Related papers: Numerical analysis with the phase field equations …
The large deformations and break up of circular 2D liquid patches in a high Reynolds number (Re=1000) gas flow are investigated numerically. The 2D, plane flow Navier--Stokes equations are directly solved with explicit tracking of the…
The purpose of this paper is to establish the well-posedness of the stochastic Stefan problem on moving hypersurfaces. Through a specially designed transformation, it turns out we need to solve stochastic partial differential equations on a…
The dynamics of solid-liquid interfaces controlled by solute precipitation and/or dissolution due to the chemical reaction at the interface were computed in two dimensions using a phase field models. Sharp-interface asymptotic analysis…
We study a nonlocal version of the two-phase Stefan problem, which models a phase transition problem between two distinct phases evolving to distinct heat equations. Mathematically speaking, this consists in deriving a theory for…
We consider a family of multi-phase Stefan problems for a certain 1-d model of cell-to-cell adhesion and diffusion, which takes the form of a nonlinear forward-backward parabolic equation. In each material phase the cell density stays…
The classical Stefan problem is one of the most studied free boundary problems of evolution type. Recently, there has been interest in treating the corresponding free boundary problem with nonlocal diffusion. We start the paper by reviewing…
The non-local in space two-phase Stefan problem (a prototype in phase change problems) can be formulated via a singular nonlinear parabolic integro-differential equation which admits a unique weak solution. This formulation makes Stefan…
Smoothed particle hydrodynamics (SPH) is developed for modelling of melting and solidification. Enthalpy method is used to solve heat conduction equations which involved moving interface between phases. At first, we study the melting of…
The dissolution of solids has created spectacular geomorphologies ranging from centimeter-scale cave scallops to the kilometer-scale "stone forests" of China and Madagascar. Mathematically, dissolution processes are modeled by a Stefan…
Modelling interfacial dynamics with soluble surfactants in a multiphase system is a challenging task. Here, we consider the numerical approximation of a phase-field surfactant model with fluid flow. The nonlinearly coupled model consists of…
A phase-field approach describing the dynamics of a strained solid in contact with its melt is developed. By rigorous asymptotic analysis we show that the sharp-interface limit of this model recovers the continuum model equations for the…
The phase-field crystal equation, a parabolic, sixth-order and nonlinear partial differential equation, has generated considerable interest as a possible solution to problems arising in molecular dynamics. This is because the phase-field…
We consider the problem of heat conduction with phase change, that is essential for permafrost modeling in Land Surface Models and Dynamic Global Vegetation Models. These models require minimal computational effort and an extremely robust…
We argue that the celebrated Stefan condition on the moving interphase, accepted in mathematical physics up to now, can not be imposed if energy sources are spatially distributed in the volume. A method based on Tikhonov and Samarskii's…
We establish certain oscillation estimates for weak solutions to nonlinear, anomalous phase transitions modeled on the nonlocal two-phase Stefan problem. The problem is singular in time, is scaling deficient and influenced by far-off…
We review some fractional free boundary problems that were recently considered for modeling anomalous phase-transitions. All problems are of Stefan type and involve fractional derivatives in time according to Caputo's definition. We survey…
We investigate the regularizing behavior of two-phase Stefan problem near initial data. The main step in the analysis is to establish that in any given scale, the scaled solution is very close to a Lipschitz profile in space-time. We…
Phase field method is playing an increasingly important role in understanding and predicting morphological evolution in materials and biological systems. Here, we develop a new analytical approach based on bifurcation analysis to explore…
We present a new phase-field model of solidification which allows efficient computations in the regime when interface kinetic effects dominate over capillary effects. The asymptotic analysis required to relate the parameters in the…
The present article is dedicated to the forward and backward solution of a transient one-phase Stefan problem. In the forward problem, we compute the evolution of the initial domain for a Stefan problem where the melting temperature varies…