Related papers: Geometrical interpretation of fluctuating hydrodyn…
Considering the example of interacting Brownian particles we present a linear response derivation of the boundary condition for the corresponding hydrodynamic description (the diffusion equation). This requires us to identify a non-analytic…
Current fluctuations in boundary-driven diffusive systems are, in many cases, studied using hydrodynamic theories. Their predictions are then expected to be valid for currents which scale inversely with the system size. To study this…
In this paper we consider a representative a priori unstable Hamiltonian system with 2+1/2 degrees of freedom, to which we apply the geometric mechanism for diffusion introduced in the paper Delshams et al., Mem. Amer. Math. Soc. 2006, and…
These are pedagogical lecture notes on hydrodynamic fluctuations in normal relativistic fluids. The lectures discuss correlation functions of conserved densities in thermal equilibrium, interactions of the hydrodynamic modes, an effective…
An infinite particle system of independent jumping particles in infinite volume is considered. Their construction is recalled,further properties are derived, the relation with hierarchical equations, Poissonian analysis, and second…
We conduct a numerical study of the dynamic behavior of a dense hard sphere fluid by deriving and integrating a set of Langevin equations. The statics of the system is described by a free energy functional of the Ramakrishnan-Yussouff form.…
The swimming trajectories of self-propelled organisms or synthetic devices in a viscous fluid can be altered by hydrodynamic interactions with nearby boundaries. We explore a multipole description of swimming bodies and provide a general…
Learning algorithms for implicit generative models can optimize a variety of criteria that measure how the data distribution differs from the implicit model distribution, including the Wasserstein distance, the Energy distance, and the…
We obtain the large scale limit of the fluctuations around its hydrodynamic limit of the density of particles of a weakly asymmetric exclusion process in dimension up to three. The proof is based upon a sharp estimate on the relative…
We consider compressible fluid flow on an evolving surface with a piecewise Lipschitz-continuous boundary from an energetic point of view. We employ both an energetic variational approach and the first law of thermodynamics to make a…
In this paper we present a novel approach to the geometric formulation of solid and fluid mechanics within the port-Hamiltonian framework, which extends the standard Hamiltonian formulation to non-conservative and open dynamical systems.…
We study the hydrodynamics of a freely-standing smectic-A film in the isothermal, incompressible limit theoretically by analyzing the linearized hydrodynamic equations of motion with proper boundary conditions. The dynamic properties for…
As an effective theory, relativistic hydrodynamics is fixed by symmetries up to a set of transport coefficients. A lot of effort has been devoted to explicit calculations of these coefficients. Here we propose a shift in perspective: we…
We discuss a dynamical theory for nematic liquid crystals describing the stage of evolution in which the hydrodynamic fluid motion has already equilibrated and the subsequent evolution proceeds via diffusive motion of the orientational…
A statistical mechanics theory for a fluid stratified in density is presented. The predicted statistical equilibrium state is the most probable outcome of turbulent stirring. The slow temporal evolution of the vertical density profile is…
A foundational question in relativistic fluid mechanics concerns the properties of the hydrodynamic gradient expansion at large orders. We establish the precise conditions under which this gradient expansion diverges for a broad class of…
We introduce Wasserstein-like dynamical transport distances between vector-valued densities on the real line. The mobility function from the scalar theory is replaced by a mobility matrix, that is subject to positivity and concavity…
Via hydrodynamics preserving molecular dynamics simulations we study growth phenomena in a phase separating symmetric binary mixture model. We quench high-temperature homogeneous configurations to state points inside the miscibility gap,…
In this paper we introduce a Wasserstein-type distance on the set of Gaussian mixture models. This distance is defined by restricting the set of possible coupling measures in the optimal transport problem to Gaussian mixture models. We…
Starting from the microscopic description of a normal fluid in terms of any kind of local interacting many-particle theory we present a well defined step by step procedure to derive the hydrodynamic equations for the macroscopic phenomena.…