Related papers: Quantitative Error Estimates for Learning Macrosco…
Assuming an effective quadratic Hamiltonian, we derive an approximate, linear stochastic equation of motion for the density-fluctuations in liquids, composed of overdamped Brownian particles. From this approach, time dependent two point…
In this paper, we present an innovative particle system characterized by moderate interactions, designed to accurately approximate kinetic flocking models that incorporate singular interaction forces and local alignment mechanisms. We…
We study coarse-grained density fluctuations in the disordered phase of the paradigmatic Vicsek-like models of self-propelled particles with alignment interactions and random self-propulsion velocities. By numerically integrating a…
The experimental search for the QCD critical point by means of relativistic heavy-ion collisions necessitates the development of dynamical models of fluctuations. In this work we study the fluctuations of the net-baryon density near the…
Fluctuations of dynamical quantities are fundamental and inevitable. For the booming research in nanotechnology, huge relative fluctuation comes with the reduction of system size, leading to large uncertainty for the estimates of dynamical…
We study an additive-noise approximation to Keller-Segel-Dean-Kawasaki dynamics, which is proposed as an approximate model to the fluctuating hydrodynamics of chemotactically interacting particles around their mean-field limit. As such, the…
We present a data-driven framework for learning hydrodynamic equations from particle-based simulations of active matter. Our method leverages coarse-graining in both space and time to bridge microscopic particle dynamics with macroscopic…
The convergence of stochastic interacting particle systems in the mean-field limit to solutions of conservative stochastic partial differential equations is established, with optimal rate of convergence. As a second main result, a…
We consider a nonlinear differential equation under the combined influence of small state-dependent Brownian perturbations of size $\varepsilon$, and fast periodic sampling with period $\delta$; $0<\varepsilon, \delta \ll 1$. Thus, state…
This article studies typical dynamics and fluctuations for a slow-fast dynamical system perturbed by a small fractional Brownian noise. Based on an ergodic theorem with explicit rates of convergence, which may be of independent interest, we…
We study a class of Hamilton-Jacobi partial differential equations in the space of probability measures. In the first part of this paper, we prove comparison principles (implying uniqueness) for this class. In the second part, we establish…
In many physical systems, degrees of freedom are coupled \emph{via} hydrodynamic forces, even in the absence of Hamiltonian interactions. A particularly important and widespread example concerns the transport of microscopic particles in…
In the hydrodynamic theory, the non-equilibrium dynamics of a many-body system is approximated, at large scales of space and time, by irreversible relaxation to local entropy maximisation. This results in a convective equation corrected by…
We study diffusion of colloids on a fluid-fluid interface using particle simulations and fluctuating hydrodynamics. Diffusion on a two-dimensional interface with three-dimensional hydrodynamics is known to be anomalous, with the collective…
Recently, many interesting features of the hydrodynamically coupled motions of the Brownian particles in a viscous fluid have been reported which are impossible for the uncoupled motions of the similar particles. However, it is expected…
This paper deals with asymptotic errors, limit theorems for errors between numerical and exact solutions of stochastic differential equation (SDE) driven by one-dimensional fractional Brownian motion (fBm). The Euler-Maruyama, higher-order…
The aim of this paper is to use large deviation theory in order to compute the entropy of macrostates for the microcanonical measure of the shallow water system. The main prediction of this full statistical mechanics computation is the…
We study fluctuations of small noise multiscale diffusions around their homogenized deterministic limit. We derive quantitative rates of convergence of the fluctuation processes to their Gaussian limits in the appropriate Wasserstein metric…
We consider the application of fluctuation relations to the dynamics of coarse-grained systems, as might arise in a hypothetical experiment in which a system is monitored with a low-resolution measuring apparatus. We analyze a stochastic,…
Large deviations of conservative interacting particle systems, such as the zero range process, about their hydrodynamic limit and their respective rate functions lead to the analysis of the skeleton equation; a degenerate…