01

For the integrable couplings of Ablowitz-Kaup-Newell-Segur (ICAKNS) equations, N-fold Darboux transformation (DT) TN, which is a 4 × 4 matrix, is constructed in this paper. Each element of this matrix is expressed by a ratio of the (4N + 1)-order determinant and 4N-order determinant of eigenfunctions. By making use of these formulae, the determinant expressions of N-transformed new solutions p [N], q [N], r [N] and s [N] are generated by this N-fold DT. Furthermore, when the reduced conditions q = ‑p* and s = ‑r* are chosen, we obtain determinant representations of N-fold DT and N-transformed solutions for the integrable couplings of nonlinear Schrödinger (ICNLS) equations. Starting from the zero seed solutions, one-soliton solutions are explicitly given as an example. Supported by the National Natural Science Foundation of China under Grant Nos. 61771174, 11371326, 11371361, 11301454, and 11271168, Natural Science Fund for Colleges and Universities of Jiangsu Province of China under Grant No. 17KJB110020, and General Research Project of Department of Education of Zhejiang Province (Y201636538)

Nonlocal constitutive equations of elasto-visco-plasticity coupled with damage and temperature

Directory of Open Access Journals (Sweden)

Liu Weijie

2016-01-01

Full Text Available In this paper, the nonlocal anisothermal elasto-visco-plastic constitutive equations strongly coupled with ductile isotropic damage, nonlinear isotropic hardening and kinematic hardening are developed to model the material behaviour under finite strain. The new micromorphic variable of damage is introduced into the principle of virtual power and new additional balance equations are obtained. Thermodynamically-consistent nonlocal constitutive equations are then deduced. The evolution equations are deduced from the generalized normality rule for the Norton-Hoff visco-plastic potential. This model is used to simulate various material responses under different velocities at high temperature. The micromorphic parameters of damage: micromorphic density and H moduli are studied to examine the effects of micromorphic damage. Biaxial tension is performed to make a comparison between the local damage model and the micromorphic damage model.

Recent symbolic summation methods to solve coupled systems of differential and difference equations

International Nuclear Information System (INIS)

Schneider, Carsten; Bluemlein, Johannes; Freitas, Abilio de

2014-07-01

We outline a new algorithm to solve coupled systems of differential equations in one continuous variable x (resp. coupled difference equations in one discrete variable N) depending on a small parameter ε: given such a system and given sufficiently many initial values, we can determine the first coefficients of the Laurent-series solutions in ε if they are expressible in terms of indefinite nested sums and products. This systematic approach is based on symbolic summation algorithms in the context of difference rings/fields and uncoupling algorithms. The proposed method gives rise to new interesting applications in connection with integration by parts (IBP) methods. As an illustrative example, we will demonstrate how one can calculate the ε-expansion of a ladder graph with 6 massive fermion lines.

Recent symbolic summation methods to solve coupled systems of differential and difference equations

Energy Technology Data Exchange (ETDEWEB)

Schneider, Carsten [Johannes Kepler Univ., Linz (Austria). Research Inst. for Symbolic Computation (RISC); Bluemlein, Johannes; Freitas, Abilio de [Deutsches Elektronen-Synchrotron (DESY), Zeuthen (Germany)

2014-07-15

We outline a new algorithm to solve coupled systems of differential equations in one continuous variable x (resp. coupled difference equations in one discrete variable N) depending on a small parameter ε: given such a system and given sufficiently many initial values, we can determine the first coefficients of the Laurent-series solutions in ε if they are expressible in terms of indefinite nested sums and products. This systematic approach is based on symbolic summation algorithms in the context of difference rings/fields and uncoupling algorithms. The proposed method gives rise to new interesting applications in connection with integration by parts (IBP) methods. As an illustrative example, we will demonstrate how one can calculate the ε-expansion of a ladder graph with 6 massive fermion lines.

Coupled replicator equations for the dynamics of learning in multiagent systems

Science.gov (United States)

Sato, Yuzuru; Crutchfield, James P.

2003-01-01

Starting with a group of reinforcement-learning agents we derive coupled replicator equations that describe the dynamics of collective learning in multiagent systems. We show that, although agents model their environment in a self-interested way without sharing knowledge, a game dynamics emerges naturally through environment-mediated interactions. An application to rock-scissors-paper game interactions shows that the collective learning dynamics exhibits a diversity of competitive and cooperative behaviors. These include quasiperiodicity, stable limit cycles, intermittency, and deterministic chaos—behaviors that should be expected in heterogeneous multiagent systems described by the general replicator equations we derive.

Coupled Dyson-Schwinger equations and effects of self-consistency

International Nuclear Information System (INIS)

Wu, S.S.; Zhang, H.X.; Yao, Y.J.

2001-01-01

Using the σ-ω model as an effective tool, the effects of self-consistency are studied in some detail. A coupled set of Dyson-Schwinger equations for the renormalized baryon and meson propagators in the σ-ω model is solved self-consistently according to the dressed Hartree-Fock scheme, where the hadron propagators in both the baryon and meson self-energies are required to also satisfy this coupled set of equations. It is found that the self-consistency affects the baryon spectral function noticeably, if only the interaction with σ mesons is considered. However, there is a cancellation between the effects due to the σ and ω mesons and the additional contribution of ω mesons makes the above effect insignificant. In both the σ and σ-ω cases the effects of self-consistency on meson spectral function are perceptible, but they can nevertheless be taken account of without a self-consistent calculation. Our study indicates that to include the meson propagators in the self-consistency requirement is unnecessary and one can stop at an early step of an iteration procedure to obtain a good approximation to the fully self-consistent results of all the hadron propagators in the model, if an appropriate initial input is chosen. Vertex corrections and their effects on ghost poles are also studied

On the coupling of systems of hyperbolic conservation laws with ordinary differential equations

International Nuclear Information System (INIS)

Borsche, Raul; Colombo, Rinaldo M; Garavello, Mauro

2010-01-01

Motivated by applications to the piston problem, to a manhole model, to blood flow and to supply chain dynamics, this paper deals with a system of conservation laws coupled with a system of ordinary differential equations. The former is defined on a domain with boundary and the coupling is provided by the boundary condition. For each of the examples considered, numerical integrations are provided

Construction of adjoint operators for coupled equations depending on different variables

International Nuclear Information System (INIS)

Hoogenboom, J.E.

1986-01-01

A procedure is described for the construction of the adjoint operator matrix in case of coupled equations defining quantities that depend on different sets of variables. This case is not properly treated in the literature. From this procedure a simple rule can be deduced for the construction of such adjoint operator matrices

Matrix Solution of Coupled Differential Equations and Looped Car Following Models

Science.gov (United States)

McCartney, Mark

2008-01-01

A simple mathematical model for the behaviour of how vehicles follow each other along a looped stretch of road is described. The resulting coupled first order differential equations are solved using appropriate matrix techniques and the physical significance of the model is discussed. A number possible classroom exercises are suggested to help…

Modulation Instability of Copropagating Optical Beams in Fractional Coupled Nonlinear Schrödinger Equations

Science.gov (United States)

Zhang, Jinggui

2018-06-01

In this paper, we investigate the dynamical behaviors of the modulation instability (MI) of copropagating optical beams in fractional coupled nonlinear Schrödinger equations (NLSE) with the aim of revealing some novel properties different from those in the conventional coupled NLSE. By applying the standard linear stability method, we first derive an expression for the gain resulting from the instability induced by cross-phase modulation (CPM) in the presence of the Lévy indexes related to fractional effects. It is found that the modulation instability of copropagating optical beams still occurs even in the fractional NLSE with self-defocusing nonlinearity. Then, the analysis of our results further reveals that such Lévy indexes increase the fastest growth frequency and the bandwidth of conventional instability not only for the self-focusing case but also for the self-defocusing case, but do not influence the corresponding maximum gain. Numerical simulations are performed to confirm theoretical predictions. These findings suggest that the novel fractional physical settings may open up new possibilities for the manipulation of MI and nonlinear waves.

Effect of wettability on scale-up of multiphase flow from core-scale to reservoir fine-grid-scale

Energy Technology Data Exchange (ETDEWEB)

Chang, Y.C.; Mani, V.; Mohanty, K.K. [Univ. of Houston, TX (United States)

1997-08-01

Typical field simulation grid-blocks are internally heterogeneous. The objective of this work is to study how the wettability of the rock affects its scale-up of multiphase flow properties from core-scale to fine-grid reservoir simulation scale ({approximately} 10{prime} x 10{prime} x 5{prime}). Reservoir models need another level of upscaling to coarse-grid simulation scale, which is not addressed here. Heterogeneity is modeled here as a correlated random field parameterized in terms of its variance and two-point variogram. Variogram models of both finite (spherical) and infinite (fractal) correlation length are included as special cases. Local core-scale porosity, permeability, capillary pressure function, relative permeability functions, and initial water saturation are assumed to be correlated. Water injection is simulated and effective flow properties and flow equations are calculated. For strongly water-wet media, capillarity has a stabilizing/homogenizing effect on multiphase flow. For small variance in permeability, and for small correlation length, effective relative permeability can be described by capillary equilibrium models. At higher variance and moderate correlation length, the average flow can be described by a dynamic relative permeability. As the oil wettability increases, the capillary stabilizing effect decreases and the deviation from this average flow increases. For fractal fields with large variance in permeability, effective relative permeability is not adequate in describing the flow.

Threshold and flavor effects in the renormalization group equations of the MSSM. II. Dimensionful couplings

International Nuclear Information System (INIS)

Box, Andrew D.; Tata, Xerxes

2009-01-01

We reexamine the one-loop renormalization group equations (RGEs) for the dimensionful parameters of the minimal supersymmetric standard model (MSSM) with broken supersymmetry, allowing for arbitrary flavor structure of the soft SUSY-breaking parameters. We include threshold effects by evaluating the β-functions in a sequence of (nonsupersymmetric) effective theories with heavy particles decoupled at the scale of their mass. We present the most general form for high-scale, soft SUSY-breaking parameters that obtains if we assume that the supersymmetry-breaking mechanism does not introduce new intergenerational couplings. This form, possibly amended to allow additional sources of flavor-violation, serves as a boundary condition for solving the RGEs for the dimensionful MSSM parameters. We then present illustrative examples of numerical solutions to the RGEs. We find that in a SUSY grand unified theory with the scale of SUSY scalars split from that of gauginos and higgsinos, the gaugino mass unification condition may be violated by O(10%). As another illustration, we show that in mSUGRA, the rate for the flavor-violating t-tilde 1 →cZ-tilde 1 decay obtained using the complete RGE solution is smaller than that obtained using the commonly used 'single-step' integration of the RGEs by a factor 10-25, and so may qualitatively change expectations for topologies from top-squark pair production at colliders. Together with the RGEs for dimensionless couplings presented in a companion paper, the RGEs in Appendix 2 of this paper form a complete set of one-loop MSSM RGEs that include threshold and flavor-effects necessary for two-loop accuracy.

Scale-up of chromatographic ion-exchange processes in biotechnology

DEFF Research Database (Denmark)

Al-Jibbouri, Sattar

2006-01-01

The van Deemter equation has been used to derive a rule of thumb guideline for scaling. The scaling is done by the concept of time scales. The time scales are kept identical for all the columns by scaling the flow rate to the total void volume and the load to the amount of the media. The verifica...

Stability of generalized Runge-Kutta methods for stiff kinetics coupled differential equations

International Nuclear Information System (INIS)

Aboanber, A E

2006-01-01

A stability and efficiency improved class of generalized Runge-Kutta methods of order 4 are developed for the numerical solution of stiff system kinetics equations for linear and/or nonlinear coupled differential equations. The determination of the coefficients required by the method is precisely obtained from the so-called equations of condition which in turn are derived by an approach based on Butcher series. Since the equations of condition are fewer in number, free parameters can be chosen for optimizing any desired feature of the process. A further related coefficient set with different values of these parameters and the region of absolute stability of the method have been introduced. In addition, the A(α) stability properties of the method are investigated. Implementing the method in a personal computer estimated the accuracy and speed of calculations and verified the good performances of the proposed new schemes for several sample problems of the stiff system point kinetics equations with reactivity feedback

OSCILLATION CRITERIA FOR A FOURTH ORDER SUBLINEAR DYNAMIC EQUATION ON TIME SCALE

Institute of Scientific and Technical Information of China (English)

无

2011-01-01

Some new criteria for the oscillation of a fourth order sublinear and/or linear dynamic equation on time scale are established. Our results are new for the corresponding fourth order differential equations as well as difference equations.

Three semi-direct sum Lie algebras and three discrete integrable couplings associated with the modified K dV lattice equation

International Nuclear Information System (INIS)

Yu Zhang; Zhang Yufeng

2009-01-01

Three semi-direct sum Lie algebras are constructed, which is an efficient and new way to obtain discrete integrable couplings. As its applications, three discrete integrable couplings associated with the modified K dV lattice equation are worked out. The approach can be used to produce other discrete integrable couplings of the discrete hierarchies of soliton equations.

Solving Coupled Gross--Pitaevskii Equations on a Cluster of PlayStation 3 Computers

Science.gov (United States)

Edwards, Mark; Heward, Jeffrey; Clark, C. W.

2009-05-01

At Georgia Southern University we have constructed an 8+1--node cluster of Sony PlayStation 3 (PS3) computers with the intention of using this computing resource to solve problems related to the behavior of ultra--cold atoms in general with a particular emphasis on studying bose--bose and bose--fermi mixtures confined in optical lattices. As a first project that uses this computing resource, we have implemented a parallel solver of the coupled time--dependent, one--dimensional Gross--Pitaevskii (TDGP) equations. These equations govern the behavior of dual-- species bosonic mixtures. We chose the split--operator/FFT to solve the coupled 1D TDGP equations. The fast Fourier transform component of this solver can be readily parallelized on the PS3 cpu known as the Cell Broadband Engine (CellBE). Each CellBE chip contains a single 64--bit PowerPC Processor Element known as the PPE and eight ``Synergistic Processor Element'' identified as the SPE's. We report on this algorithm and compare its performance to a non--parallel solver as applied to modeling evaporative cooling in dual--species bosonic mixtures.

Scaling up Telemedicine

DEFF Research Database (Denmark)

Christensen, Jannie Kristine Bang; Nielsen, Jeppe Agger; Gustafsson, Jeppe

through negotiating, mobilizing coalitions, and legitimacy building. To illustrate and further develop this conceptualization, we build on insights from a longitudinal case study (2008-2014) and provide a rich empirical account of how a Danish telemedicine pilot was transformed into a large......-scale telemedicine project through simultaneous translation and theorization efforts in a cross-sectorial, politicized social context. Although we focus on upscaling as a bottom up process (from pilot to large scale), we argue that translation and theorization, and associated political behavior occurs in a broader...

Local-in-space blow-up criteria for a class of nonlinear dispersive wave equations

Science.gov (United States)

Novruzov, Emil

2017-11-01

This paper is concerned with blow-up phenomena for the nonlinear dispersive wave equation on the real line, ut -uxxt +[ f (u) ] x -[ f (u) ] xxx +[ g (u) + f″/(u) 2 ux2 ] x = 0 that includes the Camassa-Holm equation as well as the hyperelastic-rod wave equation (f (u) = ku2 / 2 and g (u) = (3 - k) u2 / 2) as special cases. We establish some a local-in-space blow-up criterion (i.e., a criterion involving only the properties of the data u0 in a neighborhood of a single point) simplifying and precising earlier blow-up criteria for this equation.

Decoupling the NLO coupled DGLAP evolution equations: an analytic solution to pQCD

International Nuclear Information System (INIS)

Block, Martin M.; Durand, Loyal; Ha, Phuoc; McKay, Douglas W.

2010-01-01

Using repeated Laplace transforms, we turn coupled, integral-differential singlet DGLAP equations into NLO (next-to-leading) coupled algebraic equations, which we then decouple. After two Laplace inversions we find new tools for pQCD: decoupled NLO analytic solutions F s (x,Q 2 )=F s (F s0 (x),G 0 (x)), G(x,Q 2 )=G(F s0 (x), G 0 (x)). F s , G are known NLO functions and F s0 (x)≡F s (x,Q 0 2 ), G 0 (x)≡G(x,Q 0 2 ) are starting functions for evolution beginning at Q 2 =Q 0 2 . We successfully compare our u and d non-singlet valence quark distributions with MSTW results (Martin et al., Eur. Phys. J. C 63:189, 2009). (orig.)

An Efficient Numerical Approach for Solving Nonlinear Coupled Hyperbolic Partial Differential Equations with Nonlocal Conditions

Directory of Open Access Journals (Sweden)

A. H. Bhrawy

2014-01-01

Full Text Available One of the most important advantages of collocation method is the possibility of dealing with nonlinear partial differential equations (PDEs as well as PDEs with variable coefficients. A numerical solution based on a Jacobi collocation method is extended to solve nonlinear coupled hyperbolic PDEs with variable coefficients subject to initial-boundary nonlocal conservation conditions. This approach, based on Jacobi polynomials and Gauss-Lobatto quadrature integration, reduces solving the nonlinear coupled hyperbolic PDEs with variable coefficients to a system of nonlinear ordinary differential equation which is far easier to solve. In fact, we deal with initial-boundary coupled hyperbolic PDEs with variable coefficients as well as initial-nonlocal conditions. Using triangular, soliton, and exponential-triangular solutions as exact solutions, the obtained results show that the proposed numerical algorithm is efficient and very accurate.

All order running coupling BFKL evolution from GLAP (and vice versa)

International Nuclear Information System (INIS)

Ball, Richard D.; Forte, Stefano

2006-01-01

We present a systematic formalism for the derivation of the kernel of the BFKL equation from that of the GLAP equation and conversely to any given order, with full inclusion of the running of the coupling. The running coupling is treated as an operator, reducing the inclusion of running coupling effects and their factorization to a purely algebraic problem. We show how the GLAP anomalous dimensions which resum large logs of 1x can be derived from the running-coupling BFKL kernel order by order, thereby obtaining a constructive all-order proof of small x factorization. We check this result by explicitly calculating the running coupling contributions to GLAP anomalous dimensions up to next-to-next-to leading order. We finally derive an explicit expression for BFKL kernels which resum large logs of Q 2 up to next-to-leading order from the corresponding GLAP kernels, thus making possible a consistent collinear improvement of the BFKL equation up to the same order

A multi scale approximation solution for the time dependent Boltzmann-transport equation

International Nuclear Information System (INIS)

Merk, B.

2004-03-01

The basis of all transient simulations for nuclear reactor cores is the reliable calculation of the power production. The local power distribution is generally calculated by solving the space, time, energy and angle dependent neutron transport equation known as Boltzmann equation. The computation of exact solutions of the Boltzmann equation is very time consuming. For practical numerical simulations approximated solutions are usually unavoidable. The objective of this work is development of an effective multi scale approximation solution for the Boltzmann equation. Most of the existing methods are based on separation of space and time. The new suggested method is performed without space-time separation. This effective approximation solution is developed on the basis of an expansion for the time derivative of different approximations to the Boltzmann equation. The method of multiple scale expansion is used for the expansion of the time derivative, because the problem of the stiff time behaviour can't be expressed by standard expansion methods. This multiple scale expansion is used in this work to develop approximation solutions for different approximations of the Boltzmann equation, starting from the expansion of the point kinetics equations. The resulting analytic functions are used for testing the applicability and accuracy of the multiple scale expansion method for an approximation solution with 2 delayed neutron groups. The results are tested versus the exact analytical results for the point kinetics equations. Very good agreement between both solutions is obtained. The validity of the solution with 2 delayed neutron groups to approximate the behaviour of the system with 6 delayed neutron groups is demonstrated in an additional analysis. A strategy for a solution with 4 delayed neutron groups is described. A multiple scale expansion is performed for the space-time dependent diffusion equation for one homogenized cell with 2 delayed neutron groups. The result is

Coupled force-balance and particle-occupation rate equations for high-field electron transport

International Nuclear Information System (INIS)

Lei, X. L.

2008-01-01

It is pointed out that in the framework of balance-equation approach, the coupled force-balance and particle-occupation rate equations can be used as a complete set of equations to determine the high-field transport of semiconductors in both strong and weak electron-electron interaction limits. We call to attention that the occupation rate equation conserves the total particle number and maintains the energy balance of the relative electron system, and there is no need to introduce any other term in it. The addition of an energy-drift term in the particle-occupation rate equation [Phys. Rev. B 71, 195205 (2005)] is physically inadequate for the violation of the total particle-number conservation and the energy balance. It may lead to a substantial unphysical increase of the total particle number by the application of a dc electric field

Soliton interaction in the coupled mixed derivative nonlinear Schroedinger equations

International Nuclear Information System (INIS)

Zhang Haiqiang; Tian Bo; Lue Xing; Li He; Meng Xianghua

2009-01-01

The bright one- and two-soliton solutions of the coupled mixed derivative nonlinear Schroedinger equations in birefringent optical fibers are obtained by using the Hirota's bilinear method. The investigation on the collision dynamics of the bright vector solitons shows that there exists complete or partial energy switching in this coupled model. Such parametric energy exchanges can be effectively controlled and quantificationally measured by analyzing the collision dynamics of the bright vector solitons. The influence of two types of nonlinear coefficient parameters on the energy of each vector soliton, is also discussed. Based on the significant energy transfer between the two components of each vector soliton, it is feasible to exploit the future applications in the design of logical gates, fiber directional couplers and quantum information processors.

Metabolite coupling in genome-scale metabolic networks

Directory of Open Access Journals (Sweden)

Palsson Bernhard Ø

2006-03-01

Full Text Available Abstract Background Biochemically detailed stoichiometric matrices have now been reconstructed for various bacteria, yeast, and for the human cardiac mitochondrion based on genomic and proteomic data. These networks have been manually curated based on legacy data and elementally and charge balanced. Comparative analysis of these well curated networks is now possible. Pairs of metabolites often appear together in several network reactions, linking them topologically. This co-occurrence of pairs of metabolites in metabolic reactions is termed herein "metabolite coupling." These metabolite pairs can be directly computed from the stoichiometric matrix, S. Metabolite coupling is derived from the matrix ŜŜT, whose off-diagonal elements indicate the number of reactions in which any two metabolites participate together, where Ŝ is the binary form of S. Results Metabolite coupling in the studied networks was found to be dominated by a relatively small group of highly interacting pairs of metabolites. As would be expected, metabolites with high individual metabolite connectivity also tended to be those with the highest metabolite coupling, as the most connected metabolites couple more often. For metabolite pairs that are not highly coupled, we show that the number of reactions a pair of metabolites shares across a metabolic network closely approximates a line on a log-log scale. We also show that the preferential coupling of two metabolites with each other is spread across the spectrum of metabolites and is not unique to the most connected metabolites. We provide a measure for determining which metabolite pairs couple more often than would be expected based on their individual connectivity in the network and show that these metabolites often derive their principal biological functions from existing in pairs. Thus, analysis of metabolite coupling provides information beyond that which is found from studying the individual connectivity of individual

Spin-orbit couplings within the equation-of-motion coupled-cluster framework: Theory, implementation, and benchmark calculations

Energy Technology Data Exchange (ETDEWEB)

Epifanovsky, Evgeny [Department of Chemistry, University of Southern California, Los Angeles, California 90089-0482 (United States); Department of Chemistry, University of California, Berkeley, California 94720 (United States); Q-Chem Inc., 6601 Owens Drive, Suite 105, Pleasanton, California 94588 (United States); Klein, Kerstin; Gauss, Jürgen [Institut für Physikalische Chemie, Universität Mainz, D-55099 Mainz (Germany); Stopkowicz, Stella [Department of Chemistry, Centre for Theoretical and Computational Chemistry, University of Oslo, N-0315 Oslo (Norway); Krylov, Anna I. [Department of Chemistry, University of Southern California, Los Angeles, California 90089-0482 (United States)

2015-08-14

We present a formalism and an implementation for calculating spin-orbit couplings (SOCs) within the EOM-CCSD (equation-of-motion coupled-cluster with single and double substitutions) approach. The following variants of EOM-CCSD are considered: EOM-CCSD for excitation energies (EOM-EE-CCSD), EOM-CCSD with spin-flip (EOM-SF-CCSD), EOM-CCSD for ionization potentials (EOM-IP-CCSD) and electron attachment (EOM-EA-CCSD). We employ a perturbative approach in which the SOCs are computed as matrix elements of the respective part of the Breit-Pauli Hamiltonian using zeroth-order non-relativistic wave functions. We follow the expectation-value approach rather than the response-theory formulation for property calculations. Both the full two-electron treatment and the mean-field approximation (a partial account of the two-electron contributions) have been implemented and benchmarked using several small molecules containing elements up to the fourth row of the periodic table. The benchmark results show the excellent performance of the perturbative treatment and the mean-field approximation. When used with an appropriate basis set, the errors with respect to experiment are below 5% for the considered examples. The findings regarding basis-set requirements are in agreement with previous studies. The impact of different correlation treatment in zeroth-order wave functions is analyzed. Overall, the EOM-IP-CCSD, EOM-EA-CCSD, EOM-EE-CCSD, and EOM-SF-CCSD wave functions yield SOCs that agree well with each other (and with the experimental values when available). Using an EOM-CCSD approach that provides a more balanced description of the target states yields more accurate results.

Space-time coupled spectral/hp least-squares finite element formulation for the incompressible Navier-Stokes equations

International Nuclear Information System (INIS)

Pontaza, J.P.; Reddy, J.N.

2004-01-01

We consider least-squares finite element models for the numerical solution of the non-stationary Navier-Stokes equations governing viscous incompressible fluid flows. The paper presents a formulation where the effects of space and time are coupled, resulting in a true space-time least-squares minimization procedure, as opposed to a space-time decoupled formulation where a least-squares minimization procedure is performed in space at each time step. The formulation is first presented for the linear advection-diffusion equation and then extended to the Navier-Stokes equations. The formulation has no time step stability restrictions and is spectrally accurate in both space and time. To allow the use of practical C 0 element expansions in the resulting finite element model, the Navier-Stokes equations are expressed as an equivalent set of first-order equations by introducing vorticity as an additional independent variable and the least-squares method is used to develop the finite element model of the governing equations. High-order element expansions are used to construct the discrete model. The discrete model thus obtained is linearized by Newton's method, resulting in a linear system of equations with a symmetric positive definite coefficient matrix that is solved in a fully coupled manner by a preconditioned conjugate gradient method in matrix-free form. Spectral convergence of the L 2 least-squares functional and L 2 error norms in space-time is verified using a smooth solution to the two-dimensional non-stationary incompressible Navier-Stokes equations. Numerical results are presented for impulsively started lid-driven cavity flow, oscillatory lid-driven cavity flow, transient flow over a backward-facing step, and flow around a circular cylinder; the results demonstrate the predictive capability and robustness of the proposed formulation. Even though the space-time coupled formulation is emphasized, we also present the formulation and numerical results for least

Dark Energy, scalar-curvature couplings and a critical acceleration scale

CERN Document Server

Navarro, Ignacio

2008-01-01

We study the effects of coupling a cosmologically rolling scalar field to higher order curvature terms. We show that when the strong coupling scale of the theory is on the 10^{-3}-10^{-1}eV range, the model passes all experimental bounds on the existence of fifth forces even if the field has a mass of the order of the Hubble scale in vacuum and non-suppressed couplings to SM fields. The reason is that the coupling to certain curvature invariant acts as an effective mass that grows in regions of large curvature. This prevents the field from rolling down its potential near sources and makes its effects on fifth-force search experiments performed in the laboratory to be observable only at the sub-mm scale. We obtain the static spherically symmetric solutions of the theory and show that a long-range force appears but it is turned on only below a fixed Newtonian acceleration scale of the order of the Hubble constant. We comment on the possibility of using this feature of the model to alleviate the CDM small scale ...

Stability theory for dynamic equations on time scales

CERN Document Server

Martynyuk, Anatoly A

2016-01-01

This monograph is a first in the world to present three approaches for stability analysis of solutions of dynamic equations. The first approach is based on the application of dynamic integral inequalities and the fundamental matrix of solutions of linear approximation of dynamic equations. The second is based on the generalization of the direct Lyapunovs method for equations on time scales, using scalar, vector and matrix-valued auxiliary functions. The third approach is the application of auxiliary functions (scalar, vector, or matrix-valued ones) in combination with differential dynamic inequalities. This is an alternative comparison method, developed for time continuous and time discrete systems. In recent decades, automatic control theory in the study of air- and spacecraft dynamics and in other areas of modern applied mathematics has encountered problems in the analysis of the behavior of solutions of time continuous-discrete linear and/or nonlinear equations of perturbed motion. In the book “Men of Ma...

Scale-invariance underlying the logistic equation and its social applications

Energy Technology Data Exchange (ETDEWEB)

Hernando, A., E-mail: alberto.hernando@irsamc.ups-tlse.fr [Laboratoire Collisions, Agrégats, Réactivité, IRSAMC, Université Paul Sabatier, 118 Route de Narbonne, 31062 Toulouse Cedex 09 (France); Plastino, A., E-mail: plastino@fisica.unlp.edu.ar [National University La Plata, IFLP-CCT-CONICET, C.C. 727, 1900 La Plata (Argentina); Universitat de les Illes Balears and IFISC-CSIC, 07122 Palma de Mallorca (Spain)

2013-01-03

On the basis of dynamical principles we i) advance a derivation of the Logistic Equation (LE), widely employed (among multiple applications) in the simulation of population growth, and ii) demonstrate that scale-invariance and a mean-value constraint are sufficient and necessary conditions for obtaining it. We also generalize the LE to multi-component systems and show that the above dynamical mechanisms underlie a large number of scale-free processes. Examples are presented regarding city-populations, diffusion in complex networks, and popularity of technological products, all of them obeying the multi-component logistic equation in an either stochastic or deterministic way.

Scale-invariance underlying the logistic equation and its social applications

International Nuclear Information System (INIS)

Hernando, A.; Plastino, A.

2013-01-01

On the basis of dynamical principles we i) advance a derivation of the Logistic Equation (LE), widely employed (among multiple applications) in the simulation of population growth, and ii) demonstrate that scale-invariance and a mean-value constraint are sufficient and necessary conditions for obtaining it. We also generalize the LE to multi-component systems and show that the above dynamical mechanisms underlie a large number of scale-free processes. Examples are presented regarding city-populations, diffusion in complex networks, and popularity of technological products, all of them obeying the multi-component logistic equation in an either stochastic or deterministic way.

Exact solutions of fractional mBBM equation and coupled system of fractional Boussinesq-Burgers

Science.gov (United States)

Javeed, Shumaila; Saif, Summaya; Waheed, Asif; Baleanu, Dumitru

2018-06-01

The new exact solutions of nonlinear fractional partial differential equations (FPDEs) are established by adopting first integral method (FIM). The Riemann-Liouville (R-L) derivative and the local conformable derivative definitions are used to deal with the fractional order derivatives. The proposed method is applied to get exact solutions for space-time fractional modified Benjamin-Bona-Mahony (mBBM) equation and coupled time-fractional Boussinesq-Burgers equation. The suggested technique is easily applicable and effectual which can be implemented successfully to obtain the solutions for different types of nonlinear FPDEs.

MOUNTAIN-SCALE COUPLED PROCESSES (TH/THC/THM) MODELS

International Nuclear Information System (INIS)

Y.S. Wu

2005-01-01

This report documents the development and validation of the mountain-scale thermal-hydrologic (TH), thermal-hydrologic-chemical (THC), and thermal-hydrologic-mechanical (THM) models. These models provide technical support for screening of features, events, and processes (FEPs) related to the effects of coupled TH/THC/THM processes on mountain-scale unsaturated zone (UZ) and saturated zone (SZ) flow at Yucca Mountain, Nevada (BSC 2005 [DIRS 174842], Section 2.1.1.1). The purpose and validation criteria for these models are specified in ''Technical Work Plan for: Near-Field Environment and Transport: Coupled Processes (Mountain-Scale TH/THC/THM, Drift-Scale THC Seepage, and Drift-Scale Abstraction) Model Report Integration'' (BSC 2005 [DIRS 174842]). Model results are used to support exclusion of certain FEPs from the total system performance assessment for the license application (TSPA-LA) model on the basis of low consequence, consistent with the requirements of 10 CFR 63.342 [DIRS 173273]. Outputs from this report are not direct feeds to the TSPA-LA. All the FEPs related to the effects of coupled TH/THC/THM processes on mountain-scale UZ and SZ flow are discussed in Sections 6 and 7 of this report. The mountain-scale coupled TH/THC/THM processes models numerically simulate the impact of nuclear waste heat release on the natural hydrogeological system, including a representation of heat-driven processes occurring in the far field. The mountain-scale TH simulations provide predictions for thermally affected liquid saturation, gas- and liquid-phase fluxes, and water and rock temperature (together called the flow fields). The main focus of the TH model is to predict the changes in water flux driven by evaporation/condensation processes, and drainage between drifts. The TH model captures mountain-scale three-dimensional flow effects, including lateral diversion and mountain-scale flow patterns. The mountain-scale THC model evaluates TH effects on water and gas

MOUNTAIN-SCALE COUPLED PROCESSES (TH/THC/THM)MODELS

Energy Technology Data Exchange (ETDEWEB)

Y.S. Wu

2005-08-24

This report documents the development and validation of the mountain-scale thermal-hydrologic (TH), thermal-hydrologic-chemical (THC), and thermal-hydrologic-mechanical (THM) models. These models provide technical support for screening of features, events, and processes (FEPs) related to the effects of coupled TH/THC/THM processes on mountain-scale unsaturated zone (UZ) and saturated zone (SZ) flow at Yucca Mountain, Nevada (BSC 2005 [DIRS 174842], Section 2.1.1.1). The purpose and validation criteria for these models are specified in ''Technical Work Plan for: Near-Field Environment and Transport: Coupled Processes (Mountain-Scale TH/THC/THM, Drift-Scale THC Seepage, and Drift-Scale Abstraction) Model Report Integration'' (BSC 2005 [DIRS 174842]). Model results are used to support exclusion of certain FEPs from the total system performance assessment for the license application (TSPA-LA) model on the basis of low consequence, consistent with the requirements of 10 CFR 63.342 [DIRS 173273]. Outputs from this report are not direct feeds to the TSPA-LA. All the FEPs related to the effects of coupled TH/THC/THM processes on mountain-scale UZ and SZ flow are discussed in Sections 6 and 7 of this report. The mountain-scale coupled TH/THC/THM processes models numerically simulate the impact of nuclear waste heat release on the natural hydrogeological system, including a representation of heat-driven processes occurring in the far field. The mountain-scale TH simulations provide predictions for thermally affected liquid saturation, gas- and liquid-phase fluxes, and water and rock temperature (together called the flow fields). The main focus of the TH model is to predict the changes in water flux driven by evaporation/condensation processes, and drainage between drifts. The TH model captures mountain-scale three-dimensional flow effects, including lateral diversion and mountain-scale flow patterns. The mountain-scale THC model evaluates TH effects on

On the numerical solution of coupled eigenvalue differential equations arising in molecular spectroscopy

International Nuclear Information System (INIS)

Friedman, R.S.; Jamieson, M.J.; Preston, S.C.

1990-01-01

A method for solving coupled eigenvalue differential equations is given and its relation to an existing technique is shown. Use of the Gram-Schmidt process to overcome the severe instabilities arising in molecular problems is described in detail. (orig.)

Two hierarchies of multi-component Kaup-Newell equations and theirs integrable couplings

International Nuclear Information System (INIS)

Zhu Fubo; Ji Jie; Zhang Jianbin

2008-01-01

Two hierarchies of multi-component Kaup-Newell equations are derived from an arbitrary order matrix spectral problem, including positive non-isospectral Kaup-Newell hierarchy and negative non-isospectral Kaup-Newell hierarchy. Moreover, new integrable couplings of the resulting Kaup-Newell soliton hierarchies are constructed by enlarging the associated matrix spectral problem

Urban Flow and Pollutant Dispersion Simulation with Multi-scale coupling of Meteorological Model with Computational Fluid Dynamic Analysis

Science.gov (United States)

Liu, Yushi; Poh, Hee Joo

2014-11-01

The Computational Fluid Dynamics analysis has become increasingly important in modern urban planning in order to create highly livable city. This paper presents a multi-scale modeling methodology which couples Weather Research and Forecasting (WRF) Model with open source CFD simulation tool, OpenFOAM. This coupling enables the simulation of the wind flow and pollutant dispersion in urban built-up area with high resolution mesh. In this methodology meso-scale model WRF provides the boundary condition for the micro-scale CFD model OpenFOAM. The advantage is that the realistic weather condition is taken into account in the CFD simulation and complexity of building layout can be handled with ease by meshing utility of OpenFOAM. The result is validated against the Joint Urban 2003 Tracer Field Tests in Oklahoma City and there is reasonably good agreement between the CFD simulation and field observation. The coupling of WRF- OpenFOAM provide urban planners with reliable environmental modeling tool in actual urban built-up area; and it can be further extended with consideration of future weather conditions for the scenario studies on climate change impact.

Transport equations, Level Set and Eulerian mechanics. Application to fluid-structure coupling

International Nuclear Information System (INIS)

Maitre, E.

2008-11-01

My works were devoted to numerical analysis of non-linear elliptic-parabolic equations, to neutron transport equation and to the simulation of fabrics draping. More recently I developed an Eulerian method based on a level set formulation of the immersed boundary method to deal with fluid-structure coupling problems arising in bio-mechanics. Some of the more efficient algorithms to solve the neutron transport equation make use of the splitting of the transport operator taking into account its characteristics. In the present work we introduced a new algorithm based on this splitting and an adaptation of minimal residual methods to infinite dimensional case. We present the case where the velocity space is of dimension 1 (slab geometry) and 2 (plane geometry) because the splitting is simpler in the former

Dirac equation in 2-dimensional curved spacetime, particle creation, and coupled waveguide arrays

Energy Technology Data Exchange (ETDEWEB)

Koke, Christian, E-mail: christian.koke@stud.uni-heidelberg.de [Institut für theoretische Physik, Philosophenweg 16, D-69120 Heidelberg (Germany); Noh, Changsuk, E-mail: changsuk@kias.re.kr [Korea Institute for Advanced Study, 85 Hoegiro, Seoul 130-722 (Korea, Republic of); Angelakis, Dimitris G., E-mail: dimitris.angelakis@gmail.com [Centre for Quantum Technologies, National University of Singapore, 2 Science Drive 3, 117542 (Singapore); School of Electronic and Computer Engineering, Technical University of Crete, Chania, Crete, 73100 (Greece)

2016-11-15

When quantum fields are coupled to gravitational fields, spontaneous particle creation may occur similarly to when they are coupled to external electromagnetic fields. A gravitational field can be incorporated as a background spacetime if the back-action of matter on the field can be neglected, resulting in modifications of the Dirac or Klein–Gordon equations for elementary fermions and bosons respectively. The semi-classical description predicts particle creation in many situations, including the expanding-universe scenario, near the event horizon of a black hole (the Hawking effect), and an accelerating observer in flat spacetime (the Unruh effect). In this work, we give a pedagogical introduction to the Dirac equation in a general 2D spacetime and show examples of spinor wave packet dynamics in flat and curved background spacetimes. In particular, we cover the phenomenon of particle creation in a time-dependent metric. Photonic analogs of these effects are then proposed, where classical light propagating in an array of coupled waveguides provides a visualisation of the Dirac spinor propagating in a curved 2D spacetime background. The extent to which such a single-particle description can be said to mimic particle creation is discussed.

On the Effective Equation of State of Dark Energy

DEFF Research Database (Denmark)

Sloth, Martin Snoager

2010-01-01

In an effective field theory model with an ultraviolet momentum cutoff, there is a relation between the effective equation of state of dark energy and the ultraviolet cutoff scale. It implies that a measure of the equation of state of dark energy different from minus one, does not rule out vacuum...... energy as dark energy. It also indicates an interesting possibility that precise measurements of the infrared properties of dark energy can be used to probe the ultraviolet cutoff scale of effective quantum field theory coupled to gravity. In a toy model with a vacuum energy dominated universe...... with a Planck scale cutoff, the dark energy effective equation of state is -0.96....

Integrated laboratory scale demonstration experiment of the hybrid sulphur cycle and preliminary scale-up

International Nuclear Information System (INIS)

Leybros, J.; Rivalier, P.; Saturnin, A.; Charton, S.

2010-01-01

The hybrid sulphur cycle is today one of the most promising processes to produce hydrogen on a massive scale within the scope of high temperature nuclear reactors development. Thus, the Fuel Cycle Technology Department at CEA Marcoule is involved in studying the hybrid sulphur process from a technical and economical performance standpoint. Based on mass and energy balance calculations, a ProsimPlus TM flow sheet and a commercial plant design were prepared. This work includes a study on sizing of the main equipment. The capital cost has been estimated using the major characteristics of main equipment based upon formulae and charts published in literature. A specific approach has been developed for electrolysers. Operational costs are also proposed for a plant producing 1000 mol/s H 2 . Bench scale and pilot experiments must focus on the electrochemical step due to limited experimental data. Thus, a pilot plant with a hydrogen capacity of 100 NL/h was built with the aim of acquiring technical and technological data for electrolysis. This pilot plant was designed to cover a wide range of operating conditions: sulphuric acid concentrations up to 60 wt.%, temperatures up to 100 deg. C and pressures up to 10 bar. New materials and structures recently developed for fuel cells, which are expected to yield significant performance improvements when applied to classical electrochemical processes, will be tested. All experiments will be coupled with phenomenological simulation tools developed jointly with the experimental programme. (authors)

Quantum adiabatic Markovian master equations

International Nuclear Information System (INIS)

Albash, Tameem; Zanardi, Paolo; Boixo, Sergio; Lidar, Daniel A

2012-01-01

We develop from first principles Markovian master equations suited for studying the time evolution of a system evolving adiabatically while coupled weakly to a thermal bath. We derive two sets of equations in the adiabatic limit, one using the rotating wave (secular) approximation that results in a master equation in Lindblad form, the other without the rotating wave approximation but not in Lindblad form. The two equations make markedly different predictions depending on whether or not the Lamb shift is included. Our analysis keeps track of the various time and energy scales associated with the various approximations we make, and thus allows for a systematic inclusion of higher order corrections, in particular beyond the adiabatic limit. We use our formalism to study the evolution of an Ising spin chain in a transverse field and coupled to a thermal bosonic bath, for which we identify four distinct evolution phases. While we do not expect this to be a generic feature, in one of these phases dissipation acts to increase the fidelity of the system state relative to the adiabatic ground state. (paper)

Extreme Scale FMM-Accelerated Boundary Integral Equation Solver for Wave Scattering

KAUST Repository

AbdulJabbar, Mustafa Abdulmajeed

2018-03-27

Algorithmic and architecture-oriented optimizations are essential for achieving performance worthy of anticipated energy-austere exascale systems. In this paper, we present an extreme scale FMM-accelerated boundary integral equation solver for wave scattering, which uses FMM as a matrix-vector multiplication inside the GMRES iterative method. Our FMM Helmholtz kernels treat nontrivial singular and near-field integration points. We implement highly optimized kernels for both shared and distributed memory, targeting emerging Intel extreme performance HPC architectures. We extract the potential thread- and data-level parallelism of the key Helmholtz kernels of FMM. Our application code is well optimized to exploit the AVX-512 SIMD units of Intel Skylake and Knights Landing architectures. We provide different performance models for tuning the task-based tree traversal implementation of FMM, and develop optimal architecture-specific and algorithm aware partitioning, load balancing, and communication reducing mechanisms to scale up to 6,144 compute nodes of a Cray XC40 with 196,608 hardware cores. With shared memory optimizations, we achieve roughly 77% of peak single precision floating point performance of a 56-core Skylake processor, and on average 60% of peak single precision floating point performance of a 72-core KNL. These numbers represent nearly 5.4x and 10x speedup on Skylake and KNL, respectively, compared to the baseline scalar code. With distributed memory optimizations, on the other hand, we report near-optimal efficiency in the weak scalability study with respect to both the logarithmic communication complexity as well as the theoretical scaling complexity of FMM. In addition, we exhibit up to 85% efficiency in strong scaling. We compute in excess of 2 billion DoF on the full-scale of the Cray XC40 supercomputer.

Abundant families of new traveling wave solutions for the coupled Drinfel'd-Sokolov-Wilson equation

International Nuclear Information System (INIS)

Yao Yuqin

2005-01-01

The generalized Jacobi elliptic function method is further improved by introducing an elliptic function φ(ξ) as a new independent variable and it is easy to calculate the over-determined equations. Abundant new traveling wave solutions of the coupled Drinfel'd-Sokolov-Wilson equation are obtained. The solutions obtained include the kink-shaped solutions, bell-shaped solutions, singular solutions and periodic solutions

Equation-of-motion coupled cluster method for high spin double electron attachment calculations

Energy Technology Data Exchange (ETDEWEB)

Musiał, Monika, E-mail: musial@ich.us.edu.pl; Lupa, Łukasz; Kucharski, Stanisław A. [Institute of Chemistry, University of Silesia, Szkolna 9, 40-006 Katowice (Poland)

2014-03-21

The new formulation of the equation-of-motion (EOM) coupled cluster (CC) approach applicable to the calculations of the double electron attachment (DEA) states for the high spin components is proposed. The new EOM equations are derived for the high spin triplet and quintet states. In both cases the new equations are easier to solve but the substantial simplification is observed in the case of quintets. Out of 21 diagrammatic terms contributing to the standard DEA-EOM-CCSDT equations for the R{sub 2} and R{sub 3} amplitudes only four terms survive contributing to the R{sub 3} part. The implemented method has been applied to the calculations of the excited states (singlets, triplets, and quintets) energies of the carbon and silicon atoms and potential energy curves for selected states of the Na{sub 2} (triplets) and B{sub 2} (quintets) molecules.

Generalized Kapchinskij-Vladimirskij Distribution and Envelope Equation for High-intensity Beams in a Coupled Transverse Focusing Lattice

International Nuclear Information System (INIS)

Qin, Hong; Chung, Moses; Davidson, Ronald C.

2009-01-01

In an uncoupled lattice, the Kapchinskij-Vladimirskij (KV) distribution function first analyzed in 1959 is the only known exact solution of the nonlinear Vlasov-Maxwell equations for high- intensity beams including self-fields in a self-consistent manner. The KV solution is generalized here to high-intensity beams in a coupled transverse lattice using the recently developed generalized Courant-Snyder invariant for coupled transverse dynamics. This solution projects to a rotating, pulsating elliptical beam in transverse configuration space, determined by the generalized matrix envelope equation.

The stability of coupled renewal-differential equations with econometric applications

Science.gov (United States)

Rhoten, R. P.; Aggarwal, J. K.

1969-01-01

Concepts and results are presented in the fields of mathematical modeling, economics, and stability analysis. A coupled renewal-differential equation structure is presented as a modeling form for systems possessing hereditary characteristics, and this structure is applied to a model of the Austrian theory of business cycles. For realistic conditions, the system is shown to have an infinite number of poles, and conditions are presented which are both necessary and sufficient for all poles to lie strictly in the left half plane.

The plasma transport equations derived by multiple time-scale expansions and turbulent transport. I. General theory

International Nuclear Information System (INIS)

Edenstrasser, J.W.

1995-01-01

A multiple time-scale derivative expansion scheme is applied to the dimensionless Fokker--Planck equation and to Maxwell's equations, where the parameter range of a typical fusion plasma was assumed. Within kinetic theory, the four time scales considered are those of Larmor gyration, particle transit, collisions, and classical transport. The corresponding magnetohydrodynamic (MHD) time scales are those of ion Larmor gyration, Alfven, MHD collision, and resistive diffusion. The solution of the zeroth-order equations results in the force-free equilibria and ideal Ohm's law. The solution of the first-order equations leads under the assumption of a weak collisional plasma to the ideal MHD equations. On the MHD-collision time scale, not only the full set of the MHD transport equations is obtained, but also turbulent terms, where the related transport quantities are one order in the expansion parameter larger than those of classical transport. Finally, at the resistive diffusion time scale the known transport equations are arrived at including, however, also turbulent contributions. copyright 1995 American Institute of Physics

Coupled radiative transfer equation and diffusion approximation model for photon migration in turbid medium with low-scattering and non-scattering regions

International Nuclear Information System (INIS)

Tarvainen, Tanja; Vauhkonen, Marko; Kolehmainen, Ville; Arridge, Simon R; Kaipio, Jari P

2005-01-01

In this paper, a coupled radiative transfer equation and diffusion approximation model is extended for light propagation in turbid medium with low-scattering and non-scattering regions. The light propagation is modelled with the radiative transfer equation in sub-domains in which the assumptions of the diffusion approximation are not valid. The diffusion approximation is used elsewhere in the domain. The two equations are coupled through their boundary conditions and they are solved simultaneously using the finite element method. The streamline diffusion modification is used to avoid the ray-effect problem in the finite element solution of the radiative transfer equation. The proposed method is tested with simulations. The results of the coupled model are compared with the finite element solutions of the radiative transfer equation and the diffusion approximation and with results of Monte Carlo simulation. The results show that the coupled model can be used to describe photon migration in turbid medium with low-scattering and non-scattering regions more accurately than the conventional diffusion model

New matrix bounds and iterative algorithms for the discrete coupled algebraic Riccati equation

Science.gov (United States)

Liu, Jianzhou; Wang, Li; Zhang, Juan

2017-11-01

The discrete coupled algebraic Riccati equation (DCARE) has wide applications in control theory and linear system. In general, for the DCARE, one discusses every term of the coupled term, respectively. In this paper, we consider the coupled term as a whole, which is different from the recent results. When applying eigenvalue inequalities to discuss the coupled term, our method has less error. In terms of the properties of special matrices and eigenvalue inequalities, we propose several upper and lower matrix bounds for the solution of DCARE. Further, we discuss the iterative algorithms for the solution of the DCARE. In the fixed point iterative algorithms, the scope of Lipschitz factor is wider than the recent results. Finally, we offer corresponding numerical examples to illustrate the effectiveness of the derived results.

Full-scale HDR blowdown experiments as a tool for investigating dynamic fluid-structural coupling

International Nuclear Information System (INIS)

Krieg, R.; Schlechtendahl, E.G.; Scholl, K.-H.; Schumann, U.

1977-01-01

As an answer to rigorous safety requirements in reactor technology an experimental-theoretical program has been established to investigate safety-relevant mechanical aspects of LWR-blowdown accidents. Part of the program are several full-scale blowdown experiments which will be performed in the former HDR-reactor. As the conceptional study confirms, the primary goal is to find out, how big the safety margins of present LWR's in the case of a blowdown actually are, rather than simply to show that essential parts of the reactor will withstand such an accident. However, to determine the safety margins, the physical phenomena involved in the blowdown process must be understood and appropriate wave of description must be found. Therefore the experimental program is accompanied by the development of theoretical models and computer codes. A survey is given over existing methods for coupled fluid structural dynamics. The following approaches are used: - Specific finite difference-code for integrated treatment of both fluid and structure in 3D-geometry using the fast cyclic reduction scheme for solving Poisson's equation. - Modification of mass and stiffness matrices of FEM-models for shell dynamics by reducing the 3D incompressible fluid problem to 2D with the boundary integral equation method. This presently developed method has the capacity to deal with general problems in fluid-structural coupling. (Auth.)

A toolbox to solve coupled systems of differential and difference equations

International Nuclear Information System (INIS)

Ablinger, Jakob; Schneider, Carsten; Bluemlein, Johannes; Freitas, Abilio de

2016-01-01

We present algorithms to solve coupled systems of linear differential equations, arising in the calculation of massive Feynman diagrams with local operator insertions at 3-loop order, which do not request special choices of bases. Here we assume that the desired solution has a power series representation and we seek for the coefficients in closed form. In particular, if the coefficients depend on a small parameter ε (the dimensional parameter), we assume that the coefficients themselves can be expanded in formal Laurent series w.r.t. ε and we try to compute the first terms in closed form. More precisely, we have a decision algorithm which solves the following problem: if the terms can be represented by an indefinite nested hypergeometric sum expression (covering as special cases the harmonic sums, cyclotomic sums, generalized harmonic sums or nested binomial sums), then we can calculate them. If the algorithm fails, we obtain a proof that the terms cannot be represented by the class of indefinite nested hypergeometric sum expressions. Internally, this problem is reduced by holonomic closure properties to solving a coupled system of linear difference equations. The underlying method in this setting relies on decoupling algorithms, difference ring algorithms and recurrence solving. We demonstrate by a concrete example how this algorithm can be applied with the new Mathematica package SolveCoupledSystem which is based on the packages Sigma, HarmonicSums and OreSys. In all applications the representation in x-space is obtained as an iterated integral representation over general alphabets, generalizing Poincare iterated integrals.

A toolbox to solve coupled systems of differential and difference equations

Energy Technology Data Exchange (ETDEWEB)

Ablinger, Jakob; Schneider, Carsten [Linz Univ. (Austria). Research Inst. for Symbolic Computation (RISC); Bluemlein, Johannes; Freitas, Abilio de [DESY Zeuthen (Germany)

2016-01-15

We present algorithms to solve coupled systems of linear differential equations, arising in the calculation of massive Feynman diagrams with local operator insertions at 3-loop order, which do not request special choices of bases. Here we assume that the desired solution has a power series representation and we seek for the coefficients in closed form. In particular, if the coefficients depend on a small parameter ε (the dimensional parameter), we assume that the coefficients themselves can be expanded in formal Laurent series w.r.t. ε and we try to compute the first terms in closed form. More precisely, we have a decision algorithm which solves the following problem: if the terms can be represented by an indefinite nested hypergeometric sum expression (covering as special cases the harmonic sums, cyclotomic sums, generalized harmonic sums or nested binomial sums), then we can calculate them. If the algorithm fails, we obtain a proof that the terms cannot be represented by the class of indefinite nested hypergeometric sum expressions. Internally, this problem is reduced by holonomic closure properties to solving a coupled system of linear difference equations. The underlying method in this setting relies on decoupling algorithms, difference ring algorithms and recurrence solving. We demonstrate by a concrete example how this algorithm can be applied with the new Mathematica package SolveCoupledSystem which is based on the packages Sigma, HarmonicSums and OreSys. In all applications the representation in x-space is obtained as an iterated integral representation over general alphabets, generalizing Poincare iterated integrals.

Large Scale Flutter Data for Design of Rotating Blades Using Navier-Stokes Equations

Science.gov (United States)

Guruswamy, Guru P.

2012-01-01

A procedure to compute flutter boundaries of rotating blades is presented; a) Navier-Stokes equations. b) Frequency domain method compatible with industry practice. Procedure is initially validated: a) Unsteady loads with flapping wing experiment. b) Flutter boundary with fixed wing experiment. Large scale flutter computation is demonstrated for rotating blade: a) Single job submission script. b) Flutter boundary in 24 hour wall clock time with 100 cores. c) Linearly scalable with number of cores. Tested with 1000 cores that produced data in 25 hrs for 10 flutter boundaries. Further wall-clock speed-up is possible by performing parallel computations within each case.

Hierarchies of multi-component mKP equations and theirs integrable couplings

International Nuclear Information System (INIS)

Ji Jie; Yao Yuqin; Zhu Fubo; Chen Dengyuan

2008-01-01

First, a new multi-component modified Kadomtsev-Petviashvill (mKP) spectral problem is constructed by k-constraint imposed on a general pseudo-differential operator. Then, two hierarchies of multi-component mKP equations are derived, including positive non-isospectral mKP hierarchy and negative non-isospectral mKP hierarchy. Moreover, new integrable couplings of the resulting mKP soliton hierarchies are constructed by enlarging the associated matrix spectral problem

A Structural Equation Modelling of the Academic Self-Concept Scale

Science.gov (United States)

Matovu, Musa

2014-01-01

The study aimed at validating the academic self-concept scale by Liu and Wang (2005) in measuring academic self-concept among university students. Structural equation modelling was used to validate the scale which was composed of two subscales; academic confidence and academic effort. The study was conducted on university students; males and…

On the uniqueness of minimal coupling in higher-spin gauge theory

International Nuclear Information System (INIS)

Boulanger, Nicolas; Sundell, Per; Leclercq, Serge

2008-01-01

We address the uniqueness of the minimal couplings between higher-spin fields and gravity. These couplings are cubic vertices built from gauge non-invariant connections that induce non-abelian deformations of the gauge algebra. We show that Fradkin-Vasiliev's cubic 2-s-s vertex, which contains up to 2s-2 derivatives dressed by a cosmological constant Λ, has a limit where: (i) Λ → 0; (ii) the spin-2 Weyl tensor scales non-uniformly with s; and (iii) all lower-derivative couplings are scaled away. For s = 3 the limit yields the unique non-abelian spin 2-3-3 vertex found recently by two of the authors, thereby proving the uniqueness of the corresponding FV vertex. We extend the analysis to s = 4 and a class of spin 1-s-s vertices. The non-universality of the flat limit high-lightens not only the problematic aspects of higher-spin interactions with Λ = 0 but also the strongly coupled nature of the derivative expansion of the fully nonlinear higher-spin field equations with Λ≠0, wherein the standard minimal couplings mediated via the Lorentz connection are subleading at energy scales (|Λ|) 1/2 || E || M p . Finally, combining our results with those obtained by Metsaev, we give the complete list of all the manifestly covariant cubic couplings of the form 1-s-s and 2-s-s , in Minkowski background.

Description of regional blow-up in a porous-medium equation

Directory of Open Access Journals (Sweden)

Carmen Cortazar

2002-10-01

Full Text Available We describe the (finite-time blow-up phenomenon for a non-negative solution of a porous medium equation of the form $$ u_t = Delta u^m + u^m $$ in the entire space. Here $m>1$ and the initial condition is assumed compactly supported. Blow-up takes place exactly inside a finite number of balls with same radii and exhibiting the same self-similar profile.

Hierarchy problem, gauge coupling unification at the Planck scale, and vacuum stability

Directory of Open Access Journals (Sweden)

Naoyuki Haba

2015-11-01

Full Text Available From the point of view of the gauge hierarchy problem, introducing an intermediate scale in addition to TeV scale and the Planck scale (MPl=2.4×1018 GeV is unfavorable. In that way, a gauge coupling unification (GCU is expected to be realized at MPl. We explore possibilities of GCU at MPl by adding a few extra particles with TeV scale mass into the standard model (SM. When extra particles are fermions and scalars (only fermions with the same mass, the GCU at MPl can (not be realized. On the other hand, when extra fermions have different masses, the GCU can be realized around 8πMPl without extra scalars. This simple SM extension has two advantages that a vacuum becomes stable up to MPl (8πMPl and a proton lifetime becomes much longer than an experimental bound.

Decoupling the NLO coupled DGLAP evolution equations: an analytic solution to pQCD

Energy Technology Data Exchange (ETDEWEB)

Block, Martin M. [Northwestern University, Department of Physics and Astronomy, Evanston, IL (United States); Durand, Loyal [University of Wisconsin, Department of Physics, Madison, WI (United States); Ha, Phuoc [Towson University, Department of Physics, Astronomy and Geosciences, Towson, MD (United States); McKay, Douglas W. [University of Kansas, Department of Physics and Astronomy, Lawrence, KS (United States)

2010-10-15

Using repeated Laplace transforms, we turn coupled, integral-differential singlet DGLAP equations into NLO (next-to-leading) coupled algebraic equations, which we then decouple. After two Laplace inversions we find new tools for pQCD: decoupled NLO analytic solutions F{sub s}(x,Q{sup 2})=F{sub s}(F{sub s0}(x),G{sub 0}(x)), G(x,Q{sup 2})=G(F{sub s0}(x), G{sub 0}(x)). F{sub s}, G are known NLO functions and F{sub s0}(x){identical_to}F{sub s}(x,Q{sub 0}{sup 2}), G{sub 0}(x){identical_to}G(x,Q{sub 0}{sup 2}) are starting functions for evolution beginning at Q{sup 2}=Q{sub 0}{sup 2}. We successfully compare our u and d non-singlet valence quark distributions with MSTW results (Martin et al., Eur. Phys. J. C 63:189, 2009). (orig.)

Coupled Lugiato-Lefever equation for nonlinear frequency comb generation at an avoided crossing of a microresonator

Science.gov (United States)

D'Aguanno, Giuseppe; Menyuk, Curtis R.

2017-03-01

Guided-mode coupling in a microresonator generally manifests itself through avoided crossings of the corresponding resonances. This coupling can strongly modify the resonator local effective dispersion by creating two branches that have dispersions of opposite sign in spectral regions that would otherwise be characterized by either positive (normal) or negative (anomalous) dispersion. In this paper, we study, both analytically and computationally, the general properties of nonlinear frequency comb generation at an avoided crossing using the coupled Lugiato-Lefever equation. In particular, we find that bright solitons and broadband frequency combs can be excited when both branches are pumped for a suitable choice of the pump powers and the detuning parameters. A deterministic path for soliton generation is found. Contribution to the Topical Issue "Theory and applications of the Lugiato-Lefever Equation", edited by Yanne K. Chembo, Damia Gomila, Mustapha Tlidi, Curtis R. Menyuk.

A Calderón multiplicative preconditioner for coupled surface-volume electric field integral equations

KAUST Repository

Bagci, Hakan; Andriulli, Francesco P.; Cools, Kristof; Olyslager, Femke; Michielssen, Eric

2010-01-01

A well-conditioned coupled set of surface (S) and volume (V) electric field integral equations (S-EFIE and V-EFIE) for analyzing wave interactions with densely discretized composite structures is presented. Whereas the V-EFIE operator is well

Strong coupling phase in QED

International Nuclear Information System (INIS)

Aoki, Ken-ichi

1988-01-01

Existence of a strong coupling phase in QED has been suggested in solutions of the Schwinger-Dyson equation and in Monte Carlo simulation of lattice QED. In this article we recapitulate the previous arguments, and formulate the problem in the modern framework of the renormalization theory, Wilsonian renormalization. This scheme of renormalization gives the best understanding of the basic structure of a field theory especially when it has a multi-phase structure. We resolve some misleading arguments in the previous literature. Then we set up a strategy to attack the strong phase, if any. We describe a trial; a coupled Schwinger-Dyson equation. Possible picture of the strong coupling phase QED is presented. (author)

Awakened Oscillations in Coupled Consumer-Resource Pairs

Directory of Open Access Journals (Sweden)

Almaz Mustafin

2014-01-01

Full Text Available The paper concerns two interacting consumer-resource pairs based on chemostat-like equations under the assumption that the dynamics of the resource is considerably slower than that of the consumer. The presence of two different time scales enables to carry out a fairly complete analysis of the problem. This is done by treating consumers and resources in the coupled system as fast-scale and slow-scale variables, respectively, and subsequently considering developments in phase planes of these variables, fast and slow, as if they are independent. When uncoupled, each pair has unique asymptotically stable steady state and no self-sustained oscillatory behavior (although damped oscillations about the equilibrium are admitted. When the consumer-resource pairs are weakly coupled through direct reciprocal inhibition of consumers, the whole system exhibits self-sustained relaxation oscillations with a period that can be significantly longer than intrinsic relaxation time of either pair. It is shown that the model equations adequately describe locally linked consumer-resource systems of quite different nature: living populations under interspecific interference competition and lasers coupled via their cavity losses.

Similarity transformed coupled cluster response (ST-CCR) theory--a time-dependent similarity transformed equation-of-motion coupled cluster (STEOM-CC) approach.

Science.gov (United States)

Landau, Arie

2013-07-07

This paper presents a new method for calculating spectroscopic properties in the framework of response theory utilizing a sequence of similarity transformations (STs). The STs are preformed using the coupled cluster (CC) and Fock-space coupled cluster operators. The linear and quadratic response functions of the new similarity transformed CC response (ST-CCR) method are derived. The poles of the linear response yield excitation-energy (EE) expressions identical to the ones in the similarity transformed equation-of-motion coupled cluster (STEOM-CC) approach. ST-CCR and STEOM-CC complement each other, in analogy to the complementarity of CC response (CCR) and equation-of-motion coupled cluster (EOM-CC). ST-CCR/STEOM-CC and CCR/EOM-CC yield size-extensive and size-intensive EEs, respectively. Other electronic-properties, e.g., transition dipole strengths, are also size-extensive within ST-CCR, in contrast to STEOM-CC. Moreover, analysis suggests that in comparison with CCR, the ST-CCR expressions may be confined to a smaller subspace, however, the precise scope of the truncation can only be determined numerically. In addition, reformulation of the time-independent STEOM-CC using the same parameterization as in ST-CCR, as well as an efficient truncation scheme, is presented. The shown convergence of the time-dependent and time-independent expressions displays the completeness of the presented formalism.

Existence and global exponential stability of periodic solutions for n-dimensional neutral dynamic equations on time scales.

Science.gov (United States)

Li, Bing; Li, Yongkun; Zhang, Xuemei

2016-01-01

In this paper, by using the existence of the exponential dichotomy of linear dynamic equations on time scales and the theory of calculus on time scales, we study the existence and global exponential stability of periodic solutions for a class of n-dimensional neutral dynamic equations on time scales. We also present an example to illustrate the feasibility of our results. The results of this paper are completely new and complementary to the previously known results even in both the case of differential equations (time scale [Formula: see text]) and the case of difference equations (time scale [Formula: see text]).

Self-Organization in Coupled Map Scale-Free Networks

International Nuclear Information System (INIS)

Xiao-Ming, Liang; Zong-Hua, Liu; Hua-Ping, Lü

2008-01-01

We study the self-organization of phase synchronization in coupled map scale-free networks with chaotic logistic map at each node and find that a variety of ordered spatiotemporal patterns emerge spontaneously in a regime of coupling strength. These ordered behaviours will change with the increase of the average links and are robust to both the system size and parameter mismatch. A heuristic theory is given to explain the mechanism of self-organization and to figure out the regime of coupling for the ordered spatiotemporal patterns

Stability and oscillation of two coupled Duffing equations with time delay state feedback

International Nuclear Information System (INIS)

El-Bassiouny, A F

2006-01-01

This paper presents an analytical study of the simultaneous principal parametric resonances of two coupled Duffing equations with time delay state feedback. The concept of an equivalent damping related to the delay feedback is proposed and the appropriate choice of the feedback gains and the time delay is discussed from the viewpoint of vibration control. The method of multiple scales is used to determine a set of ordinary differential equations governing the modulation of the amplitudes and phases of the two modes. The first order approximation of the resonances are derived and the effect of time delay on the resonances is investigated. The fixed points correspond to a periodic motion for the starting system and we show the frequency-response curves. We analyse the effect of time delay and the other different parameters on these oscillations. The stability of the fixed points is examined by using the variational method. Numerical solutions are carried out and graphical representations of the results are presented and discussed. Increasing in the time delay τ given decreasing and increasing in the regions of definition and stability respectively and the first mode has decreased magnitudes. The multivalued solutions disappear when decreasing the coefficients of cubic nonlinearities of the second mode α 3 and the detuning parameter σ 2 respectively. Both modes shift to the left for increasing linear feedback gain v 1 and the coefficient of parametric excitation f 1 respectively

A coupling method for a cardiovascular simulation model which includes the Kalman filter.

Science.gov (United States)

Hasegawa, Yuki; Shimayoshi, Takao; Amano, Akira; Matsuda, Tetsuya

2012-01-01

Multi-scale models of the cardiovascular system provide new insight that was unavailable with in vivo and in vitro experiments. For the cardiovascular system, multi-scale simulations provide a valuable perspective in analyzing the interaction of three phenomenons occurring at different spatial scales: circulatory hemodynamics, ventricular structural dynamics, and myocardial excitation-contraction. In order to simulate these interactions, multiscale cardiovascular simulation systems couple models that simulate different phenomena. However, coupling methods require a significant amount of calculation, since a system of non-linear equations must be solved for each timestep. Therefore, we proposed a coupling method which decreases the amount of calculation by using the Kalman filter. In our method, the Kalman filter calculates approximations for the solution to the system of non-linear equations at each timestep. The approximations are then used as initial values for solving the system of non-linear equations. The proposed method decreases the number of iterations required by 94.0% compared to the conventional strong coupling method. When compared with a smoothing spline predictor, the proposed method required 49.4% fewer iterations.

Thermo-hydro-mechanical simulation of a 3D fractured porous rock: preliminary study of coupled matrix-fracture hydraulics

International Nuclear Information System (INIS)

Canamon, I.; Javier Elorza, F.; Ababou, R.

2007-01-01

We present a problem involving the modeling of coupled flow and elastic strain in a 3D fractured porous rock, which requires prior homogenization (up-scaling) of the fractured medium into an equivalent Darcian anisotropic continuum. The governing equations form a system of PDE's (Partial Differential Equations) and, depending on the case being considered, this system may involve two different types of 'couplings' (in a real system, both couplings (1) and (2) generally take place): 1) Hydraulic coupling in a single (no exchange) or in a dual matrix-fracture continuum (exchange); 2) Thermo-Hydro-Mechanical interactions between fluid flow, pressure, elastic stress, strain, and temperature. We present here a preliminary model and simulation results with FEMLAB R , for the hydraulic problem with anisotropic heterogeneous coefficients. The model is based on data collected at an instrumented granitic site (FEBEX project) for studying a hypothetical nuclear waste repository at the Grimsel Test Site in the Swiss Alps. (authors)

Thermo-hydro-mechanical simulation of a 3D fractured porous rock: preliminary study of coupled matrix-fracture hydraulics

Energy Technology Data Exchange (ETDEWEB)

Canamon, I.; Javier Elorza, F. [Universidad Politecnica de Madrid, Dept. de Matematica Aplicada y Metodos Informaticas, ETSI Minas (UPM) (Spain); Ababou, R. [Institut de Mecanique des Fluides de Toulouse (IMFT), 31 (France)

2007-07-01

We present a problem involving the modeling of coupled flow and elastic strain in a 3D fractured porous rock, which requires prior homogenization (up-scaling) of the fractured medium into an equivalent Darcian anisotropic continuum. The governing equations form a system of PDE's (Partial Differential Equations) and, depending on the case being considered, this system may involve two different types of 'couplings' (in a real system, both couplings (1) and (2) generally take place): 1) Hydraulic coupling in a single (no exchange) or in a dual matrix-fracture continuum (exchange); 2) Thermo-Hydro-Mechanical interactions between fluid flow, pressure, elastic stress, strain, and temperature. We present here a preliminary model and simulation results with FEMLAB{sup R}, for the hydraulic problem with anisotropic heterogeneous coefficients. The model is based on data collected at an instrumented granitic site (FEBEX project) for studying a hypothetical nuclear waste repository at the Grimsel Test Site in the Swiss Alps. (authors)

Multiscale Modeling of Blood Flow: Coupling Finite Elements with Smoothed Dissipative Particle Dynamics

KAUST Repository

Moreno Chaparro, Nicolas; Vignal, Philippe; Li, Jun; Calo, Victor M.

2013-01-01

A variational multi scale approach to model blood flow through arteries is proposed. A finite element discretization to represent the coarse scales (macro size), is coupled to smoothed dissipative particle dynamics that captures the fine scale features (micro scale). Blood is assumed to be incompressible, and flow is described through the Navier Stokes equation. The proposed cou- pling is tested with two benchmark problems, in fully coupled systems. Further refinements of the model can be incorporated in order to explicitly include blood constituents and non-Newtonian behavior. The suggested algorithm can be used with any particle-based method able to solve the Navier-Stokes equation.

Multiscale Modeling of Blood Flow: Coupling Finite Elements with Smoothed Dissipative Particle Dynamics

KAUST Repository

Moreno Chaparro, Nicolas

2013-06-01

A variational multi scale approach to model blood flow through arteries is proposed. A finite element discretization to represent the coarse scales (macro size), is coupled to smoothed dissipative particle dynamics that captures the fine scale features (micro scale). Blood is assumed to be incompressible, and flow is described through the Navier Stokes equation. The proposed cou- pling is tested with two benchmark problems, in fully coupled systems. Further refinements of the model can be incorporated in order to explicitly include blood constituents and non-Newtonian behavior. The suggested algorithm can be used with any particle-based method able to solve the Navier-Stokes equation.

Stochastic substitute for coupled rate equations in the modeling of highly ionized transient plasmas

International Nuclear Information System (INIS)

Eliezer, S.; Falquina, R.; Minguez, E.

1994-01-01

Plasmas produced by intense laser pulses incident on solid targets often do not satisfy the conditions for local thermodynamic equilibrium, and so cannot be modeled by transport equations relying on equations of state. A proper description involves an excessively large number of coupled rate equations connecting many quantum states of numerous species having different degrees of ionization. Here we pursue a recent suggestion to model the plasma by a few dominant states perturbed by a stochastic driving force. The driving force is taken to be a Poisson impulse process, giving a Langevin equation which is equivalent to a Fokker-Planck equation for the probability density governing the distribution of electron density. An approximate solution to the Langevin equation permits calculation of the characteristic relaxation rate. An exact stationary solution to the Fokker-Planck equation is given as a function of the strength of the stochastic driving force. This stationary solution is used, along with a Laplace transform, to convert the Fokker-Planck equation to one of Schroedinger type. We consider using the classical Hamiltonian formalism and the WKB method to obtain the time-dependent solution

From polymers to quantum gravity: Triple-scaling in rectangular random matrix models

International Nuclear Information System (INIS)

Myers, R.C.; Periwal, V.

1993-01-01

Rectangular NxM matrix models can be solved in several qualitatively distinct large-N limits, since two independent parameters govern the size of the matrix. Regarded as models of random surfaces, these matrix models interpolate between branched polymer behaviour and two-dimensional quantum gravity. We solve such models in a 'triple-scaling' regime in this paper, with N and M becoming large independently. A correspondence between phase transitions and singularities of mappings from R 2 to R 2 is indicated. At different critical points, the scaling behaviour is determined by (i) two decoupled ordinary differential equations; (ii) an ordinary differential equation and a finite-difference equation; or (iii) two coupled partial differential equations. The Painleve II equation arises (in conjunction with a difference equation) at a point associated with branched polymers. For critical points described by partial differential equations, there are dual weak-coupling/strong-coupling expansions. It is conjectured that the new physics is related to microscopic topology fluctuations. (orig.)

Neural network error correction for solving coupled ordinary differential equations

Science.gov (United States)

Shelton, R. O.; Darsey, J. A.; Sumpter, B. G.; Noid, D. W.

1992-01-01

A neural network is presented to learn errors generated by a numerical algorithm for solving coupled nonlinear differential equations. The method is based on using a neural network to correctly learn the error generated by, for example, Runge-Kutta on a model molecular dynamics (MD) problem. The neural network programs used in this study were developed by NASA. Comparisons are made for training the neural network using backpropagation and a new method which was found to converge with fewer iterations. The neural net programs, the MD model and the calculations are discussed.

Scaling up of renewable chemicals.

Science.gov (United States)

Sanford, Karl; Chotani, Gopal; Danielson, Nathan; Zahn, James A

2016-04-01

The transition of promising technologies for production of renewable chemicals from a laboratory scale to commercial scale is often difficult and expensive. As a result the timeframe estimated for commercialization is typically underestimated resulting in much slower penetration of these promising new methods and products into the chemical industries. The theme of 'sugar is the next oil' connects biological, chemical, and thermochemical conversions of renewable feedstocks to products that are drop-in replacements for petroleum derived chemicals or are new to market chemicals/materials. The latter typically offer a functionality advantage and can command higher prices that result in less severe scale-up challenges. However, for drop-in replacements, price is of paramount importance and competitive capital and operating expenditures are a prerequisite for success. Hence, scale-up of relevant technologies must be interfaced with effective and efficient management of both cell and steel factories. Details involved in all aspects of manufacturing, such as utilities, sterility, product recovery and purification, regulatory requirements, and emissions must be managed successfully. Copyright © 2016 Elsevier Ltd. All rights reserved.

GoAmazon – Scaling Amazon Carbon Water Couplings

Energy Technology Data Exchange (ETDEWEB)

Dubey, Manvendra Krishna [Los Alamos National Lab. (LANL), Los Alamos, NM (United States)

2016-09-06

Forests soak up 25% of the carbon dioxide (CO₂) emitted by anthropogenic fossil energy use (10 Gt C y^-1) moderating its atmospheric accumulation. How this terrestrial CO₂ uptake will evolve with climate change in the 21st century is largely unknown. Rainforests are the most active ecosystems with the Amazon basin storing 120 Gt C as biomass and exchanging 18 Gt C y^-1 of CO₂ via photosynthesis and respiration and fixing carbon at 2-3 kg C m^-2 y^-1. Furthermore, the intense hydrologic and carbon cycles are tightly coupled in the Amazon where about half of the water is recycled by evapotranspiration and the other half imported from the ocean by Northeasterly trade winds. Climate models predict a drying in the Amazon with reduced carbon uptake while observationally guided assessments indicate sustained uptake. We will resolve this huge discrepancy in the size and sign of the future Amazon carbon cycle by performing the first simultaneous regional scale high frequency measurements of atmospheric CO₂, H₂O, HOD, CH₄, N₂O and CO at the T3 site in Manacupuru, Brazil as part of DOE's GoAmazon project. Our data will be used to inform and develop DOE's CLM on the tropical carbon-water couplings at the appropriate grid scale (10-50km). Our measurements will also validate the CO₂ data from Japan's GOSAT and NASA's imminent OCO-2 satellite (launch date July 2014).

Scaling-up watershed discharge and sediment concentrations to regional scale: The Blue Nile Basin

Science.gov (United States)

Steenhuis, T. S.; Tilahun, S. A.; MacAlister, C.; Ayana, E. K.; Tebebu, T. Y.; Bayabil, H. K.; Zegeye, A. D.; Worqlul, A. W.

2012-12-01

Since Hewlet and Hibbert's publication there is recognition that saturated excess overland land flow is one of the main runoff mechanisms in vegetated watersheds. Predicting discharge in these watersheds can be accomplished by use of simplified models where the landscape features are grouped in potentially runoff contributing zones and permeable hillsides where the water infiltrates (and become the source of interflow and base flow). In this way each watershed can be described with nine parameters: fractional area and available water content for each of the three zones and three parameters describing subsurface flow. The information parameter values can be derived directly from the outflow hydrograph. We show that this model performs well for discharge and sediment concentration (with three additional parameters) on a 1 to 10 day time scale in the Blue Nile Basin for watersheds ranging in in size from 100 ha to 170,000 km2. Thus scaling up from watershed to regional scale can be accomplished with nine parameters for the hydrology and three additional parameters for sediment concentrations. Our hypothesis, that the model works so well, is that after the watershed wets up it drains to a characteristic moisture content distribution that is invariant in time. Wetting up is similar each time and is as a function of effective rainfall. This gives rise to a unique relationship between total storm runoff and total precipitation and surprisingly can be described by a modified form of the well-known SCS runoff equation. This approach has a direct parallel with Darcy's law in that although the average flow over several pores is described well, flow in individual pores cannot predicted. In our case the discharge can be simulated by averaging over the different runoff source area and permeable hillside in the watersheds, but processes within the zones cannot be described. This is not to say that information within the various zones cannot be simulated, but will require detailed

The Eni - IFP/Axens GTL technology. From R and D to a successful scale-up

Energy Technology Data Exchange (ETDEWEB)

Zennaro, R. [Eni S.p.A., Milan (Italy); Hugues, F. [Institut Francais du Petrole, Lyon (France); Caprani, E. [Axens, Paris (France)

2006-07-01

Proven natural gas reserves had reached about 184 Tscm in 2006 to which 36% is stranded gas far from the final market. Fischer Tropsch based GtL options today represent a viable route to develop such remote gas resources into high quality fuels and specialties. Thus opening different markets for the gas historically linked to the oil. Thanks to R and D successful improvements in the field of catalysis and reactor technology coupled with optimized integration and economies of scale have reduced the investment cost for building a Fischer Tropsch GtL complex. Basically all major Oil and Gas companies are involved in proprietary GtL development, and today several industrial projects have been announced. The most advanced is the Oryx project (QP-Sasol) which has been inaugurated the 6{sup th} of June '06 and currently in the starting up phase. Eni and IFP-Axens have developed a proprietary GtL Fischer-Tropsch and Upgrading technology in a close collaboration between the two groups. The Eni/IFP-Axens technology is based on proprietary catalysts and reactor, designed according to scale-up criteria defined in ten years of R and D activity. Unique large scale hydrodynamic facilities (bubble columns, loops) bench-scale dedicated pilot units, as well as large scale Fischer-Tropsch pilot plant, have been developed and operated to minimize reactor and ancillaries scale-up risks. The large scale Fischer-Tropsch pilot plant has been built and operated since 2001. The plant, located within the Eni refinery of Sannazzaro de' Burgondi (Pavia, Italy) is fully integrated to the refinery utilities and network. It reproduces at 20 bpd scale the overall Fischer Tropsch synthesis section: from slurry handling (loading, make-up, withdrawal), to reactor configuration and products separation units. Today the scale-up basis has been completed and the technology is ready for industrial deployment. (orig.)

Prelude to rational scale-up of penicillin production: a scale-down study.

Science.gov (United States)

Wang, Guan; Chu, Ju; Noorman, Henk; Xia, Jianye; Tang, Wenjun; Zhuang, Yingping; Zhang, Siliang

2014-03-01

Penicillin is one of the best known pharmaceuticals and is also an important member of the β-lactam antibiotics. Over the years, ambitious yields, titers, productivities, and low costs in the production of the β-lactam antibiotics have been stepwise realized through successive rounds of strain improvement and process optimization. Penicillium chrysogenum was proven to be an ideal cell factory for the production of penicillin, and successful approaches were exploited to elevate the production titer. However, the industrial production of penicillin faces the serious challenge that environmental gradients, which are caused by insufficient mixing and mass transfer limitations, exert a considerably negative impact on the ultimate productivity and yield. Scale-down studies regarding diverse environmental gradients have been carried out on bacteria, yeasts, and filamentous fungi as well as animal cells. In accordance, a variety of scale-down devices combined with fast sampling and quenching protocols have been established to acquire the true snapshots of the perturbed cellular conditions. The perturbed metabolome information stemming from scale-down studies contributed to the comprehension of the production process and the identification of improvement approaches. However, little is known about the influence of the flow field and the mechanisms of intracellular metabolism. Consequently, it is still rather difficult to realize a fully rational scale-up. In the future, developing a computer framework to simulate the flow field of the large-scale fermenters is highly recommended. Furthermore, a metabolically structured kinetic model directly related to the production of penicillin will be further coupled to the fluid flow dynamics. A mathematical model including the information from both computational fluid dynamics and chemical reaction dynamics will then be established for the prediction of detailed information over the entire period of the fermentation process and

Quadratic inner element subgrid scale discretisation of the Boltzmann transport equation

International Nuclear Information System (INIS)

Baker, C.M.J.; Buchan, A.G.; Pain, C.C.; Tollit, B.; Eaton, M.D.; Warner, P.

2012-01-01

This paper explores the application of the inner element subgrid scale method to the Boltzmann transport equation using quadratic basis functions. Previously, only linear basis functions for both the coarse scale and the fine scale were considered. This paper, therefore, analyses the advantages of using different coarse and subgrid basis functions for increasing the accuracy of the subgrid scale method. The transport of neutral particle radiation may be described by the Boltzmann transport equation (BTE) which, due to its 7 dimensional phase space, is computationally expensive to resolve. Multi-scale methods offer an approach to efficiently resolve the spatial dimensions of the BTE by separating the solution into its coarse and fine scales and formulating a solution whereby only the computationally efficient coarse scales need to be solved. In previous work an inner element subgrid scale method was developed that applied a linear continuous and discontinuous finite element method to represent the solution’s coarse and fine scale components. This approach was shown to generate efficient and stable solutions, and so this article continues its development by formulating higher order quadratic finite element expansions over the continuous and discontinuous scales. Here it is shown that a solution’s convergence can be improved significantly using higher order basis functions. Furthermore, by using linear finite elements to represent coarse scales in combination with quadratic fine scales, convergence can also be improved with only a modest increase in computational expense.

Global and exponential attractors of the three dimensional viscous primitive equations of large-scale moist atmosphere

OpenAIRE

You, Bo; Li, Fang

2016-01-01

This paper is concerned with the long-time behavior of solutions for the three dimensional viscous primitive equations of large-scale moist atmosphere. We prove the existence of a global attractor for the three dimensional viscous primitive equations of large-scale moist atmosphere by asymptotic a priori estimate and construct an exponential attractor by using the smoothing property of the semigroup generated by the three dimensional viscous primitive equations of large-scale moist atmosphere...

Development and analysis of prognostic equations for mesoscale kinetic energy and mesoscale (subgrid scale) fluxes for large-scale atmospheric models

Science.gov (United States)

Avissar, Roni; Chen, Fei

1993-01-01

Generated by landscape discontinuities (e.g., sea breezes) mesoscale circulation processes are not represented in large-scale atmospheric models (e.g., general circulation models), which have an inappropiate grid-scale resolution. With the assumption that atmospheric variables can be separated into large scale, mesoscale, and turbulent scale, a set of prognostic equations applicable in large-scale atmospheric models for momentum, temperature, moisture, and any other gaseous or aerosol material, which includes both mesoscale and turbulent fluxes is developed. Prognostic equations are also developed for these mesoscale fluxes, which indicate a closure problem and, therefore, require a parameterization. For this purpose, the mean mesoscale kinetic energy (MKE) per unit of mass is used, defined as E-tilde = 0.5 (the mean value of u'(sub i exp 2), where u'(sub i) represents the three Cartesian components of a mesoscale circulation (the angle bracket symbol is the grid-scale, horizontal averaging operator in the large-scale model, and a tilde indicates a corresponding large-scale mean value). A prognostic equation is developed for E-tilde, and an analysis of the different terms of this equation indicates that the mesoscale vertical heat flux, the mesoscale pressure correlation, and the interaction between turbulence and mesoscale perturbations are the major terms that affect the time tendency of E-tilde. A-state-of-the-art mesoscale atmospheric model is used to investigate the relationship between MKE, landscape discontinuities (as characterized by the spatial distribution of heat fluxes at the earth's surface), and mesoscale sensible and latent heat fluxes in the atmosphere. MKE is compared with turbulence kinetic energy to illustrate the importance of mesoscale processes as compared to turbulent processes. This analysis emphasizes the potential use of MKE to bridge between landscape discontinuities and mesoscale fluxes and, therefore, to parameterize mesoscale fluxes

The flow equation approach to many-particle systems

CERN Document Server

Kehrein, Stefan; Fujimori, A; Varma, C; Steiner, F

2006-01-01

This self-contained monograph addresses the flow equation approach to many-particle systems. The flow equation approach consists of a sequence of infinitesimal unitary transformations and is conceptually similar to renormalization and scaling methods. Flow equations provide a framework for analyzing Hamiltonian systems where these conventional many-body techniques fail. The text first discusses the general ideas and concepts of the flow equation method. In a second part these concepts are illustrated with various applications in condensed matter theory including strong-coupling problems and non-equilibrium systems. The monograph is accessible to readers familiar with graduate- level solid-state theory.

Numerical Simulation of Coupled Nonlinear Schrödinger Equations Using the Generalized Differential Quadrature Method

International Nuclear Information System (INIS)

Mokhtari, R.; Toodar, A. Samadi; Chegini, N. G.

2011-01-01

We the extend application of the generalized differential quadrature method (GDQM) to solve some coupled nonlinear Schrödinger equations. The cosine-based GDQM is employed and the obtained system of ordinary differential equations is solved via the fourth order Runge—Kutta method. The numerical solutions coincide with the exact solutions in desired machine precision and invariant quantities are conserved sensibly. Some comparisons with the methods applied in the literature are carried out. (general)

Multi-scale approximation of Vlasov equation

International Nuclear Information System (INIS)

Mouton, A.

2009-09-01

One of the most important difficulties of numerical simulation of magnetized plasmas is the existence of multiple time and space scales, which can be very different. In order to produce good simulations of these multi-scale phenomena, it is recommended to develop some models and numerical methods which are adapted to these problems. Nowadays, the two-scale convergence theory introduced by G. Nguetseng and G. Allaire is one of the tools which can be used to rigorously derive multi-scale limits and to obtain new limit models which can be discretized with a usual numerical method: this procedure is so-called a two-scale numerical method. The purpose of this thesis is to develop a two-scale semi-Lagrangian method and to apply it on a gyrokinetic Vlasov-like model in order to simulate a plasma submitted to a large external magnetic field. However, the physical phenomena we have to simulate are quite complex and there are many questions without answers about the behaviour of a two-scale numerical method, especially when such a method is applied on a nonlinear model. In a first part, we develop a two-scale finite volume method and we apply it on the weakly compressible 1D isentropic Euler equations. Even if this mathematical context is far from a Vlasov-like model, it is a relatively simple framework in order to study the behaviour of a two-scale numerical method in front of a nonlinear model. In a second part, we develop a two-scale semi-Lagrangian method for the two-scale model developed by E. Frenod, F. Salvarani et E. Sonnendrucker in order to simulate axisymmetric charged particle beams. Even if the studied physical phenomena are quite different from magnetic fusion experiments, the mathematical context of the one-dimensional paraxial Vlasov-Poisson model is very simple for establishing the basis of a two-scale semi-Lagrangian method. In a third part, we use the two-scale convergence theory in order to improve M. Bostan's weak-* convergence results about the finite

Scales and scaling in turbulent ocean sciences; physics-biology coupling

Science.gov (United States)

Schmitt, Francois

2015-04-01

Geophysical fields possess huge fluctuations over many spatial and temporal scales. In the ocean, such property at smaller scales is closely linked to marine turbulence. The velocity field is varying from large scales to the Kolmogorov scale (mm) and scalar fields from large scales to the Batchelor scale, which is often much smaller. As a consequence, it is not always simple to determine at which scale a process should be considered. The scale question is hence fundamental in marine sciences, especially when dealing with physics-biology coupling. For example, marine dynamical models have typically a grid size of hundred meters or more, which is more than 105 times larger than the smallest turbulence scales (Kolmogorov scale). Such scale is fine for the dynamics of a whale (around 100 m) but for a fish larvae (1 cm) or a copepod (1 mm) a description at smaller scales is needed, due to the nonlinear nature of turbulence. The same is verified also for biogeochemical fields such as passive and actives tracers (oxygen, fluorescence, nutrients, pH, turbidity, temperature, salinity...) In this framework, we will discuss the scale problem in turbulence modeling in the ocean, and the relation of Kolmogorov's and Batchelor's scales of turbulence in the ocean, with the size of marine animals. We will also consider scaling laws for organism-particle Reynolds numbers (from whales to bacteria), and possible scaling laws for organism's accelerations.

The πHe3H3 coupling constant estimation using the Chew-Low equation

International Nuclear Information System (INIS)

Mach, R.; Nichitiu, F.

1975-01-01

In this paper it is presented an estimation of the πHe 3 H 3 coupling constant using the Chew-Low equation and a semi-phenomenological analysis of the π -+ He 3 elastic differential cross sections at 98, 120, 135 and 156 MeV

'Scaling-up is a craft not a science': Catalysing scale-up of health innovations in Ethiopia, India and Nigeria.

Science.gov (United States)

Spicer, Neil; Bhattacharya, Dipankar; Dimka, Ritgak; Fanta, Feleke; Mangham-Jefferies, Lindsay; Schellenberg, Joanna; Tamire-Woldemariam, Addis; Walt, Gill; Wickremasinghe, Deepthi

2014-11-01

Donors and other development partners commonly introduce innovative practices and technologies to improve health in low and middle income countries. Yet many innovations that are effective in improving health and survival are slow to be translated into policy and implemented at scale. Understanding the factors influencing scale-up is important. We conducted a qualitative study involving 150 semi-structured interviews with government, development partners, civil society organisations and externally funded implementers, professional associations and academic institutions in 2012/13 to explore scale-up of innovative interventions targeting mothers and newborns in Ethiopia, the Indian state of Uttar Pradesh and the six states of northeast Nigeria, which are settings with high burdens of maternal and neonatal mortality. Interviews were analysed using a common analytic framework developed for cross-country comparison and themes were coded using Nvivo. We found that programme implementers across the three settings require multiple steps to catalyse scale-up. Advocating for government to adopt and finance health innovations requires: designing scalable innovations; embedding scale-up in programme design and allocating time and resources; building implementer capacity to catalyse scale-up; adopting effective approaches to advocacy; presenting strong evidence to support government decision making; involving government in programme design; invoking policy champions and networks; strengthening harmonisation among external programmes; aligning innovations with health systems and priorities. Other steps include: supporting government to develop policies and programmes and strengthening health systems and staff; promoting community uptake by involving media, community leaders, mobilisation teams and role models. We conclude that scale-up has no magic bullet solution - implementers must embrace multiple activities, and require substantial support from donors and governments in

Toward a Common Ontology of Scaling Up in Development

Directory of Open Access Journals (Sweden)

April N. Frake

2018-03-01

Full Text Available Scaling up development measures to target global food insecurity has a distinctly spatial character and is often cited as a solution to the global hunger crisis. Development does not occur without scaling and consensus on the ontological meaning of scaling up is a vital component to developing sustainable solutions to the global hunger crisis across geographical scales. Yet ‘scaling up’, while frequently used throughout Research and Development (R&D and Natural Resource Management (NRM literature, lacks ontological agreement. We begin by considering the noun, ‘scale’ and existing literature on scaling up, then present a visual analysis of definitions provided for scaling up across development institutions. Our study finds that the organization of terms used across these definitions falls into three distinct categories: Interventions, Mechanisms, and Outcomes. Further, we contend that the continued uncertainty is linked to scale being applied in two fashions: as a noun (outcome and verb (process. Rather than calling for reformed definitions, we argue for precision of definitions. To that end, we present a conceptual framework of scaling up that gives greater emphasis on separating the noun scale, from the verb, to scale. Further, Monitoring and Evaluation (M&E in our model complements scaling efforts beginning with how scaling up is defined by program, through to final evaluation of success.

Up scaling two-phase flow in heterogeneous porous media; Mise a l'echelle des ecoulements diphasiques dans les milieux poreux heterogenes

Energy Technology Data Exchange (ETDEWEB)

Artus, V.

2003-11-01

For two-phase flow in heterogeneous media, the emergence of different flow regimes at large-scale is driven by local interactions between the viscous coupling and the heterogeneity. In particular, when the viscosity ratio is favorable, viscous effects induce a transverse flow that stabilizes the front while flooding. However, most of recent stochastic models neglect the influence of the viscous coupling. We developed a stochastic model for the dynamics of the front, taking the viscous coupling into account. For stable cases, this model relates the statistical properties of the front to the statistical properties of the permeability field. For stable flow in stratified media, we show that the front is stationary by parts in the reservoir. These parts can be identified as large-scale hydrodynamic layers and separately coarsened in the large-scale simulation model. For flows with favorable viscosity ratios in isotropic reservoirs, we show that a stationary front occurs, in a statistical sense. For unfavorable viscosity ratios, the flow is driven by the development of viscous fingering. These different regimes lead to different large-scale saturation profiles that can be matched with a macro-dispersion equation, if the effective convective flux is modified to take into account stabilizing or destabilizing viscous effects. (author)

Effective average action for gauge theories and exact evolution equations

International Nuclear Information System (INIS)

Reuter, M.; Wetterich, C.

1993-11-01

We propose a new nonperturbative evolution equation for Yang-Mills theories. It describes the scale dependence of an effective action. The running of the nonabelian gauge coupling in arbitrary dimension is computed. (orig.)

The non-linear coupled spin 2-spin 3 Cotton equation in three dimensions

Energy Technology Data Exchange (ETDEWEB)

Linander, Hampus; Nilsson, Bengt E.W. [Department of Physics, Theoretical PhysicsChalmers University of Technology, S-412 96 Göteborg (Sweden)

2016-07-05

In the context of three-dimensional conformal higher spin theory we derive, in the frame field formulation, the full non-linear spin 3 Cotton equation coupled to spin 2. This is done by solving the corresponding Chern-Simons gauge theory system of equations, that is, using F=0 to eliminate all auxiliary fields and thus expressing the Cotton equation in terms of just the spin 3 frame field and spin 2 covariant derivatives and tensors (Schouten). In this derivation we neglect the spin 4 and higher spin sectors and approximate the star product commutator by a Poisson bracket. The resulting spin 3 Cotton equation is complicated but can be related to linearized versions in the metric formulation obtained previously by other authors. The expected symmetry (spin 3 “translation”, “Lorentz” and “dilatation”) properties are verified for Cotton and other relevant tensors but some perhaps unexpected features emerge in the process, in particular in relation to the non-linear equations. We discuss the structure of this non-linear spin 3 Cotton equation but its explicit form is only presented here, in an exact but not completely refined version, in appended files obtained by computer algebra methods. Both the frame field and metric formulations are provided.

On similarity and scaling of the radiative transfer equation

International Nuclear Information System (INIS)

Mitrescu, C.; Stephens, G.L.

2004-01-01

The present paper shows how the well-known similarity and scaling concepts are properties of the radiative transfer equation and not specifically of the degree of anisotropy of the phase function. It is shown that the key assumption regarding the angular dependence of the radiative field is essential in determining both the value for the parameter used to scale the radiative transfer, as well as the number of streams used in calculating the radiances for various atmospheric problems. Simulations performed on realistic type of cirrus clouds, characterized by strongly anisotropic functions, demonstrates the superior computational advantage for accurately simulating radiances. A new approach for determining the scaling parameter is introduced

Lagrangian derivation of the two coupled field equations in the Janus cosmological model

Science.gov (United States)

Petit, Jean-Pierre; D'Agostini, G.

2015-05-01

After a review citing the results obtained in previous articles introducing the Janus Cosmological Model, consisting of a set of two coupled field equations, where one metrics refers to the positive masses and the other to the negative masses, which explains the observed cosmic acceleration and the nature of dark energy, we present the Lagrangian derivation of the model.

Modulational instability of coupled waves

International Nuclear Information System (INIS)

McKinstrie, C.J.; Bingham, R.

1989-01-01

The collinear propagation of an arbitrary number of finite-amplitude waves is modeled by a system of coupled nonlinear Schroedinger equations; one equation for each complex wave amplitude. In general, the waves are modulationally unstable with a maximal growth rate larger than the modulational growth rate of any wave alone. Moreover, waves that are modulationally stable by themselves can be driven unstable by the nonlinear coupling. The general theory is then applied to the relativistic modulational instability of two laser beams in a beat-wave accelerator. For parameters typical of a proposed beat-wave accelerator, this instability can seriously distort the incident laser pulse shapes on the particle-acceleration time scale, with detrimental consequences for particle acceleration

Treatability and scale-up protocols for polynuclear aromatic hydrocarbon bioremediation of manufactured-gas-plant soils. Final report, September 1987-July 1991

International Nuclear Information System (INIS)

Blackburn, J.W.; DiGrazia, P.M.; Sanseverino, J.

1991-07-01

The report describes activities to develop a framework to reliably scale-up and apply challenging bioremediation processes to polynuclear aromatic hydrocarbons in Manufactured Gas Plant (MGP) soils. It includes: a discussion of the accuracy needed for competitive application of bioremediation; a framework and examples for treatability and scale-up protocols for selection, design and application of these processes; both batch and continuous testing protocols for developing predictive rate data; and special predictive relationships that may be used in process selection/scale-up. The work, coupled with subsequent work (as recommended) to develop an MGP soil desorption/diffusion protocol and new scale-up methods, and with subsequent scale-up testing should lead to the capability for improved selection of MGP sites for bioremediation and improved performance, success, and reliability of field applications. With this greater predictive reliability, bioremediation will be used more often in the field on the most favorable applications and its cost advantages over other remediation options will be realized

A Coupled System of Integrodifferential Equations Arising in Liquidity Risk Model

International Nuclear Information System (INIS)

Pham, Huyen; Tankov, Peter

2009-01-01

We study the mathematical aspects of the portfolio/consumption choice problem in a market model with liquidity risk introduced in (Pham and Tankov, Math. Finance, 2006, to appear). In this model, the investor can trade and observe stock prices only at exogenous Poisson arrival times. He may also consume continuously from his cash holdings, and his goal is to maximize his expected utility from consumption. This is a mixed discrete/continuous time stochastic control problem, nonstandard in the literature. We show how the dynamic programming principle leads to a coupled system of Integro-Differential Equations (IDE), and we prove an analytic characterization of this control problem by adapting the concept of viscosity solutions. This coupled system of IDE may be numerically solved by a decoupling algorithm, and this is the topic of a companion paper (Pham and Tankov, Math. Finance, 2006, to appear)

Scale up risk of developing oil shale processing units

International Nuclear Information System (INIS)

Oepik, I.

1991-01-01

The experiences in oil shale processing in three large countries, China, the U.S.A. and the U.S.S.R. have demonstrated, that the relative scale up risk of developing oil shale processing units is related to the scale up factor. On the background of large programmes for developing the oil shale industry branch, i.e. the $30 billion investments in colorado and Utah or 50 million t/year oil shale processing in Estonia and Leningrad Region planned in the late seventies, the absolute scope of the scale up risk of developing single retorting plants, seems to be justified. But under the conditions of low crude oil prices, when the large-scale development of oil shale processing industry is stopped, the absolute scope of the scale up risk is to be divided between a small number of units. Therefore, it is reasonable to build the new commercial oil shale processing plants with a minimum scale up risk. For example, in Estonia a new oil shale processing plant with gas combustion retorts projected to start in the early nineties will be equipped with four units of 1500 t/day enriched oil shale throughput each, designed with scale up factor M=1.5 and with a minimum scale up risk, only r=2.5-4.5%. The oil shale retorting unit for the PAMA plant in Israel [1] is planned to develop in three steps, also with minimum scale up risk: feasibility studies in Colorado with Israel's shale at Paraho 250 t/day retort and other tests, demonstration retort of 700 t/day and M=2.8 in Israel, and commercial retorts in the early nineties with the capacity of about 1000 t/day with M=1.4. The scale up risk of the PAMA project r=2-4% is approximately the same as that in Estonia. the knowledge of the scope of the scale up risk of developing oil shale processing retorts assists on the calculation of production costs in erecting new units. (author). 9 refs., 2 tabs

BRST, generalized Maurer-Cartan equations and CFT

Energy Technology Data Exchange (ETDEWEB)

Zeitlin, Anton M. [Department of Mathematics, Yale University, 442 Dunham Lab, 10 Hillhouse Ave., New Haven, CT 06511 (United States); St. Petersburg Department of Steklov Mathematical Institute, Fontanka, 27, St. Petersburg 191023 (Russian Federation)]. E-mail: zam@math.ipme.ru

2006-12-25

The paper is devoted to the study of BRST charge in perturbed two-dimensional conformal field theory. The main goal is to write the operator equation expressing the conservation law of BRST charge in perturbed theory in terms of purely algebraic operations on the corresponding operator algebra, which are defined via the OPE. The corresponding equations are constructed and their symmetries are studied up to the second order in formal coupling constant. It appears that the obtained equations can be interpreted as generalized Maurer-Cartan ones. We study two concrete examples in detail: the bosonic nonlinear sigma model and perturbed first order theory. In particular, we show that the Einstein equations, which are the conformal invariance conditions for both these perturbed theories, expanded up to the second order, can be rewritten in such generalized Maurer-Cartan form.

Equation of state at finite net-baryon density using Taylor coefficients up to sixth order

International Nuclear Information System (INIS)

Huovinen, Pasi; Petreczky, Péter; Schmidt, Christian

2014-01-01

We employ the lattice QCD data on Taylor expansion coefficients up to sixth order to construct an equation of state at finite net-baryon density. When we take into account how hadron masses depend on lattice spacing and quark mass, the coefficients evaluated using the p4 action are equal to those of hadron resonance gas at low temperature. Thus the parametrised equation of state can be smoothly connected to the hadron resonance gas equation of state. We see that the equation of state using Taylor coefficients up to second order is realistic only at low densities, and that at densities corresponding to s/n B ≳40, the expansion converges by the sixth order term

Electrokinetic coupling in unsaturated porous media

Energy Technology Data Exchange (ETDEWEB)

Revil, A.; Linde, N.; Cerepi, A.; Jougnot, D.; Matthai, S.; Finsterle, S.

2007-02-27

We consider a charged porous material that is saturated bytwo fluid phases that are immiscible and continuous on the scale of arepresentative elementary volume. The wetting phase for the grains iswater and the nonwetting phase is assumed to be an electricallyinsulating viscous fluid. We use a volume-averaging approach to derivethe linear constitutive equations for the electrical current density aswell as the seepage velocities of the wetting and nonwetting phases onthe scale of a representative elementary volume. These macroscopicconstitutive equations are obtained by volume-averaging Ampere's lawtogether with the Nernst Planck equation and the Stokes equations. Thematerial properties entering the macroscopic constitutive equations areexplicitly described as functions of the saturation of the water phase,the electrical formation factor, and parameters that describe thecapillary pressure function, the relative permeability function, and thevariation of electrical conductivity with saturation. New equations arederived for the streaming potential and electro-osmosis couplingcoefficients. A primary drainage and imbibition experiment is simulatednumerically to demonstrate that the relative streaming potential couplingcoefficient depends not only on the water saturation, but also on thematerial properties of the sample, as well as the saturation history. Wealso compare the predicted streaming potential coupling coefficients withexperimental data from four dolomite core samples. Measurements on thesesamples include electrical conductivity, capillary pressure, thestreaming potential coupling coefficient at various level of saturation,and the permeability at saturation of the rock samples. We found verygood agreement between these experimental data and the modelpredictions.

Excited states by analytic continuation of TBA equations

International Nuclear Information System (INIS)

Dorey, P.; Tateo, R.

1996-01-01

We suggest an approach to the problem of finding integral equations for the excited states of an integrable model, starting from the thermodynamic Bethe ansatz equations for its ground state. The idea relies on analytic continuation through complex values of the coupling constant, and an analysis of the monodromies that the equations and their solutions undergo. For the scaling Lee-Yang model, we find equations in this way for the one- and two-particle states in the spin-zero sector, and suggest various generalisations. Numerical results show excellent agreement with the truncated conformal space approach, and we also treat some of the ultraviolet and infrared asymptotics analytically. (orig.)

Coupled geochemical and solute transport code development

International Nuclear Information System (INIS)

Morrey, J.R.; Hostetler, C.J.

1985-01-01

A number of coupled geochemical hydrologic codes have been reported in the literature. Some of these codes have directly coupled the source-sink term to the solute transport equation. The current consensus seems to be that directly coupling hydrologic transport and chemical models through a series of interdependent differential equations is not feasible for multicomponent problems with complex geochemical processes (e.g., precipitation/dissolution reactions). A two-step process appears to be the required method of coupling codes for problems where a large suite of chemical reactions must be monitored. Two-step structure requires that the source-sink term in the transport equation is supplied by a geochemical code rather than by an analytical expression. We have developed a one-dimensional two-step coupled model designed to calculate relatively complex geochemical equilibria (CTM1D). Our geochemical module implements a Newton-Raphson algorithm to solve heterogeneous geochemical equilibria, involving up to 40 chemical components and 400 aqueous species. The geochemical module was designed to be efficient and compact. A revised version of the MINTEQ Code is used as a parent geochemical code

Coupled energy-drift and force-balance equations for high-field hot-carrier transport

International Nuclear Information System (INIS)

Huang, Danhong; Alsing, P.M.; Apostolova, T.; Cardimona, D.A.

2005-01-01

Coupled energy-drift and force-balance equations that contain a frictional force for the center-of-mass motion of electrons are derived for hot-electron transport under a strong dc electric field. The frictional force is found to be related to the net rate of phonon emission, which takes away the momentum of a phonon from an electron during each phonon-emission event. The net rate of phonon emission is determined by the Boltzmann scattering equation, which depends on the distribution of electrons interacting with phonons. The work done by the frictional force is included into the energy-drift equation for the electron-relative scattering motion and is found to increase the thermal energy of the electrons. The importance of the hot-electron effect in the energy-drift term under a strong dc field is demonstrated in reducing the field-dependent drift velocity and mobility. The Doppler shift in the energy conservation of scattering electrons interacting with impurities and phonons is found to lead to an anisotropic distribution of electrons in the momentum space along the field direction. The importance of this anisotropic distribution is demonstrated through a comparison with the isotropic energy-balance equation, from which we find that defining a state-independent electron temperature becomes impossible. To the leading order, the energy-drift equation is linearized with a distribution function by expanding it into a Fokker-Planck-type equation, along with the expansions of both the force-balance equation and the Boltzmann scattering equation for hot phonons

Mountain-Scale Coupled Processes (TH/THC/THM)

International Nuclear Information System (INIS)

Dixon, P.

2004-01-01

The purpose of this Model Report is to document the development of the Mountain-Scale Thermal-Hydrological (TH), Thermal-Hydrological-Chemical (THC), and Thermal-Hydrological-Mechanical (THM) Models and evaluate the effects of coupled TH/THC/THM processes on mountain-scale UZ flow at Yucca Mountain, Nevada. This Model Report was planned in ''Technical Work Plan (TWP) for: Performance Assessment Unsaturated Zone'' (BSC 2002 [160819], Section 1.12.7), and was developed in accordance with AP-SIII.10Q, Models. In this Model Report, any reference to ''repository'' means the nuclear waste repository at Yucca Mountain, and any reference to ''drifts'' means the emplacement drifts at the repository horizon. This Model Report provides the necessary framework to test conceptual hypotheses for analyzing mountain-scale hydrological/chemical/mechanical changes and predict flow behavior in response to heat release by radioactive decay from the nuclear waste repository at the Yucca Mountain site. The mountain-scale coupled TH/THC/THM processes models numerically simulate the impact of nuclear waste heat release on the natural hydrogeological system, including a representation of heat-driven processes occurring in the far field. The TH simulations provide predictions for thermally affected liquid saturation, gas- and liquid-phase fluxes, and water and rock temperature (together called the flow fields). The main focus of the TH Model is to predict the changes in water flux driven by evaporation/condensation processes, and drainage between drifts. The TH Model captures mountain-scale three dimensional (3-D) flow effects, including lateral diversion at the PTn/TSw interface and mountain-scale flow patterns. The Mountain-Scale THC Model evaluates TH effects on water and gas chemistry, mineral dissolution/precipitation, and the resulting impact to UZ hydrological properties, flow and transport. The THM Model addresses changes in permeability due to mechanical and thermal disturbances in

Mathematical analysis of the dimensional scaling technique for the Schroedinger equation with power-law potentials

International Nuclear Information System (INIS)

Ding Zhonghai; Chen, Goong; Lin, Chang-Shou

2010-01-01

The dimensional scaling (D-scaling) technique is an innovative asymptotic expansion approach to study the multiparticle systems in molecular quantum mechanics. It enables the calculation of ground and excited state energies of quantum systems without having to solve the Schroedinger equation. In this paper, we present a mathematical analysis of the D-scaling technique for the Schroedinger equation with power-law potentials. By casting the D-scaling technique in an appropriate variational setting and studying the corresponding minimization problem, the D-scaling technique is justified rigorously. A new asymptotic dimensional expansion scheme is introduced to compute asymptotic expansions for ground state energies.

Enhanced treatment of Fischer-Tropsch wastewater using up-flow anaerobic sludge blanket system coupled with micro-electrolysis cell: A pilot scale study.

Science.gov (United States)

Wang, Dexin; Han, Yuxing; Han, Hongjun; Li, Kun; Xu, Chunyan

2017-08-01

The coupling of micro-electrolysis cell (MEC) with an up-flow anaerobic sludge blanket (UASB) system in pilot scale was established for enhanced treatment of Fischer-Tropsch (F-T) wastewater. The lowest influent pH (4.99±0.10) and reduced alkali addition were accomplished under the assistance of anaerobic effluent recycling of 200% (stage 5). Simultaneously, the optimum COD removal efficiency (93.5±1.6%) and methane production (2.01±0.13m 3 /m 3 ·d) at the lower hydraulic retention time (HRT) were achieved in this stage. In addition, the dissolved iron from MEC could significantly increase the protein content of tightly bound extracellular polymeric substances (TB-EPS), which was beneficial to formation of stable granules. Furthermore, the high-throughput 16S rRNA gene pyrosequencing in this study further confirmed that Geobacter species could utilize iron oxides particles as electron conduit to perform the direct interspecies electron transfer (DIET) with Methanothrix, finally facilitating the syntrophic degradation of propionic acid and butyric acid and contributing completely methane production. Copyright © 2017 Elsevier Ltd. All rights reserved.

Scaling up: Assessing social impacts at the macro-scale

International Nuclear Information System (INIS)

Schirmer, Jacki

2011-01-01

Social impacts occur at various scales, from the micro-scale of the individual to the macro-scale of the community. Identifying the macro-scale social changes that results from an impacting event is a common goal of social impact assessment (SIA), but is challenging as multiple factors simultaneously influence social trends at any given time, and there are usually only a small number of cases available for examination. While some methods have been proposed for establishing the contribution of an impacting event to macro-scale social change, they remain relatively untested. This paper critically reviews methods recommended to assess macro-scale social impacts, and proposes and demonstrates a new approach. The 'scaling up' method involves developing a chain of logic linking change at the individual/site scale to the community scale. It enables a more problematised assessment of the likely contribution of an impacting event to macro-scale social change than previous approaches. The use of this approach in a recent study of change in dairy farming in south east Australia is described.

Solutions of system of P1 equations without use of auxiliary differential equations coupled; Solucoes do sistema de equacoes P1 sem o uso de equacoes diferenciais auxiliares acopladas

Energy Technology Data Exchange (ETDEWEB)

Martinez, Aquilino Senra; Silva, Fernando Carvalho da; Cardoso, Carlos Eduardo Santos [Universidade Federal, Rio de Janeiro, RJ (Brazil). Coordenacao dos Programas de Pos-graduacao de Engenharia. Programa de Engenharia Nuclear

2000-07-01

The system of P1 equations is composed by two equations coupled itself one for the neutron flux and other for the current. Usually this system is solved by definitions of two integrals parameters, which are named slowing down densities of the flux and the current. Hence, the system P1 can be change from integral to only two differential equations. However, there are two new differentials equations that may be solved with the initial system. The present work analyzes this procedure and studies a method, which solve the P1 equations directly, without definitions of slowing down densities. (author)

Basic Equations Interrelate Atomic and Nuclear Properties to Patterns at the Size Scales of the Cosmos, Extended Clusters of Galaxies, Galaxies, and Nebulae

Science.gov (United States)

Allen, Rob

2016-09-01

Structures within molecules and nuclei have relationships to astronomical patterns. The COBE cosmic scale plots, and large scale surveys of galaxy clusters have patterns also repeating and well known at atomic scales. The Induction, Strong Force, and Nuclear Binding Energy Periods within the Big Bang are revealed to have played roles in the formation of these large scale distributions. Equations related to the enormous patterns also model chemical bonds and likely nucleus and nucleon substructures. ratios of the forces that include gravity are accurately calculated from the distributions and shapes. In addition, particle masses and a great many physical constants can be derived with precision and accuracy from astrophysical shapes. A few very basic numbers can do modelling from nucleon internals to molecules to super novae, and up to the Visible Universe. Equations are also provided along with possible structural configurations for some Cold Dark Matter and Dark Energy.

Polyethylene encapsulation of mixed wastes: Scale-up feasibility

International Nuclear Information System (INIS)

Kalb, P.D.; Heiser, J.H.; Colombo, P.

1991-01-01

A polyethylene process for the improved encapsulation of radioactive, hazardous, and mixed wastes have been developed at Brookhaven National Laboratory (BNL). Improvements in waste loading and waste form performance have been demonstrated through bench-scale development and testing. Maximum waste loadings of up to 70 dry wt % mixed waste nitrate salt were achieved, compared with 13--20 dry wt % using conventional cement processes. Stability under anticipated storage and disposal conditions and compliance with applicable hazardous waste regulations were demonstrated through a series of lab-scale waste form performance tests. Full-scale demonstration of this process using actual or surrogate waste is currently planned. A scale-up feasibility test was successfully conducted, demonstrating the ability to process nitrate salts at production rates (up to 450 kg/hr) and the close agreement between bench- and full-scale process parameters. Cored samples from the resulting pilot-scale (114 liter) waste form were used to verify homogeneity and to provide additional specimens for confirmatory performance testing

Monlinear fish-scale metamaterial via coupled duffing oscillators

OpenAIRE

Kochetov, Bogdan; Tuz, Vladimir; Mladyonov, Pavel; Prosvirnin, Sergey; Kochetova, Lyudmila

2012-01-01

The dynamic system of two coupled Duffing oscillators is considered in order to predict the optical response of the nonlinear planar fish-scale metamaterial. The direct numerical calculation of meta material response confirms the correctness of the proposed model

A Calderón multiplicative preconditioner for coupled surface-volume electric field integral equations

KAUST Repository

Bagci, Hakan

2010-08-01

A well-conditioned coupled set of surface (S) and volume (V) electric field integral equations (S-EFIE and V-EFIE) for analyzing wave interactions with densely discretized composite structures is presented. Whereas the V-EFIE operator is well-posed even when applied to densely discretized volumes, a classically formulated S-EFIE operator is ill-posed when applied to densely discretized surfaces. This renders the discretized coupled S-EFIE and V-EFIE system ill-conditioned, and its iterative solution inefficient or even impossible. The proposed scheme regularizes the coupled set of S-EFIE and V-EFIE using a Calderón multiplicative preconditioner (CMP)-based technique. The resulting scheme enables the efficient analysis of electromagnetic interactions with composite structures containing fine/subwavelength geometric features. Numerical examples demonstrate the efficiency of the proposed scheme. © 2006 IEEE.

Nonlocal symmetries of a class of scalar and coupled nonlinear ordinary differential equations of any order

International Nuclear Information System (INIS)

Pradeep, R Gladwin; Chandrasekar, V K; Senthilvelan, M; Lakshmanan, M

2011-01-01

In this paper, we devise a systematic procedure to obtain nonlocal symmetries of a class of scalar nonlinear ordinary differential equations (ODEs) of arbitrary order related to linear ODEs through nonlocal relations. The procedure makes use of the Lie point symmetries of the linear ODEs and the nonlocal connection to deduce the nonlocal symmetries of the corresponding nonlinear ODEs. Using these nonlocal symmetries, we obtain reduction transformations and reduced equations to specific examples. We find that the reduced equations can be explicitly integrated to deduce the general solutions for these cases. We also extend this procedure to coupled higher order nonlinear ODEs with specific reference to second-order nonlinear ODEs. (paper)

Three-Year Follow-Up of Same-Sex Couples Who Had Civil Unions in Vermont, Same-Sex Couples Not in Civil Unions, and Heterosexual Married Couples

Science.gov (United States)

Balsam, Kimberly F.; Beauchaine, Theodore P.; Rothblum, Esther D.; Solomon, Sondra E.

2008-01-01

This study was a 3-year follow-up of 65 male and 138 female same-sex couples who had civil unions in Vermont during the 1st year of that legislation. These couples were compared with 23 male and 61 female same-sex couples in their friendship circles who did not have civil unions and with 55 heterosexual married couples (1 member of each was a…

Scale transformations, the energy-momentum tensor, and the equation of state

International Nuclear Information System (INIS)

Carruthers, P.

1989-01-01

The Equation of State (EOS) relates diagonal elements of the energy-momentum tensor θ μν . The first moment of the energy-momentum tensor generates scale transformations. The virial theorem, a consequence of the behavior of the energy density under scale transformations, allows one to eliminate the kinetic energy in terms of the potential terms. The trace theorem for the energy-momentum tensor expresses ε-3p in terms of ensemble averages of scale-breaking operators, allowing a new approach to the EOS. 10 refs

Blow-Up Criterion of Weak Solutions for the 3D Boussinesq Equations

Directory of Open Access Journals (Sweden)

Zhaohui Dai

2015-01-01

Full Text Available The Boussinesq equations describe the three-dimensional incompressible fluid moving under the gravity and the earth rotation which come from atmospheric or oceanographic turbulence where rotation and stratification play an important role. In this paper, we investigate the Cauchy problem of the three-dimensional incompressible Boussinesq equations. By commutator estimate, some interpolation inequality, and embedding theorem, we establish a blow-up criterion of weak solutions in terms of the pressure p in the homogeneous Besov space Ḃ∞,∞0.

A burn-up module coupling to an AMPX system

International Nuclear Information System (INIS)

Salvatore Duque, M.; Gomez, S.E.; Patino, N.E.; Abbate, M.J.; Sbaffoni, M.M.

1990-01-01

The Reactors and Neutrons Division of the Bariloche Atomic Center uses the AMPX system for the study of high conversion reactors (HCR). Such system allows to make neutronic calculations from the nuclear data library (ENDF/B-IV). The Nuclear Engineering career of the Balseiro Institute developed and implemented a burn-up module at a μ-cell level (BUM: Burn-up Module) which agrees with the requirement to be coupled to the AMPX system. (Author) [es

Hole-vibrational coupling in Pentacene thin films detected by UPS

International Nuclear Information System (INIS)

Yamame, H.; Fukagawa, H.; Honda, H.; Ono, M.; Okudaira, K.K.; Ueno, N.; Kera, S.; Ishii, H.

2004-01-01

Full text:The hole/electron-vibrational coupling plays a crucial rule in the hole/electron transport in organic devices. In this work, fine structure of the highest occupied molecular orbital (HOMO) band in oriented thin films of pentacene on graphite (HOPG) was studied by using high-resolution ultraviolet photoelectron spectroscopy (UPS). Figure 1 shows the comparison of UPS spectra between pentacene thin films (circles) and gas-phase pentacene (dashed line). We observed a very sharp HOMO band, which consists of at least three components, as observed for Cu-phthalocyanine monolayer on HOPG. It is of note that the relative intensities of fine structures are different between the condensed phase and gas phase, while their energy separations are the same for the two phases (∼ 0.17 eV / 1400 cm -1 ). Furthermore, the relative intensity of fine structures showed remarkable dependence on photoelectron-take-off angle. Judging from these results, the observed fine structures in UPS originate from the hole-vibrational (molecular C-C stretching) coupling in pentacene thin films. At the conference, temperature and thickness dependences of UPS will be discussed

Two- and four-component relativistic generalized-active-space coupled cluster method: implementation and application to BiH.

Science.gov (United States)

Sørensen, Lasse K; Olsen, Jeppe; Fleig, Timo

2011-06-07

A string-based coupled-cluster method of general excitation rank and with optimal scaling which accounts for special relativity within the four-component framework is presented. The method opens the way for the treatment of multi-reference problems through an active-space inspired single-reference based state-selective expansion of the model space. The evaluation of the coupled-cluster vector function is implemented by considering contractions of elementary second-quantized operators without setting up the amplitude equations explicitly. The capabilities of the new method are demonstrated in application to the electronic ground state of the bismuth monohydride molecule. In these calculations simulated multi-reference expansions with both doubles and triples excitations into the external space as well as the regular coupled-cluster hierarchy up to full quadruples excitations are compared. The importance of atomic outer core-correlation for obtaining accurate results is shown. Comparison to the non-relativistic framework is performed throughout to illustrate the additional work of the transition to the four-component relativistic framework both in implementation and application. Furthermore, an evaluation of the highest order scaling for general-order expansions is presented. © 2011 American Institute of Physics

Growth kinetics and scale-up of Agrobacterium tumefaciens.

Science.gov (United States)

Leth, Ingrid K; McDonald, Karen A

2017-06-01

Production of recombinant proteins in plants through Agrobacterium-mediated transient expression is a promising method of producing human therapeutic proteins, vaccines, and commercial enzymes. This process has been shown to be viable at a large scale and involves growing large quantities of wild-type plants and infiltrating the leaf tissue with a suspension of Agrobacterium tumefaciens bearing the genes of interest. This study examined one of the steps in this process that had not yet been optimized: the scale-up of Agrobacterium production to sufficient volumes for large-scale plant infiltration. Production of Agrobacterium strain C58C1 pTFS40 was scaled up from shake flasks (50-100 mL) to benchtop (5 L) scale with three types of media: Lysogeny broth (LB), yeast extract peptone (YEP) media, and a sucrose-based defined media. The maximum specific growth rate (μ max ) of the strain in the three types of media was 0.46 ± 0.04 h -1 in LB media, 0.43 ± 0.03 h -1 in YEP media, and 0.27 ± 0.01 h -1 in defined media. The maximum biomass concentration reached at this scale was 2.0 ± 0.1, 2.8 ± 0.1, and 2.6 ± 0.1 g dry cell weight (DCW)/L for the three media types. Production was successfully scaled up to a 100-L working volume reactor with YEP media, using k L a as the scale-up parameter.

Wave equations on a de Sitter fiber bundle. [Semiclassical wave function, bundle space, L-S coupling

Energy Technology Data Exchange (ETDEWEB)

Drechsler, W [Max-Planck-Institut fuer Physik und Astrophysik, Muenchen (F.R. Germany)

1975-01-01

A gauge theory of strong interaction is developed based on fields defined on a fiber bundle. The structural group of the bundle is taken to be the Lsub(4,1) de Sitter group. An internal variable xi, varying in the fiber over a space-time point x, is introduced as a means to describe - with the help of a semiclassical wave function psi(x,xi) defined on the bundle space - the internal structure of extended hadrons in a framework using differential geometric techniques. Three basic nonlinear wave equations for psi(x,xi) are established which are of integro-differential type. The nonlinear coupling terms in these de Sitter gauge invariant equations represent physically a generalized spin orbit coupling or a generalized spin coupling for the motion taking place in the fiber. The motivation for using a bigger space for the definition of hadronic matter wave functions as well as the implications of this geometric approach to strong interaction physics is discussed in detail, in particular with respect to the problem of hadronic constituents. The proposed fiber bundle formalism allows a dynamical description of extended structures for hadrons without implying the necessity of introducing any constituents.

Instantaneous equations for multiphase flow in porous media without length-scale restrictions using a non-local averaging volume

International Nuclear Information System (INIS)

Espinosa-Paredes, Gilberto

2010-01-01

The aim of this paper is to propose a framework to obtain a new formulation for multiphase flow conservation equations without length-scale restrictions, based on the non-local form of the averaged volume conservation equations. The simplification of the local averaging volume of the conservation equations to obtain practical equations is subject to the following length-scale restrictions: d << l << L, where d is the characteristic length of the dispersed phases, l is the characteristic length of the averaging volume, and L is the characteristic length of the physical system. If the foregoing inequality does not hold, or if the scale of the problem of interest is of the order of l, the averaging technique and therefore, the macroscopic theories of multiphase flow should be modified in order to include appropriate considerations and terms in the corresponding equations. In these cases the local form of the averaged volume conservation equations are not appropriate to describe the multiphase system. As an example of the conservation equations without length-scale restrictions, the natural circulation boiling water reactor was consider to study the non-local effects on the thermal-hydraulic core performance during steady-state and transient behaviors, and the results were compared with the classic local averaging volume conservation equations.

Minimal gravitational coupling in the Newtonian theory and the covariant Schroedinger equation

International Nuclear Information System (INIS)

Duval, C.; Kuenzle, H.P.

1983-02-01

The role of the Bargmann group (11-dimensional extended Galilei group) in non relativistic gravitation theory is investigated. The generalized Newtonian gravitation theory (Newton-Cartan theory) achieves the status of a gauge theory about as much as General Relativity and couples minimally to a complex scalar field leading to a fourdimensionally covariant Schroedinger equation. Matter current and stress-energy tensor follow correctly from the Lagrangian. This theory on curved Newtonian space-time is also shown to be a limit of the Einstein-Klein-Gordon theory

Minimal gravitational coupling in the Newtonian theory and the covariant Schroedinger equation

International Nuclear Information System (INIS)

Duval, C.; Kuenzle, H.P.

1984-01-01

The role of the Bargmann group (11-dimensional extended Galilei group) in nonrelativistic gravitation theory is investigated. The generalized Newtonian gravitation theory (Newton-Cartan theory) achieves the status of a gauge theory about as much as general relativity and couples minimally to a complex scalar field leading to a four-dimensionally covariant Schroedinger equation. Matter current and stress-energy tensor follow correctly from the Lagrangian. This theory on curved Newtonian space-time is also shown to be a limit of the Einstein-Klein-Gordon theory. (author)

Running coupling corrections to high energy inclusive gluon production

International Nuclear Information System (INIS)

Horowitz, W.A.; Kovchegov, Yuri V.

2011-01-01

We calculate running coupling corrections for the lowest-order gluon production cross section in high energy hadronic and nuclear scattering using the BLM scale-setting prescription. In the final answer for the cross section the three powers of fixed coupling are replaced by seven factors of running coupling, five in the numerator and two in the denominator, forming a 'septumvirate' of running couplings, analogous to the 'triumvirate' of running couplings found earlier for the small-x BFKL/BK/JIMWLK evolution equations. It is interesting to note that the two running couplings in the denominator of the 'septumvirate' run with complex-valued momentum scales, which are complex conjugates of each other, such that the production cross section is indeed real. We use our lowest-order result to conjecture how running coupling corrections may enter the full fixed-coupling k T -factorization formula for gluon production which includes nonlinear small-x evolution.

Scale-up of heterogeneous catalytic reactions

Energy Technology Data Exchange (ETDEWEB)

Heggs, P; Sunderland, P

1979-12-01

This report on the Institution of Chemical Engineers ''Problems in Applied Catalysis'' Meeting (Bath, U.K. 1/4-5/78) covers papers on the nature of the catalyst surface, including the use of IR spectroscopy, electron energy loss spectroscopy, low-energy electron diffraction, electron spectroscopy, secondary ion mass spectroscopy, and modular-beam scattering for investigating solid surfaces and their relevance to catalysis; study of the reaction mechanisms by which catalysis takes place; use of mechanistic models to determine the true chemical kinetics illustrated for the oxidation of benzene to maleic anhydride over a vanadium pentoxide/molybdenum trioxide catalyst; the study with respect to the importance of transport effects in catalyst pellets on scale-up, falsification of true kinetics, and the design of laboratory reactors; full-scale reactor design of packed-bed reactors; and practical scale-up problems illustrated for methanol synthesis over a copper catalyst, ammonia oxidation over a cobalt oxide catalyst, and the steam reforming of naphtha.

The SCALE-UP Project

Science.gov (United States)

Beichner, Robert

2015-03-01

The Student Centered Active Learning Environment with Upside-down Pedagogies (SCALE-UP) project was developed nearly 20 years ago as an economical way to provide collaborative, interactive instruction even for large enrollment classes. Nearly all research-based pedagogies have been designed with fairly high faculty-student ratios. The economics of introductory courses at large universities often precludes that situation, so SCALE-UP was created as a way to facilitate highly collaborative active learning with large numbers of students served by only a few faculty and assistants. It enables those students to learn and succeed not only in acquiring content, but also to practice important 21st century skills like problem solving, communication, and teamsmanship. The approach was initially targeted at undergraduate science and engineering students taking introductory physics courses in large enrollment sections. It has since expanded to multiple content areas, including chemistry, math, engineering, biology, business, nursing, and even the humanities. Class sizes range from 24 to over 600. Data collected from multiple sites around the world indicates highly successful implementation at more than 250 institutions. NSF support was critical for initial development and dissemination efforts. Generously supported by NSF (9752313, 9981107) and FIPSE (P116B971905, P116B000659).

Physics on all scales. Scalar-tensor theories of quantum gravity in particle physics and cosmology

Energy Technology Data Exchange (ETDEWEB)

Henz, Tobias

2016-05-10

In this thesis, we investigate dilaton quantum gravity using a functional renormalization group approach. We derive and discuss flow equations both in the background field approximation and using a vertex expansion as well as solve the fixed point equations globally to show how realistic gravity, connecting ultraviolet and infrared physics, can be realized on a pure fixed point trajectory by virtue of spontaneous breaking of scale invariance. The emerging physical system features a dynamically generated moving Planck scale resembling the Newton coupling as well as slow roll inflation with an exponentially decreasing effective cosmological constant that vanishes completely in the infrared. The moving Planck scale might make quantum gravity experimentally accessible at a different energy scale than previously believed. We therefore not only provide further evidence for the existence of a consistent quantum theory of gravity based on general relativity, but also offer potential solutions towards the hierarchy and cosmological constant problems, thereby opening up exciting opportunities for further research.

A mass-energy preserving Galerkin FEM for the coupled nonlinear fractional Schrödinger equations

Science.gov (United States)

Zhang, Guoyu; Huang, Chengming; Li, Meng

2018-04-01

We consider the numerical simulation of the coupled nonlinear space fractional Schrödinger equations. Based on the Galerkin finite element method in space and the Crank-Nicolson (CN) difference method in time, a fully discrete scheme is constructed. Firstly, we focus on a rigorous analysis of conservation laws for the discrete system. The definitions of discrete mass and energy here correspond with the original ones in physics. Then, we prove that the fully discrete system is uniquely solvable. Moreover, we consider the unconditionally convergent properties (that is to say, we complete the error estimates without any mesh ratio restriction). We derive L2-norm error estimates for the nonlinear equations and L^{∞}-norm error estimates for the linear equations. Finally, some numerical experiments are included showing results in agreement with the theoretical predictions.

Scaling-up antiretroviral therapy in Malawi.

Science.gov (United States)

Jahn, Andreas; Harries, Anthony D; Schouten, Erik J; Libamba, Edwin; Ford, Nathan; Maher, Dermot; Chimbwandira, Frank

2016-10-01

In Malawi, health-system constraints meant that only a fraction of people infected with human immunodeficiency virus (HIV) and in immediate need of antiretroviral treatment (ART) received treatment. In 2004, the Malawian Ministry of Health launched plans to scale-up ART nationwide, adhering to the principle of equity to ensure fair geographical access to therapy. A public health approach was used with standardized training and treatment and regular supervision and monitoring of the programme. Before the scale-up, an estimated 930 000 people in Malawi were HIV-infected, with 170 000 in immediate need of ART. About 3000 patients were on ART in nine clinics. By December 2015, cumulatively 872 567 patients had been started on ART from 716 clinics, following national treatment protocols and using the standard monitoring system. Strong national leadership allowed the ministry of health to implement a uniform system for scaling-up ART and provided benchmarks for implementation on the ground. New systems of training staff and accrediting health facilities enabled task-sharing and decentralization to peripheral health centres and a standardized approach to starting and monitoring ART. A system of quarterly supervision and monitoring, into which operational research was embedded, ensured stocks of drug supplies at facilities and adherence to national treatment guidelines.

A geometrical multi-scale numerical method for coupled hygro-thermo-mechanical problems in photovoltaic laminates.

Science.gov (United States)

Lenarda, P; Paggi, M

A comprehensive computational framework based on the finite element method for the simulation of coupled hygro-thermo-mechanical problems in photovoltaic laminates is herein proposed. While the thermo-mechanical problem takes place in the three-dimensional space of the laminate, moisture diffusion occurs in a two-dimensional domain represented by the polymeric layers and by the vertical channel cracks in the solar cells. Therefore, a geometrical multi-scale solution strategy is pursued by solving the partial differential equations governing heat transfer and thermo-elasticity in the three-dimensional space, and the partial differential equation for moisture diffusion in the two dimensional domains. By exploiting a staggered scheme, the thermo-mechanical problem is solved first via a fully implicit solution scheme in space and time, with a specific treatment of the polymeric layers as zero-thickness interfaces whose constitutive response is governed by a novel thermo-visco-elastic cohesive zone model based on fractional calculus. Temperature and relative displacements along the domains where moisture diffusion takes place are then projected to the finite element model of diffusion, coupled with the thermo-mechanical problem by the temperature and crack opening dependent diffusion coefficient. The application of the proposed method to photovoltaic modules pinpoints two important physical aspects: (i) moisture diffusion in humidity freeze tests with a temperature dependent diffusivity is a much slower process than in the case of a constant diffusion coefficient; (ii) channel cracks through Silicon solar cells significantly enhance moisture diffusion and electric degradation, as confirmed by experimental tests.

Laboratory investigation of constitutive property up-scaling in volcanic tuffs

International Nuclear Information System (INIS)

Tidwell, V.C.

1996-08-01

One of the critical issues facing the Yucca Mountain site characterization and performance assessment programs is the manner in which property up-scaling is addressed. Property up-scaling becomes an issue whenever heterogeneous media properties are measured at one scale but applied at another. A research program has been established to challenge current understanding of property up-scaling with the aim of developing and testing improved models that describe up-scaling behavior in a quantitative manner. Up-scaling of constitutive rock properties is investigated through physical experimentation involving the collection of suites of gas-permeability data measured over a range of discrete scales. To date, up-scaling studies have been performed on a series of tuff and sandstone (used as experimental controls) blocks. Samples include a welded, anisotropic tuff (Tiva Canyon Member of the Paintbrush Tuff, upper cliff microstratigraphic unit), and a moderately welded tuff (Tiva Canyon Member of the Paintbrush Tuff, Caprock microstratigraphic unit). A massive fluvial sandstone (Berea Sandstone) was also investigated as a means of evaluating the experimental program and to provide a point of comparison for the tuff data. Because unsaturated flow is of prime interest to the Yucca Mountain Program, scoping studies aimed at investigating the up-scaling of hydraulic properties under various saturated conditions were performed to compliment these studies of intrinsic permeability. These studies focused on matrix sorptivity, a constitutive property quantifying the capillarity of a porous medium. 113 refs

A note on Burgers' equation with time delay: Instability via finite-time blow-up

International Nuclear Information System (INIS)

Jordan, P.M.

2008-01-01

Burgers' equation with time delay is considered. Using the Cole-Hopf transformation, the exact solution of this nonlinear partial differential equation (PDE) is determined in the context of a (seemingly) well-posed initial-boundary value problem (IBVP) involving homogeneous Dirichlet data. The solution obtained, however, is shown to exhibit a delay-induced instability, suffering blow-up in finite-time

Scaled parametric equation of state for steam in the critical region

International Nuclear Information System (INIS)

Murphy, T.A.; Sengers, J.V.

1975-01-01

The anomalous thermodynamic behavior of fluids near the critical point can be described in terms of scaling laws. In recent years a parametric equation of state, the so-called Linear Model, has been proposed that satisfies the scaling laws and contains only a small number of adjustable parameters. It is shown that the Linear Model yields a satisfactory representation of the experimental P-V-T data for steam in the critical region. (29 references)

Biases and statistical errors in Monte Carlo burnup calculations: an unbiased stochastic scheme to solve Boltzmann/Bateman coupled equations

International Nuclear Information System (INIS)

Dumonteil, E.; Diop, C.M.

2011-01-01

External linking scripts between Monte Carlo transport codes and burnup codes, and complete integration of burnup capability into Monte Carlo transport codes, have been or are currently being developed. Monte Carlo linked burnup methodologies may serve as an excellent benchmark for new deterministic burnup codes used for advanced systems; however, there are some instances where deterministic methodologies break down (i.e., heavily angularly biased systems containing exotic materials without proper group structure) and Monte Carlo burn up may serve as an actual design tool. Therefore, researchers are also developing these capabilities in order to examine complex, three-dimensional exotic material systems that do not contain benchmark data. Providing a reference scheme implies being able to associate statistical errors to any neutronic value of interest like k(eff), reaction rates, fluxes, etc. Usually in Monte Carlo, standard deviations are associated with a particular value by performing different independent and identical simulations (also referred to as 'cycles', 'batches', or 'replicas'), but this is only valid if the calculation itself is not biased. And, as will be shown in this paper, there is a bias in the methodology that consists of coupling transport and depletion codes because Bateman equations are not linear functions of the fluxes or of the reaction rates (those quantities being always measured with an uncertainty). Therefore, we have to quantify and correct this bias. This will be achieved by deriving an unbiased minimum variance estimator of a matrix exponential function of a normal mean. The result is then used to propose a reference scheme to solve Boltzmann/Bateman coupled equations, thanks to Monte Carlo transport codes. Numerical tests will be performed with an ad hoc Monte Carlo code on a very simple depletion case and will be compared to the theoretical results obtained with the reference scheme. Finally, the statistical error propagation

On the structure of the master equation for a two-level system coupled to a thermal bath

International Nuclear Information System (INIS)

Vega, Inés de

2015-01-01

We derive a master equation from the exact stochastic Liouville–von-Neumann (SLN) equation (Stockburger and Grabert 2002 Phys. Rev. Lett. 88 170407). The latter depends on two correlated noises and describes exactly the dynamics of an oscillator (which can be either harmonic or present an anharmonicity) coupled to an environment at thermal equilibrium. The newly derived master equation is obtained by performing analytically the average over different noise trajectories. It is found to have a complex hierarchical structure that might be helpful to explain the convergence problems occurring when performing numerically the stochastic average of trajectories given by the SLN equation (Koch et al 2008 Phys. Rev. Lett. 100 230402, Koch 2010 PhD thesis Fakultät Mathematik und Naturwissenschaften der Technischen Universitat Dresden). (paper)

On the structure of the master equation for a two-level system coupled to a thermal bath

Science.gov (United States)

de Vega, Inés

2015-04-01

We derive a master equation from the exact stochastic Liouville-von-Neumann (SLN) equation (Stockburger and Grabert 2002 Phys. Rev. Lett. 88 170407). The latter depends on two correlated noises and describes exactly the dynamics of an oscillator (which can be either harmonic or present an anharmonicity) coupled to an environment at thermal equilibrium. The newly derived master equation is obtained by performing analytically the average over different noise trajectories. It is found to have a complex hierarchical structure that might be helpful to explain the convergence problems occurring when performing numerically the stochastic average of trajectories given by the SLN equation (Koch et al 2008 Phys. Rev. Lett. 100 230402, Koch 2010 PhD thesis Fakultät Mathematik und Naturwissenschaften der Technischen Universitat Dresden).

High Agreement was Obtained Across Scores from Multiple Equated Scales for Social Anxiety Disorder using Item Response Theory.

Science.gov (United States)

Sunderland, Matthew; Batterham, Philip; Calear, Alison; Carragher, Natacha; Baillie, Andrew; Slade, Tim

2018-04-10

There is no standardized approach to the measurement of social anxiety. Researchers and clinicians are faced with numerous self-report scales with varying strengths, weaknesses, and psychometric properties. The lack of standardization makes it difficult to compare scores across populations that utilise different scales. Item response theory offers one solution to this problem via equating different scales using an anchor scale to set a standardized metric. This study is the first to equate several scales for social anxiety disorder. Data from two samples (n=3,175 and n=1,052), recruited from the Australian community using online advertisements, were utilised to equate a network of 11 self-report social anxiety scales via a fixed parameter item calibration method. Comparisons between actual and equated scores for most of the scales indicted a high level of agreement with mean differences <0.10 (equivalent to a mean difference of less than one point on the standardized metric). This study demonstrates that scores from multiple scales that measure social anxiety can be converted to a common scale. Re-scoring observed scores to a common scale provides opportunities to combine research from multiple studies and ultimately better assess social anxiety in treatment and research settings. Copyright © 2018. Published by Elsevier Inc.

Up-scaling expectations among Pakistan's HIV bureaucrats: entrepreneurs of the self and job precariousness post-scale-up.

Science.gov (United States)

Qureshi, Ayaz

2014-01-01

Existing research has documented how the expansion of HIV programming has produced new subjectivities among the recipients of interventions. However, this paper contends that changes in politics, power and subjectivities may also be seen among the HIV bureaucracy in the decade of scale-up. One year's ethnographic fieldwork was conducted among AIDS control officials in Pakistan at a moment of rolling back a World Bank-financed Enhanced Programme. In 2003, the World Bank convinced the Musharraf regime to scale up the HIV response, offering a multimillion dollar soft loan package. I explore how the Enhanced Programme initiated government employees into a new transient work culture and turned the AIDS control programmes into a hybrid bureaucracy. However, the donor money did not last long and individuals' entrepreneurial abilities were tested in a time of crisis engendered by dependence on aid, leaving them precariously exposed to job insecurity, and undermining the continuity of AIDS prevention and treatment in the country. I do not offer a story of global 'best practices' thwarted by local 'lack of capacity', but an ethnographic critique of the transnational HIV apparatus and its neoliberal underpinning. I suggest that this Pakistan-derived analysis is more widely relevant in the post-scale-up decade.

Coupling of discrete ordinates methods by transmission of boundary conditions in solving the neutron transport equation in slab geometry; Couplage de discretisations aux ordonnees discretes d`equations de transport 1D par passage de conditions frontieres

Energy Technology Data Exchange (ETDEWEB)

Bal, G. [Departement MMN, Service IMA, Direction des Etudes et Recherches, Electricite de France (EDF), 92 - Clamart (France)

1995-10-01

Neutron transport in nuclear reactors is quite well modelled by the linear Boltzmann transport equation. Its solution is relatively easy, but unfortunately too expensive to achieve whole core computations. Thus, we have to simplify it, for example by homogenizing some physical characteristics. However, the solution may then be inaccurate. Moreover, in strongly homogeneous areas, the error may be too big. Then we would like to deal with such an inconvenient by solving the equation accurately on this area, but more coarsely away from it, so that the computation is not too expensive. This problem is the subject of a thesis. We present here some results obtained for slab geometry. The couplings between the fine and coarse discretization regions could be conceived in a number of approaches. Here, we only deal with the coupling at crossing the interface between two sub-domains. In the first section, we present the coupling of discrete ordinate methods for solving the homogeneous, isotropic and mono-kinetic equation. Coupling operators are defined and shown to be optimal. The second and the third sections are devoted to an extension of the previous results when the equation is non-homogeneous, anisotropic and multigroup (under some restrictive assumptions). Some numerical results are given in the case of isotropic and mono-kinetic equations. (author) 15 refs.

On the stability, the periodic solutions and the resolution of certain types of non linear equations, and of non linearly coupled systems of these equations, appearing in betatronic oscillations

International Nuclear Information System (INIS)

Valat, J.

1960-12-01

Universal stability diagrams have been calculated and experimentally checked for Hill-Meissner type equations with square-wave coefficients. The study of these equations in the phase-plane has then made it possible to extend the periodic solution calculations to the case of non-linear differential equations with periodic square-wave coefficients. This theory has been checked experimentally. For non-linear coupled systems with constant coefficients, a search was first made for solutions giving an algebraic motion. The elliptical and Fuchs's functions solve such motions. The study of non-algebraic motions is more delicate, apart from the study of nonlinear Lissajous's motions. A functional analysis shows that it is possible however in certain cases to decouple the system and to find general solutions. For non-linear coupled systems with periodic square-wave coefficients it is then possible to calculate the conditions leading to periodic solutions, if the two non-linear associated systems with constant coefficients fall into one of the categories of the above paragraph. (author) [fr

Weak KAM theory for a weakly coupled system of Hamilton–Jacobi equations

KAUST Repository

Figalli, Alessio; Gomes, Diogo A.; Marcon, Diego

2016-01-01

Here, we extend the weak KAM and Aubry–Mather theories to optimal switching problems. We consider three issues: the analysis of the calculus of variations problem, the study of a generalized weak KAM theorem for solutions of weakly coupled systems of Hamilton–Jacobi equations, and the long-time behavior of time-dependent systems. We prove the existence and regularity of action minimizers, obtain necessary conditions for minimality, extend Fathi’s weak KAM theorem, and describe the asymptotic limit of the generalized Lax–Oleinik semigroup. © 2016, Springer-Verlag Berlin Heidelberg.

Weak KAM theory for a weakly coupled system of Hamilton–Jacobi equations

KAUST Repository

Figalli, Alessio

2016-06-23

Here, we extend the weak KAM and Aubry–Mather theories to optimal switching problems. We consider three issues: the analysis of the calculus of variations problem, the study of a generalized weak KAM theorem for solutions of weakly coupled systems of Hamilton–Jacobi equations, and the long-time behavior of time-dependent systems. We prove the existence and regularity of action minimizers, obtain necessary conditions for minimality, extend Fathi’s weak KAM theorem, and describe the asymptotic limit of the generalized Lax–Oleinik semigroup. © 2016, Springer-Verlag Berlin Heidelberg.

Generalized hyperbolic functions to find soliton-like solutions for a system of coupled nonlinear Schroedinger equations

International Nuclear Information System (INIS)

Yomba, Emmanuel

2008-01-01

With the aid of symbolic computation, we demonstrate that the known method which is based on the new generalized hyperbolic functions and the new kinds of generalized hyperbolic function transformations, generates classes of exact solutions to a system of coupled nonlinear Schroedinger equations. This system includes the modified Hubbard model and the system of coupled nonlinear Schroedinger derived by Lazarides and Tsironis. Four types of solutions for this system are given explicitly, namely: new bright-bright, new dark-dark, new bright-dark and new dark-bright solitons

Analytical Solutions for Multi-Time Scale Fractional Stochastic Differential Equations Driven by Fractional Brownian Motion and Their Applications

Directory of Open Access Journals (Sweden)

Xiao-Li Ding

2018-01-01

Full Text Available In this paper, we investigate analytical solutions of multi-time scale fractional stochastic differential equations driven by fractional Brownian motions. We firstly decompose homogeneous multi-time scale fractional stochastic differential equations driven by fractional Brownian motions into independent differential subequations, and give their analytical solutions. Then, we use the variation of constant parameters to obtain the solutions of nonhomogeneous multi-time scale fractional stochastic differential equations driven by fractional Brownian motions. Finally, we give three examples to demonstrate the applicability of our obtained results.

Disrupted coupling of large-scale networks is associated with relapse behaviour in heroin-dependent men

Science.gov (United States)

Li, Qiang; Liu, Jierong; Wang, Wei; Wang, Yarong; Li, Wei; Chen, Jiajie; Zhu, Jia; Yan, Xuejiao; Li, Yongbin; Li, Zhe; Ye, Jianjun; Wang, Wei

2018-01-01

Background It is unknown whether impaired coupling among 3 core large-scale brain networks (salience [SN], default mode [DMN] and executive control networks [ECN]) is associated with relapse behaviour in treated heroin-dependent patients. Methods We conducted a prospective resting-state functional MRI study comparing the functional connectivity strength among healthy controls and heroin-dependent men who had either relapsed or were in early remission. Men were considered to be either relapsed or in early remission based on urine drug screens during a 3-month follow-up period. We also examined how the coupling of large-scale networks correlated with relapse behaviour among heroin-dependent men. Results We included 20 controls and 50 heroin-dependent men (26 relapsed and 24 early remission) in our analyses. The relapsed men showed greater connectivity than the early remission and control groups between the dorsal anterior cingulate cortex (key node of the SN) and the dorsomedial prefrontal cortex (included in the DMN). The relapsed men and controls showed lower connectivity than the early remission group between the left dorsolateral prefrontal cortex (key node of the left ECN) and the dorsomedial prefrontal cortex. The percentage of positive urine drug screens positively correlated with the coupling between the dorsal anterior cingulate cortex and dorsomedial prefrontal cortex, but negatively correlated with the coupling between the left dorsolateral prefrontal cortex and dorsomedial prefrontal cortex. Limitations We examined deficits in only 3 core networks leading to relapse behaviour. Other networks may also contribute to relapse. Conclusion Greater coupling between the SN and DMN and lower coupling between the left ECN and DMN is associated with relapse behaviour. These findings may shed light on the development of new treatments for heroin addiction. PMID:29252165

Travelling Wave Solutions of Coupled Burger’s Equations of Time-Space Fractional Order by Novel (Gʹ/G-Expansion Method

Directory of Open Access Journals (Sweden)

Rashida Hussain

2017-04-01

Full Text Available In this paper, Novel (Gʹ/G-expansion method is used to find new generalized exact travelling wave solutions of fractional order coupled Burger’s equations in terms of trigonometric functions, rational functions and hyperbolic functions with arbitrary parameters. For the conversion of the partial differential equation to the ordinary differential equation, complex transformation method is used. Novel (Gʹ/G-expansion method is very effective and provides a powerful mathematical tool to solve nonlinear equations. Moreover, for the representation of these exact solutions we have plotted graphs for different values of parameters which were in travelling waveform.

Effects of system-bath coupling on a photosynthetic heat engine: A polaron master-equation approach

Science.gov (United States)

Qin, M.; Shen, H. Z.; Zhao, X. L.; Yi, X. X.

2017-07-01

Stimulated by suggestions of quantum effects in energy transport in photosynthesis, the fundamental principles responsible for the near-unit efficiency of the conversion of solar to chemical energy became active again in recent years. Under natural conditions, the formation of stable charge-separation states in bacteria and plant reaction centers is strongly affected by the coupling of electronic degrees of freedom to a wide range of vibrational motions. These inspire and motivate us to explore the effects of the environment on the operation of such complexes. In this paper, we apply the polaron master equation, which offers the possibilities to interpolate between weak and strong system-bath coupling, to study how system-bath couplings affect the exciton-transfer processes in the Photosystem II reaction center described by a quantum heat engine (QHE) model over a wide parameter range. The effects of bath correlation and temperature, together with the combined effects of these factors are also discussed in detail. We interpret these results in terms of noise-assisted transport effect and dynamical localization, which correspond to two mechanisms underpinning the transfer process in photosynthetic complexes: One is resonance energy transfer and the other is the dynamical localization effect captured by the polaron master equation. The effects of system-bath coupling and bath correlation are incorporated in the effective system-bath coupling strength determining whether noise-assisted transport effect or dynamical localization dominates the dynamics and temperature modulates the balance of the two mechanisms. Furthermore, these two mechanisms can be attributed to one physical origin: bath-induced fluctuations. The two mechanisms are manifestations of the dual role played by bath-induced fluctuations depending on the range of parameters. The origin and role of coherence are also discussed. It is the constructive interplay between noise and coherent dynamics, rather

Coupled Higgs field equation and Hamiltonian amplitude equation ...

Indian Academy of Sciences (India)

the rational functions are obtained. Keywords. ... differential equations as is evident by the number of research papers, books and a new symbolic software .... Now using (2.11), (2.14) in (2.8) with C1 = 0 and integrating once we get. P. 2 = − β.

The networks scale and coupling parameter in synchronization of neural networks with diluted synapses

International Nuclear Information System (INIS)

Li Yanlong; Ma Jun; Chen Yuhong; Xu Wenke; Wang Yinghai

2008-01-01

In this paper the influence of the networks scale on the coupling parameter in the synchronization of neural networks with diluted synapses is investigated. Using numerical simulations, an exponential decay form is observed in the extreme case of global coupling among networks and full connection in each network; the larger linked degree becomes, the larger critical coupling intensity becomes; and the oscillation phenomena in the relationship of critical coupling intensity and the number of neural networks layers in the case of small-scale networks are found

Density scaling for multiplets

International Nuclear Information System (INIS)

Nagy, A

2011-01-01

Generalized Kohn-Sham equations are presented for lowest-lying multiplets. The way of treating non-integer particle numbers is coupled with an earlier method of the author. The fundamental quantity of the theory is the subspace density. The Kohn-Sham equations are similar to the conventional Kohn-Sham equations. The difference is that the subspace density is used instead of the density and the Kohn-Sham potential is different for different subspaces. The exchange-correlation functional is studied using density scaling. It is shown that there exists a value of the scaling factor ζ for which the correlation energy disappears. Generalized OPM and Krieger-Li-Iafrate (KLI) methods incorporating correlation are presented. The ζKLI method, being as simple as the original KLI method, is proposed for multiplets.

Smooth, cusped, and discontinuous traveling waves in the periodic fluid resonance equation

Science.gov (United States)

Kruse, Matthew Thomas

The principal motivation for this dissertation is to extend the study of small amplitude high frequency wave propagation in solutions for hyperbolic conservation laws begun by A. Majda and R. Rosales in 1984. It was then that Majda and Rosales obtained equations governing the leading order wave amplitudes of resonantly interacting weakly nonlinear high frequency wave trains in the compressible Euler equations. The equations were obtained through systematic application of multiple scales and result in a pair of nonlinear acoustic wave equations coupled through a convolution operator. The extended solutions satisfy a pair of inviscid Burgers' equations coupled via a spatial convolution operator. Since then, many mathematicians have used this technique to extend the time validity of solutions to systems of equations other than the Euler equations and have arrived at similar nonlinear non-local systems. This work attempts to look at some of the basic features of the linear and nonlinear coupled and decoupled non- local equations, offering some analytic solutions and numerical insight into the phenomena associated with these equations. We do so by examining a single non-local linear equation, and then a single equation coupling a Burgers' nonlinearity with a linear convolution operator. The linear case is completely solvable. Analytic solutions are provided along with numerical results showing the fundamental properties of the linear non- local equations. In the nonlinear case some analytic solutions, including steady state profiles and traveling wave solutions, are provided along with a battery of numerical simulations. Evidence indicates the existence of attractors for solutions of the single equation with a single mode kernel. Provided resonant interaction takes place, the profile of the attractor is uniquely dependent on the kernel alone. Hamiltonian equations are obtained for both the linear and nonlinear equations with the condition that the resonant kernel must

Molecular dynamics on diffusive time scales from the phase-field-crystal equation.

Science.gov (United States)

Chan, Pak Yuen; Goldenfeld, Nigel; Dantzig, Jon

2009-03-01

We extend the phase-field-crystal model to accommodate exact atomic configurations and vacancies by requiring the order parameter to be non-negative. The resulting theory dictates the number of atoms and describes the motion of each of them. By solving the dynamical equation of the model, which is a partial differential equation, we are essentially performing molecular dynamics simulations on diffusive time scales. To illustrate this approach, we calculate the two-point correlation function of a fluid.

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

Large-scale instability in interacting dark energy and dark matter fluids

International Nuclear Information System (INIS)

Väliviita, Jussi; Majerotto, Elisabetta; Maartens, Roy

2008-01-01

If dark energy interacts with dark matter, this gives a new approach to the coincidence problem. But interacting dark energy models can suffer from pathologies. We consider the case where the dark energy is modelled as a fluid with constant equation of state parameter w. Non-interacting constant-w models are well behaved in the background and in the perturbed universe. But the combination of constant w and a simple interaction with dark matter leads to an instability in the dark sector perturbations at early times: the curvature perturbation blows up on super-Hubble scales. Our results underline how important it is to carefully analyse the relativistic perturbations when considering models of coupled dark energy. The instability that we find has been missed in some previous work where the perturbations were not consistently treated. The unstable mode dominates even if adiabatic initial conditions are used. The instability also arises regardless of how weak the coupling is. This non-adiabatic instability is different from previously discovered adiabatic instabilities on small scales in the strong-coupling regime

Synchronous bursts on scale-free neuronal networks with attractive and repulsive coupling.

Directory of Open Access Journals (Sweden)

Qingyun Wang

Full Text Available This paper investigates the dependence of synchronization transitions of bursting oscillations on the information transmission delay over scale-free neuronal networks with attractive and repulsive coupling. It is shown that for both types of coupling, the delay always plays a subtle role in either promoting or impairing synchronization. In particular, depending on the inherent oscillation period of individual neurons, regions of irregular and regular propagating excitatory fronts appear intermittently as the delay increases. These delay-induced synchronization transitions are manifested as well-expressed minima in the measure for spatiotemporal synchrony. For attractive coupling, the minima appear at every integer multiple of the average oscillation period, while for the repulsive coupling, they appear at every odd multiple of the half of the average oscillation period. The obtained results are robust to the variations of the dynamics of individual neurons, the system size, and the neuronal firing type. Hence, they can be used to characterize attractively or repulsively coupled scale-free neuronal networks with delays.

Pin level neutronic - thermal hydraulic two-way-coupling using DYN3D-SP3 and SUBCHANFLOW

International Nuclear Information System (INIS)

Torres, Armando Gomez; Espinoza, Victor Sanchez; Imke, Uwe; Juan, Rafael Macian

2011-01-01

Nowadays several Reactor Dynamic Codes, (RDC) are able to solve the diffusion equation or even the transport equation (SP3 approximation) considering feedback parameters coming from the thermalhydraulic (TH) core behavior. These kinds of codes (DYN3D, PARCS, among others) usually contain a 1D two phase flow thermalhydraulic model capable to pass them assembly averaged feedback parameters. At fuel assembly base this nodal coupling is completely a two way coupling. The Neutronic part calculates the mean power of the whole assembly and passes it to the TH part in order to actualize the heat source. In turn, the TH model passes the assembly-based feedback parameters to the neutronic code for actualizing the nodal cross sections. The process will be repeated until convergence. At pin level, the current situation is somehow different. Although the neutronic solver can pass the pin power distribution in every sub - node (pin distribution), the 1-D TH model will average the pin power distribution to assembly-based scale and will give back assembly averaged feedbacks to the neutronic part for cross sections up-date (one and a half way coupling), leading to information loss in the calculation. A new coupled program system DYNSUB was developed by coupling DYN3D-SP3 and SUBCHANFLOW at pin level. DYNSUB was used to analyze stationary PWR minicore problems at pin-level. The comparison of the Keff predicted by DYNSUB with the one calculated by DYN3D-SP3 (coarse TH solution) shows small differences of up to 26 pcm. Differences up to 4.5% were found in the radial distribution of the pin power. The local safety parameters such as cladding and fuel temperature predicted with DYNSUB shows larger deviations compared with the ones obtained with DYN3D-SP3. These differences may increase when analyzing transients. (author)

Sparse maps—A systematic infrastructure for reduced-scaling electronic structure methods. II. Linear scaling domain based pair natural orbital coupled cluster theory

International Nuclear Information System (INIS)

Riplinger, Christoph; Pinski, Peter; Becker, Ute; Neese, Frank; Valeev, Edward F.

2016-01-01

Domain based local pair natural orbital coupled cluster theory with single-, double-, and perturbative triple excitations (DLPNO-CCSD(T)) is a highly efficient local correlation method. It is known to be accurate and robust and can be used in a black box fashion in order to obtain coupled cluster quality total energies for large molecules with several hundred atoms. While previous implementations showed near linear scaling up to a few hundred atoms, several nonlinear scaling steps limited the applicability of the method for very large systems. In this work, these limitations are overcome and a linear scaling DLPNO-CCSD(T) method for closed shell systems is reported. The new implementation is based on the concept of sparse maps that was introduced in Part I of this series [P. Pinski, C. Riplinger, E. F. Valeev, and F. Neese, J. Chem. Phys. 143, 034108 (2015)]. Using the sparse map infrastructure, all essential computational steps (integral transformation and storage, initial guess, pair natural orbital construction, amplitude iterations, triples correction) are achieved in a linear scaling fashion. In addition, a number of additional algorithmic improvements are reported that lead to significant speedups of the method. The new, linear-scaling DLPNO-CCSD(T) implementation typically is 7 times faster than the previous implementation and consumes 4 times less disk space for large three-dimensional systems. For linear systems, the performance gains and memory savings are substantially larger. Calculations with more than 20 000 basis functions and 1000 atoms are reported in this work. In all cases, the time required for the coupled cluster step is comparable to or lower than for the preceding Hartree-Fock calculation, even if this is carried out with the efficient resolution-of-the-identity and chain-of-spheres approximations. The new implementation even reduces the error in absolute correlation energies by about a factor of two, compared to the already accurate

A multiscale finite element method for modeling fully coupled thermomechanical problems in solids

KAUST Repository

Sengupta, Arkaprabha; Papadopoulos, Panayiotis; Taylor, Robert L.

2012-01-01

This article proposes a two-scale formulation of fully coupled continuum thermomechanics using the finite element method at both scales. A monolithic approach is adopted in the solution of the momentum and energy equations. An efficient implementation of the resulting algorithm is derived that is suitable for multicore processing. The proposed method is applied with success to a strongly coupled problem involving shape-memory alloys. © 2012 John Wiley & Sons, Ltd.

A multiscale finite element method for modeling fully coupled thermomechanical problems in solids

KAUST Repository

Sengupta, Arkaprabha

2012-05-18

This article proposes a two-scale formulation of fully coupled continuum thermomechanics using the finite element method at both scales. A monolithic approach is adopted in the solution of the momentum and energy equations. An efficient implementation of the resulting algorithm is derived that is suitable for multicore processing. The proposed method is applied with success to a strongly coupled problem involving shape-memory alloys. © 2012 John Wiley & Sons, Ltd.

Three-scale expansion of the solution of MHD and Reynolds equations for tokamak

International Nuclear Information System (INIS)

Maslov, V.P.; Omel'yanov, G.A.

1994-01-01

An asymptotic solution of the magnetohydrodynamic equations is constructed. The three scales asymptotic solution describes the non-linear evolution of small, rapidly varying perturbations of equilibrium. It is shown, that an anisotropic coherent structure appears in the linear nonstability situation, and the structures evolution directs to energy interaction between high-frequency and low-frequency waves. The closed system of MHD Reynolds equations for anisotropic structure is derived

Equal-Time and Equal-Space Poisson Brackets of the N -Component Coupled NLS Equation

International Nuclear Information System (INIS)

Zhou Ru-Guang; Li Pei-Yao; Gao Yuan

2017-01-01

Two Poisson brackets for the N-component coupled nonlinear Schrödinger (NLS) equation are derived by using the variantional principle. The first one is called the equal-time Poisson bracket which does not depend on time but only on the space variable. Actually it is just the usual one describing the time evolution of system in the traditional theory of integrable Hamiltonian systems. The second one is equal-space and new. It is shown that the spatial part of Lax pair with respect to the equal-time Poisson bracket and temporal part of Lax pair with respect to the equal-space Poisson bracket share the same r-matrix formulation. These properties are similar to that of the NLS equation. (paper)

Multiple Positive Symmetric Solutions to p-Laplacian Dynamic Equations on Time Scales

Directory of Open Access Journals (Sweden)

You-Hui Su

2009-01-01

two examples are given to illustrate the main results and their differences. These results are even new for the special cases of continuous and discrete equations, as well as in the general time-scale setting.

From global circulation to flood loss: Coupling models across the scales

Science.gov (United States)

Felder, Guido; Gomez-Navarro, Juan Jose; Bozhinova, Denica; Zischg, Andreas; Raible, Christoph C.; Ole, Roessler; Martius, Olivia; Weingartner, Rolf

2017-04-01

The prediction and the prevention of flood losses requires an extensive understanding of underlying meteorological, hydrological, hydraulic and damage processes. Coupled models help to improve the understanding of such underlying processes and therefore contribute the understanding of flood risk. Using such a modelling approach to determine potentially flood-affected areas and damages requires a complex coupling between several models operating at different spatial and temporal scales. Although the isolated parts of the single modelling components are well established and commonly used in the literature, a full coupling including a mesoscale meteorological model driven by a global circulation one, a hydrologic model, a hydrodynamic model and a flood impact and loss model has not been reported so far. In the present study, we tackle the application of such a coupled model chain in terms of computational resources, scale effects, and model performance. From a technical point of view, results show the general applicability of such a coupled model, as well as good model performance. From a practical point of view, such an approach enables the prediction of flood-induced damages, although some future challenges have been identified.

Traveling waves and the renormalization group improvedBalitsky-Kovchegov equation

Energy Technology Data Exchange (ETDEWEB)

Enberg, Rikard

2006-12-01

I study the incorporation of renormalization group (RG)improved BFKL kernels in the Balitsky-Kovchegov (BK) equation whichdescribes parton saturation. The RG improvement takes into accountimportant parts of the next-to-leading and higher order logarithmiccorrections to the kernel. The traveling wave front method for analyzingthe BK equation is generalized to deal with RG-resummed kernels,restricting to the interesting case of fixed QCD coupling. The resultsshow that the higher order corrections suppress the rapid increase of thesaturation scale with increasing rapidity. I also perform a "diffusive"differential equation approximation, which illustrates that someimportant qualitative properties of the kernel change when including RGcorrections.

Nonstandard scaling law of fluctuations in finite-size systems of globally coupled oscillators.

Science.gov (United States)

Nishikawa, Isao; Tanaka, Gouhei; Aihara, Kazuyuki

2013-08-01

Universal scaling laws form one of the central issues in physics. A nonstandard scaling law or a breakdown of a standard scaling law, on the other hand, can often lead to the finding of a new universality class in physical systems. Recently, we found that a statistical quantity related to fluctuations follows a nonstandard scaling law with respect to the system size in a synchronized state of globally coupled nonidentical phase oscillators [I. Nishikawa et al., Chaos 22, 013133 (2012)]. However, it is still unclear how widely this nonstandard scaling law is observed. In the present paper, we discuss the conditions required for the unusual scaling law in globally coupled oscillator systems and validate the conditions by numerical simulations of several different models.

NUMERICAL TECHNIQUES TO SOLVE CONDENSATIONAL AND DISSOLUTIONAL GROWTH EQUATIONS WHEN GROWTH IS COUPLED TO REVERSIBLE REACTIONS (R823186)

Science.gov (United States)

Noniterative, unconditionally stable numerical techniques for solving condensational anddissolutional growth equations are given. Growth solutions are compared to Gear-code solutions forthree cases when growth is coupled to reversible equilibrium chemistry. In all cases, ...

The gambling follow-up scale: development and reliability testing of a scale for pathological gamblers under treatment.

Science.gov (United States)

de Castro, Viviane; Fuentes, Daniel; Tavares, Hermano

2005-02-01

To provide preliminary data on the Gambling Follow-Up Scale (GFS), a new scale assessing recovering gamblers. Secondary goals included assessing the impact of "work status," "family relationship," "leisure," and "enrolment in Gamblers Anonymous (GA)" on gambling (all items from the scale), together with the impact of treatment. Using the GFS, 3 independent raters interviewed gamblers under treatment. The sample was collected in 2 university centres in the city of São Paulo, Brazil. Patients attended psychotherapy coupled with psychiatric follow-up, participation in GA, or both. We interviewed 47 pathological gamblers; 13 were interviewed twice, with a minimum interval of 6 months, for a total of 60 GFS interviews. Interviews took on average 6.0 minutes, SD 2.7. Interrater concordance ranged from 82% to 95% (intraclass correlation coefficient range 0.85 to 0.99, P < 0.001). A factorial analysis showed a 1-factor solution (Eigenvalue = 2.4, 47.6% of total variance accounted). "Leisure," "frequency and time gambling," and "family relationship" showed considerable loadings (0.84; 0.71; 0.71),whereas "enrolment in GA" and "work status" showed moderate loadings (0.59; 0.56). A linear regression model significantly correlated gambling (R2 = 0.356; P < 0.001) with "leisure" and length of treatment. Treatment modalities affected "leisure" (F2,43 = 5.00, P = 0.011), with GA attendees reporting more regular and gratifying activities. The GFS showed interrater reliability and construct validity. More leisure and lengthier treatment were significantly relAted to less gambling. GA enrolment seemed to particularly benefit the quality of leisure. Future studies could profit from the quickness and simple structure of the GFS in providing shareable outcome measures.

The renormalization scale-setting problem in QCD

Energy Technology Data Exchange (ETDEWEB)

Wu, Xing-Gang [Chongqing Univ. (China); Brodsky, Stanley J. [SLAC National Accelerator Lab., Menlo Park, CA (United States); Mojaza, Matin [SLAC National Accelerator Lab., Menlo Park, CA (United States); Univ. of Southern Denmark, Odense (Denmark)

2013-09-01

A key problem in making precise perturbative QCD predictions is to set the proper renormalization scale of the running coupling. The conventional scale-setting procedure assigns an arbitrary range and an arbitrary systematic error to fixed-order pQCD predictions. In fact, this ad hoc procedure gives results which depend on the choice of the renormalization scheme, and it is in conflict with the standard scale-setting procedure used in QED. Predictions for physical results should be independent of the choice of the scheme or other theoretical conventions. We review current ideas and points of view on how to deal with the renormalization scale ambiguity and show how to obtain renormalization scheme- and scale-independent estimates. We begin by introducing the renormalization group (RG) equation and an extended version, which expresses the invariance of physical observables under both the renormalization scheme and scale-parameter transformations. The RG equation provides a convenient way for estimating the scheme- and scale-dependence of a physical process. We then discuss self-consistency requirements of the RG equations, such as reflexivity, symmetry, and transitivity, which must be satisfied by a scale-setting method. Four typical scale setting methods suggested in the literature, i.e., the Fastest Apparent Convergence (FAC) criterion, the Principle of Minimum Sensitivity (PMS), the Brodsky–Lepage–Mackenzie method (BLM), and the Principle of Maximum Conformality (PMC), are introduced. Basic properties and their applications are discussed. We pay particular attention to the PMC, which satisfies all of the requirements of RG invariance. Using the PMC, all non-conformal terms associated with the β-function in the perturbative series are summed into the running coupling, and one obtains a unique, scale-fixed, scheme-independent prediction at any finite order. The PMC provides the principle underlying the BLM method, since it gives the general rule for extending

Spin-orbit splitted excited states using explicitly-correlated equation-of-motion coupled-cluster singles and doubles eigenvectors

Science.gov (United States)

Bokhan, Denis; Trubnikov, Dmitrii N.; Perera, Ajith; Bartlett, Rodney J.

2018-04-01

An explicitly-correlated method of calculation of excited states with spin-orbit couplings, has been formulated and implemented. Developed approach utilizes left and right eigenvectors of equation-of-motion coupled-cluster model, which is based on the linearly approximated explicitly correlated coupled-cluster singles and doubles [CCSD(F12)] method. The spin-orbit interactions are introduced by using the spin-orbit mean field (SOMF) approximation of the Breit-Pauli Hamiltonian. Numerical tests for several atoms and molecules show good agreement between explicitly-correlated results and the corresponding values, calculated in complete basis set limit (CBS); the highly-accurate excitation energies can be obtained already at triple- ζ level.

A range of formulations to couple mass and momentum equations

International Nuclear Information System (INIS)

Darbandi, M.; Schneider, G.E.

2002-01-01

Since the innovation of control-volume-based methods, the issue of pressure-velocity decoupling has prompted the researcher to develop and employ staggered grid arrangement. The difficulties and disadvantages of staggered-grid-based schemes have encouraged the workers to investigate more in alternative scheme, i.e., the collocated-grid-based scheme. The primitive idea in collocated scheme is to couple the mass and momentum equations with the help of two types of velocity definitions instead of two types of grid arrangements. Following the work of preceding workers, we introduce a general strategy which enables the workers to develop a wide range of velocity definitions which can be properly used in collocated formulations. The developed formulations are then tested in a domain with source and sink. The results of the extended formulations are eventually discussed. (author)

Renormalization group equation for interacting Thirring fields in dimensional regularization scheme

International Nuclear Information System (INIS)

Chowdhury, A.R.; Roy, T.; Kar, S.

1976-01-01

The dynamics of two interacting Thirring fields has been investigated within the dimensional regularization framework. The coupling constants are renormalized in the same way as observed in the non-perturbative approach of Ansel'm et al (Sov. Phys. - JETP 36: 608 (1959)). Functionsβsub(i)(g 1 , g 2 , g 3 ) and γsub(i)(g 1 , g 2 , g 3 ), pertaining to the stability and anomalous behaviour of the problem, are computed up to a third order in the coupling parameters. With the help of these, subsidiary non-linear differential equations of the renormalization group are studied in 2-epsilon dimension. The results show up some peculiar features of the theory: a zero of βsub(i)(g 1 , g 2 , g 3 ) corresponding to g 2 approximately α√epsilon, a characteristic of phi theory. The scale invariant limit is reached when g 2 → 0 (i.e. the two Thirring fields are decoupled) and also when g 1 = xg 2 = g 3 , where x is a root of 2x 3 + 2x 2 - 1 = 0. The branch-point zero makes the transition to the epsilon tends to 0 limit non-unique. The anomalous dimensions are obtained and seen to match that of the Dashen-Frishman model (Phys. Lett.; 46B 439 (1973)). The existence of a non-trivial scale invariant limit distinguishes the model from many simple field theories. (author)

Scale-up on electrokinetic remediation: Engineering and technological parameters

Energy Technology Data Exchange (ETDEWEB)

López-Vizcaíno, Rubén [Department of Chemical Engineering, Institute of Chemical & Environmental Technologies, University of Castilla-La Mancha, Campus Universitario s/n, 13071 Ciudad Real (Spain); Navarro, Vicente; León, María J. [Geoenvironmental Group, Civil Engineering School, University of Castilla-La Mancha, Avda. Camilo José Cela s/n, 13071 Ciudad Real (Spain); Risco, Carolina [Department of Chemical Engineering, Institute of Chemical & Environmental Technologies, University of Castilla-La Mancha, Campus Universitario s/n, 13071 Ciudad Real (Spain); Rodrigo, Manuel A., E-mail: manuel.rodrigo@uclm.es [Department of Chemical Engineering, Faculty of Chemical Sciences & Technologies, University of Castilla-La Mancha, Campus Universitario s/n, 13071 Ciudad Real (Spain); Sáez, Cristina; Cañizares, Pablo [Department of Chemical Engineering, Faculty of Chemical Sciences & Technologies, University of Castilla-La Mancha, Campus Universitario s/n, 13071 Ciudad Real (Spain)

2016-09-05

Highlights: • Moisture and compaction of soil must be re-establish in Scale-up of EKR. • Degree of compaction of soil depends on moisture, type of soil and EKR reactor. • Scale of EKR process determines the energy consumption in the treatment. • Electroosmosis and electromigration processes are favoured in prototype scale. • In real scale EKR processes it is important determine evaporation and leaks effects. - Abstract: This study analyses the effect of the scale-up of electrokinetic remediation (EKR) processes in natural soils. A procedure is proposed to prepare soils based on a compacting process to obtaining soils with similar moisture content and density to those found in real soils in the field. The soil used here was from a region with a high agrarian activity (Mora, Spain). The scale-up study was performed in two installations at different scales: a mock-up pilot scale (0.175 m{sup 3}) and a prototype with a scale that was very similar to a real application (16 m{sup 3}). The electrode configuration selected consisted of rows of graphite electrodes facing each other located in electrolyte wells. The discharge of 20 mg of 2,4-dichlorophenoxyacetic acid [2,4-D] per kg of dry soil was treated by applying an electric potential gradient of 1 V cm{sup −1}. An increase in scale was observed to directly influence the amount of energy supplied to the soil being treated. As a result, electroosmotic and electromigration flows and electric heating are more intense than in smaller-scale tests (24%, 1% and 25%, respectively respect to the values in prototype). In addition, possible leaks were evaluated by conducting a watertightness test and quantifying evaporation losses.

3-D pore-scale resolved model for coupled species/charge/fluid transport in a vanadium redox flow battery

International Nuclear Information System (INIS)

Qiu Gang; Joshi, Abhijit S.; Dennison, C.R.; Knehr, K.W.; Kumbur, E.C.; Sun Ying

2012-01-01

The vanadium redox flow battery (VRFB) has emerged as a viable grid-scale energy storage technology that offers cost-effective energy storage solutions for renewable energy applications. In this paper, a novel methodology is introduced for modeling of the transport mechanisms of electrolyte flow, species and charge in the VRFB at the pore scale of the electrodes; that is, at the level where individual carbon fiber geometry and electrolyte flow are directly resolved. The detailed geometry of the electrode is obtained using X-ray computed tomography (XCT) and calibrated against experimentally determined pore-scale characteristics (e.g., pore and fiber diameter, porosity, and surface area). The processed XCT data is then used as geometry input for modeling of the electrochemical processes in the VRFB. The flow of electrolyte through the pore space is modeled using the lattice Boltzmann method (LBM) while the finite volume method (FVM) is used to solve the coupled species and charge transport and predict the performance of the VRFB under various conditions. An electrochemical model using the Butler–Volmer equations is used to provide species and charge coupling at the surfaces of the carbon fibers. Results are obtained for the cell potential distribution, as well as local concentration, overpotential and current density profiles under galvanostatic discharge conditions. The cell performance is investigated as a function of the electrolyte flow rate and external drawing current. The model developed here provides a useful tool for building the structure–property–performance relationship of VRFB electrodes.

Numerical solution of the point reactor kinetics equations with fuel burn-up and temperature feedback

International Nuclear Information System (INIS)

Tashakor, S.; Jahanfarnia, G.; Hashemi-Tilehnoee, M.

2010-01-01

Point reactor kinetics equations are solved numerically using one group of delayed neutrons and with fuel burn-up and temperature feedback included. To calculate the fraction of one-group delayed neutrons, a group of differential equations are solved by an implicit time method. Using point reactor kinetics equations, changes in mean neutrons density, temperature, and reactivity are calculated in different times during the reactor operation. The variation of reactivity, temperature, and maximum power with time are compared with the predictions by other methods.

Up and down or down and up? The process of change in constructive couple behavior during Traditional and Integrative Behavioral Couple Therapy.

Science.gov (United States)

Sevier, Mia; Atkins, David C; Doss, Brian D; Christensen, Andrew

2015-01-01

Observed positive and negative spouse behavior during sessions of Traditional (TBCT) and Integrative Behavioral Couples Therapy (IBCT) were compared for couples with successful outcomes and their unsuccessful counterparts. One hundred and thirty-four married chronically and seriously distressed couples (on average in their forties and 80% Caucasian) were randomly assigned to TBCT or IBCT. Trained observers made ratings of 1224 segments from approximately 956 sessions sampled from the course of up to 26 sessions. Multilevel modeling was used to examine change over time. TBCT treatment responders demonstrated a boost-drop pattern, increasing in constructive behaviors early (more positive behaviors and less negative behaviors) but decreasing later. IBCT responders demonstrated an opposite, drop-boost pattern, decreasing in constructive behaviors early and increasing later. Patterns were significant for positive behaviors (p behaviors (p = .05). In both treatments, nonresponders showed a significant pattern of decline in positive and increase in negative behaviors over time, although a trend (p = .05) indicates that TBCT nonresponders initially declined in negative behaviors. This study helps clarify the different process of change in two behavioral couple therapies, which may assist in treatment development and provide a guide for therapists in considering behavioral markers of change during treatment. © 2013 American Association for Marriage and Family Therapy.

Differential equations extended to superspace

International Nuclear Information System (INIS)

Torres, J.; Rosu, H.C.

2003-01-01

We present a simple SUSY Ns = 2 superspace extension of the differential equations in which the sought solutions are considered to be real superfields but maintaining the common derivative operators and the coefficients of the differential equations unaltered. In this way, we get self consistent systems of coupled differential equations for the components of the superfield. This procedure is applied to the Riccati equation, for which we obtain in addition the system of coupled equations corresponding to the components of the general superfield solution. (Author)

Differential equations extended to superspace

Energy Technology Data Exchange (ETDEWEB)

Torres, J. [Instituto de Fisica, Universidad de Guanajuato, A.P. E-143, Leon, Guanajuato (Mexico); Rosu, H.C. [Instituto Potosino de Investigacion Cientifica y Tecnologica, A.P. 3-74, Tangamanga, San Luis Potosi (Mexico)

2003-07-01

We present a simple SUSY Ns = 2 superspace extension of the differential equations in which the sought solutions are considered to be real superfields but maintaining the common derivative operators and the coefficients of the differential equations unaltered. In this way, we get self consistent systems of coupled differential equations for the components of the superfield. This procedure is applied to the Riccati equation, for which we obtain in addition the system of coupled equations corresponding to the components of the general superfield solution. (Author)

Unbiased minimum variance estimator of a matrix exponential function. Application to Boltzmann/Bateman coupled equations solving

International Nuclear Information System (INIS)

Dumonteil, E.; Diop, C. M.

2009-01-01

This paper derives an unbiased minimum variance estimator (UMVE) of a matrix exponential function of a normal wean. The result is then used to propose a reference scheme to solve Boltzmann/Bateman coupled equations, thanks to Monte Carlo transport codes. The last section will present numerical results on a simple example. (authors)

Analytical Solutions for Multi-Time Scale Fractional Stochastic Differential Equations Driven by Fractional Brownian Motion and Their Applications

OpenAIRE

Xiao-Li Ding; Juan J. Nieto

2018-01-01

In this paper, we investigate analytical solutions of multi-time scale fractional stochastic differential equations driven by fractional Brownian motions. We firstly decompose homogeneous multi-time scale fractional stochastic differential equations driven by fractional Brownian motions into independent differential subequations, and give their analytical solutions. Then, we use the variation of constant parameters to obtain the solutions of nonhomogeneous multi-time scale fractional stochast...

On non-linear dynamics of a coupled electro-mechanical system

DEFF Research Database (Denmark)

Darula, Radoslav; Sorokin, Sergey

2012-01-01

Electro-mechanical devices are an example of coupled multi-disciplinary weakly non-linear systems. Dynamics of such systems is described in this paper by means of two mutually coupled differential equations. The first one, describing an electrical system, is of the first order and the second one...... excitation. The results are verified using a numerical model created in MATLAB Simulink environment. Effect of non-linear terms on dynamical response of the coupled system is investigated; the backbone and envelope curves are analyzed. The two phenomena, which exist in the electro-mechanical system: (a......, for mechanical system, is of the second order. The governing equations are coupled via linear and weakly non-linear terms. A classical perturbation method, a method of multiple scales, is used to find a steadystate response of the electro-mechanical system exposed to a harmonic close-resonance mechanical...

Fractional Sobolev’s Spaces on Time Scales via Conformable Fractional Calculus and Their Application to a Fractional Differential Equation on Time Scales

Directory of Open Access Journals (Sweden)

Yanning Wang

2016-01-01

Full Text Available Using conformable fractional calculus on time scales, we first introduce fractional Sobolev spaces on time scales, characterize them, and define weak conformable fractional derivatives. Second, we prove the equivalence of some norms in the introduced spaces and derive their completeness, reflexivity, uniform convexity, and compactness of some imbeddings, which can be regarded as a novelty item. Then, as an application, we present a recent approach via variational methods and critical point theory to obtain the existence of solutions for a p-Laplacian conformable fractional differential equation boundary value problem on time scale T:  Tα(Tαup-2Tα(u(t=∇F(σ(t,u(σ(t, Δ-a.e.  t∈a,bTκ2, u(a-u(b=0, Tα(u(a-Tα(u(b=0, where Tα(u(t denotes the conformable fractional derivative of u of order α at t, σ is the forward jump operator, a,b∈T,  01, and F:[0,T]T×RN→R. By establishing a proper variational setting, we obtain three existence results. Finally, we present two examples to illustrate the feasibility and effectiveness of the existence results.

Exact renormalization group equation for the Lifshitz critical point

Science.gov (United States)

Bervillier, C.

2004-10-01

An exact renormalization equation (ERGE) accounting for an anisotropic scaling is derived. The critical and tricritical Lifshitz points are then studied at leading order of the derivative expansion which is shown to involve two differential equations. The resulting estimates of the Lifshitz critical exponents compare well with the O(ε) calculations. In the case of the Lifshitz tricritical point, it is shown that a marginally relevant coupling defies the perturbative approach since it actually makes the fixed point referred to in the previous perturbative calculations O(ε) finally unstable.

Scaling Features of Multimode Motions in Coupled Chaotic Oscillators

DEFF Research Database (Denmark)

Pavlov, A.N.; Sosnovtseva, Olga; Mosekilde, Erik

2003-01-01

Two different methods (the WTMM- and DFA-approaches) are applied to investigate the scaling properties in the return-time sequences generated by a system of two coupled chaotic oscillators. Transitions from twomode asynchronous dynamics (torus or torus-Chaos) to different states of chaotic phase ...

On blow-up of solutions of the Kuramoto-Sivashinsky equation

International Nuclear Information System (INIS)

Pokhozhaev, S I

2008-01-01

The problem of the absence of global solutions of initial-boundary value problems for the Kuramoto-Sivashinsky equation is considered. Sufficient conditions for the absence of global solutions of the problems under consideration are obtained both for bounded and unbounded domains. These conditions imply a priori the blow-up of the solution of the corresponding initial-boundary value problem. The proof uses a generalization of the method of non-linear capacity based on the choice of asymptotically optimal test functions. Bibliography: 20 titles.

Direct Computation of Sound Radiation by Jet Flow Using Large-scale Equations

Science.gov (United States)

Mankbadi, R. R.; Shih, S. H.; Hixon, D. R.; Povinelli, L. A.

1995-01-01

Jet noise is directly predicted using large-scale equations. The computational domain is extended in order to directly capture the radiated field. As in conventional large-eddy-simulations, the effect of the unresolved scales on the resolved ones is accounted for. Special attention is given to boundary treatment to avoid spurious modes that can render the computed fluctuations totally unacceptable. Results are presented for a supersonic jet at Mach number 2.1.

Multi-Scale Coupling Between Monte Carlo Molecular Simulation and Darcy-Scale Flow in Porous Media

KAUST Repository

Saad, Ahmed Mohamed; Kadoura, Ahmad Salim; Sun, Shuyu

2016-01-01

In this work, an efficient coupling between Monte Carlo (MC) molecular simulation and Darcy-scale flow in porous media is presented. The cell centered finite difference method with non-uniform rectangular mesh were used to discretize the simulation

Nonlinear analysis of 0-3 polarized PLZT microplate based on the new modified couple stress theory

Science.gov (United States)

Wang, Liming; Zheng, Shijie

2018-02-01

In this study, based on the new modified couple stress theory, the size- dependent model for nonlinear bending analysis of a pure 0-3 polarized PLZT plate is developed for the first time. The equilibrium equations are derived from a variational formulation based on the potential energy principle and the new modified couple stress theory. The Galerkin method is adopted to derive the nonlinear algebraic equations from governing differential equations. And then the nonlinear algebraic equations are solved by using Newton-Raphson method. After simplification, the new model includes only a material length scale parameter. In addition, numerical examples are carried out to study the effect of material length scale parameter on the nonlinear bending of a simply supported pure 0-3 polarized PLZT plate subjected to light illumination and uniform distributed load. The results indicate the new model is able to capture the size effect and geometric nonlinearity.

A Study On the Effectiveness of Emotionally Focused Couple Therapy and Integrated Systemic Couple Therapy on reducing Intimacy Anxiety

Directory of Open Access Journals (Sweden)

هاجر فلاح زاده

2015-04-01

Full Text Available This study examined the effectiveness of emotionally focused couple therapy (EFT and integrated systemic couple therapy (IST on resolving intimacy anxiety. For this purpose, 30 couples were randomly selected and based on their pretests were assigned into two experimental and one control groups. Research instruments were Fear of Intimacy Scale (FIS (Descutner & Thelen, and the Dyadic Adjustment Scale (DAS (Spanier, 1976. A Nine-session of EFT was conducted for one experiment group and eight sessions of IST for the other. The control group did not receive any treatment. These three groups completed post test at the end of the experiment, and follow-up test 3 months later. Results indicated that EFT and IST significantly decreased intimacy anxiety in couples, and the treatment effect was consistent after 3 months follow-up.

Treatment of pairing correlations based on the equations of motion for zero-coupled pair operators

International Nuclear Information System (INIS)

Andreozzi, F.; Covello, A.; Gargano, A.; Ye, L.J.; Porrino, A.

1985-01-01

The pairing problem is treated by means of the equations of motion for zero-coupled pair operators. Exact equations for the seniority-v states of N particles are derived. These equations can be solved by a step-by-step procedure which consists of progressively adding pairs of particles to a core. The theory can be applied at several levels of approximation depending on the number of core states which are taken into account. Some numerical applications to the treatment of v = 0, v = 1, and v = 2 states in the Ni isotopes are performed. The accuracy of various approximations is tested by comparison with exact results. For the seniority-one and seniority-two problems it turns out that the results obtained from the first-order theory are very accurate, while those of higher order calculations are practically exact. Concerning the seniority-zero problem, a fifth-order calculation reproduces quite well the three lowest states

Mode coupling in spin torque oscillators

International Nuclear Information System (INIS)

Zhang, Steven S.-L.; Zhou, Yan; Li, Dong; Heinonen, Olle

2016-01-01

A number of recent experimental works have shown that the dynamics of a single spin torque oscillator can exhibit complex behavior that stems from interactions between two or more modes of the oscillator, such as observed mode-hopping or mode coexistence. There has been some initial work indicating how the theory for a single-mode (macro-spin) spin torque oscillator should be generalized to include several modes and the interactions between them. In the present work, we rigorously derive such a theory starting with the Landau–Lifshitz–Gilbert equation for magnetization dynamics by expanding up to third-order terms in deviation from equilibrium. Our results show how a linear mode coupling, which is necessary for observed mode-hopping to occur, arises through coupling to a magnon bath. The acquired temperature dependence of this coupling implies that the manifold of orbits and fixed points may shift with temperature. - Highlights: • Deriving equations for coupled modes in spin torque oscillators. • Including Hamiltonian formalism and elimination of three–magnon processes. • Thermal bath of magnons central to mode coupling. • Numerical examples of circular and elliptical devices.

Mode coupling in spin torque oscillators

Energy Technology Data Exchange (ETDEWEB)

Zhang, Steven S.-L., E-mail: ZhangShule@missouri.edu [Department of Physics and Astronomy, University of Missouri, Columbia, MO 65211 (United States); Zhou, Yan, E-mail: yanzhou@hku.hk [Department of Physics, The University of Hong Kong, Hong Kong (China); Center of Theoretical and Computational Physics, University of Hong Kong, Hong Kong (China); Li, Dong, E-mail: geodesic.ld@gmail.com [Department of Physics, Centre for Nonlinear Studies, and Beijing-Hong Kong-Singapore Joint Centre for Nonlinear and Complex Systems, Hong Kong Baptist University, Kowloon Tong, Hong Kong (China); Heinonen, Olle, E-mail: heinonen@anl.gov [Material Science Division, Argonne National Laboratory, Lemont, IL 60439 (United States); Northwestern-Argonne Institute of Science and Technology, 2145 Sheridan Road, Evanston, IL 60208 (United States); Computation Institute, The Unversity of Chicago, 5735 S Ellis Avenue, Chicago, IL 60637 (United States)

2016-09-15

A number of recent experimental works have shown that the dynamics of a single spin torque oscillator can exhibit complex behavior that stems from interactions between two or more modes of the oscillator, such as observed mode-hopping or mode coexistence. There has been some initial work indicating how the theory for a single-mode (macro-spin) spin torque oscillator should be generalized to include several modes and the interactions between them. In the present work, we rigorously derive such a theory starting with the Landau–Lifshitz–Gilbert equation for magnetization dynamics by expanding up to third-order terms in deviation from equilibrium. Our results show how a linear mode coupling, which is necessary for observed mode-hopping to occur, arises through coupling to a magnon bath. The acquired temperature dependence of this coupling implies that the manifold of orbits and fixed points may shift with temperature. - Highlights: • Deriving equations for coupled modes in spin torque oscillators. • Including Hamiltonian formalism and elimination of three–magnon processes. • Thermal bath of magnons central to mode coupling. • Numerical examples of circular and elliptical devices.

Scaling up complex interventions: insights from a realist synthesis.

Science.gov (United States)

Willis, Cameron D; Riley, Barbara L; Stockton, Lisa; Abramowicz, Aneta; Zummach, Dana; Wong, Geoff; Robinson, Kerry L; Best, Allan

2016-12-19

Preventing chronic diseases, such as cancer, cardiovascular disease and diabetes, requires complex interventions, involving multi-component and multi-level efforts that are tailored to the contexts in which they are delivered. Despite an increasing number of complex interventions in public health, many fail to be 'scaled up'. This study aimed to increase understanding of how and under what conditions complex public health interventions may be scaled up to benefit more people and populations.A realist synthesis was conducted and discussed at an in-person workshop involving practitioners responsible for scaling up activities. Realist approaches view causality through the linkages between changes in contexts (C) that activate mechanisms (M), leading to specific outcomes (O) (CMO configurations). To focus this review, three cases of complex interventions that had been successfully scaled up were included: Vibrant Communities, Youth Build USA and Pathways to Education. A search strategy of published and grey literature related to each case was developed, involving searches of relevant databases and nominations from experts. Data extracted from included documents were classified according to CMO configurations within strategic themes. Findings were compared and contrasted with guidance from diffusion theory, and interpreted with knowledge users to identify practical implications and potential directions for future research.Four core mechanisms were identified, namely awareness, commitment, confidence and trust. These mechanisms were activated within two broad scaling up strategies, those of renewing and regenerating, and documenting success. Within each strategy, specific actions to change contexts included building partnerships, conducting evaluations, engaging political support and adapting funding models. These modified contexts triggered the identified mechanisms, leading to a range of scaling up outcomes, such as commitment of new communities, changes in relevant

Simulation for Supporting Scale-Up of a Fluidized Bed Reactor for Advanced Water Oxidation

Directory of Open Access Journals (Sweden)

Farhana Tisa

2014-01-01

Full Text Available Simulation of fluidized bed reactor (FBR was accomplished for treating wastewater using Fenton reaction, which is an advanced oxidation process (AOP. The simulation was performed to determine characteristics of FBR performance, concentration profile of the contaminants, and various prominent hydrodynamic properties (e.g., Reynolds number, velocity, and pressure in the reactor. Simulation was implemented for 2.8 L working volume using hydrodynamic correlations, continuous equation, and simplified kinetic information for phenols degradation as a model. The simulation shows that, by using Fe3+ and Fe2+ mixtures as catalyst, TOC degradation up to 45% was achieved for contaminant range of 40–90 mg/L within 60 min. The concentration profiles and hydrodynamic characteristics were also generated. A subsequent scale-up study was also conducted using similitude method. The analysis shows that up to 10 L working volume, the models developed are applicable. The study proves that, using appropriate modeling and simulation, data can be predicted for designing and operating FBR for wastewater treatment.

Impact of the inherent separation of scales in the Navier-Stokes- alphabeta equations.

Science.gov (United States)

Kim, Tae-Yeon; Cassiani, Massimo; Albertson, John D; Dolbow, John E; Fried, Eliot; Gurtin, Morton E

2009-04-01

We study the effect of the length scales alpha and beta in the Navier-Stokes- alphabeta equations on the energy spectrum and the alignment between the vorticity and the eigenvectors of the stretching tensor in three-dimensional homogeneous and isotropic turbulent flows in a periodic cubic domain, including the limiting cases of the Navier-Stokes- alpha and Navier-Stokes equations. A significant increase in the accuracy of the energy spectrum at large wave numbers arises for betaNavier-Stokes- alphabeta equations also improve as beta decreases away from alpha . However, optimal choices for alpha and beta depend not only on the problem of interest but also on the grid resolution.

A SCALE-UP Mock-Up: Comparison of Student Learning Gains in High- and Low-Tech Active-Learning Environments

Science.gov (United States)

Soneral, Paula A. G.; Wyse, Sara A.

2017-01-01

Student-centered learning environments with upside-down pedagogies (SCALE-UP) are widely implemented at institutions across the country, and learning gains from these classrooms have been well documented. This study investigates the specific design feature(s) of the SCALE-UP classroom most conducive to teaching and learning. Using pilot survey data from instructors and students to prioritize the most salient SCALE-UP classroom features, we created a low-tech “Mock-up” version of this classroom and tested the impact of these features on student learning, attitudes, and satisfaction using a quasi-­experimental setup. The same instructor taught two sections of an introductory biology course in the SCALE-UP and Mock-up rooms. Although students in both sections were equivalent in terms of gender, grade point average, incoming ACT, and drop/fail/withdraw rate, the Mock-up classroom enrolled significantly more freshmen. Controlling for class standing, multiple regression modeling revealed no significant differences in exam, in-class, preclass, and Introduction to Molecular and Cellular Biology Concept Inventory scores between the SCALE-UP and Mock-up classrooms. Thematic analysis of student comments highlighted that collaboration and whiteboards enhanced the learning experience, but technology was not important. Student satisfaction and attitudes were comparable. These results suggest that the benefits of a SCALE-UP experience can be achieved at lower cost without technology features. PMID:28213582

Scaling up ITO-Free solar cells

NARCIS (Netherlands)

Galagan, Y.O.; Coenen, E.W.C.; Zimmermann, B.; Slooff, L.H.; Verhees, W.J.H.; Veenstra, S.C.; Kroon, J.M.; Jørgensen, M.; Krebs, F.C.; Andriessen, H.A.J.M.

2014-01-01

Indium-tin-oxide-free (ITO-free) polymer solar cells with composite electrodes containing current-collecting grids and a semitransparent poly(3,4-ethylenedioxythiophene):polystyrenesulfonate) (PEDOT:PSS) conductor are demonstrated. The up-scaling of the length of the solar cell from 1 to 6 cm and

Hydrodynamics at the smallest scales: a solvability criterion for Navier-Stokes equations in high dimensions.

Science.gov (United States)

Viswanathan, T M; Viswanathan, G M

2011-01-28

Strong global solvability is difficult to prove for high-dimensional hydrodynamic systems because of the complex interplay between nonlinearity and scale invariance. We define the Ladyzhenskaya-Lions exponent α(L)(n)=(2+n)/4 for Navier-Stokes equations with dissipation -(-Δ)(α) in R(n), for all n≥2. We review the proof of strong global solvability when α≥α(L)(n), given smooth initial data. If the corresponding Euler equations for n>2 were to allow uncontrolled growth of the enstrophy (1/2)∥∇u∥(L²)(2), then no globally controlled coercive quantity is currently known to exist that can regularize solutions of the Navier-Stokes equations for α<α(L)(n). The energy is critical under scale transformations only for α=α(L)(n).

UP-scaling of inverted small molecule based organic solar cells

DEFF Research Database (Denmark)

Patil, Bhushan Ramesh; Madsen, Morten

Organic solar cells (OSC), in spite of being a promising technology, still face challenges regarding large-scale fabrication. Although efficiencies of up to 12 % has been reached for small molecule OSC, their performance, both in terms of device efficiency and stability, is significantly reduced...... during up-scaling processes. The work presented here is focused on an approach towards up-scaling of small molecule based OSC with inverted device configuration. Bilayer OSC from Tetraphenyldibenzoperiflanthene (DBP) and Fullerenes (C70), as electron donor and acceptor respectively, with cell area...

Identification of a time-varying point source in a system of two coupled linear diffusion-advection- reaction equations: application to surface water pollution

International Nuclear Information System (INIS)

Hamdi, Adel

2009-01-01

This paper deals with the identification of a point source (localization of its position and recovering the history of its time-varying intensity function) that constitutes the right-hand side of the first equation in a system of two coupled 1D linear transport equations. Assuming that the source intensity function vanishes before reaching the final control time, we prove the identifiability of the sought point source from recording the state relative to the second coupled transport equation at two observation points framing the source region. Note that at least one of the two observation points should be strategic. We establish an identification method that uses these records to identify the source position as the root of a continuous and strictly monotonic function. Whereas the source intensity function is recovered using a recursive formula without any need of an iterative process. Some numerical experiments on a variant of the surface water pollution BOD–OD coupled model are presented

Dynamical symmetries of semi-linear Schrodinger and diffusion equations

International Nuclear Information System (INIS)

Stoimenov, Stoimen; Henkel, Malte

2005-01-01

Conditional and Lie symmetries of semi-linear 1D Schrodinger and diffusion equations are studied if the mass (or the diffusion constant) is considered as an additional variable. In this way, dynamical symmetries of semi-linear Schrodinger equations become related to the parabolic and almost-parabolic subalgebras of a three-dimensional conformal Lie algebra (conf 3 ) C . We consider non-hermitian representations and also include a dimensionful coupling constant of the non-linearity. The corresponding representations of the parabolic and almost-parabolic subalgebras of (conf 3 ) C are classified and the complete list of conditionally invariant semi-linear Schrodinger equations is obtained. Possible applications to the dynamical scaling behaviour of phase-ordering kinetics are discussed

Simulation in full-scale mock-ups: an ergonomics evaluation method?

DEFF Research Database (Denmark)

Andersen, Simone Nyholm; Broberg, Ole

2014-01-01

This paper presents and exploratory study of four simulation sessions in full-scale mock-ups of future hospital facilities.......This paper presents and exploratory study of four simulation sessions in full-scale mock-ups of future hospital facilities....

Improving laboratory efficiencies to scale-up HIV viral load testing.

Science.gov (United States)

Alemnji, George; Onyebujoh, Philip; Nkengasong, John N

2017-03-01

Viral load measurement is a key indicator that determines patients' response to treatment and risk for disease progression. Efforts are ongoing in different countries to scale-up access to viral load testing to meet the Joint United Nations Programme on HIV and AIDS target of achieving 90% viral suppression among HIV-infected patients receiving antiretroviral therapy. However, the impact of these initiatives may be challenged by increased inefficiencies along the viral load testing spectrum. This will translate to increased costs and ineffectiveness of scale-up approaches. This review describes different parameters that could be addressed across the viral load testing spectrum aimed at improving efficiencies and utilizing test results for patient management. Though progress is being made in some countries to scale-up viral load, many others still face numerous challenges that may affect scale-up efficiencies: weak demand creation, ineffective supply chain management systems; poor specimen referral systems; inadequate data and quality management systems; and weak laboratory-clinical interface leading to diminished uptake of test results. In scaling up access to viral load testing, there should be a renewed focus to address efficiencies across the entire spectrum, including factors related to access, uptake, and impact of test results.

MgB2 magnetometer with directly coupled pick-up loop

NARCIS (Netherlands)

Portesi, C.; Mijatovic, D.; Veldhuis, Dick; Brinkman, Alexander; Monticone, E.; Gonnelli, R.S.

2006-01-01

magnetometer with a directly coupled pick-up loop. We used an all in situ technique for fabricating magnesium diboride films, which consists of the co-evaporation of B and Mg by means of an e-gun and a resistive heater respectively. Consequently, we realized the superconducting device, which

A model-based framework for incremental scale-up of wastewater treatment processes

DEFF Research Database (Denmark)

Mauricio Iglesias, Miguel; Sin, Gürkan

Scale-up is traditionally done following specific ratios or rules of thumb which do not lead to optimal results. We present a generic framework to assist in scale-up of wastewater treatment processes based on multiscale modelling, multiobjective optimisation and a validation of the model at the new...... large scale. The framework is illustrated by the scale-up of a complete autotropic nitrogen removal process. The model based multiobjective scaleup offers a promising improvement compared to the rule of thumbs based emprical scale up rules...

Transport-diffusion coupling for Candu reactor core follow-Up

International Nuclear Information System (INIS)

Varin, E.; Marleau, G.; Chambon, R.

2003-01-01

We couple the finite reactor diffusion code DONJON and the lattice code DRAGON, called for simplicity DD, to perform reactor follow-up calculations using a history-based approach. In order to do this, a new DD module is developed. This module manages the transfer of information between standard DONJON and DRAGON data structures. Moreover, it stores in a history data structure the global and local parameters required for cell calculations as well as the isotopic composition of the various materials present in each cell of the reactor. We then implement in DD a parallel algorithm to perform history-based Candu reactor calculations. Here, we assign to each processor a specific number of fuel channels to be analyzed. The DRAGON cell calculations for each of the fuel bundles associated with the specified channels are performed on the same processor in order to minimize communication time. Only the macroscopic cross section libraries are exchanged between the processor. Since the amount of data exchanged is relatively small, we expect to obtain an ideal speed-up. The coupling is tested for the analysis of a simplified Candu reactor model with 4 x 4 channels each containing 4 bundles. A 100 full-power days core tracking sequence with 16 refueling steps is studied. Results are coherent with those obtained using more approximate approaches. Parallel speed-up is near optimal indicating that the use of this approach for more realistic reactor calculations should be pursued. (authors)

New tuberculosis technologies: challenges for retooling and scale-up.

Science.gov (United States)

Pai, M; Palamountain, K M

2012-10-01

The availability of new tools does not mean that they will be adopted, used correctly, scaled up or have public health impact. Experience to date with new diagnostics suggests that many national tuberculosis programmes (NTPs) in high-burden countries are reluctant to adopt and scale up new tools, even when these are backed by evidence and global policy recommendations. We suggest that there are several common barriers to effective national adoption and scale-up of new technologies: global policy recommendations that do not provide sufficient information for scale-up, complex decision-making processes and weak political commitment at the country level, limited engagement of and support to NTP managers, high cost of tools and poor fit with user needs, unregulated markets and inadequate business models, limited capacity for laboratory strengthening and implementation research, and insufficient advocacy and donor support. Overcoming these barriers will require enhanced country-level advocacy, resources, technical assistance and political commitment. Some of the BRICS (Brazil, Russia, India, China, South Africa) countries are emerging as early adopters of policies and technologies, and are increasing their investments in TB control. They may provide the first opportunities to fully assess the public health impact of new tools.

Drift-Scale Coupled Processes (DST and THC Seepage) Models

International Nuclear Information System (INIS)

Dixon, P.

2004-01-01

The purpose of this Model Report (REV02) is to document the unsaturated zone (UZ) models used to evaluate the potential effects of coupled thermal-hydrological-chemical (THC) processes on UZ flow and transport. This Model Report has been developed in accordance with the ''Technical Work Plan for: Performance Assessment Unsaturated Zone'' (Bechtel SAIC Company, LLC (BSC) 2002 [160819]). The technical work plan (TWP) describes planning information pertaining to the technical scope, content, and management of this Model Report in Section 1.12, Work Package AUZM08, ''Coupled Effects on Flow and Seepage''. The plan for validation of the models documented in this Model Report is given in Attachment I, Model Validation Plans, Section I-3-4, of the TWP. Except for variations in acceptance criteria (Section 4.2), there were no deviations from this TWP. This report was developed in accordance with AP-SIII.10Q, ''Models''. This Model Report documents the THC Seepage Model and the Drift Scale Test (DST) THC Model. The THC Seepage Model is a drift-scale process model for predicting the composition of gas and water that could enter waste emplacement drifts and the effects of mineral alteration on flow in rocks surrounding drifts. The DST THC model is a drift-scale process model relying on the same conceptual model and much of the same input data (i.e., physical, hydrological, thermodynamic, and kinetic) as the THC Seepage Model. The DST THC Model is the primary method for validating the THC Seepage Model. The DST THC Model compares predicted water and gas compositions, as well as mineral alteration patterns, with observed data from the DST. These models provide the framework to evaluate THC coupled processes at the drift scale, predict flow and transport behavior for specified thermal-loading conditions, and predict the evolution of mineral alteration and fluid chemistry around potential waste emplacement drifts. The DST THC Model is used solely for the validation of the THC

Drift-Scale Coupled Processes (DST and THC Seepage) Models

Energy Technology Data Exchange (ETDEWEB)

E. Gonnenthal; N. Spyoher

2001-02-05

The purpose of this Analysis/Model Report (AMR) is to document the Near-Field Environment (NFE) and Unsaturated Zone (UZ) models used to evaluate the potential effects of coupled thermal-hydrologic-chemical (THC) processes on unsaturated zone flow and transport. This is in accordance with the ''Technical Work Plan (TWP) for Unsaturated Zone Flow and Transport Process Model Report'', Addendum D, Attachment D-4 (Civilian Radioactive Waste Management System (CRWMS) Management and Operating Contractor (M and O) 2000 [153447]) and ''Technical Work Plan for Nearfield Environment Thermal Analyses and Testing'' (CRWMS M and O 2000 [153309]). These models include the Drift Scale Test (DST) THC Model and several THC seepage models. These models provide the framework to evaluate THC coupled processes at the drift scale, predict flow and transport behavior for specified thermal loading conditions, and predict the chemistry of waters and gases entering potential waste-emplacement drifts. The intended use of this AMR is to provide input for the following: (1) Performance Assessment (PA); (2) Abstraction of Drift-Scale Coupled Processes AMR (ANL-NBS-HS-000029); (3) UZ Flow and Transport Process Model Report (PMR); and (4) Near-Field Environment (NFE) PMR. The work scope for this activity is presented in the TWPs cited above, and summarized as follows: continue development of the repository drift-scale THC seepage model used in support of the TSPA in-drift geochemical model; incorporate heterogeneous fracture property realizations; study sensitivity of results to changes in input data and mineral assemblage; validate the DST model by comparison with field data; perform simulations to predict mineral dissolution and precipitation and their effects on fracture properties and chemistry of water (but not flow rates) that may seep into drifts; submit modeling results to the TDMS and document the models. The model development, input data

Drift-Scale Coupled Processes (DST and THC Seepage) Models

International Nuclear Information System (INIS)

Sonnenthale, E.

2001-01-01

The purpose of this Analysis/Model Report (AMR) is to document the Near-Field Environment (NFE) and Unsaturated Zone (UZ) models used to evaluate the potential effects of coupled thermal-hydrologic-chemical (THC) processes on unsaturated zone flow and transport. This is in accordance with the ''Technical Work Plan (TWP) for Unsaturated Zone Flow and Transport Process Model Report'', Addendum D, Attachment D-4 (Civilian Radioactive Waste Management System (CRWMS) Management and Operating Contractor (M and O) 2000 [1534471]) and ''Technical Work Plan for Nearfield Environment Thermal Analyses and Testing'' (CRWMS M and O 2000 [153309]). These models include the Drift Scale Test (DST) THC Model and several THC seepage models. These models provide the framework to evaluate THC coupled processes at the drift scale, predict flow and transport behavior for specified thermal loading conditions, and predict the chemistry of waters and gases entering potential waste-emplacement drifts. The intended use of this AMR is to provide input for the following: Performance Assessment (PA); Near-Field Environment (NFE) PMR; Abstraction of Drift-Scale Coupled Processes AMR (ANL-NBS-HS-000029); and UZ Flow and Transport Process Model Report (PMR). The work scope for this activity is presented in the TWPs cited above, and summarized as follows: Continue development of the repository drift-scale THC seepage model used in support of the TSPA in-drift geochemical model; incorporate heterogeneous fracture property realizations; study sensitivity of results to changes in input data and mineral assemblage; validate the DST model by comparison with field data; perform simulations to predict mineral dissolution and precipitation and their effects on fracture properties and chemistry of water (but not flow rates) that may seep into drifts; submit modeling results to the TDMS and document the models. The model development, input data, sensitivity and validation studies described in this AMR are

Equation for the superfluid gap obtained by coarse graining the Bogoliubov-de Gennes equations throughout the BCS-BEC crossover

Science.gov (United States)

Simonucci, S.; Strinati, G. C.

2014-02-01

We derive a nonlinear differential equation for the gap parameter of a superfluid Fermi system by performing a suitable coarse graining of the Bogoliubov-de Gennes (BdG) equations throughout the BCS-BEC crossover, with the aim of replacing the time-consuming solution of the original BdG equations by the simpler solution of this novel equation. We perform a favorable numerical test on the validity of this new equation over most of the temperature-coupling phase diagram, by an explicit comparison with the full solution of the original BdG equations for an isolated vortex. We also show that the new equation reduces both to the Ginzburg-Landau equation for Cooper pairs in weak coupling close to the critical temperature and to the Gross-Pitaevskii equation for composite bosons in strong coupling at low temperature.

A quasi-Newton algorithm for large-scale nonlinear equations

Directory of Open Access Journals (Sweden)

Linghua Huang

2017-02-01

Full Text Available Abstract In this paper, the algorithm for large-scale nonlinear equations is designed by the following steps: (i a conjugate gradient (CG algorithm is designed as a sub-algorithm to obtain the initial points of the main algorithm, where the sub-algorithm’s initial point does not have any restrictions; (ii a quasi-Newton algorithm with the initial points given by sub-algorithm is defined as main algorithm, where a new nonmonotone line search technique is presented to get the step length α k $\\alpha_{k}$ . The given nonmonotone line search technique can avoid computing the Jacobian matrix. The global convergence and the 1 + q $1+q$ -order convergent rate of the main algorithm are established under suitable conditions. Numerical results show that the proposed method is competitive with a similar method for large-scale problems.

Variational method for the derivative nonlinear Schroedinger equation with computational applications

Energy Technology Data Exchange (ETDEWEB)

Helal, M A [Mathematics Department, Faculty of Science, Cairo University (Egypt); Seadawy, A R [Mathematics Department, Faculty of Science, Beni-Suef University (Egypt)], E-mail: mahelal@yahoo.com, E-mail: aly742001@yahoo.com

2009-09-15

The derivative nonlinear Schroedinger equation (DNLSE) arises as a physical model for ultra-short pulse propagation. In this paper, the existence of a Lagrangian and the invariant variational principle (i.e. in the sense of the inverse problem of calculus of variations through deriving the functional integral corresponding to a given coupled nonlinear partial differential equations) for two-coupled equations describing the nonlinear evolution of the Alfven wave with magnetosonic waves at a much larger scale are given and the functional integral corresponding to those equations is derived. We found the solutions of DNLSE by choice of a trial function in a region of a rectangular box in two cases, and using this trial function, we find the functional integral and the Lagrangian of the system without loss. Solution of the general case for the two-box potential can be obtained on the basis of a different ansatz where we approximate the Jost function using polynomials of order n instead of the piecewise linear function. An example for the third order is given for illustrating the general case.

The effective field theory of cosmological large scale structures

Energy Technology Data Exchange (ETDEWEB)

Carrasco, John Joseph M. [Stanford Univ., Stanford, CA (United States); Hertzberg, Mark P. [Stanford Univ., Stanford, CA (United States); SLAC National Accelerator Lab., Menlo Park, CA (United States); Senatore, Leonardo [Stanford Univ., Stanford, CA (United States); SLAC National Accelerator Lab., Menlo Park, CA (United States)

2012-09-20

Large scale structure surveys will likely become the next leading cosmological probe. In our universe, matter perturbations are large on short distances and small at long scales, i.e. strongly coupled in the UV and weakly coupled in the IR. To make precise analytical predictions on large scales, we develop an effective field theory formulated in terms of an IR effective fluid characterized by several parameters, such as speed of sound and viscosity. These parameters, determined by the UV physics described by the Boltzmann equation, are measured from N-body simulations. We find that the speed of sound of the effective fluid is c²_s ≈ 10^–6c² and that the viscosity contributions are of the same order. The fluid describes all the relevant physics at long scales k and permits a manifestly convergent perturbative expansion in the size of the matter perturbations δ(k) for all the observables. As an example, we calculate the correction to the power spectrum at order δ(k)⁴. As a result, the predictions of the effective field theory are found to be in much better agreement with observation than standard cosmological perturbation theory, already reaching percent precision at this order up to a relatively short scale k ≃ 0.24h Mpc^–1.

High-field transport of electrons and radiative effects using coupled force-balance and Fokker-Planck equations beyond the relaxation-time approximation

International Nuclear Information System (INIS)

Huang, Danhong; Apostolova, T.; Alsing, P.M.; Cardimona, D.A.

2004-01-01

The dynamics of a many-electron system under both dc and infrared fields is separated into a center-of-mass and a relative motion. The first-order force-balance equation is employed for the slow center-of-mass motion of electrons, and the Fokker-Planck equation is used for the ultrafast relative scattering motion of degenerate electrons. This approach allows us to include the anisotropic energy-relaxation process which has been neglected in the energy-balance equation in the past. It also leads us to include the anisotropic coupling to the incident infrared field with different polarizations. Based on this model, the transport of electrons is explored under strong dc and infrared fields by going beyond the relaxation-time approximation. The anisotropic dependence of the electron distribution function on the parallel and perpendicular kinetic energies of electrons is displayed with respect to the dc field direction, and the effect of anisotropic coupling to an incident infrared field with polarizations parallel and perpendicular to the applied dc electric field is shown. The heating of electrons is more accurately described beyond the energy-balance equation with the inclusion of an anisotropic coupling to the infrared field. The drift velocity of electrons is found to increase with the amplitude of the infrared field due to a suppressed momentum-relaxation process (or frictional force) under parallel polarization but decreases with the amplitude due to an enhanced momentum-relaxation process under perpendicular polarization

Equations of motion of test particles for solving the spin-dependent Boltzmann–Vlasov equation

Energy Technology Data Exchange (ETDEWEB)

Xia, Yin [Shanghai Institute of Applied Physics, Chinese Academy of Sciences, Shanghai 201800 (China); University of Chinese Academy of Science, Beijing 100049 (China); Xu, Jun, E-mail: xujun@sinap.ac.cn [Shanghai Institute of Applied Physics, Chinese Academy of Sciences, Shanghai 201800 (China); Li, Bao-An [Department of Physics and Astronomy, Texas A& M University-Commerce, Commerce, TX 75429-3011 (United States); Department of Applied Physics, Xi' an Jiao Tong University, Xi' an 710049 (China); Shen, Wen-Qing [Shanghai Institute of Applied Physics, Chinese Academy of Sciences, Shanghai 201800 (China)

2016-08-10

A consistent derivation of the equations of motion (EOMs) of test particles for solving the spin-dependent Boltzmann–Vlasov equation is presented. The resulting EOMs in phase space are similar to the canonical equations in Hamiltonian dynamics, and the EOM of spin is the same as that in the Heisenburg picture of quantum mechanics. Considering further the quantum nature of spin and choosing the direction of total angular momentum in heavy-ion reactions as a reference of measuring nucleon spin, the EOMs of spin-up and spin-down nucleons are given separately. The key elements affecting the spin dynamics in heavy-ion collisions are identified. The resulting EOMs provide a solid foundation for using the test-particle approach in studying spin dynamics in heavy-ion collisions at intermediate energies. Future comparisons of model simulations with experimental data will help to constrain the poorly known in-medium nucleon spin–orbit coupling relevant for understanding properties of rare isotopes and their astrophysical impacts.

Performance and scaling of locally-structured grid methods forpartial differential equations

Energy Technology Data Exchange (ETDEWEB)

Colella, Phillip; Bell, John; Keen, Noel; Ligocki, Terry; Lijewski, Michael; Van Straalen, Brian

2007-07-19

In this paper, we discuss some of the issues in obtaining high performance for block-structured adaptive mesh refinement software for partial differential equations. We show examples in which AMR scales to thousands of processors. We also discuss a number of metrics for performance and scalability that can provide a basis for understanding the advantages and disadvantages of this approach.

Scaling-Up the Functional Diagnostic Systems

International Nuclear Information System (INIS)

Mohamed, A.H.

2008-01-01

Functional diagnostic systems received a lot of attention in the last decade. They have proven their powerful for diagnosis the new faults of some complex systems. But, they still have some complexity in both the representation and reasoning about the large-scale systems. This paper introduces a new functional diagnostic system that can divide its small functions into main and auxiliary ones. This process enables the diagnostic system to scale -up the representation of the tested system and simplify the diagnostic mechanism tasks. Thus, it can improve both the representation and reasoning complexity. Also,it can decrease the required analysis, cost, and time. Proposed system can be applied for a wide area of the large-scale systems. It has been proven its acceptance to be applied practically for the Complex real-time systems

On the stability, the periodic solutions and the resolution of certain types of non linear equations, and of non linearly coupled systems of these equations, appearing in betatronic oscillations; Sur la stabilite, les solutions periodiques et la resolution de certaines categories d'equations et systemes d'equations differentielles couplees non lineaires apparaissant dans les oscillations betatroniques

Energy Technology Data Exchange (ETDEWEB)

Valat, J [Commissariat a l' Energie Atomique, Saclay (France). Centre d' Etudes Nucleaires

1960-12-15

Universal stability diagrams have been calculated and experimentally checked for Hill-Meissner type equations with square-wave coefficients. The study of these equations in the phase-plane has then made it possible to extend the periodic solution calculations to the case of non-linear differential equations with periodic square-wave coefficients. This theory has been checked experimentally. For non-linear coupled systems with constant coefficients, a search was first made for solutions giving an algebraic motion. The elliptical and Fuchs's functions solve such motions. The study of non-algebraic motions is more delicate, apart from the study of nonlinear Lissajous's motions. A functional analysis shows that it is possible however in certain cases to decouple the system and to find general solutions. For non-linear coupled systems with periodic square-wave coefficients it is then possible to calculate the conditions leading to periodic solutions, if the two non-linear associated systems with constant coefficients fall into one of the categories of the above paragraph. (author) [French] Pour les equations du genre de Hill-Meissner a coefficients creneles, on a calcule des diagrammes universels de stabilite et ceux-ci ont ete verifies experimentalement. L'etude de ces equations dans le plan de phase a permis ensuite d'etendre le calcul des solutions periodiques au cas des equations differentielles non lineaires a coefficients periodiques creneles. Cette theorie a ete verifiee experimentalement. Pour Jes systemes couples non lineaires a coefficients constants, on a d'abord cherche les solutions menant a des mouvements algebriques. Les fonctions elliptiques et fuchsiennes uniformisent de tels mouvements. L'etude de mouvements non algebriques est plus delicate, a part l'etude des mouvements de Lissajous non lineaires. Une analyse fonctionnelle montre qu'il est toutefois possible dans certains cas de decoupler le systeme et de trouver des solutions generales. Pour les

A scale-entropy diffusion equation to describe the multi-scale features of turbulent flames near a wall

Science.gov (United States)

Queiros-Conde, D.; Foucher, F.; Mounaïm-Rousselle, C.; Kassem, H.; Feidt, M.

2008-12-01

Multi-scale features of turbulent flames near a wall display two kinds of scale-dependent fractal features. In scale-space, an unique fractal dimension cannot be defined and the fractal dimension of the front is scale-dependent. Moreover, when the front approaches the wall, this dependency changes: fractal dimension also depends on the wall-distance. Our aim here is to propose a general geometrical framework that provides the possibility to integrate these two cases, in order to describe the multi-scale structure of turbulent flames interacting with a wall. Based on the scale-entropy quantity, which is simply linked to the roughness of the front, we thus introduce a general scale-entropy diffusion equation. We define the notion of “scale-evolutivity” which characterises the deviation of a multi-scale system from the pure fractal behaviour. The specific case of a constant “scale-evolutivity” over the scale-range is studied. In this case, called “parabolic scaling”, the fractal dimension is a linear function of the logarithm of scale. The case of a constant scale-evolutivity in the wall-distance space implies that the fractal dimension depends linearly on the logarithm of the wall-distance. We then verified experimentally, that parabolic scaling represents a good approximation of the real multi-scale features of turbulent flames near a wall.

Application of Exploratory Structural Equation Modeling to Evaluate the Academic Motivation Scale

Science.gov (United States)

Guay, Frédéric; Morin, Alexandre J. S.; Litalien, David; Valois, Pierre; Vallerand, Robert J.

2015-01-01

In this research, the authors examined the construct validity of scores of the Academic Motivation Scale using exploratory structural equation modeling. Study 1 and Study 2 involved 1,416 college students and 4,498 high school students, respectively. First, results of both studies indicated that the factor structure tested with exploratory…

Three-mode resonant coupling of collective excitations in a Bose-Einstein condensate

International Nuclear Information System (INIS)

Ma Yongli; Huang, Guoxiang; Hu Bambi

2005-01-01

We make a systematic study of the resonant mode coupling of the collective excitations at zero temperature in a Bose-Einstein condensate (BEC). (i) Based on the Gross-Pitaevskii equation we derive a set of nonlinearly coupled envelope equations for a three-mode resonant interaction (TMRI) by means of a method of multiple scales. (ii) We calculate the coupling matrix elements for the TMRI and show that the divergence appearing in previous studies can be eliminated completely by using a Fetter-like variational approximation for the ground-state wave function of the condensate. (iii) We provide the selection rules in mode-mode interaction processes [including TMRI and second-harmonic generation (SHG)] according to the symmetry of the excitations. (iv) By solving the nonlinearly coupled envelope equations we obtain divergence-free nonlinear amplitudes for the TMRI and SHG processes and show that our theoretical results on the shape oscillations of the condensate agree well with the experimental ones. We suggest also an experiment to check the theoretical prediction of the present study on the TMRI of collective excitations in a BEC

Millions Learning: Scaling up Quality Education in Developing Countries

Science.gov (United States)

Robinson, Jenny Perlman; Winthrop, Rebecca

2016-01-01

"Millions Learning: Scaling up Quality Education in Developing Countries" tells the story of where and how quality education has scaled in low- and middle-income countries. The story emerges from wide-ranging research on scaling and learning, including 14 in-depth case studies from around the globe. Ultimately, "Millions…

The coupling of fluids, dynamics, and controls on advanced architecture computers

Science.gov (United States)

Atwood, Christopher

1995-01-01

This grant provided for the demonstration of coupled controls, body dynamics, and fluids computations in a workstation cluster environment; and an investigation of the impact of peer-peer communication on flow solver performance and robustness. The findings of these investigations were documented in the conference articles.The attached publication, 'Towards Distributed Fluids/Controls Simulations', documents the solution and scaling of the coupled Navier-Stokes, Euler rigid-body dynamics, and state feedback control equations for a two-dimensional canard-wing. The poor scaling shown was due to serialized grid connectivity computation and Ethernet bandwidth limits. The scaling of a peer-to-peer communication flow code on an IBM SP-2 was also shown. The scaling of the code on the switched fabric-linked nodes was good, with a 2.4 percent loss due to communication of intergrid boundary point information. The code performance on 30 worker nodes was 1.7 (mu)s/point/iteration, or a factor of three over a Cray C-90 head. The attached paper, 'Nonlinear Fluid Computations in a Distributed Environment', documents the effect of several computational rate enhancing methods on convergence. For the cases shown, the highest throughput was achieved using boundary updates at each step, with the manager process performing communication tasks only. Constrained domain decomposition of the implicit fluid equations did not degrade the convergence rate or final solution. The scaling of a coupled body/fluid dynamics problem on an Ethernet-linked cluster was also shown.

Comparison of different Maxwell solvers coupled to a PIC resolution method of Maxwell-Vlasov equations

International Nuclear Information System (INIS)

Fochesato, Ch.; Bouche, D.

2007-01-01

The numerical solution of Maxwell equations is a challenging task. Moreover, the range of applications is very wide: microwave devices, diffraction, to cite a few. As a result, a number of methods have been proposed since the sixties. However, among all these methods, none has proved to be free of drawbacks. The finite difference scheme proposed by Yee in 1966, is well suited for Maxwell equations. However, it only works on cubical mesh. As a result, the boundaries of complex objects are not properly handled by the scheme. When classical nodal finite elements are used, spurious modes appear, which spoil the results of simulations. Edge elements overcome this problem, at the price of rather complex implementation, and computationally intensive simulations. Finite volume methods, either generalizing Yee scheme to a wider class of meshes, or applying to Maxwell equations methods initially used in the field of hyperbolic systems of conservation laws, are also used. Lastly, 'Discontinuous Galerkin' methods, generalizing to arbitrary order of accuracy finite volume methods, have recently been applied to Maxwell equations. In this report, we more specifically focus on the coupling of a Maxwell solver to a PIC (Particle-in-cell) method. We analyze advantages and drawbacks of the most widely used methods: accuracy, robustness, sensitivity to numerical artefacts, efficiency, user judgment. (authors)

Soliton on a cnoidal wave background in the coupled nonlinear Schroedinger equation

International Nuclear Information System (INIS)

Shin, H J

2004-01-01

An application of the Darboux transformation on a cnoidal wave background in the coupled nonlinear Schroedinger equation gives a new solution which describes a soliton moving on a cnoidal wave. This is a generalized version of the previously known soliton solutions of dark-bright pair. Here a dark soliton resides on a cnoidal wave instead of on a constant background. It also exhibits a new type of soliton solution in a self-focusing medium, which describes a breakup of a generalized dark-bright pair into another generalized dark-bright pair and an 'oscillating' soliton. We calculate the shift of the crest of the cnoidal wave along a soliton and the moving direction of the soliton on a cnoidal wave

Scaling up Effects in the Organic Laboratory

Science.gov (United States)

Persson, Anna; Lindstrom, Ulf M.

2004-01-01

A simple and effective way of exposing chemistry students to some of the effects of scaling up an organic reaction is described. It gives the student an experience that may encounter in an industrial setting.

Integrable discretization s of derivative nonlinear Schroedinger equations

International Nuclear Information System (INIS)

Tsuchida, Takayuki

2002-01-01

We propose integrable discretizations of derivative nonlinear Schroedinger (DNLS) equations such as the Kaup-Newell equation, the Chen-Lee-Liu equation and the Gerdjikov-Ivanov equation by constructing Lax pairs. The discrete DNLS systems admit the reduction of complex conjugation between two dependent variables and possess bi-Hamiltonian structure. Through transformations of variables and reductions, we obtain novel integrable discretizations of the nonlinear Schroedinger (NLS), modified KdV (mKdV), mixed NLS, matrix NLS, matrix KdV, matrix mKdV, coupled NLS, coupled Hirota, coupled Sasa-Satsuma and Burgers equations. We also discuss integrable discretizations of the sine-Gordon equation, the massive Thirring model and their generalizations. (author)

A SCALE-UP Mock-Up: Comparison of Student Learning Gains in High- and Low-Tech Active-Learning Environments.

Science.gov (United States)

Soneral, Paula A G; Wyse, Sara A

2017-01-01

Student-centered learning environments with upside-down pedagogies (SCALE-UP) are widely implemented at institutions across the country, and learning gains from these classrooms have been well documented. This study investigates the specific design feature(s) of the SCALE-UP classroom most conducive to teaching and learning. Using pilot survey data from instructors and students to prioritize the most salient SCALE-UP classroom features, we created a low-tech "Mock-up" version of this classroom and tested the impact of these features on student learning, attitudes, and satisfaction using a quasi--experimental setup. The same instructor taught two sections of an introductory biology course in the SCALE-UP and Mock-up rooms. Although students in both sections were equivalent in terms of gender, grade point average, incoming ACT, and drop/fail/withdraw rate, the Mock-up classroom enrolled significantly more freshmen. Controlling for class standing, multiple regression modeling revealed no significant differences in exam, in-class, preclass, and Introduction to Molecular and Cellular Biology Concept Inventory scores between the SCALE-UP and Mock-up classrooms. Thematic analysis of student comments highlighted that collaboration and whiteboards enhanced the learning experience, but technology was not important. Student satisfaction and attitudes were comparable. These results suggest that the benefits of a SCALE-UP experience can be achieved at lower cost without technology features. © 2017 P. A. G. Soneral and S. A. Wyse. CBE—Life Sciences Education © 2017 The American Society for Cell Biology. This article is distributed by The American Society for Cell Biology under license from the author(s). It is available to the public under an Attribution–Noncommercial–Share Alike 3.0 Unported Creative Commons License (http://creativecommons.org/licenses/by-nc-sa/3.0).

A variational master equation approach to quantum dynamics with off-diagonal coupling in a sub-Ohmic environment

Energy Technology Data Exchange (ETDEWEB)

Sun, Ke-Wei [School of Science, Hangzhou Dianzi University, Hangzhou 310018 (China); Division of Materials Science, Nanyang Technological University, 50 Nanyang Avenue, Singapore 639798 (Singapore); Fujihashi, Yuta; Ishizaki, Akihito [Institute for Molecular Science, National Institutes of Natural Sciences, Okazaki 444-8585 (Japan); Zhao, Yang, E-mail: YZhao@ntu.edu.sg [Division of Materials Science, Nanyang Technological University, 50 Nanyang Avenue, Singapore 639798 (Singapore)

2016-05-28

A master equation approach based on an optimized polaron transformation is adopted for dynamics simulation with simultaneous diagonal and off-diagonal spin-boson coupling. Two types of bath spectral density functions are considered, the Ohmic and the sub-Ohmic. The off-diagonal coupling leads asymptotically to a thermal equilibrium with a nonzero population difference P{sub z}(t → ∞) ≠ 0, which implies localization of the system, and it also plays a role in restraining coherent dynamics for the sub-Ohmic case. Since the new method can extend to the stronger coupling regime, we can investigate the coherent-incoherent transition in the sub-Ohmic environment. Relevant phase diagrams are obtained for different temperatures. It is found that the sub-Ohmic environment allows coherent dynamics at a higher temperature than the Ohmic environment.

Coupling biomechanics to a cellular level model: an approach to patient-specific image driven multi-scale and multi-physics tumor simulation.

Science.gov (United States)

May, Christian P; Kolokotroni, Eleni; Stamatakos, Georgios S; Büchler, Philippe

2011-10-01

Modeling of tumor growth has been performed according to various approaches addressing different biocomplexity levels and spatiotemporal scales. Mathematical treatments range from partial differential equation based diffusion models to rule-based cellular level simulators, aiming at both improving our quantitative understanding of the underlying biological processes and, in the mid- and long term, constructing reliable multi-scale predictive platforms to support patient-individualized treatment planning and optimization. The aim of this paper is to establish a multi-scale and multi-physics approach to tumor modeling taking into account both the cellular and the macroscopic mechanical level. Therefore, an already developed biomodel of clinical tumor growth and response to treatment is self-consistently coupled with a biomechanical model. Results are presented for the free growth case of the imageable component of an initially point-like glioblastoma multiforme tumor. The composite model leads to significant tumor shape corrections that are achieved through the utilization of environmental pressure information and the application of biomechanical principles. Using the ratio of smallest to largest moment of inertia of the tumor material to quantify the effect of our coupled approach, we have found a tumor shape correction of 20% by coupling biomechanics to the cellular simulator as compared to a cellular simulation without preferred growth directions. We conclude that the integration of the two models provides additional morphological insight into realistic tumor growth behavior. Therefore, it might be used for the development of an advanced oncosimulator focusing on tumor types for which morphology plays an important role in surgical and/or radio-therapeutic treatment planning. Copyright © 2011 Elsevier Ltd. All rights reserved.

Critical initial-slip scaling for the noisy complex Ginzburg–Landau equation

International Nuclear Information System (INIS)

Liu, Weigang; Täuber, Uwe C

2016-01-01

We employ the perturbative fieldtheoretic renormalization group method to investigate the universal critical behavior near the continuous non-equilibrium phase transition in the complex Ginzburg–Landau equation with additive white noise. This stochastic partial differential describes a remarkably wide range of physical systems: coupled nonlinear oscillators subject to external noise near a Hopf bifurcation instability; spontaneous structure formation in non-equilibrium systems, e.g., in cyclically competing populations; and driven-dissipative Bose–Einstein condensation, realized in open systems on the interface of quantum optics and many-body physics, such as cold atomic gases and exciton-polaritons in pumped semiconductor quantum wells in optical cavities. Our starting point is a noisy, dissipative Gross–Pitaevski or nonlinear Schrödinger equation, or equivalently purely relaxational kinetics originating from a complex-valued Landau–Ginzburg functional, which generalizes the standard equilibrium model A critical dynamics of a non-conserved complex order parameter field. We study the universal critical behavior of this system in the early stages of its relaxation from a Gaussian-weighted fully randomized initial state. In this critical aging regime, time translation invariance is broken, and the dynamics is characterized by the stationary static and dynamic critical exponents, as well as an independent ‘initial-slip’ exponent. We show that to first order in the dimensional expansion about the upper critical dimension, this initial-slip exponent in the complex Ginzburg–Landau equation is identical to its equilibrium model A counterpart. We furthermore employ the renormalization group flow equations as well as construct a suitable complex spherical model extension to argue that this conclusion likely remains true to all orders in the perturbation expansion. (paper)

Fundamental burn-up mode in a pebble-bed type reactor

International Nuclear Information System (INIS)

Chen, Xue-Nong; Kiefhaber, Edgar; Maschek, Werner

2008-01-01

This paper deals with a pebble-bed type reactor, in which the fuel is loaded from one side (top) and discharged from the other side (bottom). A boundary value problem of a single group diffusion equation coupled with simplified burn-up equations is studied, where the natural radioactive decay processes are neglected in the burn-up modelling. An asymptotic burning wave solution is found analytically in the one-dimensional case, which is called as fundamental burn-up mode. Among this solution family there are two particular cases, namely, a classic fundamental solution with a zero burn-up and a partial solitary burn-up wave solution with a highest burn-up. An example of Th-U conversion is considered and the solutions are presented in order to show the mechanism of the burning wave. (author)

Constraints on hyperon couplings from neutron star equations of state

CERN Document Server

Miyazaki, K

2005-01-01

Based on the constituent quark picture of baryons and taking into account the contributions of isovector and strange mesons, we have developed the extended Zimanyi-Moszkowski model of dense baryon matter for studying neutron star (NS) equations of state (EOSs). Four sets of meson-hyperons coupling constants are investigated. The first is characterized by strong attractive N\\Sigma interaction while the others have repulsive N\\Sigma interactions. The second is characterized by strong attractive \\Lambda\\Lambda interaction. The third has weak \\Lambda\\Lambda but strong attractive \\Sigma\\Sigma interactions. The last one has much weaker \\Sigma\\Sigma interaction than the third one. By systematic analyses of the EOSs and mass sequences of NSs, it has been found that the strong attractive N\\Sigma, \\Lambda\\Lambda and \\Sigma\\Sigma interactions are ruled out. The result is consistent to the most recent information on hyperon interactions from the experimental and theoretical i! nvestigations of hypernuclei.

Hardy inequality on time scales and its application to half-linear dynamic equations

Directory of Open Access Journals (Sweden)

Řehák Pavel

2005-01-01

Full Text Available A time-scale version of the Hardy inequality is presented, which unifies and extends well-known Hardy inequalities in the continuous and in the discrete setting. An application in the oscillation theory of half-linear dynamic equations is given.

Three-Dimensional Coupled NLS Equations for Envelope Gravity Solitary Waves in Baroclinic Atmosphere and Modulational Instability

Directory of Open Access Journals (Sweden)

Baojun Zhao

2018-01-01

Full Text Available Envelope gravity solitary waves are an important research hot spot in the field of solitary wave. And the weakly nonlinear model equations system is a part of the research of envelope gravity solitary waves. Because of the lack of technology and theory, previous studies tried hard to reduce the variable numbers and constructed the two-dimensional model in barotropic atmosphere and could only describe the propagation feature in a direction. But for the propagation of envelope gravity solitary waves in real ocean ridges and atmospheric mountains, the three-dimensional model is more appropriate. Meanwhile, the baroclinic problem of atmosphere is also an inevitable topic. In the paper, the three-dimensional coupled nonlinear Schrödinger (CNLS equations are presented to describe the evolution of envelope gravity solitary waves in baroclinic atmosphere, which are derived from the basic dynamic equations by employing perturbation and multiscale methods. The model overcomes two disadvantages: (1 baroclinic problem and (2 propagation path problem. Then, based on trial function method, we deduce the solution of the CNLS equations. Finally, modulational instability of wave trains is also discussed.

Existence and Uniqueness of Solutions for Coupled Systems of Higher-Order Nonlinear Fractional Differential Equations

Directory of Open Access Journals (Sweden)

Ahmad Bashir

2010-01-01

Full Text Available We study an initial value problem for a coupled Caputo type nonlinear fractional differential system of higher order. As a first problem, the nonhomogeneous terms in the coupled fractional differential system depend on the fractional derivatives of lower orders only. Then the nonhomogeneous terms in the fractional differential system are allowed to depend on the unknown functions together with the fractional derivative of lower orders. Our method of analysis is based on the reduction of the given system to an equivalent system of integral equations. Applying the nonlinear alternative of Leray-Schauder, we prove the existence of solutions of the fractional differential system. The uniqueness of solutions of the fractional differential system is established by using the Banach contraction principle. An illustrative example is also presented.

Theory of collisions between an atom and a diatomic molecule in the body-fixed coordinate system.)/sup a/ I. Coupled differential equation and asymptotic boundary conditions

International Nuclear Information System (INIS)

Choi, B.H.; Poe, R.T.; Tang, K.T.

1978-01-01

The body-fixed (BF) formulation for atom--diatom scatterings is developed to the extent that one can use it to perform accurate close-coupling calculation, without introducing further approximation except truncating a finite basis set of the target molecular wave function, on the same ground as one use the space-fixed (SF) formulation. In this formulation, the coupled differential equations are solved an the boundary conditions matched entirely in the BF coordinate system. A unitary transformation is used to obtain both the coupled differential equation and the boundary condition in BF system system from SF system. All properties of the solution with respect to parity are derived entirely from the transformation, without using the parity eignfunctions of the BF frame. Boundary conditions that yield the scattering (S) matrix and the reactance (R) matrix are presented for each parity in both the far asymptotic region (where the interaction and the centrifugal potentials are both negligible) and the near asymptotic region (where the interaction potential is negligible but the centrifugal potential is not). While our differential equations are the same as those derived by others with different methods, our asymptotic boundary conditions disagree with some existing ones. With a given form of the BF coupled differential equations, the acceptable boundary conditions are discussed

Scaling Optimization of the SIESTA MHD Code

Science.gov (United States)

Seal, Sudip; Hirshman, Steven; Perumalla, Kalyan

2013-10-01

SIESTA is a parallel three-dimensional plasma equilibrium code capable of resolving magnetic islands at high spatial resolutions for toroidal plasmas. Originally designed to exploit small-scale parallelism, SIESTA has now been scaled to execute efficiently over several thousands of processors P. This scaling improvement was accomplished with minimal intrusion to the execution flow of the original version. First, the efficiency of the iterative solutions was improved by integrating the parallel tridiagonal block solver code BCYCLIC. Krylov-space generation in GMRES was then accelerated using a customized parallel matrix-vector multiplication algorithm. Novel parallel Hessian generation algorithms were integrated and memory access latencies were dramatically reduced through loop nest optimizations and data layout rearrangement. These optimizations sped up equilibria calculations by factors of 30-50. It is possible to compute solutions with granularity N/P near unity on extremely fine radial meshes (N > 1024 points). Grid separation in SIESTA, which manifests itself primarily in the resonant components of the pressure far from rational surfaces, is strongly suppressed by finer meshes. Large problem sizes of up to 300 K simultaneous non-linear coupled equations have been solved on the NERSC supercomputers. Work supported by U.S. DOE under Contract DE-AC05-00OR22725 with UT-Battelle, LLC.

Electromagnetic topology: Characterization of internal electromagnetic coupling

Science.gov (United States)

Parmantier, J. P.; Aparicio, J. P.; Faure, F.

1991-01-01

The main principles are presented of a method dealing with the resolution of electromagnetic internal problems: Electromagnetic Topology. A very interesting way is to generalize the multiconductor transmission line network theory to the basic equation of the Electromagnetic Topology: the BLT equation. This generalization is illustrated by the treatment of an aperture as a four port junction. Analytical and experimental derivations of the scattering parameters are presented. These concepts are used to study the electromagnetic coupling in a scale model of an aircraft, and can be seen as a convenient means to test internal electromagnetic interference.

Scaling Equation of State for Ferroelectric Triglycine Selenate at T ≈ Tc

NARCIS (Netherlands)

Iglesias, T.; Noheda, B.; Gallego, B.; Fernández del Castillo, J.R.; Lifante, G.; Gonzalo, J.A.

1994-01-01

Digital data of polarization vs. field on triglycine selenate at closely spaced temperature intervals (ΔT ≈ 0.015) in the vicinity of the quasi-tricritical point of triglycine selenate have been collected. These data fulfill very well the scaling equation of state ê± = ±p + (1/5)p5 (where ê- and ê+

Low-frequency scaling of the standard and mixed magnetic field and Müller integral equations

KAUST Repository

Bogaert, Ignace

2014-02-01

The standard and mixed discretizations for the magnetic field integral equation (MFIE) and the Müller integral equation (MUIE) are investigated in the context of low-frequency (LF) scattering problems involving simply connected scatterers. It is proved that, at low frequencies, the frequency scaling of the nonsolenoidal part of the solution current can be incorrect for the standard discretization. In addition, it is proved that the frequency scaling obtained with the mixed discretization is correct. The reason for this problem in the standard discretization scheme is the absence of exact solenoidal currents in the rotated RWG finite element space. The adoption of the mixed discretization scheme eliminates this problem and leads to a well-conditioned system of linear equations that remains accurate at low frequencies. Numerical results confirm these theoretical predictions and also show that, when the frequency is lowered, a finer and finer mesh is required to keep the accuracy constant with the standard discretization. © 1963-2012 IEEE.

Quality Assessment of Physical and Organoleptic Instant Corn Rice on Scale-Up Process

Science.gov (United States)

Kumalasari, R.; Ekafitri, R.; Indrianti, N.

2017-12-01

Development of instant corn rice product has been successfully conducted on a laboratory scale. Corn has high carbohydrate content but low in fiber. The addition of fiber in instant corn rice, intended to improve the functioning of the product, and replace fiber loss during the process. Scale up process of Instant corn rice required to increase the production capacity. Scale up was the process to get identic output on a larger scale based on predetermined production scale. This study aimed to assess the changes and differences in the quality of instant corn rice during scale up. Instant corn rice scale up was done on production capacity 3 kg, 4 kg and 5 kg. Results showed that scale up of instant corn rice producing products with rehydration ratio ranges between 514% - 570%, the absorption rate ranged between 414% - 470%, swelling rate ranging between 119% - 134%, bulk density ranged from 0.3661 to 0.4745 (g/ml) and porosity ranging between 30-37%. The physical quality of instant corn rice on scale up were stable from the ones at laboratory scale on swelling rate, rehydration ratio, and absorption rate but not stable on bulk density and porosity. Organoleptic qualities were stable at increased scale compared on a laboratory scale. Bulk density was higher than those at laboratory scale, and the porosity was lower than those at laboratory scale.

On lower bounds for possible blow-up solutions to the periodic Navier-Stokes equation

International Nuclear Information System (INIS)

Cortissoz, Jean C.; Montero, Julio A.; Pinilla, Carlos E.

2014-01-01

We show a new lower bound on the H .3/2 (T 3 ) norm of a possible blow-up solution to the Navier-Stokes equation, and also comment on the extension of this result to the whole space. This estimate can be seen as a natural limiting result for Leray's blow-up estimates in L p (R 3 ), 3 .5/2 (T 3 ), and give the corresponding extension to the case of the whole space

BHR equations re-derived with immiscible particle effects

Energy Technology Data Exchange (ETDEWEB)

Schwarzkopf, John Dennis [Los Alamos National Lab. (LANL), Los Alamos, NM (United States); Horwitz, Jeremy A. [Stanford Univ., CA (United States)

2015-05-01

Compressible and variable density turbulent flows with dispersed phase effects are found in many applications ranging from combustion to cloud formation. These types of flows are among the most challenging to simulate. While the exact equations governing a system of particles and fluid are known, computational resources limit the scale and detail that can be simulated in this type of problem. Therefore, a common method is to simulate averaged versions of the flow equations, which still capture salient physics and is relatively less computationally expensive. Besnard developed such a model for variable density miscible turbulence, where ensemble-averaging was applied to the flow equations to yield a set of filtered equations. Besnard further derived transport equations for the Reynolds stresses, the turbulent mass flux, and the density-specific volume covariance, to help close the filtered momentum and continuity equations. We re-derive the exact BHR closure equations which include integral terms owing to immiscible effects. Physical interpretations of the additional terms are proposed along with simple models. The goal of this work is to extend the BHR model to allow for the simulation of turbulent flows where an immiscible dispersed phase is non-trivially coupled with the carrier phase.

Generating reference evapotranspiration surfaces from the Hargreaves equation at watershed scale

Directory of Open Access Journals (Sweden)

C. Aguilar

2011-08-01

Full Text Available In this study, Hargreaves' formulation is considered to be appropriate for the water and energy balance at a daily scale due to its simplicity of application once the distributed values of temperature are available at cell scale. However, the coefficient of the Hargreaves equation must be previously calibrated. The interplay of different factors at different temporal scales became evident in the calibration process at the local scale of weather stations. The best fits against daily estimates by ASCE-PM were achieved when differentiating between the wet and the dry season. For the spatial distribution of Hargreaves coefficient at watershed scale, a regionalization in the area around each weather station was proposed in terms of areas of influence. The best results at watershed scale were obtained after a spatial correction for alpine areas, when the average of the difference cell by cell between ASCE-PM and Hargreaves's distributed daily estimates were 0.02 and 0.15 mm day⁻¹ for the wet and the dry seasons, respectively. In all the cases, the best interpolation results were obtained using C-I (calculate and interpolate procedures.

Application of the graphical unitary group approach to the energy second derivative for CI wave functions via the coupled perturbed CI equations

International Nuclear Information System (INIS)

Fox, D.J.

1983-10-01

Analytic derivatives of the potential energy for Self-Consistent-Field (SCF) wave functions have been developed in recent years and found to be useful tools. The first derivative for configuration interaction (CI) wave functions is also available. This work details the extension of analytic methods to energy second derivatives for CI wave functions. The principal extension required for second derivatives is evaluation of the first order change in the CI wave function with respect to a nuclear perturbation. The shape driven graphical unitary group approach (SDGUGA) direct CI program was adapted to evaluate this term via the coupled-perturbed CI equations. Several iterative schemes are compared for use in solving these equations. The pilot program makes no use of molecular symmetry but the timing results show that utilization of molecular symmetry is desirable. The principles for defining and solving a set of symmetry adapted equations are discussed. Evaluation of the second derivative also requires the solution of the second order coupled-perturbed Hartree-Fock equations to obtain the correction to the molecular orbitals due to the nuclear perturbation. This process takes a consistently higher percentage of the computation time than for the first order equations alone and a strategy for its reduction is discussed

Running coupling constant of a gauge theory in the framework of the Schwinger-Dyson equation: Infrared behavior of three-dimensional quantum electrodynamics

International Nuclear Information System (INIS)

Kondo, K.

1997-01-01

We discuss how to define and obtain the running coupling of a gauge theory in the approach of the Schwinger-Dyson (SD) equation, in order to perform a nonperturbative study of the theory. For this purpose, we introduce the nonlocally generalized gauge fixing into the SD equation, which is used to define the running coupling constant (this method is applicable only to a gauge theory). Some advantages and the validity of this approach are exemplified in QED 3 . This confirms the slowing down of the rate of decrease of the running coupling and the existence of the nontrivial infrared fixed point (in the normal phase) of QED 3 , claimed recently by Aitchison and Mavromatos, without so many of their approximations. We also argue that the conventional approach is recovered by applying the (inverse) Landau-Khalatnikov transformation to the nonlocal gauge result. copyright 1997 The American Physical Society

A family of conjugate gradient methods for large-scale nonlinear equations.

Science.gov (United States)

Feng, Dexiang; Sun, Min; Wang, Xueyong

2017-01-01

In this paper, we present a family of conjugate gradient projection methods for solving large-scale nonlinear equations. At each iteration, it needs low storage and the subproblem can be easily solved. Compared with the existing solution methods for solving the problem, its global convergence is established without the restriction of the Lipschitz continuity on the underlying mapping. Preliminary numerical results are reported to show the efficiency of the proposed method.

Hovering of model insects: simulation by coupling equations of motion with Navier-Stokes equations.

Science.gov (United States)

Wu, Jiang Hao; Zhang, Yan Lai; Sun, Mao

2009-10-01

When an insect hovers, the centre of mass of its body oscillates around a point in the air and its body angle oscillates around a mean value, because of the periodically varying aerodynamic and inertial forces of the flapping wings. In the present paper, hover flight including body oscillations is simulated by coupling the equations of motion with the Navier-Stokes equations. The equations are solved numerically; periodical solutions representing the hover flight are obtained by the shooting method. Two model insects are considered, a dronefly and a hawkmoth; the former has relatively high wingbeat frequency (n) and small wing mass to body mass ratio, whilst the latter has relatively low wingbeat frequency and large wing mass to body mass ratio. The main results are as follows. (i) The body mainly has a horizontal oscillation; oscillation in the vertical direction is about 1/6 of that in the horizontal direction and oscillation in pitch angle is relatively small. (ii) For the hawkmoth, the peak-to-peak values of the horizontal velocity, displacement and pitch angle are 0.11 U (U is the mean velocity at the radius of gyration of the wing), 0.22 c=4 mm (c is the mean chord length) and 4 deg., respectively. For the dronefly, the corresponding values are 0.02 U, 0.05 c=0.15 mm and 0.3 deg., much smaller than those of the hawkmoth. (iii) The horizontal motion of the body decreases the relative velocity of the wings by a small amount. As a result, a larger angle of attack of the wing, and hence a larger drag to lift ratio or larger aerodynamic power, is required for hovering, compared with the case of neglecting body oscillations. For the hawkmoth, the angle of attack is about 3.5 deg. larger and the specific power about 9% larger than that in the case of neglecting the body oscillations; for the dronefly, the corresponding values are 0.7 deg. and 2%. (iv) The horizontal oscillation of the body consists of two parts; one (due to wing aerodynamic force) is proportional to

Scale-up of a Luminescent Solar Concentrator-Based Photomicroreactor via Numbering-up.

Science.gov (United States)

Zhao, Fang; Cambié, Dario; Janse, Jeroen; Wieland, Eric W; Kuijpers, Koen P L; Hessel, Volker; Debije, Michael G; Noël, Timothy

2018-01-02

The use of solar energy to power chemical reactions is a long-standing dream of the chemical community. Recently, visible-light-mediated photoredox catalysis has been recognized as the ideal catalytic transformation to convert solar energy into chemical bonds. However, scaling photochemical transformations has been extremely challenging due to Bouguer-Lambert-Beer law. Recently, we have pioneered the development of luminescent solar concentrator photomicroreactors (LSC-PMs), which display an excellent energy efficiency. These devices harvest solar energy, convert the broad solar energy spectrum to a narrow-wavelength region, and subsequently waveguide the re-emitted photons to the reaction channels. Herein, we report on the scalability of such LSC-PMs via a numbering-up strategy. Paramount in our work was the use of molds that were fabricated via 3D printing. This allowed us to rapidly produce many different prototypes and to optimize experimentally key design aspects in a time-efficient fashion. Reactors up to 32 parallel channels have been fabricated that display an excellent flow distribution using a bifurcated flow distributor (standard deviations below 10%). This excellent flow distribution was crucial to scale up a model reaction efficiently, displaying yields comparable to those obtained in a single-channel device. We also found that interchannel spacing is an important and unique design parameter for numbered-up LSC-PMs, which influences greatly the photon flux experienced within the reaction channels.

The Integrative Psychotherapy Alliance: Family, Couple and Individual Therapy Scales.

Science.gov (United States)

Pinsof, William M.; Catherall, Donald R.

1986-01-01

Presents an integrative definition of the therapeutic alliance that conceptualizes individual, couple and family therapy as occurring within the same systemic framework. The implications of this concept for therapy reserach are examined. Three new systematically oriented scales to measure the alliance are presented along with some preliminary data…

User's Guide of TOUGH2-EGS. A Coupled Geomechanical and Reactive Geochemical Simulator for Fluid and Heat Flow in Enhanced Geothermal Systems Version 1.0

Energy Technology Data Exchange (ETDEWEB)

Fakcharoenphol, Perapon [Colorado School of Mines, Golden, CO (United States); Xiong, Yi [Colorado School of Mines, Golden, CO (United States); Hu, Litang [Colorado School of Mines, Golden, CO (United States); Winterfeld, Philip H. [Colorado School of Mines, Golden, CO (United States); Xu, Tianfu [Lawrence Berkeley National Lab. (LBNL), Berkeley, CA (United States); Wu, Yu-Shu [Colorado School of Mines, Golden, CO (United States)

2013-05-01

TOUGH2-EGS is a numerical simulation program coupling geomechanics and chemical reactions for fluid and heat flows in porous media and fractured reservoirs of enhanced geothermal systems. The simulator includes the fully-coupled geomechanical (THM) module, the fully-coupled geochemical (THC) module, and the sequentially coupled reactive geochemistry (THMC) module. The fully-coupled flow-geomechanics model is developed from the linear elastic theory for the thermo-poro-elastic system and is formulated with the mean normal stress as well as pore pressure and temperature. The chemical reaction is sequentially coupled after solution of flow equations, which provides the flow velocity and phase saturation for the solute transport calculation at each time step. In addition, reservoir rock properties, such as porosity and permeability, are subjected to change due to rock deformation and chemical reactions. The relationships between rock properties and geomechanical and chemical effects from poro-elasticity theories and empirical correlations are incorporated into the simulator. This report provides the user with detailed information on both mathematical models and instructions for using TOUGH2-EGS for THM, THC or THMC simulations. The mathematical models include the fluid and heat flow equations, geomechanical equation, reactive geochemistry equations, and discretization methods. Although TOUGH2-EGS has the capability for simulating fluid and heat flows coupled with both geomechanical and chemical effects, it is up to the users to select the specific coupling process, such as THM, THC, or THMC in a simulation. There are several example problems illustrating the applications of this program. These example problems are described in details and their input data are presented. The results demonstrate that this program can be used for field-scale geothermal reservoir simulation with fluid and heat flow, geomechanical effect, and chemical reaction in porous and fractured media.

Solution of the Eliashberg equations for a very strong electron-phonon coupling with a low-energy cutoff

International Nuclear Information System (INIS)

Weger, M.; Barbiellini, B.; Jarlborg, T.; Peter, M.; Santi, G.

1995-01-01

We solve the Eliashberg equations for the case of an explicit vector k dependence of the interactions, and of the resulting self-energies Σ 1 ( vector k,ω), Σ 2 ( vector k,ω). We consider a strong energy-dependence of the electron-electron scattering-rate τ ee -1 , which is associated with a strong energy-dependence of the electron-phonon matrix element g(k,k'). We characterize this energy-dependence by a cutoff ξ 1 , which is of the order of the phonon frequency ω ph . We find that we can account for a large number of unexpected features of the superconductivity of the cuprates by the BCS electron-phonon theory, if we consider very large values of the McMillan coupling constant λ ph , and small values of the cutoff ξ 1 . Specifically, the Coulomb interaction is found not to depress T c ; the isotope effect is strongly reduced when ξ 1 ph . We find solutions in which the gap function Δ( vector k,ω) has extended s-wave symmetry but is very anisotropic. We suggest that the underlying cause of the strong energy-dependence is a very small electronic screening parameter at the Fermi surface; the electron-phonon matrix element g is abnormally large, and this accounts for the high transition temperatures of the cuprates. An order of magnitude estimate suggests that the electron-phonon mechanism can account for transition temperatures up to about 200 K. We thus propose a very-strong-coupling theory, in which the renormalization functions, in particular the energy-renormalization X, depend very strongly on the superconducting gap Δ, and thus display a very strong temperature-dependence between T c and T=0. An experimental manifestation of the very strong coupling with a small cutoff is a zero bias anomaly sometimes observed in tunneling experiments. (orig.)

Analysis of global multiscale finite element methods for wave equations with continuum spatial scales