相关论文: TASEP hydrodynamics using microscopic characterist…
Solutions to finite-dimensional (all spatial Fourier modes set to zero beyond a finite wavenumber $K_G$), inviscid equations of hydrodynamics at long times are known to be at variance with those obtained for the original infinite…
The $n$-species particle-exchange process (PEP($n$)) is an exclusion process in which particles of $n$ different species exchange positions on neighbouring sites with rates chosen such that the invariant measure on the discrete torus is a…
We show that the thermal subadditivity of entropy provides a common basis to derive a strong form of the bounded difference inequality and related results as well as more recent inequalities applicable to convex Lipschitz functions, random…
The paper is concerned with the steady-state Burgers equation of fractional dissipation on the real line. We first prove the global existence of viscosity weak solutions to the fractal Burgers equation driven by the external force. Then the…
We obtain hydrodynamic descriptions of a broad class of conserved-mass transport processes on a ring. These processes are governed by chipping, diffusion and coalescence of masses, where microscopic probability weights in their…
The new mathematical framework based on the free energy of pure classical fluids presented in [R. D. Rohrmann, Physica A 347, 221 (2005)] is extended to multi-component systems to determine thermodynamic and structural properties of…
We identify the ballistically and diffusively rescaled limit distribution of the second class particle position in a wide range of asymmetric and symmetric interacting particle systems with established hydrodynamic behavior, respectively…
We investigate the dynamics of the asymmetric simple exclusion process (ASEP) on a ring. The ASEP is equivalent to the derivative nonlinear Schr\"{o}dinger equation (DNLS), which is integrable quantum field theory, in the continuous limit.…
We prove that the hydrodynamic limit of the symmetric exclusion process (SEP) is a Fokker-Planck equation in the setting of Poisson random neighborhood graphs approximating a weighted Riemannian manifold with Ricci curvature bounded from…
This paper represents the full version of a paper published earlier in Physica A [246 (1997), 275]. The present paper includes argumentation, proofs and details omitted in the shortened version. The papers are a further development of the…
We derive the second-order hydrodynamic equation and the microscopic formulae of the relaxation times as well as the transport coefficients systematically from the relativistic Boltzmann equation. Our derivation is based on a novel…
We study the periodic homogenization of a reaction-diffusion problem with large nonlinear drift and Robin boundary condition posed in an unbounded perforated domain. The nonlinear problem is associated with the hydrodynamic limit of a…
We consider the family of two-sided Bernoulli initial conditions for TASEP which, as the left and right densities ($\rho_-,\rho_+$) are varied, give rise to shock waves and rarefaction fans---the two phenomena which are typical to TASEP. We…
In this paper we will show how the results found in Cator and Pimentel 2009, about the Busemann functions in last-passage percolation, can be used to calculate the asymptotic distribution of the speed of a single second class particle…
We summarise a selection of results on the inviscid limit of the stochastic Burgers equation emphasising geometric properties of the caustic, Maxwell set and Hamilton-Jacobi level surfaces and relating these results to a discussion of…
Similarity solutions play an important role in many fields of science: we consider here similarity in stochastic dynamics. Important issues are not only the existence of stochastic similarity, but also whether a similarity solution is…
The one-dimensional totally asymmetric simple exclusion process (TASEP) with $N$ particles on a periodic lattice of $L$ sites is an interacting particle system with hopping rates breaking detailed balance. The total time-integrated current…
Statistical mechanics descriptions of the second law of thermodynamics generally imply point-like particles driven by a dissipative overall mechanism for their simultaneous time-evolution. As the number of involved particles grows larger,…
Under appropriate conditions for the initial configuration, the empirical measure of the $N$-particle Dyson model with parameter $\beta \geq 1$ converges to a unique measure-valued process as $N$ goes to infinity, which is independent of…
Using the matrix product formalism we formulate a natural p-species generalization of the asymmetric simple exclusion process. In this model particles hop with their own specific rate and fast particles can overtake slow ones with a rate…