Related papers: Determining the collision kernel in the Boltzmann …
A linear Boltzmann equation is derived in the Boltzmann-Grad scaling for the deterministic dynamics of many interacting particles with random initial data. We study a Rayleigh gas where a tagged particle is undergoing hard-sphere collisions…
The Boltzmann equation has been a driving force behind significant mathematical research over the years. Its challenging theoretical complexity, combined with a wide variety of current scientific and technological problems that require…
Inconsistencies are pointed out in a recent proposal [L. Diosi, Phys. Rev. A 80, 064104 (2009); arXiv:0905.3908v1] for a quantum version of the classical linear Boltzmann equation.
This paper describes a simple and general method for deriving the inelastic collision term in the electron Boltzmann equation for scattering from a coupled electron-phonon system, and applies the method to the case of doped polar…
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…
In transport theory, physical phenomena are well described using the Boltzmann equation, which is efficiently simulated and discretized with the lattice Boltzmann method. The collision step defines the microscopic molecules behavior, and…
The quantum version of the Boltzmann transport equation (Wigner-Boltzmann equation) is a quite useful tool to investigate the effects of energy dissipation in quantum systems. Numerical approaches uses to be employed in order to stablish a…
The linearized Boltzmann collision operator is fundamental in many studies of the Boltzmann equation and its main properties are of substantial importance. The decomposition into a sum of a positive multiplication operator, the collision…
We consider non-colliding Brownian motions with two starting points and two endpoints. The points are chosen so that the two groups of Brownian motions just touch each other, a situation that is referred to as a tacnode. The extended kernel…
The iterative Boltzmann inversion is an iterative scheme to determine an effective pair potential for an ensemble of identical particles in thermal equilibrium from the corresponding radial distribution function. Although the method is…
In this work, we study the formal connections between the non-linear Fokker-Planck Equation associated with the non-additive entropy and the Boltzmann Equation with the non-additive correlation functional. The collisional term following the…
We consider a semiclassical linear Boltzmann model with a non local collision operator. We provide sharp spectral asymptotics for the small spectrum in the low temperature regime from which we deduce the rate of return to equilibrium as…
A semiconductor Boltzmann equation with a non-linear BGK-type collision operator is analyzed for a cloud of ultracold atoms in an optical lattice: \[ \partial_t f + \nabla_p\epsilon(p)\cdot\nabla_x f - \nabla_x n_f\cdot\nabla_p f = n_f(1-…
We find a near detailed balance solution to the relativistic Boltzmann equation under the relaxation time approximation with a collision term which differs from the Anderson-Witting model and is dependent on the stationary observer. Using…
This work is concerned with an inverse elastic scattering problem of identifying the unknown rigid obstacle embedded in an open space filled with a homogeneous and isotropic elastic medium. A Newton-type iteration method relying on the…
A survey is given of the various aspects of W-boson physics at the next generation of linear colliders. In particular, it is indicated how the W boson can help us improve our understanding of the mechanism of mass generation and the…
We present an alternative way of solving the steerable kernel constraint that appears in the design of steerable equivariant convolutional neural networks. We find explicit real and complex bases which are ready to use, for different…
We present a numerical algorithm to solve the Boltzmann equation for the electron distribution function in magnetic multilayer heterostructures with non-collinear magnetizations. The solution is based on a scattering matrix formalism for…
This study employs the isospin-dependent Boltzmann-Uehling-Uhlenbeck model to simulate intermediate-energy heavy-ion collisions between prolate nuclei $^{24}$Mg. The emphasis is on investigating the influence of centrality and orientation…
We prove the existence of a class of large global scattering solutions of Boltzmann's equation with constant collision kernel in two dimensions. These solutions are found for $L^2$ perturbations of an underlying initial data which is…