Related papers: Hydrodynamic limit for a chain with thermal and me…
We consider attractive irreducible conservative particle systems on $\mathbb{Z}$, without necessarily nearest-neighbor jumps or explicit invariant measures. We prove that for such systems, the hydrodynamic limit under Euler time scaling…
Hydrodynamic interactions between particles confined in a liquid-filled linear channel are known to be screened beyond a distance comparable to the channel width. Using a simple analytical theory and lattice-Boltzmann simulations, we show…
The dynamics of short 1D nonlinear Hamiltonian chains is analyzed numerically at different temperatures (energy per particle). The boundary temperature $T_b$ separating the regular (quasiperiodic) and the stochastic (chaotic) chain motion…
In this chapter, we illustrate recently obtained thermodynamic bounds for a number of enzymatic networks by focusing on simple examples of unicyclic or multi-cyclic networks. We also derive complementary relations which constrain the…
Continuum mechanics (e.g., hydrodynamics, elasticity theory) is based on the assumption that a small set of fields provides a closed description on large space and time scales. Conditions governing the choice for these fields are discussed…
We prove an explicit, non-local hydrodynamic closure for the linear one-dimensional kinetic equation independent on the size of the relaxation time. We compare this dynamical equation to the local approximations obtained from the…
This paper presents our study of the asymptotic behavior of a two-component system of Brownian motions undergoing certain singular interactions. In particular, the system is a combination of two different types of particles and the…
A fourth-order nonlinear evolution equation is derived from a microscopic model for surface diffusion, namely, the continuum solid-on-solid model. We use the method developed by Varadhan for the computation of hydrodynamic scaling limit of…
We study a hydrodynamic limit approach to move-to-front rules, namely, a scaling limit as the number of items tends to infinity, of the joint distribution of jump rate and position of items. As an application of the limit formula, we…
Nonlinear fluctuating hydrodynamics (NFHD) is a powerful framework for understanding transport, but checking its validity with molecular dynamics is still challenging. Here, we overcome this challenge by developing an effective scheme for…
We consider two-species exclusion processes on the d-dimensional discrete torus taking the effects of exchange, creation and annihilation into account. The model is, in general, of nongradient type. We prove that the (charged) particle…
We consider a one-dimensional, weakly asymmetric, boundary driven exclusion process on the interval $[0,N]\cap Z$ in the super-diffusive time scale $N^2 \epsilon^{-1}_N$, where $1\ll \epsilon^{-1}_N \ll N^{1/4}$. We assume that the external…
We analyze the generalized symmetric exclusion process, which allows at most $\alpha$ particles per site, and we put it in contact with stochastic reservoirs whose strength is regulated by a parameter $\theta\in\mathbb R$. We prove that the…
We consider current statistics for a two species exclusion process of particles hopping in opposite directions on a one-dimensional lattice. We derive an exact formula for the Green's function as well as for a joint current distribution of…
We consider relativistic hydrodynamics in the limit where the number of spatial dimensions is very large. We show that under certain restrictions, the resulting equations of motion simplify significantly. Holographic theories in a large…
We study the non-equilibrium steady-states of a one-dimensional ($1D1V$) fluid in a finite space region of length $L$. Particles interact among themselves by multi-particle collisions and are in contact with two thermal-wall heat…
We obtain macroscopic isothermal thermodynamic transformations by space-time scalings of a microscopic Hamiltonian dynamics in contact with a heat bath. The microscopic dynamics is given by a chain of anharmonic oscillators subject to a…
The phenomenological equations of hydrodynamics describe emergent behavior in many body systems. Their forms and the associated phenomena are well established when the quiescent state of the system is one of thermodynamic equilibrium, yet…
Under partial confinement, the motion of colloidal particles is restricted to a plane but their dynamics is influenced by hydrodynamic interactions mediated by the unconfined, three--dimensional flow of the embedding fluid. We demonstrate…
We study the Langevin dynamics of flux lines of high--T$_c$ superconductors in the presence of random quenched pinning. The hydrodynamic theory for the densities is derived by starting with the microscopic model for the flux-line liquid.…