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We study properties of the solutions of a family of second order integro-differential equations, which describe the large scale dynamics of a class of microscopic phase segregation models with particle conserving dynamics. We first…
A thermodynamic approach to rapid phase transformations within a diffuse interface in a binary system is developed. Assuming an extended set of independent thermodynamic variables formed by the union of the classic set of slow variables and…
We consider a reaction-diffusion system for two densities lying in adjacent domains of $\mathbb{R}^N$. We treat two configurations: either a cylinder and its complement, or two half-spaces. Diffusion and reaction heterogeneities for the two…
The nonequilibrium dynamics of the chiral phase transition expected during the expansion of the quark-qluon plasma produced in a high energy hadron or heavy ion collision is studied in the O(4) linear sigma model to leading order in a large…
The temperature phase transition in the N-component scalar field theory with spontaneous symmetry breaking is investigated in the perturbative approach. The second Legendre transform is used together with the consideration of the gap…
We investigate the phase diagram of a relativistic, parametrically driven O($N$)-symmetric theory coupled to a Markovian thermal bath. Our analysis reveals a rich variety of phases, including both uniform and spatially modulated…
With the aim to understand the role of the constraints in the thermalisation of quantum systems, we study the dynamics of a family of kinetically constrained models arising through duality from the XXZ spin chain. We find that integrable…
We consider a kinetic model of two species of particles interacting with a reservoir at fixed temperature, described by two coupled Vlasov-Fokker-Plank equations. We prove that in the diffusive limit the evolution is described by a…
Spontaneous symmetry breaking occurs in various equilibrium and nonequilibrium systems, where phase transitions are typically marked by a single critical point that separates ordered and disordered regimes. We reveal a novel phenomenon in…
Interactions of the uniform mode with higher order modes due to incommensurately modulated equilibrium state change the usual relaxation behaviour to a more complex one. A multirelaxation character should be present even in the…
We investigate the relaxational dynamics of the order parameter of chiral symmetry breaking, the sigma mean-field, with a heat bath consisting of quarks and antiquarks. A semiclassical stochastic Langevin equation of motion is obtained from…
In the last two decades, many phase-field models for solid-state sintering have been published. Two groups of models have emerged, with and without the contribution of rigid body motion. This paper first describes the previously published…
Numerical simulations of phase ordering under dissipative dynamics in a (2+1)-dimensional 3-vector model with O(3) symmetry are reported. The energy functional includes terms which stabilize the size of extended topological defects. They…
Via hydrodynamics preserving molecular dynamics simulations we study growth phenomena in a phase separating symmetric binary mixture model. We quench high-temperature homogeneous configurations to state points inside the miscibility gap,…
We discuss a dynamical theory for nematic liquid crystals describing the stage of evolution in which the hydrodynamic fluid motion has already equilibrated and the subsequent evolution proceeds via diffusive motion of the orientational…
We study the probability distribution of a current flowing through a diffusive system connected to a pair of reservoirs at its two ends. Sufficient conditions for the occurrence of a host of possible phase transitions both in and out of…
We study a stochastic lattice gas of particles undergoing asymmetric diffusion in two dimensions. Transitions between a low-density uniform phase and high-density non-uniform phases characterized by localized or extended structure are…
The hindered diffusion model is introduced. It is a continuum model giving the dynamics of a conserved density. Similar to the spin-facilitated models, the kinetics are hindered by a fluctuating diffusion coefficient that decreases as the…
The multicritical points of the $O(N)$ invariant $N$ vector model in the large $N$ limit are reexamined. Of particular interest are the subtleties involved in the stability of the phase structure at critical dimensions. In the limit $N \to…
The phase transition patterns displayed by a model of two coupled complex scalar fields are studied at finite temperature and chemical potential. Possible phenomena like symmetry persistence and inverse symmetry breaking at high…