Related papers: Second class particles as microscopic characterist…
Natural phenomena frequently involve a very large number of interacting molecules moving in confined regions of space. Cellular transport by motor proteins is an example of such collective behavior. We derive a deterministic compartmental…
We show uniqueness and stability in $L^2$ and for all time for piecewise-smooth solutions to hyperbolic balance laws. We have in mind applications to gas dynamics, the isentropic Euler system and the full Euler system for a polytropic gas…
We consider a system of two conservation laws and provide a detailed description of both classical and non-classical self-similar Riemann solutions. In particular, we demonstrate the existence of overcompressive delta shocks as singular…
The observed general time-asymmetric behavior of macroscopic systems -- embodied in the second law of thermodynamics -- arises naturally from time-symmetric microscopic laws due to the great disparity between macro and micro-scales. More…
In textbooks on statistical mechanics, one finds often arguments based on classical mechanics, phase space and ergodicity in order to justify the second law of thermodynamics. However, the basic equations of motion of classical mechanics…
We deal with a class of abstract nonlinear stochastic models, which covers many 2D hydrodynamical models including 2D Navier-Stokes equations, 2D MHD models and 2D magnetic B\'enard problem and also some shell models of turbulence. We first…
We introduce a general class of stochastic lattice gas models, and derive their fluctuating hydrodynamics description in the large size limit under a local equilibrium hypothesis. The model consists in energetic particles on a lattice…
Quantum hydrodynamic (QHD) model of charged spin-1/2 particles contains physical quantities defined for all particles of a species including particles with spin-up and with spin-down. Different population of states with different spin…
For general second order evolution equations, we prove an optimal condition on the degree of unboundedness of the damping, that rules out finite-time extinction. We show that control estimates give energy decay rates that explicitly depend…
Existence and admissibility of $\delta$-shock type solution is discussed for the following nonconvex strictly hyperbolic system arising in studues of plasmas: \pa_t u + \pa_x \big(\Sfrac{u^2+v^2}{2} \big) &=0 \pa_t v +\pa_x(v(u-1))&=0. The…
We consider an exclusion process representing a reactive dynamics of a pulled front on the integer lattice, describing the dynamics of first class $X$ particles moving as a simple symmetric exclusion process, and static second class $Y$…
In case of spinless particles there appear additional (singular) solutions in the framework of relativistic Klein-Gordon equation for Coulomb potential. These solutions obey to all requirements of quantum mechanical general principles.…
Time-asymmetric behavior as embodied in the second law of thermodynamics is observed in {\it individual macroscopic} systems. It can be understood as arising naturally from time-symmetric microscopic laws when account is taken of a) the…
We consider the scalar conservation law in one space dimension with a genuinely nonlinear flux. We assume that an appropriate velocity function depending on the entropy solution of the conservation law is given for the comprising particles,…
We propose that particles are associated both with localized macroscopic states at point vertices and with extended microscopic states at all vacuum points. The self-fields screen the microscopic particle currents everywhere except at the…
The equations of fluid motions are considered in the case of internal energy depending on mass density, volume entropy and their spatial derivatives. The model corresponds to domains with large density gradients in which the temperature is…
It is shown that the laws of thermodynamics are extremely robust under generalizations of the form of entropy. Using the Bregman-type relative entropy, the Clausius inequality is proved to be always valid. This implies that thermodynamics…
An "exact" method for scalar one-dimensional hyperbolic conservation laws is presented. The approach is based on the evolution of shock particles, separated by local similarity solutions. The numerical solution is defined everywhere, and is…
We introduce a stochastic system of interacting particles which is expected to furnish as the number of particles goes to infinity a stochastic approach of the 2-D Keller-Segel model. In this note, we prove existence and some uniqueness for…
We consider two particles performing continuous-time nearest neighbor random walk on $\mathbb Z$ and interacting with each other when they are at neighboring positions. Typical examples are two particles in the partial exclusion process or…