Related papers: Characteristic power spectrum of the diffusive int…
We consider numerically the depinning transition in the random-field Ising model. Our analysis reveals that the three and four dimensional model displays a simple scaling behavior whereas the five dimensional scaling behavior is affected by…
We consider a two dimensional Turing like system with two diffusing species which interact with each other. Considering the species to be charged, we include the effect of an electric field along a given direction which can lead to a drift…
Enchanting ripple pattern exist on interface, and manifest them self in it's fluctuation profile as well. These ripples apparently flow as the interface struck with inhomogeneous externally driven field interface, moves fluctuating about it…
A phase transition indicates a sudden change in the properties of a large system. For temperature-driven phase transitions this is related to non-analytic behavior of the free energy density at the critical temperature: The knowledge of the…
Diffuse interface models are widely used to describe evolution of multi-phase systems of different nature. Dispersed "inclusions", described by the phase field distribution, are usually three dimensional objects. When describing elastic…
To investigate novel aspects of pattern formation in spin systems, we use a mapping between reactive concentrations in a reaction-diffusion system and spin orientations in a dynamic multiple-spin Ising model. While pattern formation in…
A long-standing goal of materials science is to understand, predict and control the evolution of microstructures in crystalline materials. Most microstructure evolution is controlled by interface motion; hence, the establishment of rigorous…
Diffusion in a multidimensional energy surface with minima and barriers is a problem of importance in statistical mechanics and also has wide applications, such as protein folding. To understand it in such a system, we carry out theory and…
We study a diffusion approximation for a model of stochastic motion of a particle in one spatial dimension. The velocity of the particle is constant but the direction of the motion undergoes random changes with a Poisson clock. Moreover,…
We study the structure of an interface in a three dimensional Ising system created by an external non-uniform field $H({\bf r},t)$. $H$ changes sign over a two dimensional plane of arbitrary orientation. When the field is pulled with…
The interface separating a liquid from its vapor phase is diffuse: the composition varies continuously from one phase to the other over a finite length. Recent experiments on dynamic jamming fronts in two dimensions [Waitukaitis et al.,…
We consider a thermodynamically consistent diffuse interface model describing two-phase flows of incompressible fluids in a non-isothermal setting. This model was recently introduced in a previous paper of ours, where we proved existence of…
We study the motion of phase interfaces in a diffusive lattice equation with bistable nonlinearity and derive a free boundary problem with hysteresis to describe the macroscopic evolution in the parabolic scaling limit. The first part of…
We consider interface fluctuations on a two-dimensional layered lattice where the couplings follow a hierarchical sequence. This problem is equivalent to the diffusion process of a quantum particle in the presence of a one-dimensional…
We consider d=2 Ising strip with surface fields acting on boundary spins. Using the properties of the transfer matrix spectrum we identify two pseudotransition temperatures and show that they satisfy similar scaling relations as expected…
A non-equilibrium theory of isothermal and diffusionless evolution of incoherent interfaces within a plastically deforming solid is developed. The irreversible dynamics of the interface are driven by its normal motion, incoherency (slip and…
We investigate the interface dynamics of the two-dimensional stochastic Ising model in an external field under helicoidal boundary conditions. At sufficiently low temperatures and fields, the dynamics of the interface is described by an…
The influence of nonequilibrium bulk conditions on the properties of the interfaces exhibited by a kinetic Ising--like model system with nonequilibrium steady states is studied. The system is maintained out of equilibrium by perturbing the…
The dynamics based on information transfer is proposed as an underlying mechanism for the scale-invariant dynamic critical behavior observed in a variety of systems. We apply the dynamics to the globally-coupled Ising model, which is…
We introduce a thermal dynamics for the Ising ferromagnet where the energy variations occurring within the system exhibit a diffusive character typical of thermalizing agents such as e.g. localized excitations. Time evolution is provided by…