相关论文: Boltzmann to Landau from the Gradient Flow Perspec…

We are concerned with a mixture of Boltzmann and McKean-Vlasov type equations, this means (in probabilistic terms) equations with coefficients depending on the law of the solution itself,and driven by a Poisson point measure with the…

This paper is devoted to the grazing collision limit of the inelastic Kac model introduced in [A. Pulvirenti and G. Toscani. J. Statist. Phys., 114(5-6):1453--1480, 2004], when the equilibrium distribution function is a heavy-tailed…

We consider a test particle moving in a random distribution of obstacles in the plane, under the action of a uniform magnetic field, orthogonal to the plane. We show that, in a weak coupling limit, the particle distribution behaves…

This paper extends the results regarding entropic convergence and the strong linearized limit for the Boltzmann equation (without external force) in [C. David Levermore. Entropic convergence and the linearized limit for the Boltzmann…

We study the convergence of the system of the Allen-Cahn equations to the weak solution for the multi-phase mean curvature flow in the sense of Brakke. The Landau-Lifshitz equation in this paper can be regarded as a system of Allen-Cahn…

In this manuscript we derive the quantum Landau operator as the weak-coupling limit of the quantum Boltzmann operator (also known as the Uehling-Uhlenbeck operator). We consider both Fermi-Dirac and Bose-Einstein statistics. Our approach is…

We introduce two new concepts of convergence of gradient systems $(\mathbf Q, \mathcal E_\varepsilon,\mathcal R_\varepsilon)$ to a limiting gradient system $(\mathbf Q, \mathcal E_0,\mathcal R_0)$. These new concepts are called `EDP…

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…

The displacement $\lambda$-convexity of a nonstandard entropy with respect to a nonlocal transportation metric in finite state spaces is shown using a gradient flow approach. The constant $\lambda$ is computed explicitly in terms of a…

We derive the Boltzmann equation for scalar fields using the Schwinger-Keldysh formalism. The focus lies on the derivation of the collision term. We show that the relevant self-energy diagrams have a factorization property. The collision…

In this paper we consider a nonlinear Fokker-Planck equation with asymptotically small parameters. It describes the diffusion of finite-size particles in the presence of a fixed distribution of obstacles in the limit of low-volume fraction.…

This is the final version of the author's diploma thesis written at the Humboldt University of Berlin in 1995. The topic is the flow of granular material in narrow vertical pipes, driven by the gravity, that is described by Langevin…

Consider the motion of a charged, point particle moving in the complement of a Poisson distribution of hard sphere scatterers in two dimensions under the effect of a fixed magnetic field. Building on, and extending a coupling method…

We prove a superdiffusive central limit theorem for the displacement of a test particle in the periodic Lorentz gas in the limit of large times $t$ and low scatterer densities (Boltzmann-Grad limit). The normalization factor is $\sqrt{t\log…

The influence and validity of wall boundary conditions for non-equilibrium fluid flows described by the Boltzmann equation remains an open problem. The substantial computational cost of directly solving the Boltzmann equation has limited…

The Boltzmann kinetic equation is obtained from an integro-differential master equation that describes a stochastic dynamics in phase space of an isolated thermodynamic system. The stochastic evolution yields a generation of entropy,…

Motivated by the numerical investigation by Aoki et al. [1], we study a rarefied gas flow between two parallel infinite plates of the same temperature governed by the Boltzmann equation with diffuse reflection boundaries, where one plate is…

In our previous paper (Hunana et al. 2022) we have employed the Landau collisional operator together with the moment method of Grad and considered various generalizations of the Braginskii model, such as a multi-fluid formulation of the 21-…

A kinetic inhomogeneous Boltzmann-type equation is proposed to model the dynamics of the number of agents in a large market depending on the estimated value of an asset and the rationality of the agents. The interaction rules take into…

A lattice Boltzmann model is introduced which simulates oil-water-surfactant mixtures. The model is based on a Ginzburg-Landau free energy with two scalar order parameters. Diffusive and hydrodynamic transport is included. Results are…