Related papers: Phase field approach for modeling intracellular dy…
The interface dynamics of a 3D cell immersed in a 3D extracellular matrix is investigated. We suggest a 3D generalization of a known 2D minimal phase field model suggested in [1] for the description of keratocyte motility. Our model…
Exact characterization of phase transitions requires sufficient configurational sampling, necessitating efficient and accurate potential energy surfaces. Molecular force fields with computational efficiency and physical interpretability are…
A new approach is developed for computational modelling of microstructure evolution problems. The approach combines the phase-field method with the recently-developed laminated element technique (LET) which is a simple and efficient method…
This contribution presents a diffuse framework for modeling cracks in heterogeneous media. Interfaces are depicted by static phase-fields. This concept allows the use of non-conforming meshes. Another phase-field is used to describe the…
The kinetic behavior of a phase field model of electrochemistry is explored for advancing (electrodeposition) and receding (electrodissolution) conditions in one dimension. We described the equilibrium behavior of this model in [J. E.…
We present the first application of phase field modeling to electrochemistry. A free energy functional that includes the electrostatic effect of charged particles leads to rich interactions between concentration, electrostatic potential,…
A consistent treatment of the coupling of surface energy and elasticity within the multi-phase- field framework is presented. The model accurately reproduces stress distribution in a number of analytically tractable, yet non-trivial, cases…
Reaction-diffusion processes play an important role in a variety of physical, chemical, and biological systems. Conventionally, the kinetics of these processes are described by the law of mass action. However, there are various cases where…
Here, we review the basic concepts and applications of the phase-field-crystal (PFC) method, which is one of the latest simulation methodologies in materials science for problems, where atomic- and microscales are tightly coupled. The PFC…
In this article we consider the widely used immersed finite element method (IFEM), in both explicit and implicit form, and its relationship to our more recent one-field fictitious domain method (FDM). We review and extend the formulation of…
Phase field models for two-phase flow with a surfactant soluble in possibly both fluids are derived from balance equations and an energy inequality so that thermodynamic consistency is guaranteed. Via a formal asymptotic analysis, they are…
Based on static and dynamical density functional theory, a phase-field-crystal model is derived which involves both the translational density and the orientational degree of ordering as well as a local director field. The model exhibits…
A diffusion process for charge distributions in a phase space is examined. The corresponding charge moves in a force field and under an action of a random field. There are the diffusion motions for coordinates and for momenta. In our model,…
This paper presents an overview of the theories and computer implementation aspects of phase field models (PFM) of fracture. The advantage of PFM over discontinuous approaches to fracture is that PFM can elegantly simulate complicated…
The phase field approach to modeling fracture uses a diffuse damage field to represent a crack. This addresses the singularities that arise at the crack tip in computations with sharp interface models, mollifying some of the difficulties…
An important component in studying mathematical models in many biochemical systems, such as those found in developmental biology, is phase transition. The purpose of this work is to analyze the phase transition property of a…
Spontaneous rhythmic oscillations are widely observed in various real-world systems. In particular, biological rhythms, which typically arise via synchronization of many self-oscillatory cells, often play important functional roles in…
We investigate the convergence of solutions of a recently proposed diffuse interface/phase field model for cell blebbing by means of matched asymptotic expansions. It is a biological phenomenon that increasingly attracts attention by both…
We present a new multiphase-field theory for describing pattern formation in multi-domain and/or multi-component systems. The construction of the free energy functional and the dynamic equations is based on criteria that ensure mathematical…
We extend the phase field crystal model to accommodate exact atomic configurations and vacancies by requiring the order parameter to be non-negative. The resulting theory dictates the number of atoms and describes the motion of each of…