Related papers: Dynamics of a cell motility model near the sharp i…
We analyze a phase-field approximation of a sharp-interface model for two- phase materials proposed by M. Silhavy [32, 33]. The distinguishing trait of the model resides in the fact that the interfacial term is Eulerian in nature, for it is…
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…
The Rayleigh--Taylor instability of two immiscible fluids in the limit of small Atwood numbers is studied by means of a phase-field description. In this method the sharp fluid interface is replaced by a thin, yet finite, transition layer…
We suggest a 3D phase field model to describe 3D cell spreading on a flat substrate. The model is a simplified version of a minimal model that was developed in [1]. Our model couples the order parameter $u$ with 3D polarization…
We describe a general phase-field model for hyperelastic multiphase materials. The model features an elastic energy functional that depends on the phase-field variable and a surface energy term that depends in turn on the elastic…
A phase-field model that allows for quantitative simulations of low-speed eutectic and peritectic solidification under typical experimental conditions is developed. Its cornerstone is a smooth free-energy functional, designed so that the…
We use a sharp interface model for active cells to study the jamming transition point and behavior near it by varying cell concentration, active velocity and elasticity, including a binary mixture of soft and stiff cells. We determine the…
The flow near a moving contact line depends on the dynamic contact angle, viscosity ratio, and capillary number. We report experiments involving immersing a plate into a liquid bath, concurrently measuring the interface shape, interfacial…
The description of surface-diffusion controlled dynamics via the phase-field method is less trivial than it appears at first sight. A seemingly straightforward approach from the literature is shown to fail to produce the correct…
In this paper, we propose an improved phase field model for interface capturing in simulating two-phase incompressible flows. The model incorporates a second-order diffusion term, which utilizes a nonlinear coefficient to assess the degree…
The phase-field method is reviewed from the general perspective of converting a free boundary problem into a set of coupled partial differential equations. Its main advantage is that it avoids front tracking by using phase fields to locate…
We analyze a two-dimensional phase field model designed to describe the dynamics of crystalline grains. The phenomenological free energy is a functional of two order parameters. The first one reflects the orientational order while the…
We present a continuum theory to describe elastically induced phase transitions between coherent solid phases. In the limit of vanishing elastic constants in one of the phases, the model can be used to describe fracture on the basis of the…
Phase field modelling offers an extremely general framework to predict microstructural evolutions in complex systems. However, its computational implementation requires a discretisation scheme with a grid spacing small enough to preserve…
This article presents a new phase-field formulation for non-equilibrium interface conditions in rapid phase transformations. With a particular way of defining concentration fields, the classical sharp and diffuse (thick) interface theories…
Interactions between crawling cells, which are essential for many biological processes, can be quantified by measuring cell-cell collisions. Conventionally, experiments of cell-cell collisions are conducted on two-dimensional flat…
In this paper, a thermal-dynamical consistent model for mass transfer across permeable moving interfaces is proposed by using the energy variation method. We consider a restricted diffusion problem where the flux across the interface…
Cell motility is fundamental to many biological processes, and cells exhibit a variety of migration patterns. Many motile cell types follow a universal law that connects their speed and persistency, a property that can originate from the…
We present a derivation of the sharp-interface limit of a generic fluctuating phase-field model for solidification. As a main result, we obtain a sharp-interface projection which presents noise terms in both the diffusion equation and in…
We introduce a new phase-field model which allows for simulation of incoherent solid/solid transformations. Contrary to previous models which impose coherency at the interface, the zero shear-stress condition characteristic of incoherent…