Related papers: Integer Lattice Gas with a sampling collision oper…
In this paper we consider an approach to improve the performance of exponential Runge--Kutta integrators and Lawson schemes} in cases where the solution of a related, but usually much simpler, problem can be computed efficiently. While for…
We develop and implement new probabilistic strategy for proving exponential ergodicity for interacting diffusion processes on unbounded lattice. The concept of the solution used is rather weak as we construct the process in infinite…
We present a mathematical theory of dynamical fluctuations for the hard sphere gas in the Boltzmann-Grad limit. We prove that: (1) fluctuations of the empirical measure from the solution of the Boltzmann equation, scaled with the square…
The equilibrium statistical mechanics of one-dimensional lattice gases with interactions of arbitrary range and shape between first-neighbor atoms is solved exactly on the basis of statistically interacting vacancy particles. Two sets of…
This paper provides an introduction to some stochastic models of lattice gases out of equilibrium and a discussion of results of various kinds obtained in recent years. Although these models are different in their microscopic features, a…
Suppose that an infinite lattice gas of constant density $n_0$, whose dynamics are described by the symmetric simple exclusion process, is brought in contact with a spherical absorber of radius $R$. Employing the macroscopic fluctuation…
We present a novel mechanism for thermalizing a system of particles in equilibrium and nonequilibrium situations, based on specifically modeling energy transfer at the boundaries via a microscopic collision process. We apply our method to…
In the current work we propose a theory for an additional mass diffusion effect in the conventional gas dynamics equations. We find that this effect appears as a homogenization time limit correction, when the deterministic interaction…
We study current fluctuations in lattice gases in the macroscopic limit extending the dynamic approach to density fluctuations developed in previous articles. More precisely, we derive large deviation estimates for the space--time…
We highlight the importance of long-range correlations in active matter systems of self-propelling particles even in the absence of global order or steric interactions by demonstrating that long-range density fluctuations are reduced. We…
The large deviation properties of equilibrium (reversible) lattice gases are mathematically reasonably well understood. Much less is known in non--equilibrium, namely for non reversible systems. In this paper we consider a simple example of…
In this paper we study the problem of computing the effective diffusivity for a particle moving in chaotic and stochastic flows. In addition we numerically investigate the residual diffusion phenomenon in chaotic advection. The residual…
This paper concerns the use of the expectation-maximisation (EM) algorithm for inference in partially observed diffusion processes. In this context, a well known problem is that all except a few diffusion processes lack closed-form…
The Boltzmann equation becomes invalid as the size of gas molecules is comparable with the average intermolecular distance. A better description is provided by the Enskog collision operator, which takes into account the finite size of gas…
The semi-Lagrangian methods with the improved number of one-dimensional advections are proposed for a plasma hybrid model with kinetic ions and mass-less electrons. Two subsystems with mass, momentum, and energy conservation are obtained by…
In this paper we present a novel particle method for the Vlasov--Poisson equation. Unlike in conventional particle methods, the particles are not interpreted as point charges, but as point values of the distribution function. In between the…
We develop diffusion models for simulating lattice gauge theories, where stochastic quantization is explicitly incorporated as a physical condition for sampling. We demonstrate the applicability of this novel sampler to U(1) gauge theory in…
In this presentation we overview some recent results on biased tracer diffusion in lattice gases. We consider both models in which the gas particles density is explicitly conserved and situations in which the lattice gas particles undergo…
Combining analytical and numerical methods, we study within the framework of the homogeneous non-linear Boltzmann equation, a broad class of models relevant for the dynamics of dissipative fluids, including granular gases. We use the new…
Lattice Boltzmann methods are numerical schemes derived as a kinetic approximation of an underlying lattice gas. A numerical convergence theory for nonlinear convective-diffusive lattice Boltzmann methods is established. Convergence,…