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Abstract: Focusing on the local geometric properties of the shockpeakon for the Degasperis–Procesi equation, a multi-symplectic method for the quasi-Degasperis–Procesi equation is proposed to reveal the jump discontinuity of the shockpeakon for the Degasperis–Procesi equation numerically in this paper. The main contribution of this paper lies in the following: (1) the uniform multi-symplectic structure of the b-family equation is constructed; (2) the stable jump discontinuity of the shockpeakon for the Degasperis–Procesi equation is reproduced by simulating the peakon–antipeakon collision process of the quasi-Degasperis–Procesi equation. First, the multi-symplectic structure and several local conservation laws are presented for the b-family equation with two exceptions ( and ). And then, the Preissman Box multi-symplectic scheme for the multi-symplectic structure is constructed and the mathematical proofs for the discrete local conservation laws of the multi-symplectic structure are given. Finally, the numerical experiments on the peakon–antipeakon collision of the quasi-Degasperis–Procesi equation are reported to investigate the jump discontinuity of shockpeakon of the Degasperis–Procesi equation. From the numerical results, it can be concluded that the peakon–antipeakon collision of the quasi-Degasperis–Procesi equation can be simulated well by the multi-symplectic method and the simulation results can reveal the jump discontinuity of shockpeakon of the Degasperis–Procesi equation approximately. [Copyright &y& Elsevier]

We consider the relativistic Vlasov–Maxwell (RVM) equations in the limit when the light velocity c goes to infinity. In this regime, the RVM system converges towards the Vlasov–Poisson system and the aim of this paper is to construct asymptotic preserving numerical schemes that are robust with respect to this limit. Our approach relies on a time splitting approach for the RVM system employing an implicit time integrator for Maxwell’s equations in order to damp the higher and higher frequencies present in the numerical solution. A number of numerical simulations are conducted in order to investigate the performances of our numerical scheme both in the relativistic as well as in the classical limit regime. In addition, we derive the dispersion relation of the Weibel instability for the continuous and the discretized problem. [ABSTRACT FROM AUTHOR]

Abstract: In some recent papers Li, Voskoboynikov, Lee, Sze and Tretyak suggested an iterative scheme for computing the electronic states of quantum dots and quantum rings taking into account an electron effective mass which depends on the position and electron energy level. In this paper we prove that this method converges globally and linearly in an alternating way, i.e. yielding lower and upper bounds of a predetermined energy level in turn. Moreover, taking advantage of the Rayleigh functional of the governing nonlinear eigenproblem, we propose a variant which converges even quadratically thereby reducing the computational cost substantially. Two examples of finite element models of quantum dots of different shapes demonstrate the efficiency of the method. [Copyright &y& Elsevier]

Numerical kinetic models of plasma turbulence require careful treatment of conserved quantities. In the collisionless limit, numerical dissipation can impact entropy in a non-controlled manner. In this paper, the impact of the error in entropy conservation is investigated. In a simulation of ion-acoustic turbulence, a large error ( 15 % ) in entropy conservation is found. Surprisingly, this error is independent of the numerical method, scheme, or number of grid points. Adding a collision operator resolves this issue, but only if the collision frequency is large enough that it modifies the qualitative time evolution of observables, such as electric field amplitude, anomalous resistivity, or phase-space structures. [ABSTRACT FROM AUTHOR]

OpenSMOKE++ is a general framework for numerical simulations of reacting systems with detailed kinetic mechanisms, including thousands of chemical species and reactions. The framework is entirely written in object-oriented C++ and can be easily extended and customized by the user for specific systems, without having to modify the core functionality of the program. The OpenSMOKE++ framework can handle simulations of ideal chemical reactors (plug-flow, batch, and jet stirred reactors), shock-tubes, rapid compression machines, and can be easily incorporated into multi-dimensional CFD codes for the modeling of reacting flows. OpenSMOKE++ provides useful numerical tools such as the sensitivity and rate of production analyses, needed to recognize the main chemical paths and to interpret the numerical results from a kinetic point of view. Since simulations involving large kinetic mechanisms are very time consuming, OpenSMOKE++ adopts advanced numerical techniques able to reduce the computational cost, without sacrificing the accuracy and the robustness of the calculations. In the present paper we give a detailed description of the framework features, the numerical models available, and the implementation of the code. The possibility of coupling the OpenSMOKE++ functionality with existing numerical codes is discussed. The computational performances of the framework are presented, and the capabilities of OpenSMOKE++ in terms of integration of stiff ODE systems are discussed and analyzed with special emphasis. Some examples demonstrating the ability of the OpenSMOKE++ framework to successfully manage large kinetic mechanisms are eventually presented. Program summary Program title: OpenSMOKE++ Catalogue identifier: AEVY_v1_0 Program summary URL: http://cpc.cs.qub.ac.uk/summaries/AEVY_v1_0.html Program obtainable from: CPC Program Library, Queen’s University, Belfast, N. Ireland Licensing provisions: GNU General Public License, version 3 No. of lines in distributed program, including test data, etc.: 146353 No. of bytes in distributed program, including test data, etc.: 4890534 Distribution format: tar.gz Programming language: C++. Computer: Any computer that can run a C++ Compiler. Operating system: Tested on Microsoft Windows 7, Ubuntu 14.4. RAM: From a few Mb to several Gb depending on the size of the system being simulated. Classification: 22. External routines: Eigen, Boost C++ Libraries, RapidXML Nature of problem: Evolution of reacting gas mixtures with detailed description of thermodynamic, kinetic and transport data. Solution method: Stiff systems of Ordinary differential Equations, whose solution is obtained using methods based on the Backward Differentiation Formulas (BDF) (LU factorization of dense matrices is required). Additional comments: The code was specifically conceived for managing homogeneous, reacting mixtures including thousands of species and reactions. Running time: Problem-dependent, from seconds (small kinetics) to hours [ABSTRACT FROM AUTHOR]

Abstract: Event-driven algorithms are a powerful and efficient simulation method that can be used to numerically study the behavior of particulate systems, such as granular materials or powders. Its superior efficiency originates from only considering analytically calculable points in time, where physically relevant events occur. This, however, is only possible for pairs of trajectories whose relative distance can be expressed as a polynomial of order less than or equal to four. For more complex trajectories, like a sinusoidal motion of a wall, the collision times have to be calculated numerically, which dramatically reduces the efficiency. In this paper we present a tabulation method implemented in an event-driven algorithm, which is able to efficiently handle the one-dimensional motion of a periodically moving wall. By demonstrating this for a sinusoidally moving wall, we enhance the comparability of simulations with (usually sinusoidally driven) experiments. Because granular materials or powders are systems which are easily accessible through both experiments and simulations, our work enhances the growing field of statistical physics far from equilibrium. [Copyright &y& Elsevier]

Abstract: In a heterogeneous granular material, viscous flow concentrates to regions with lower particle number density, or higher permeability region, denoted here by “macroscopic cavity”. This in turn enhances the normal stress toward the fluid region on the upstream boundary, which destroys the boundary if the local stress exceeds a certain magnitude. The latter may further enhance the concentration of flow into the cavity region, which is repeated to form a large scale fluidized region toward upstream direction. These processes have been elucidated in our previous experiment using glass beads layer confined between two parallel plane walls. In this paper, a numerical simulation taking into account of the global flow field on the basis of the generalized Darcyʼs equation as well as the local stick-slip equation on the basis of the Newtonʼs equation of motion is performed. Our numerical simulation can successfully reproduce our experimental findings by imposing a suitable pressure gradient and frictional coefficient. The present numerical method can be applied to more general distribution of cavities, including three-dimensional ones, which may predict the formation of long underground waterways or creation of the passage of blood flows (angiogenesis). [Copyright &y& Elsevier]

Abstract: This paper is concerned with the numerical simulation of highly relativistic beams. We developed a particle-in-cell code for highly relativistic beams, based on the paraxial Vlasov–Maxwell formulation of Laval et al. This formulation follows the beam in a speed-of-light frame. It is fourth order accurate in the small characteristic velocity of the beam. The formulation is simpler than standard particle-in-cell codes in the lab frame or in the beam frame and gives a fast and easy to implement algorithm. Numerical examples illustrate the accuracy of the method. [Copyright &y& Elsevier]

In this paper we present a novel computational method for calculating the heterojunction bipolar transistor (HBT) physical characteristics in the time domain. To calculate the HBT high frequency properties, the Gummel–Poon equivalent circuit model is applied to replace the HBT in the circuit and a set of governing ordinary differential equations (ODEs) is formulated. We directly decouple the system ODEs and solve each decoupled ODE with the monotone iterative method in the time domain. This solution methodology proposed here has been applied to semiconductor device simulation by us earlier, and we find this method for the HBT simulation has good accuracy and converges globally. Compared with the HSPICE circuit simulator results, our results present the accuracy, efficiency, and robustness of the method. [Copyright &y& Elsevier]