Related papers: Gradient flow dynamics of two-phase biomembranes: …
Interfaces in two-dimensional systems exhibit unexpected complex dynamical behaviors, the dynamics of a border connecting a stripe pattern and a uniform state is studied. Numerical simulations of a prototype isotropic model, the subcritical…
We consider an Ising model on a square grid with ferromagnetic spin-spin interactions spanning beyond nearest neighbors. Starting from initial states with a single unbounded interface separating ordered phases, we investigate the evolution…
A new time discretization scheme for the numerical simulation of two-phase flow governed by a thermodynamically consistent diffuse interface model is presented. The scheme is consistent in the sense that it allows for a discrete in time…
We investigate the nonlinear dynamics of a moving interface in a Hele-Shaw cell subject to an in-plane applied electric field. We develop a spectrally accurate boundary integral method where a coupled integral equation system is formulated.…
We investigate dynamics of large scale and slow deformations of layered structures. Starting from the respective model equations for a non-conserved system, a conserved system and a binary fluid, we derive the interface equations which are…
The dynamics of sharp interfaces separating two non-hydrostatically stressed solids is analyzed using the idea that the rate of mass transport across the interface is proportional to the thermodynamic potential difference across the…
We develop an embedded boundary method (EBM) to solve the two-phase incompressible flow with piecewise constant density. The front tracking method is used to track the interface. The fractional step methods are used to solve the…
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…
Stably stratified fluids subject to sustained forcing are known to develop step-like density "staircases", where nearly homogeneous layers alternate with thin interfaces of strong stratification. However, long-time numerical investigations…
The dynamics of a membrane is a coupled system comprising a moving elastic surface and an incompressible membrane fluid. We will consider a reduced elastic surface model, which involves the evolution equations of the moving surface, the…
We consider the spreading of a thin two-dimensional droplet on a planar substrate as a prototype system to compare the contemporary model for contact line motion based on interface formation of Shikhmurzaev [Int. J. Multiphas. Flow 19, 589…
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…
When a colloidal particle adheres to a fluid membrane, it induces elastic deformations in the membrane which oppose its own binding. The structural and energetic aspects of this balance are theoretically studied within the framework of a…
In this paper, we consider the numerical approximation for a diffuse interface model of the two-phase incompressible inductionless magnetohydrodynamics problem. This model consists of Cahn-Hilliard equations, Navier-Stokes equations and…
We propose an efficient and accurate parametric finite element method (PFEM) for solving sharp-interface continuum models for solid-state dewetting of thin films with anisotropic surface energies. The governing equations of the…
We present an adaptive simulation framework for binary-fluid flows, based on the Abels-Garcke-Gr\"un Navier-Stokes-Cahn-Hilliard (AGG NSCH) diffuse-interface model. The adaptive-refinement procedure is guided by a two-level hierarchical…
We introduce variational approximations for curve evolutions in two-dimensional Riemannian manifolds that are conformally flat, i.e.\ conformally equivalent to the Euclidean space. Examples include the hyperbolic plane, the hyperbolic disk,…
We introduce a non-local $L^2$-gradient flow for the Willmore energy of immersed surfaces which preserves the isoperimetric ratio. For spherical initial data with energy below an explicit threshold, we show long-time existence and…
The Ohta-Kawasaki model for diblock-copolymers is well known to the scientific community of diffuse-interface methods. To accurately capture the long-time evolution of the moving interfaces, we present a derivation of the corresponding…
Fluid flow applications can involve a number of coupled problems. One is the simulation of free-surface flows, which require the solution of a free-boundary problem. Within this problem, the governing equations of fluid flow are coupled…