Related papers: Isotropic matrix elements of the Boltzmann equatio…
We describe a three-stage procedure to analyze the dependence of Poisson Boltzmann calculations on the shape, size and geometry of the boundary between solute and solvent. Our study is carried out within the boundary element formalism, but…
The homogeneous isotropic Boltzmann equation (HIBE) is a fundamental dynamic model for many applications in thermodynamics, econophysics and sociodynamics. Despite recent hardware improvements, the solution of the Boltzmann equation remains…
An orbit following code is developed to calculate ion beam trajectories in magnetized plasmas. The equation of motion (the Newton's equation) is solved including the Lorentz force term and Coulomb collisional relaxation term. Furthermore, a…
The Poisson--Boltzmann equation is widely used to model electrostatics in molecular systems. Available software packages solve it using finite difference, finite element, and boundary element methods, where the latter is attractive due to…
We derive approximate iterative analytical solutions of the non-extensive Boltzmann transport equation in the relaxation time approximation. The approximate solutions almost overlap with the exact solution for a considerably wide range of…
In this paper, explicit method of constructing approximations (the Triangle Entropy Method) is developed for nonequilibrium problems. This method enables one to treat any complicated nonlinear functionals that fit best the physics of a…
The linearized collision operator of the Boltzmann equation for single species can be written as a sum of a positive multiplication operator, the collision frequency, and a compact integral operator. This classical result has more recently,…
A complete classification of isotropic vector equations of the geometric type that possess higher symmetries is proposed. New examples of integrable multi-component systems of the geometric type and their auto-Backlund transformations are…
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 implementation of the finite element method for linear elliptic equations requires to assemble the stiffness matrix and the load vector. In general, the entries of this matrix-vector system are not known explicitly but need to be…
We study the kinetics of nonlinear irreversible fragmentation. Here fragmentation is induced by interactions/collisions between pairs of particles, and modelled by general classes of interaction kernels, and for several types of breakage…
In this paper, we present a splitting algorithm to solve multicomponent transport models. These models are related to plasma simulations, in which we consider the local thermodynamic equilibrium and weakly ionised plasma-mixture models that…
We compute and analyze isotropy subgroups of the complex orthogonal group with respect to the similarity transformation on itself and on skew-symmetric matrices. Their group structure is related to a group of certain nonsingular block…
The anisotropic Cahn-Hilliard equation is often used to model the formation of faceted pyramids on nanoscale crystal surfaces. In comparison to the isotropic Cahn-Hilliard model, the nonlinear terms associated with strong anisotropic…
We analytically determine all the eigenvalues and eigenfunctions of the linearized Boltzmann collision operator in massless scalar $\lambda \phi^4$ theory in the high-temperature (classical) regime. This is used to exactly compute the shear…
We describe a practical procedure to calculate the Coulomb matrix elements of 2D spatially separated and confined charge carriers, which are needed for detailed theoretical descriptions of important condensed matter finite systems. We…
We consider an inverse problem for the nonlinear Boltzmann equation near the equilibrium. Our goal is to determine the collision kernel in the Boltzmann equation from the knowledge of the Albedo operator. Our approach relies on a…
A linear Boltzmann equation with nonautonomous collision operator is rigorously derived in the Boltzmann-Grad limit for the deterministic dynamics of a Rayleigh gas where a tagged particle is undergoing hard-sphere collisions with…
Kinetic theories constitute one of the most promising tools to decipher the characteristic spatio-temporal dynamics in systems of actively propelled particles. In this context, the Boltzmann equation plays a pivotal role, since it provides…
On the basis of pure gauge sector of Blaizot-Iancu equation, we derive kinetic equation of Boltzmann type, taking into account 2n+2-colorless plasmon decay processes, n=1,2,.... Using so-called Tsytovich correspondence principle, a direct…