Related papers: Isotropic matrix elements of the Boltzmann equatio…
This article deals with the numerical integration in time of nonlinear Schr\"odinger equations. The main application is the numerical simulation of rotating Bose-Einstein condensates. The authors perform a change of unknown so that the…
This articles first investigates boundary integral operators for the three-dimensional isotropic linear elasticity of a biphasic model with piecewise constant Lam\'e coefficients in the form of a bounded domain of arbitrary shape surrounded…
We present a procedure for finding the exact solution to the linear-response Boltzmann equation for two-dimensional anisotropic systems and demonstrate it on examples of non-crystalline anisotropic magnetoresistance in a system with…
This article describes methods for the deterministic simulation of the collisional Boltzmann equation. It presumes that the transport and collision parts of the equation are to be simulated separately in the time domain. Time stepping…
In this paper, we study the polyatomic Boltzmann equation based on continuous internal energy, focusing on physically relevant collision kernels of the hard potentials type with integrable angular part. We establish three main results:…
We derive the spin Boltzmann equations for spin-1/2 fermions in a non-relativistic model with four-fermion contact interaction which conserves spin degrees of freedom. A great advantage of the model is that the spin matrix elements in…
Coulomb integrals, i.e., matrix elements of bare or screened Coulomb interaction between one-electron orbitals, are fundamental objects in many approaches developed to tackle the challenging problem of calculating the electronic structure…
In this paper a spectral-Lagrangian method for the Boltzmann equation for a multi-energy level gas is proposed. Internal energy levels are treated as separate species and inelastic collisions (leading to internal energy excitation and…
Isotropization occurs on time scales much shorter than the thermal equilibration time. This is a crucial ingredient for the understanding of collision experiments of heavy nuclei or other nonequilibrium phenomena in complex many body…
An explicit solution of the stationary one dimensional half-space boundary value problem for the linear Boltzmann equation is presented in the presence of an arbitrarily high constant external field. The collision kernel is assumed to be…
QCD kinetic theory simulations are a prominent tool for studying the nonequilibrium initial stages in heavy-ion collisions. Despite their success, all implementations rely on approximations of the hard thermal loop (HTL) screened matrix…
At higher altitudes, for high temperature gases, for instance near space shuttles moving at hypersonic speed, not only mechanical collisions are affecting the gas flow, but also chemical reactions have an impact on such hypersonic flows. In…
We propose a multiple relaxation time Boltzmann equation collision model by systematically assigning a separate relaxation time to each of the central moments of the distribution function. The Chapman-Enskog calculation leads to correct…
In this paper we discuss the analytical properties of the binary collision integral for a gas of ultrarelativistic particles interacting via a constant cross-section. Starting from a near-equilibrium expansion over a complete basis of…
For the non cutoff radially symmetric homogeneous Boltzmann equation with Maxwellian molecules, we give the numerical solutions using symbolic manipulations and spectral decomposition of Hermit functions. The initial data can belong to some…
The matrix element method utilizes ab initio calculations of probability densities as powerful discriminants for processes of interest in experimental particle physics. The method has already been used successfully at previous and current…
We introduce a new iterative method for computing solutions of elliptic equations with random rapidly oscillating coefficients. Similarly to a multigrid method, each step of the iteration involves different computations meant to address…
The Boltzmann equation without an angular cutoff is considered when the initial data is a small perturbation of a global Maxwellian with an algebraic decay in the velocity variable. A well-posedness theory in the perturbative framework is…
We find a recursive algorithm for computing the precise centralizers of the complex orthogonal and symplectic groups, and hence the isotropy groups, with respect to the similarity transformation on the spaces of skew-symmetric and…
In this work, we investigate the numerical reconstruction of inclusions in a semilinear elliptic equation arising in the mathematical modeling of cardiac ischemia. We propose an adaptive finite element method for the resulting constrained…