相关论文: Sharp-interface limits of Cahn-Hilliard models and…
In this work, the sharp interface limit of the degenerate Cahn-Hilliard equation (in two space dimensions) with a polynomial double well free energy and a quadratic mobility is derived via a matched asymptotic analysis involving…
The sharp-interface limits of a phase-field model with a generalized Navier slip boundary condition for moving contact line problem are studied by asymptotic analysis and numerical simulations. The effects of the {mobility} number as well…
We discuss the sharp interface limit of a diffuse interface model for a two-phase flow of two partly miscible viscous Newtonian fluids of different densities, when a certain parameter \epsilon>0 related to the interface thickness tends to…
We discuss the sharp interface limit of a diffuse interface model for a coupled Cahn-Hilliard--Darcy system that models tumor growth when a certain parameter $\varepsilon>0$, related to the interface thickness, tends to zero. In particular,…
In this letter, we derive the sharp-interface limit of the Cahn-Hilliard-Biot equations using formal matched asymptotic expansions. We find that in each sub-domain, the quasi-static Biot equations are obtained with domain-specific material…
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 use of continuum phase-field models to describe the motion of well-defined interfaces is discussed for a class of phenomena, that includes order/disorder transitions, spinodal decomposition and Ostwald ripening, dendritic growth, and…
We consider the sharp interface limit of a coupled Stokes/Cahn\textendash Hilliard system in a two dimensional, bounded and smooth domain, i.e., we consider the limiting behavior of solutions when a parameter $\epsilon>0$ corresponding to…
In this paper, we aim to study the motions of interfaces and coarsening rates governed by the time-fractional Cahn--Hilliard equation (TFCHE). It is observed by many numerical experiments that the microstructure evolution described by the…
In this paper, we study the sharp interface limit for solutions of the Cahn-Hilliard equation with disparate mobilities. This means that the mobility function degenerates in one of the two energetically favorable configurations, suppressing…
We consider a system of two coupled parabolic PDEs introduced in [1] to model motility of eukaryotic cells. We study the asymptotic behavior of solutions in the limit of a small parameter related to the width of the interface in phase field…
We consider the sharp interface limit of a coupled Stokes/Allen-Cahn system, when a parameter $\varepsilon>0$ that is proportional to the thickness of the diffuse interface tends to zero, in a two dimensional bounded domain. For…
We consider sharp interface asymptotics for a phase field model of two phase near spherical biomembranes involving a coupling between the local mean curvature and the local composition proposed by the first and second authors. The model is…
Phase field models frequently provide insight to phase transitions, and are robust numerical tools to solve free boundary problems corresponding to the motion of interfaces. A body of prior literature suggests that interface motion via…
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…
We investigate the limiting behavior of the Navier-Stokes-Cahn-Hilliard model for binary-fluid flows as the diffuse-interface thickness passes to zero, in the presence of fluid-fluid-solid contact lines. Allowing for motion of such contact…
We consider a system of two PDEs arising in modeling of motility of eukariotic cells on substrates. This system consists of the Allen-Cahn equation for the scalar phase field function coupled with another vectorial parabolic equation for…
We consider the sharp interface limit of a convective Allen-Cahn equation, which can be part of a Navier-Stokes/Allen-Cahn system, for different scalings of the mobility $m_\varepsilon=m_0\varepsilon^\theta$ as $\varepsilon\to 0$. In the…
A main challenge in numerical simulations of moving contact line problems is that the adherence, or no-slip boundary condition leads to a non-integrable stress singularity at the contact line. In this report we perform the first steps in…
In this paper, the sharp interface limit for the compressible non-isentropic Navier-Stokes/Allen-Cahn system is derived by the method of matched asymptotic expansion. We show that the leading order problem satisfies the compressible…