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Fluctuating hydrodynamics provides a quantitative, large-scale description of many-body systems in terms of smooth variables, with microscopic details entering only through a small set of transport coefficients. Although this framework has…
We study the role of fluctuations in particle systems modeled by Dean-Kawasaki-type equations, which describe the evolution of particle densities in systems with Brownian motion. By comparing microscopic simulations, stochastic partial…
A procedure for model reduction of stochastic ordinary differential equations with additive noise was recently introduced in [Colangeli-Duong-Muntean, Journal of Physics A: Mathematical and Theoretical, 2022], based on the Invariant…
The formulation of a fluctuating hydrodynamic theory for interacting particles is a crucial step in the theoretical description of liquids. The microscopic mappings proposed decades ago by Dean and Kawasaki have played a central role in the…
Inspired by [Fehrman, Gess; Invent. Math., 2023], we provide a fine analysis of the McKean-Vlasov PDE with singular interactions and drift terms of square root form. As the corresponding skeleton equation of Dean-Kawasaki equation with…
The purpose of this paper is to establish a well-posedness theory for conservative stochastic partial differential equations on the whole space. This class of stochastic PDEs arises in fluctuating hydrodynamics, and includes the…
Computing analytically the $n$-point density correlations in systems of interacting particles is a long-standing problem of statistical physics, with a broad range of applications, from the interpretation of scattering experiments in simple…
We present predictions for the statistical error due to finite sampling in the presence of thermal fluctuations in molecular simulation algorithms. Specifically, we establish how these errors depend on Mach number, Knudsen number, number of…
At the macroscopic scale, many important models of collective motion fall into the class of kinematic flows for which both velocity and diffusion terms depend only on particle density. When total particle numbers are fixed and finite,…
We consider hydrodynamic scaling limits for a class of reversible interacting particle systems, which includes the symmetric simple exclusion process and certain zero-range processes. We study a (non-quadratic) microscopic action functional…
The Dean-Kawasaki equation - one of the most fundamental SPDEs of fluctuating hydrodynamics - has been proposed as a model for density fluctuations in weakly interacting particle systems. In its original form it is highly singular and fails…
Computational fluctuating hydrodynamics aims at understanding the impact of thermal fluctuations on fluid motions at small scales through numerical exploration. These fluctuations are modeled as stochastic flux terms and incorporated into…
In this paper, we provide a continuum model for the fluctuations of the symmetric simple exclusion process about its hydrodynamic limit. The model is based on an approximating sequence of stochastic PDEs with nonlinear, conservative noise.…
Characterising the statistical properties of classical interacting particle systems is a long-standing question. For Brownian particles the microscopic density obeys a stochastic evolution equation, known as the Dean--Kawasaki equation.…
We consider a general class of nonlinear diffusive models with bulk dissipation and boundary driving, and derive its hydrodynamic description in the large size limit. Both the average macroscopic behavior and the fluctuating properties of…
We establish a central limit theorem and large deviations principle that characterises small noise fluctuations of the generalised Dean--Kawasaki stochastic PDE. The fluctuations agree to first order with fluctuations of certain interacting…
We develop stochastic mixed finite element methods for spatially adaptive simulations of fluid-structure interactions when subject to thermal fluctuations. To account for thermal fluctuations, we introduce a discrete fluctuation-dissipation…
We consider the weak-error rate of the SPDE approximation by regularized Dean-Kawasaki equation with It\^o noise for particle systems with mean-field interactions both on the drift and the noise. The global existence and uniqueness of the…
We consider a class of interacting particle systems in continuous space of non-gradient type, which are reversible with respect to Poisson point processes with constant density. For these models, a rate of convergence was recently obtained…
We investigate the fluctuations around the average density profile in the weakly asymmetric exclusion process with open boundaries in the steady state. We show that these fluctuations are given, in the macroscopic limit, by a centered…