Related papers: Linearized Boltzmann Collision Operator: I. Polyat…
The homogenization of elliptic divergence-type fourth-order operators with periodic coefficients is studied in a (periodic) domain. The aim is to find an operator with constant coefficients and represent the equation through a perturbation…
We review the quantum version of the linear Boltzmann equation, which describes in a non-perturbative fashion, by means of scattering theory, how the quantum motion of a single test particle is affected by collisions with an ideal…
We introduce a structured approach to the construction of linear BGK-type collision operators ensuring that the resulting Lattice-Boltzmann methods are stable with respect to a weighted $L^2$-norm. The results hold for particular boundary…
The paper proves existence of renormalized solutions for a class of velocity-discrete coplanar stationary Boltzmann equations with given indata. The proof is based on the construction of a sequence of approximations with L1 compactness for…
Using the theory of Hilbert direct integrals, we introduce and study a monotonicity-preserving operation, termed the integral resolvent mixture. It combines arbitrary families of monotone operators acting on different spaces and linear…
In this paper, we study composition operators on Hilbert space of complex-valued harmonic functions. In particular, we explore isometries, the type of self-map that generate bounded composition operator, and characterize the boundedness of…
The paper considers a class of linear Boltzmann transport equations which models a charged particle transport. The equation is an approximation of the original exact transport equation which involves hyper-singular integrals in their…
We derive a master equation for the motion of a polarizable particle weakly interacting with one or several strongly pumped cavity modes. We focus here on massive particles with complex internal structure such as large molecules and…
A novel lattice Boltzmann (LB) model for multiphase flows is developed that complies with the thermodynamic foundations of kinetic theory. By directly devising the collision term for LB equation at the discrete level, a self-tuning equation…
A granular gas is a collection of macroscopic particles that interact through energy-dissipating collisions, also known as inelastic collisions. This inelasticity is characterized by a collision mechanics in which mass and momentum are…
We introduce the notion of joint torsion for several commuting operators satisfying a Fredholm condition. This new secondary invariant takes values in the group of invertibles of a field. It is constructed by comparing determinants…
Over the last decades, several types of collision models have been proposed to extend the validity domain of the lattice Boltzmann method (LBM), each of them being introduced in its own formalism. The present article proposes a formalism…
In this paper, the sharp quantitative weighted bounds for the iterated commutators of a class of multilinear operators were systematically studied. This class of operators contains multilinear Calder\'{o}n-Zygmund operators, multilinear…
In this paper, we characterize all closed linear operators in a separable Hilbert space which are unitarily equivalent to an integral bi-Carleman operator in $L_2(R)$ with bounded and arbitrarily smooth kernel on $R^2$. In addition, we give…
We consider a modified Boltzmann equation which contains, together with the collision operator, an additional drift term that is characterized by a matrix A. Furthermore, we consider a Maxwell gas, where the collision kernel has an angular…
The paper presents a solution to the Boltzmann kinetic equation based on the construction of its discrete conservative model. Discrete analogue of the collision integral is presented as a contraction of a tensor, which is independent from…
We study a catching-up algorithm for a class of differential inclusions driven by maximal monotone operators with continuous perturbations. Using a decomposition of the monotone operator into the closed convex hull of its single-valued part…
In this article, we study the convergence of algorithms for solving monotone inclusions in the presence of adjoint mismatch. The adjoint mismatch arises when the adjoint of a linear operator is replaced by an approximation, due to…
An algorithm for sequential calculation of non-isotropic matrix elements of the collision integral which are necessary for the solution of the non-linear Boltzmann equation by moment method is proposed. Isotropic matrix elements that we…
This work is devoted to the analysis of the linear Boltzmann equation in a bounded domain, in the presence of a force deriving from a potential. The collision operator is allowed to be degenerate in the following two senses: (1) the…