相关论文: Long time behavior of dynamic solution to Peierls-…

An extension of the Kinetic Ising model with nonuniform coupling constants on a one-dimensional lattice with boundaries is investigated, and the relaxation of such a system towards its equilibrium is studied. Using a transfer matrix method,…

We consider a diffuse interface model which describes the motion of an incompressible isothermal mixture of two immiscible fluids. This model consists of the Navier-Stokes equations coupled with a convective nonlocal Cahn-Hilliard equation.…

We study the long-time behaviour of a nonlinear Fokker-Planck equation, which models the evolution of rigid polymers in a given flow, after a closure approximation. The aim of this work is twofold: first, we propose a microscopic derivation…

A finite element discretization using a method of lines approached is proposed for approximately solving the Poisson-Nernst-Planck (PNP) equations. This discretization scheme enforces positivity of the computed solutions, corresponding to…

We deal with a system of two coupled differential equations, describing the evolution of a first order phase transition. In particular, we have two non-linear parabolic equations: the first one is deduced from a balance law for entropy and…

We study the evolution of closed inextensible planar curves under a second order flow that decreases the $p$-elastic energy. A short time existence result for $p \in (1,\infty)$ is obtained via a minimizing movements method. For $p = 2$,…

The question whether a nonlinear localized mode (discrete soliton/breather) can be mobile in a lattice has a standard interpretation in terms of the Peierls-Nabarro (PN) potential barrier. For the most commonly studied cases, the PN barrier…

In seeking to understand at a microscopic level the response of dislocations to stress we have undertaken to study as completely as possible the simplest case: a single dislocation in a two dimensional crystal. The intention is that results…

We study a simplified system of the original Ericksen--Leslie equations for the flow of nematic liquid crystals. This is a coupled non-parabolic dissipative dynamic system. We show the convergence of global classical solutions to single…

The general scheme for the treatment of relaxation processes and temporal autocorrelations of dynamical variables for many particle systems is presented in framework of the recurrence relations approach. The time autocorrelation functions…

This work studies a stabilization technique for first-order hyperbolic differential equations used in DNA transcription modeling. Specifically we use the Lighthill-Whitham-Richards Model with a nonlinear Greenshield's velocity proposed in…

We introduce a class of continuum mechanical models aimed at describing the behaviour of viscoelastic fluids by incorporating concepts originated in the theory of solid plasticity. Within this class, even a simple model with constant…

We study localization, pinning, and mobility in the fractional discrete nonlinear Schr\"odinger equation (fDNLS) with generalized power-law coupling. A finite-dimensional spatial-dynamics reduction of the nonlocal recurrence yields onsite…

The motion of a deformable active particle in linear shear flow is explored theoretically. Based on symmetry considerations, in two spatial dimensions, we propose coupled nonlinear dynamical equations for the particle position, velocity,…

We study a continuum model of dislocation transport in order to investigate the formation of heterogeneous dislocation patterns. We propose a physical mechanism which relates the formation of heterogeneous patterns to the dynamics of a…

We present a dynamical description of slow relaxation processes based on the extension of Onsager's fluctuation theory to systems in local quasi-equilibrium. A non-Markovian Fokker-Planck equation for the conditional probability density is…

Results of broadband dielectric spectroscopy and rheological studies of poly(propylene glycol) + SiO${_2}$ nanocomposites are presented. They show that the dynamics in high-concentrated composite is determined by confinement and adsorption…

This paper studies global existence, hydrodynamic limit, and large-time behavior of weak solutions to a kinetic flocking model coupled to the incompressible Navier-Stokes equations. The model describes the motion of particles immersed in a…

In the present study we investigate analytically the process of velocity and energy relaxation in two-phase flows. We begin our exposition by considering the so-called six equations two-phase model [Ishii1975, Rovarch2006]. This model…

In this work the issue of whether key energetic properties (nonlinear, exponential-type dissipation in the abscence of forcing and long-term stability under conditions of time dependent loading) are automatically inherited by deforming…