Related papers: A consistency-stability approach to scaling limits…
Dynamics of many-particle systems with long-range interaction is collisionless and governed by the Vlasov equation. This dynamics is a flow of a six-dimensional incompressible liquid with uncountable integrals of motion. If the flow…
We propose a multiple relaxation time entropic realization of a two-phase flow lattice Boltzmann model we introduced in earlier works arXiv:2112.01975 S.A. Hosseini, B. Dorschner, and I. V. Karlin, arXiv preprint, arXiv:2112.01975 (2021).…
We propose a method for approximating solutions to optimization problems involving the global stability properties of parameter-dependent continuous-time autonomous dynamical systems. The method relies on an approximation of the…
This paper presents, in a unified fashion, deterministic as well as statistical Lagrangian-verification techniques. They formally quantify the behavioral robustness of any time-continuous process, formulated as a continuous-depth model. To…
We investigate the hydrodynamic limit for weakly asymmetric simple exclusion processes in crystal lattices. We construct a suitable scaling limit by using a discrete harmonic map. As we shall observe, the quasi-linear parabolic equation in…
Recently, a minimal kinetic model for fluid flow, known as entropic lattice Boltzmann method, has been proposed for the simulation of isothermal hydrodynamic flows. At variance with previous Lattice Boltzmann methods, the entropic version…
We present {\it block analysis}, an efficient method to perform finite-size scaling for obtaining the length scale of dynamic heterogeneity and the point-to-set length scale for generic glass-forming liquids. This method involves…
Characterizing current fluctuations in a steady state is of fundamental interest and has attracted considerable attention in the recent past. However, the bulk of the studies are limited to systems that either do not exhibit a phase…
We consider one-dimensional, interacting spinless bosons on a tight-binding lattice described by the Bose-Hubbard model. Besides attractive on-site two-body interactions, we include a three-body repulsive term such that the competition…
We argue that the coarse-grained dynamics of the zero-range process in the condensation regime can be described by an extension of the standard hydrodynamic equation obtained from Eulerian scaling even though the system is not locally…
We study central limit theorems for a totally asymmetric, one-dimensional interacting random system. The models we work with are the Aldous-Diaconis-Hammersley process and the related stick model. The A-D-H process represents a particle…
We study dynamical behaviors of one-dimensional stochastic lattice gases with repulsive interactions whose span can be arbitrary large. We endow the system with a zero-temperature dynamics, so that the hops to empty sites which would have…
Convergence of a system of particles, interacting with a fluid, to Navier-Stokes-Vlasov-Fokker-Planck system is studied. The interaction between particles and fluid is described by Stokes drag force. The empirical measure of particles is…
These notes are based on lectures delivered by the authors at a Langeoog seminar of SFB/TR12 "Symmetries and universality in mesoscopic systems" to a mixed audience of mathematicians and theoretical physicists. After a brief outline of the…
We establish the equivalence of a recently introduced discrete model of the hydrophobic interaction, as well as its extension to continuous state variables, with the Ising model in a magnetic field with temperature-dependent strength. In…
We investigate the scaling of the R\'{e}nyi entanglement entropies for a particle bipartition of interacting spinless fermions in one spatial dimension. In the Tomonaga-Luttinger liquid regime, we calculate the second R\'{e}nyi entanglement…
We introduce a novel approach to simulate the interaction between fluids and thin elastic solids without any penetration. Our approach is centered around an optimization system augmented with barriers, which aims to find a configuration…
In this paper, we study the asymptotic behaviors of solutions to the inhomogeneous Navier-Stokes-Vlasov system in $\mathbb{R}^{3}\times\mathbb{R}^{3}$, where the initial fluid density is allowed to vanish. We establish the uniform bound of…
We study a kinetic toy model for a spray of particles immersed in an ambient fluid, subject to some additional random forcing given by a mixing, space-dependent Markov process. Using the perturbed test function method, we derive the…
We obtain a fast diffusion equation (FDE) as scaling limit of a sequence of zero-range process with symmetric unit rate. Fast diffusion effect comes from the fact that the diffusion coefficient goes to infinity as the density goes to zero.…