Related papers: Boltzmann-type kinetic equations and discrete mode…
Self-similarity in general relativity is briefly reviewed and the differences between self-similarity of the first kind and generalized self-similarity are discussed. The covariant notion of a kinematic self-similarity in the context of…
We present a general method of solving the Cauchy problem for multidimensional parabolic (diffusion type) equation with variable coefficients which depend on spatial variable but do not change over time. We assume the existence of the…
The differential equations of chemical kinetics are systems of nonlinear (polynomial) differential equations, therefore their solutions cannot usually be found in symbolic form. Here we offer a method to solve classes of kinetic…
A kind of fluid dynamic description for the collective movement of pedestrians is developed on the basis of a Boltzmann-like gaskinetic model. The differences between these pedestrian specific equations and those for ordinary fluids are…
The non-equilibrium gas dynamics is described by the Boltzmann equation, which can be solved numerically through the deterministic and stochastic methods. Due to the complicated collision term of the Boltzmann equation, many kinetic…
The equation of motion for the reduced Wigner function of a system coupled to an external quantum system is presented for the specific case when the external quantum system can be modeled as a set of harmonic oscillators. The result is…
Lattice kinetic equations incorporating the effects of external/internal force fields via a shift of the local fields in the local equilibria, are placed within the framework of continuum kinetic theory. The mathematical treatment reveals…
We derive minimal discrete models of the Boltzmann equation consistent with equilibrium thermodynamics, and which recover correct hydrodynamics in arbitrary dimensions. A simple analytical procedure of constructing the equilibrium for the…
In this paper, global well-posedness of the non-Markovian Unruh-Zurek and Hu-Paz-Zhang master equations with nonlinear electrostatic coupling is demonstrated. They both consist of a Wigner-Poisson like equation subjected to a dissipative…
By a further investigation on the structure of the coefficient matrix of the globally hyperbolic regularized moment equations for Boltzmann equation in [Z. Cai, Y. Fan and R. Li, Comm. Math. Sci., 11 (2013), pp. 547-571], we propose a…
We study the Korteweg-de Vries-type equation dt u=-dx(dx^2 u+f(u)-B(t,x)u), where B is a small and bounded, slowly varying function and f is a nonlinearity. Many variable coefficient KdV-type equations can be rescaled into this equation. We…
We present a robust scheme for solving the electrokinetic equations. This goal is achieved by combining the lattice-Boltzmann method (LB) with a discrete solution of the convection-diffusion equation for the different charged and neutral…
We present a concise derivation of the Boltzmann form for single-particle energy distributions in classical many-body Hamiltonian systems. The derivation relies on two physical facts: coarse-graining-scale invariance of the empirical…
We review the traditional derivation of the fluid-dynamical equations from kinetic theory according to Israel and Stewart. We show that their procedure to close the fluid-dynamical equations of motion is not unique. Their approach contains…
Paradoxes in the Boltzmann kinetic theory are presented. Firstly, it is pointed out that the usual notion concerning the perfect continuity of distribution function is not generally valid; in many important situations using certain types of…
We develop the kinetic theory of Hamiltonian systems with weak long-range interactions. Starting from the Klimontovich equation and using a quasilinear theory, we obtain a general kinetic equation that can be applied to spatially…
In kinetic theory, a system is usually described by its one-particle distribution function $f(\mathbf{r},\mathbf{v},t)$, such that $f(\mathbf{r},\mathbf{v},t)d\mathbf{r} d\mathbf{v}$ is the fraction of particles with positions and…
This contribution presents a comprehensive overview of of lattice Boltzmann models for non-ideal fluids, covering both theoretical concepts at both kinetic and macroscopic levels and more practical discussion of numerical nature. In that…
This paper deals with the existence and uniqueness of solutions to kinetic equations describing alignment of self-propelled particles. The particularity of these models is that the velocity variable is not on the euclidean space but…
By a further study of the mechanism of the hyperbolic regularization of the moment system for Boltzmann equation proposed in [Z. Cai, Y. Fan, R. Li, Comm. Math. Sci. 11(2): 547-571, 2013], we point out that the key point is treating the…