Related papers: Global existence for a singular phase field system…

Spontaneous symmetry-breaking in phase transitions occurs when the system Hamiltonian is symmetric under a certain transformation, but the equilibrium states observed in nature are not. Here, we prove that when a discrete symmetry is…

We consider a very complicated system of some latticized differential equations that is considered as equations of motion for a field theory. We define macro state restrictions for such a system analogous to thermodynamical states of a…

We consider countable system of harmonic oscillators on the real line with quadratic interaction potential with finite support and local external force (stationary stochastic process) acting only on one fixed particle. In the case of…

When a system's parameter is abruptly changed, a relaxation towards the new equilibrium of the system follows. We show that a crossing between the second and third eigenvalues of the relaxation matrix results in a relaxation trajectory…

The classification of the ground-state phases of complex one-dimensional electronic systems is considered in the context of a fixed-point strategy. Examples are multichain Hubbard models, the Kondo-Heisenberg model, and the one-dimensional…

We study phase transition behavior of the Heisenberg model on a distorted triangular lattice with competing interactions. The ground-state phase diagram indicates that underlying symmetry can be changed by tuning parameters. We focus on two…

When placed on an inclined plane, a perfect 2D disk or 3D sphere simply rolls down in a straight line under gravity. But how is the rolling affected if these shapes are irregular or random? Treating the terminal rolling speed as an order…

The phase diagram of a system of monodispersed hard rectangles of size $m\times m k$ on a square lattice is numerically determined for $m=2,3$ and aspect ratio $k= 1,2,\ldots, 7$. We show the existence of a disordered phase, a nematic phase…

We consider the two-phase flow model with slip boundary condition in a 3D exterior domains whose boundary is smooth. We establish the global existence of classical solutions of this system provided that the initial energy is suitably small.…

The investigation of quantum gravity effects in order to avoid the big bang singularity is a requisite, so that the idea of oscillating universes is introduced as an alternative for standard cosmological model. Therefore, the Friedmann…

We study a multiscale stochastic optimal control problem subject to state constraints on the slow variable. To address this class of problems, we develop a rigorous theoretical framework based on singular perturbation analysis, tailored to…

We propose a stability analysis method for sampled-data switched linear systems with finite-level static quantizers. In the closed-loop system, information on the active mode of the plant is transmitted to the controller only at each…

The fundamental problem of phase saturation of electrons in a disordered mesoscopic system at very low temperatures is addressed. The disorder in the medium has both static and dynamic components, the latter being in the form of two-level…

We investigate the traveling front solutions of a nonlocal Lotka Volterra system to illustrate the outcome of the competition between two species. The existence of the front solution is obtained through a new monotone iteration scheme, the…

We consider the overdamped dynamics of a paradigmatic long-range system of particles residing on the sites of a one-dimensional lattice, in the presence of thermal noise. The internal degree of freedom of each particle is a periodic…

We prove the existence and uniqueness of solutions for a family of nonlinear parabolic systems related to phase field models taking in account variations of temperature and the possibility of a general class of nonlinearities. The present…

Here we investigate how the positions of a condensed phase can be controlled by using concentration gradients of a regulator that influences phase separation. We consider a mean field model of a ternary mixture where a concentration…

We study solutions to a one-phase singular perturbation problem that arises in combustion theory and that formally approximates the classical one-phase free boundary problem. We introduce a natural density condition on the transition layers…

Recent theoretical work has shown that the competition between coherent unitary dynamics and stochastic measurements, performed by the environment, along wavefunction trajectories can give rise to transitions in the entanglement scaling. In…

Traditionally, phase transitions are defined in the thermodynamic limit only. We discuss how phase transitions of first order (with phase separation and surface tension), continuous transitions and (multi)-critical points can be seen and…