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Modeling the chemical, electric, and thermal transport as well as phase transitions and the accompanying mesoscale microstructure evolution within a material in an electronic device setting involves the solution of partial differential…
A fundamental problem of non-equilibrium statistical mechanics is the derivation of macroscopic transport equations in the hydrodynamic limit. The rigorous study of such limits requires detailed information about rates of convergence to…
The theory of first order density-driven phase transitions with frustration due to the long range Coulomb (LRC) interaction develop on paper I of this series is applied to the following physical systems: i) the low density electron gas ii)…
Phase separation and coarsening is a phenomenon commonly seen in binary physical and chemical systems that occur in nature. Often times, thermal fluctuations, modeled as stochastic noise, are present in the system and the phase segregation…
We study the dynamics of a strongly interacting bosonic quantum gas in an optical lattice potential under the effect of a dissipative environment. We show that the interplay between the dissipative process and the Hamiltonian evolution…
The superradiant phase transition in the dissipative Dicke lattice model, driven by on-site collective atom-photon interactions and inter-site photon hopping, is a cornerstone of nonequilibrium quantum many-body physics. However, little is…
We comprehensively study external forcing-driven dynamical structure formation in a binary dusty plasma mixture. Using two-dimensional driven-dissipative molecular dynamics simulations, we demonstrate phase segregation into bands and lanes…
This article presents a new phase-field formulation for non-equilibrium interface conditions in rapid phase transformations. With a particular way of defining concentration fields, the classical sharp and diffuse (thick) interface theories…
In this paper we propose a mathematical model of phase separation for a quasi-incompressible binary mixture where the spinodal decomposition is induced by an heat flux governed by the Cattaneo-Maxwell equation. As usual, the phase…
Low temperature analysis of nonequilibrium systems requires finding the states with the longest lifetime and that are most accessible from other states. We determine these dominant states for a one-dimensional diffusive lattice gas subject…
The nonextensivity of a classical long-range Hamiltonian system is discussed. The system is the so-called $\alpha$-XY model, a lattice of inertial rotators with an adjustable parameter $\alpha$ controlling the range of the interactions.…
We investigate the time evolution of a model system of interacting particles, moving in a $d$-dimensional torus. The microscopic dynamics are first order in time with velocities set equal to the negative gradient of a potential energy term…
Numerical experiments of the statistical evolution of an ensemble of non-interacting particles in a time-dependent billiard with inelastic collisions, reveals the existence of three statistical regimes for the evolution of the speeds…
We present an adequate analytical approach to the description of nonlinear vibration with strong energy exchange between weakly coupled oscillators and oscillatory chains. The fundamental notion of the limiting phase trajectory (LPT)…
We propose an open-boundary molecular dynamics method in which an atomistic system is in contact with an infinite particle reservoir at constant temperature, volume and chemical potential. In practice, following the Hamiltonian adaptive…
One-dimensional, boundary-driven lattice gases with local interactions are studied in the weakly interacting limit. The density profiles and the correlation functions are calculated to first order in the interaction strength for zero-range…
The Cahn-Hilliard equation with an externally-prescribed chaotic shear flow is studied in two and three dimensions. The main goal is to compare and contrast the phase separation in two and three dimensions, using high-resolution numerical…
This article is devoted to the study of the dynamical behavior of a collisionless kinetic gas in d=1,2,3 space dimensions which is trapped in a rotationally symmetric potential well. Although at the microscopic level the trajectories of…
A lattice gas with infinite repulsion between particles separated by $\leq 1$ lattice spacing, and nearest-neighbor hopping dynamics, is subject to a drive favoring movement along one axis of the square lattice. The equilibrium (zero drive)…
We revisit the Lieb-Liniger model for $n$ bosons in one dimension with attractive delta interaction in a half-space $\mathbb{R}^+$ with diagonal boundary conditions. This model is integrable for arbitrary value of $b \in \mathbb{R}$, the…