Related papers: Sharp interface limits of phase-field models
We discuss the sharp interface limit, leading to a mean curvature flow energy, for the rate function of the large deviation principle of a Glauber+Kawasaki process with speed change. We provide an explicit formula of the limiting functional…
We consider the sharp interface limit for the scalar-valued and vector-valued Allen-Cahn equation with homogeneous Neumann boundary condition in a bounded smooth domain $\Omega$ of arbitrary dimension $N\geq 2$ in the situation when a…
We characterize both analytically and numerically short-range forces between spatially diffuse interfaces in multi-phase-field models of polycrystalline materials. During late-stage solidification, crystal-melt interfaces may attract or…
We present a unified approach to thermodynamic description of one, two and three dimensional phases and phase transformations among them. The approach is based on a rigorous definition of a phase applicable to thermodynamic systems of any…
Two phase flows that include phase transition, especially phase creation, with a sharp interface remain a challenging task for numerics. We consider the isothermal Euler equations with phase transition between a liquid and a vapor phase.…
We rigorously prove the convergence of weak solutions to a model for lipid raft formation in cell membranes which was recently proposed by Garcke et al. to weak (varifold) solutions of the corresponding sharp-interface problem for a…
A new diffuse interface model for a two-phase flow of two incompressible fluids with different densities is introduced using methods from rational continuum mechanics. The model fulfills local and global dissipation inequalities and is…
Phase field models are powerful tools to tackle free boundary problems. For phase transformations involving diffusion, the evolution of the non conserved phase field is coupled to the evolution of the conserved diffusion field. Introducing…
The effect of nonequilibrium solute trapping by a growing solid under rapid solidification conditions is studied using a phase-field model. Considering a continuous steady-state concentration profile across the diffuse solid-liquid…
A novel thermodynamically consistent diffuse interface model is derived for compressible electrolytes with phase transitions. The fluid mixtures may consist of N constituents with the phases liquid and vapor, where both phases may coexist.…
We consider a moving interface that is coupled to an elliptic equation in a heterogeneous medium. The problem is motivated by the study of displacive solid-solid phase transformations. We show that a nearly flat interface is given by the…
We consider the sharp interface limit of the Allen-Cahn equation with Dirichlet or dynamic boundary conditions and give a varifold characterization of its limit which is formally a mean curvature flow with Dirichlet or dynamic boundary…
In this paper, we propose and analyze a diffuse interface model for inductionless magnetohydrodynamic fluids. The model couples a convective Cahn-Hilliard equation for the evolution of the interface, the Navier-Stokes system for fluid flow…
We consider the dynamics and kinetic roughening of wetting fronts in the case of forced wetting driven by a constant mass flux into a 2D disordered medium. We employ a coarse-grained phase field model with local conservation of density,…
We study the two and three dimensional stochastic Cahn-Hilliard equation in the sharp interface limit, where the positive parameter $\epsilon$ tends to zero, which measures the width of transition layers generated during phase separation.…
The near-rapid solidification conditions during additive manufacturing can lead to selection of non-equilibrium phases. Sharp interface models via interface response functions have been used earlier to explain the microstructure selection…
Phase-field models are a popular choice in computational physics to describe complex dynamics of substances with multiple phases and are widely used in various applications. We present nonlocal non-isothermal phase-field models of…
Dynamic wetting poses a well-known challenge in classical sharp-interface formulation as the no-slip wall condition leads to a contact line singularity that is typically regularized with a Navier boundary condition, often requiring…
Interactions between an evolving solid and inviscid flow can result in substantial computational complexity, particularly in circumstances involving varied boundary conditions between the solid and fluid phases. Examples of such…
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…