Related papers: Dynamics of Interfaces in Superconductors
We investigate the evolution of interfaces among phases of the interstellar medium with different temperature. It is found that, for some initial conditions, the dynamical effects related to conductive fronts are very important even if…
In this paper we consider scalar parabolic equations in a general non-smooth setting with emphasis on mixed interface and boundary conditions. In particular, we allow for dynamics and diffusion on a Lipschitz interface and on the boundary,…
The time-dependent Ginzburg-Landau approach is used to investigate nonlinear response of a strongly type-II superconductor. The dissipation takes a form of the flux flow which is quantitatively studied beyond linear response. Thermal…
The explicit form of the interface equation of motion derived assuming a minimal surface is extended to general bicontinuous interfaces that appear in the diffusion limited stage of the phase separation process of binary mixtures. The…
The evolution of the interface separating a conduit of light, viscous fluid rising buoyantly through a heavy, more viscous, exterior fluid at small Reynolds numbers is governed by the interplay between nonlinearity and dispersion. Previous…
The diffusion equation is the primary tool to study the movement dynamics of a free Brownian particle, but when spatial heterogeneities in the form of permeable interfaces are present, no fundamental equation has been derived. Here we…
This work presents a comprehensive framework for enhanced diffusion modeling in fluid-structure interactions by combining the Immersed Boundary Method (IBM) with stochastic trajectories and high-order spectral boundary conditions. Using…
The evolution of interfaces is intrinsic to many physical processes ranging from cavitation in fluids to recrystallization in solids. Computational modeling of interface motion entails a number of challenges, many of which are related to…
We investigate the dynamics of a nonequilibrium interface between coexisting phases in a system described by a Cahn-Hilliard equation with an additional driving term. By means of a matched asymptotic expansion we derive equations for the…
The general problem of two-phase transport in phase-field models is analyzed: the flux of a conserved quantity is driven by the gradient of a potential through a medium that consists of domains of two distinct phases which are separated by…
The flow in a Hele-Shaw cell with a time-increasing gap poses a unique shrinking interface problem. When the upper plate of the cell is lifted perpendicularly at a prescribed speed, the exterior less viscous fluid penetrates the interior…
We consider an Ising model on a square grid with ferromagnetic spin-spin interactions spanning beyond nearest neighbors. Starting from initial states with a single unbounded interface separating ordered phases, we investigate the evolution…
We study the dynamics of an interface (active domain) between different absorbing regions in models with two absorbing states in one dimension; probabilistic cellular automata models and interacting monomer-dimer models. These models…
We derive the nonlinear fractional surface wave equation that governs compression waves at an interface that is coupled to a viscous bulk medium. The fractional character of the differential equation comes from the fact that the effective…
We consider the critical behavior at an interface which separates two semi-infinite subsystems belonging to different universality classes, thus having different set of critical exponents, but having a common transition temperature. We…
The nonequilibrium process in dislocation dynamics and its relaxation to the metastable transition profile is crucial for understanding the plastic deformation caused by line defects in materials. In this paper, we consider the full…
We study phase separation in two dimensions in the scaling limit below criticality. The general form of the magnetization profile as the volume goes to infinity is determined exactly within the field theoretical framework which explicitly…
We introduce a diffuse interface model describing the evolution of a mixture of two different viscous incompressible fluids of equal density. The main novelty of the present contribution consists in the fact that the effects of temperature…
We study the mixing in the presence of convective flow in a porous medium. Convection is characterized by the formation of vortices and stagnation points, where the fluid interface is stretched and compressed enhancing mixing. We analyze…
We study the appearance of a boundary condition along an interface between two regions, one with constant diffusivity $1$ and the other with diffusivity $\eps>0$, when $\eps\to0$. In particular, we take Fick's diffusion law in a context of…