A boundary value problem for cold plasma dynamics.
A Coherent Derivation of an Average Ion Model Including the Evolution of Correlations Between Different Shells
We propose in this short note a method enabling to write in a systematic way a set of refined equations for average ion models in which correlations between populations are taken into account, starting from a microscopic model for the evolution of the electronic configuration probabilities. Numerical simulations illustrating the improvements with respect to standard average ion models are presented at the end of the paper.
A condition for weak disorder for directed polymers in random environment.
A direct and accurate adaptive semi-Lagrangian scheme for the Vlasov-Poisson equation
This article aims at giving a simplified presentation of a new adaptive semi-Lagrangian scheme for solving the (1+1)-dimensional Vlasov-Poisson system, which was developed in 2005 with Michel Mehrenberger and first described in (Campos Pinto and Mehrenberger, 2007). The main steps of the analysis are also given, which yield the first error estimate for an adaptive scheme in the context of the Vlasov equation. This article focuses on a key feature of our method, which is a new algorithm to transport...
A dual mesh method for a nonlocal thermistor problem.
A geometric derivation of the linear Boltzmann equation for a particle interacting with a Gaussian random field, using a Fock space approach
In this article the linear Boltzmann equation is derived for a particle interacting with a Gaussian random field, in the weak coupling limit, with renewal in time of the random field. The initial data can be chosen arbitrarily. The proof is geometric and involves coherent states and semi-classical calculus.
A Hamiltonian approach to the discrete-continuous dynamical systems in diamond-type crystals.
A Hermite-type adaptive semi-Lagrangian scheme
We study a new Hermite-type interpolating operator arising in a semi-Lagrangian scheme for solving the Vlasov equation in the D phase space. Numerical results on uniform and adaptive grids are shown and compared with the biquadratic Lagrange interpolation introduced in (Campos Pinto and Mehrenberger, 2004) in the case of a rotating Gaussian.
A heterogeneous alternating-direction method for a micro-macro dilute polymeric fluid model
We examine a heterogeneous alternating-direction method for the approximate solution of the FENE Fokker–Planck equation from polymer fluid dynamics and we use this method to solve a coupled (macro-micro) Navier–Stokes–Fokker–Planck system for dilute polymeric fluids. In this context the Fokker–Planck equation is posed on a high-dimensional domain and is therefore challenging from a computational point of view. The heterogeneous alternating-direction scheme combines a spectral Galerkin method for...
A Langevin Description for Driven Granular Gases
The study of the fluctuations in the steady state of a heated granular system is reviewed. A Boltzmann-Langevin description can be built requiring consistency with the equations for the one- and two-particle correlation functions. From the Boltzmann-Langevin equation, Langevin equations for the total energy and the transverse velocity field are derived. The existence of a fluctuation-dissipation relation for the transverse velocity field is also...
A linear mixed finite element scheme for a nematic Ericksen–Leslie liquid crystal model
In this work we study a fully discrete mixed scheme, based on continuous finite elements in space and a linear semi-implicit first-order integration in time, approximating an Ericksen–Leslie nematic liquid crystal model by means of a Ginzburg–Landau penalized problem. Conditional stability of this scheme is proved via a discrete version of the energy law satisfied by the continuous problem, and conditional convergence towards generalized Young measure-valued solutions to the Ericksen–Leslie problem...
A local limit theorem for directed polymers in random media : the continuous and the discrete case
A lower bound for the principal eigenvalue of the Stokes operator in a random domain
This article is dedicated to localization of the principal eigenvalue (PE) of the Stokes operator acting on solenoidal vector fields that vanish outside a large random domain modeling the pore space in a cubic block of porous material with disordered micro-structure. Its main result is an asymptotically deterministic lower bound for the PE of the sum of a low compressibility approximation to the Stokes operator and a small scaled random potential term, which is applied to produce a similar bound...
A model of dense fluids
We obtain coupled reaction-diffusion equations for the density and temperature of a dense fluid, starting from a discrete model in which at most one particle can be present at each site. The model is constructed by the methods of statistical dynamics. We verify that the theory obeys the first and second laws of thermodynamics. Some remarks on measurement theory for the position of a particle are offered.
A model of evolution of temperature and density of ions in an electrolyte
We study existence and nonexistence of solutions (both stationary and evolution) for a parabolic-elliptic system describing the electrodiffusion of ions. In this model the evolution of temperature is also taken into account. For stationary states the existence of an external potential is also assumed.
A model of frontal polymerization including the gel effect.
A new exponentially fitted triangular finite element method for the continuity equations in the drift-diffusion model of semiconductor devices
A new exponentially fitted triangular finite element method for the continuity equations in the drift-diffusion model of semiconductor devices
In this paper we present a novel exponentially fitted finite element method with triangular elements for the decoupled continuity equations in the drift-diffusion model of semiconductor devices. The continuous problem is first formulated as a variational problem using a weighted inner product. A Bubnov-Galerkin finite element method with a set of piecewise exponential basis functions is then proposed. The method is shown to be stable and can be regarded as an extension to two dimensions of the...
A new perspective on some approximations used in neutron transport modeling
In this contribution, we will use the Maxwell-Cartesian spherical harmonics (introduced in [1,2]) to derive a system of partial differential equations governing transport of neutrons within an interacting medium. This system forms an alternative to the well known approximation, which is based on the expansion of the directional dependence into tesseral spherical harmonics ([3,p.197]). In comparison with this latter set of equations, the Maxwell-Cartesian system posesses a much more regular structure,...
A new solution for the director relaxation problem in twisted nematic film based on wavelet analysis.