Related papers: Phase Segregation Dynamics in Particle Systems wit…
The aim of this paper is to discuss the mathematical modeling of Brownian active particle systems, a recently popular paradigmatic system for self-propelled particles. We present four microscopic models with different types of repulsive…
We study a family of conservative interacting particle systems with degenerate rates called noncooperative kinetically constrained lattice gases. We prove for all models in this family the diffusive scaling of the relaxation time, the…
We study the steady state resulting from instabilities in crystals driven through a dissipative medium, for instance, a colloidal crystal which is steadily sedimenting through a viscous fluid. The problem involves two coupled fields, the…
We first survey some open questions concerning stochastic interacting particle systems with open boundaries. Then an asymmetric exclusion process with open boundaries that generalizes the lattice gas model of Katz, Lebowitz, and Spohn (KLS)…
We derive the hydrodynamic limit of Glauber-Kawasaki dynamics. The Kawasaki part is simple and describes independent movement of the particles with hard core exclusive interactions. It is speeded up in a diffusive space-time scaling. The…
Mixtures of glass-forming fluids sometimes exhibit glass-glass phase separation at low temperatures. Here, we use a molecular dynamics simulation to study one of the simplest examples of the glass-glass phase separation. We consider a…
In this paper, we study a model for phase segregation taking place in a spatial domain that was introduced by Podio-Guidugli in Ric. Mat. 55 (2006), pp. 105-118. The model consists of a strongly coupled system of nonlinear parabolic…
Using an analytically tractable lattice model for reaction-diffusion processes of hard-core particles we demonstrate that under nonequilibrium conditions phase coexistence may arise even if the system is effectively one-dimensional as e.g.…
We investigate a novel variant of the exclusion process in which particles perform asymmetric nearest-neighbor jumps across a bond \((k, k+1)\) only if the preceding site \((k-1)\) is unoccupied. This next-nearest-neighbor constraint…
Conjecture II.3.6 of Spohn in [Spohn '91] and Lecture 7 of Jensen-Yau in [Jensen-Yau '99] ask for a general derivation of universal fluctuations of hydrodynamic limits in large-scale stochastic interacting particle systems. However, the…
We prove the dynamical large deviations for a particle system in which particles may have different velocities. We assume that we have two infinite reservoirs of particles at the boundary: this is the so-called boundary driven process. The…
We prove that the stochastic Burgers equation, which is related to the Kardar-Parisi-Zhang/KPZ equation via weak derivative, is a "critical" scaling limit for density fluctuations for a family of non-integrable and non-stationary…
We study an alloy system where short-ranged, thermally-driven diffusion competes with externally imposed, finite-ranged, athermal atomic exchanges, as is the case in alloys under irradiation. Using a Cahn-Hilliard-type approach, we show…
A conserved lattice gas with random neighbor hopping of active particles is introduced which exhibits a continuous phase transition from an active state to an absorbing non-active state. Since the randomness of the particle hopping breaks…
We derive a novel thermodynamically consistent Navier--Stokes--Cahn--Hilliard system with dynamic boundary conditions. This model describes the motion of viscous incompressible binary fluids with different densities. In contrast to previous…
We analyse the process of energy exchanges generated by the elastic collisions between a point-particle, confined to a two-dimensional cell with convex boundaries, and a `piston', i.e. a line-segment, which moves back and forth along a…
In this paper we present a mathematical model to describe the phenomenon of phase separation, which is modelled as space regions where an order parameter changes smoothly. The model proposed, including thermal and mixing effects, is deduced…
We perform a linear perturbation analysis of expanding shells driven by expansions of HII regions. The ambient gas is assumed to be uniform. As an unperturbed state, we develop a semi-analytic method for deriving the time evolution of the…
In this work, we analytically investigate a degenerating PDE system for phase separation and complete damage processes considered on a nonsmooth time-dependent domain with mixed boundary conditions. The evolution of the system is described…
The hysteretic behavior of many-particle systems with non-convex free energy can be modeled by nonlocal Fokker-Planck equations that involve two small parameters and are driven by a time- dependent constraint. In this paper we consider the…