Related papers: On Hydrodynamic Equations at the Limit of Infinite…
Multiparticle collision dynamics (MPCD) enables to simulate fluid dynamics including both hydrodynamics and thermal fluctuations. Its main use concerns complex fluids, where the solvent interacts with concentrated solutes, may they be…
Many features of granular media can be modeled by a fluid of hard spheres with inelastic collisions. Under rapid flow conditions, the macroscopic behavior of grains can be described through hydrodynamic equations accounting for dissipation…
Standard textbooks will state that hydrodynamics requires near-equilibrium to be applicable. Recently, however, out-of-equilibrium attractor solutions for hydrodynamics have been found in kinetic theory and holography in systems with a high…
In this paper, we consider suitable weak solutions of the four dimensional incompressible magneto-hydrodynamic equations. We give two different kind $\varepsilon$-regularity criteria. One only requires the smallness of scaling $L^{p,q}$…
This is the first of two articles on the study of a particle system model that exhibits a Turing instability type effect. The model is based on two discrete lines (or toruses) with Ising spins, that evolve according to a continuous time…
In this paper we study the hydrodynamic (small mass approximation) limit of a Fokker-Planck equation. This equation arises in the kinetic description of the evolution of a particle system immersed in a viscous Stokes flow. We discuss two…
The hydrodynamic description of probabilistic ballistic annihilation, for which no conservation laws hold, is an intricate problem with hard sphere-like dynamics for which no exact solution exists. We consequently focus on simplified…
We establish the global existence of weak solutions of the isentropic compressible magnetohydrodynamic equations with ripped density in the whole plane provided the bulk viscosity coefficient is properly large. Moreover, we show that such…
Two questions connected to the macroscopic Maxwell equations are addressed: First, which form do they assume in the hydrodynamic regime, for low frequencies, strong dissipation and arbitrary field strengths. Second, what does this tell us…
The observation of seeming hydrodynamic-like behavior in proton-proton and proton-nucleus collisions presents us with the conceptual problem of how the initial state of such a hydrodynamic evolution should be characterized. This is an issue…
The rigorous derivation of the Uehling-Uhlenbeck equation from more fundamental quantum many-particle systems is a challenging open problem in mathematics. In this paper, we exam the weak coupling limit of quantum N-particle dynamics. We…
In the classical work by Irving and Zwanzig [Irving J.H. and Zwanzig R.W., J. Chem. Phys. 19 (1951), 1173-1180 ] it has been shown that quantum observables for macroscopic density, momentum and energy satisfy the conservation laws of fluid…
We propose a new concept of weak solution to the equations of compressible magnetohydrodynamics driven by large boundary data. The system of the underlying field equations is solvable globally in time in the out of equilibrium regime…
This article considers some classes of models dealing with the dynamics of discrete curves subjected to stochastic deformations. It turns out that the problems of interest can be set in terms of interacting exclusion processes, the ultimate…
Consider an interacting particle system indexed by the vertices of a (possibly random) locally finite graph whose vertices and edges are equipped with marks representing parameters of the model such as the environment and initial…
This paper proves the existence of weak solutions to the spatially homogeneous Boltzmann equation for Maxwellian molecules, when the initial data are chosen from the space of all Borel probability measures on R^3 with finite second moments…
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…
Consider the overdamped limit for a system of interacting particles in the presence of hydrodynamic interactions. For two-body hydrodynamic interactions and one- and two-body potentials, a Smoluchowski-type evolution equation is rigorously…
Starting from the non-relativistic Pauli description of spin-1/2 particles, a set of fluid equations, governing the dynamics of such particles interacting with external fields and other particles, is derived. The equations describe…
Under the hydrodynamic equilibrium Buchdahl's conditions on the behavior of the density and the pressure, for regular fluid static circularly symmetric star in (2 + 1) dimensions in the presence of a cosmological constant, is established…