Related papers: Hydrodynamic and hydrostatic limit for a generaliz…
We study the diffusive scaling limit for a chain of $N$ coupled oscillators. In order to provide the system with good ergodic properties, we perturb the Hamiltonian dynamics with random flips of velocities, so that the energy is locally…
Transport is one of the most important physical processes in all energy and length scales. Ideal gases and hydrodynamics are, respectively, two opposite limits of transport. Here, we present an unexpected mathematical connection between…
We present an analytical calculation of the hydrodynamic interaction between two spherical particles near an elastic interface such as a cell membrane. The theory predicts the frequency dependent self- and pair-mobilities accounting for the…
Motivated by recent simulations and by experiments on aggregation of gliding bacteria, we study a model of the collective dynamics of self-propelled hard rods on a substrate in two dimensions. The rods have finite size, interact via…
In this paper, we are concerned with a class of conservative systems including asymmetric exclusion processes and zero-range processes as examples, where some particles are initially placed on $N$ positions. A particle jumps from a position…
We extend the usual hydrodynamic description of the symmetric exclusion process by keeping track of collision events corresponding to jumps into already occupied sites, thereby quantifying the dissipated part of the microscopic activity…
This article deals with the issues of global-in-time existence and asymptotic analysis of a fluid-particle interaction model in the so-called bubbling regime. The mixture occupies the physical space $\Omega \subset \mathbb{R}^3$ which may…
The thermodynamic limit of the internal energy and the entropy of the system of quantum interacting particles in random medium is shown to exist under the crucial requirements of stability and temperedness of interactions. The energy turns…
We consider macroscopic systems in weak contact with boundary reservoirs and under the action of external fields. We present an explicit formula for the Hamiltonian of such systems, from which we deduce the equation of motions, the action…
We investigate the coupled dynamics of charge and energy in interacting lattice models with dipole conservation. We formulate a generic hydrodynamic theory for this combination of fractonic constraints and numerically verify its…
The population dynamics and stability of ecosystems of interacting species is studied from the perspective of non-equilibrium thermodynamics by assuming that species, through their biotic and abiotic interactions, are units of entropy…
We propose an open-boundary molecular dynamics method in which an atomistic system is in contact with an infinite particle reservoir at constant temperature, volume and chemical potential. In practice, following the Hamiltonian adaptive…
This article is concerned with rigorously justifying the hydrostatic limit for continuously stratified incompressible fluids under the influence of gravity. The main distinction of this work compared to previous studies is the absence of…
In 2001, Knight constructed a stochastic process modeling the one dimensional interaction of two particles, one being Newtonian in the sense that it obeys Newton's laws of motion, and the other particle being Brownian. We construct a…
A new computational method is presented to resolve hydrodynamic interactions acting on solid particles immersed in incompressible host fluids. In this method, boundaries between solid particles and host fluids are replaced with a continuous…
Hydrodynamics provides a concise but powerful description of long-time and long-distance physics of correlated systems out of thermodynamic equilibrium. Here we construct hydrodynamic equations for nonrelativistic particles with a…
Non-equilibrium thermodynamics has long been an area of substantial interest to ecologists because most fundamental biological processes, such as protein synthesis and respiration, are inherently energy-consuming. Microbial communities are…
Kinetic and hydrodynamic theories are widely employed for describing the collective behaviour of active matter systems. At the fluctuating level, these have been obtained from explicit coarse-graining procedures in the limit where each…
Recent microfluidic experiments revealed that large particles advected in a fluidic loop display long-range hydrodynamic interactions. However, the consequences of such couplings on the traffic dynamics in more complex networks remain…
Numerous experimental and theoretical results in liquids and plasmas suggest the presence of a critical momentum at which the shear diffusion mode collides with a non-hydrodynamic relaxation mode, giving rise to propagating shear waves.…