相关论文: Modelling Silicosis: The Structure of Equilibria
The evolution of inhomogeneities in a spherical collapse model is studied by expanding the Einstein equation in powers of inverse radial parameter. In the linear regime, the density contrast is obtained for flat, closed and open universes.…
We present a new approach to the problem of proving global stability, based on symplectic geometry and with a focus on systems with several conserved quantities. We also provide a proof of instability for integrable systems whose momentum…
We study relaxation properties of two-body collisions in infinite spatial dimension. We show that this process exhibits multiscaling asymptotic behavior as the underlying distribution is characterized by an infinite set of nontrivial…
We study the cosmological Burgers model, as we call it, which is a nonlinear hyperbolic balance law (in one and two spatial variables) posed on an expanding or contracting background. We design a finite volume scheme that is fourth-order in…
As the quantification of metabolism, nonequilibrium steady states play a central role in living matter, but are beyond the purview of equilibrium statistical mechanics. Here we develop a fermionic theory of nonequilibrium steady states in…
We discuss an exact analytical solution of a simplified version of the statistical multifragmentation model with the restriction that the largest fragment size cannot exceed the finite volume of the system. A complete analysis of the…
We consider the general problem of determining the steady state of stochastic nonequilibrium systems such as those that have been used to model (among other things) biological transport and traffic flow. We begin with a broad overview of…
We study real space condensation in aggregation-fragmentation models where the total mass is not conserved, as in phenomena like cloud formation and intracellular trafficking. We study the scaling properties of the system with influx and…
We study infinite systems of particles which undergo coalescence and fragmentation, in a manner determined solely by their masses. A pair of particles having masses $x$ and $y$ coalesces at a given rate $K(x,y)$. A particle of mass $x$…
The aim of this paper is to show an existence theorem for a kinetic model of coagulation-fragmentation with initial data satisfying the natural physical bounds, and assumptions of finite number of particles and finite $L^p$-norm. We use the…
In this work, we illustrate the underlying mathematical structure of mixed-dimensional models arising from the composition of graphs and continuous domains. Such models are becoming popular in applications, in particular, to model the human…
An exact analytical solution of the statistical multifragmentation model is found in thermodynamic limit. The system of nuclear fragments exhibits a 1-st order liquid-gas phase transition. The peculiar thermodynamic properties of the model…
Although coarse-grained models have been widely used to explain exotic phenomena in complex fluids, such as droplet formation in living cells, these conventional approaches often fail to capture the intricate microscopic degrees of freedom…
The issue of symmetry and symmetry breaking is fundamental in all areas of science. Symmetry is often assimilated to order and beauty while symmetry breaking is the source of many interesting phenomena such as phase transitions,…
A five-dimensional cosmological model including a single perfect fluid is studied in the framework of dynamical system analysis. All the critical points of the system with their stability properties are listed and some representative phase…
The cosmological many-body problem is effectively an infinite system of gravitationally interacting masses in an expanding universe. Despite the interactions' long-range nature, an analytical theory of statistical mechanics describes the…
We study an analytically tractable model with long-range interactions for which an out-of-equilibrium very long-lived coherent structure spontaneously appears. The dynamics of this model is indeed very peculiar: a bicluster forms at low…
We analyze the collective behavior of a lattice model of pulse-coupled oscillators. By studying the intrinsic dynamics of each member of the population and their mutual interactions we observe the emergence of either spatio-temporal…
Using the formalism of rigorous statistical mechanics, we study the phenomena of phase separation and freezing-point depression upon freezing of solutions. Specifically, we devise an Ising-based model of a solvent-solute system and show…
The phase diagrams and transitions of nonequilibrium systems with multiplicative noise are studied theoretically. We show the existence of both strong and weak-coupling critical behavior, of two distinct active phases, and of a nonzero…