Related papers: Interacting phase fields yielding phase separation…
We use a simple and efficient computer model to investigate the physical properties of bilayer membranes. The amphiphilic molecules are modeled as short rigid trimers with finite range pair interactions between them. The pair potentials…
It is demonstrated that 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 previously used in the literature is shown to…
Phase-field models have recently had great success in describing the dynamic morphologies and motility of eukaryotic cells. In this work we investigate the minimal phase-field model introduced in [Berlyand, Potomkin, Rybalko (2017)].…
Fluid flow through layered materials with different wetting behavior is observed in a wide range of applications in biological, environmental and technical systems. Therefore, it is necessary to understand the occuring transport mechanisms…
Motivated by recent experimental work on multicomponent lipid membranes supported by colloidal scaffolds, we report an exhaustive theoretical investigation of the equilibrium configurations of binary mixtures on curved substrates. Starting…
We consider a continuum mechanical model for the migration of multiple cell populations through parts of tissue separated by thin membranes. In this model, cells belonging to different populations may be characterised by different…
We investigate a two-species Fermi gas in which one species is confined in two parallel layers and interacts with the other species in the three-dimensional space by a tunable short-range interaction. Based on the controlled weak coupling…
The effect of screening of the coulomb interaction between two layers of two-dimensional electrons, such as in graphene, by a highly doped semiconducting substrate is investigated. We employ the random-phase approximation to calculate the…
We analyze a diffuse interface model for multi-phase flows of $N$ incompressible, viscous Newtonian fluids with different densities. In the case of a bounded and sufficiently smooth domain existence of weak solutions in two and three space…
We derive a phase field crystal model that couples the diffusive evolution of a microscopic structure with the fast dynamics of a macroscopic velocity field, explicitly accounting for the relaxation of elastic excitations. This model…
The modeling of crack propagation in a heterogeneous material using a phase field model is studied numerically in a simple test case: the crack meets a wedge of higher fracture energy. It is shown that when the crack cannot enter the wedge,…
Tubular and membranous shapes display a wide range of morphologies that are difficult to analyze within a common framework. By generalizing the classical Helfrich energy of biomembranes, we model them as solutions to a curvature…
We review recent simulation studies of interfaces between immiscible homopolymer phases. Special emphasis is given to the presentation of efficient simulation techniques and powerful methods of data analysis, such as the analysis of…
Common models for two-phase lipid bilayer membranes are based on an energy that consists of an elastic term for each lipid phase and a line energy at interfaces. Although such an energy controls only the length of interfaces, the membrane…
A diffused-interface approach based on the Allen-Cahn phase field equation is developed within a high-order Discontinuous Galerkin framework. The interface capturing technique is based on the balance between explicit diffusion and…
Two-phase flow of two Newtonian incompressible viscous fluids with a soluble surfactant and different densities of the fluids can be modeled within the diffuse interface approach. We consider a Navier-Stokes/Cahn-Hilliard type system…
We study closed liquid membranes that segregate into three phases due to differences in the chemical and physical properties of its components. The shape and in-plane membrane arrangement of the phases are coupled through phase-specific…
Adhesion between membranes is studied using a phenomenological model, where the inter-membrane distance is coupled to the concentration of sticker molecules on the membranes. The model applies to both for adhesion of two flexible membranes…
We investigate the phase-field approximation of the Willmore flow. This is a fourth-order diffusion equation with a parameter $\epsilon>0$ that is proportional to the thickness of the diffuse interface. We show rigorously that for…
Using an interface displacement model derived from a microscopic density functional theory we investigate thin liquidlike wetting layers adsorbed on flat substrates with an embedded chemical heterogeneity forming a stripe. For a wide range…