Related papers: Dynamics of Interfaces in the Two-Dimensional Wave…
We consider a diffuse interface model for tumor growth recently proposed in [Y. Chen, S.M. Wise, V.B. Shenoy, J.S. Lowengrub, A stable scheme for a nonlinear, multiphase tumor growth model with an elastic membrane, Int. J. Numer. Methods…
We study the interface dynamics of a binary particle mixture in a rotating cylinder numerically. By considering only the particle motion in axial direction, it is shown that the initial dynamics can be well described by a one-dimensional…
We consider a porous media equation with balanced bistable reactions, equipped with some general nonlinear boundary condition. When the coefficient of the reaction term is much larger than that of the diffusion term, we see that, besides…
Various molecules exclusively accumulate at the front or back of migrating eukaryotic cells in response to a shallow gradient of extracellular signals. Directional sensing and signal amplification highlight the essential properties in the…
We propose to model physical effects at the sharp density interface between atmosphere and ocean with the help of diffuse interface approaches for multiphase flows with variable densities. We use the variable-density model proposed in…
Diffuse-interface theory provides a foundation for the modeling and simulation of microstructure evolution in a very wide range of materials, and for the tracking/capturing of dynamic interfaces between different materials on larger scales.…
We present a method for studying the evolution of plasma turbulence by tracking dispersion relations in the energy spectrum in the wavenumber-frequency domain. We apply hybrid plasma simulations in a simplified two-dimensional geometry to…
We perform an analytical investigation of the cell interface dynamics in the framework of a minimal phase field model of cell motility suggested in [1], which consists of two coupled evolution equations for the order parameter and a…
Intracellular protein patterns regulate a variety of vital cellular processes such as cell division and motility, which often involve dynamic changes of cell shape. These changes in cell shape may in turn affect the dynamics of…
This paper deals with the evolution equation of a curve obtained as the sharp interface limit of a non-linear system of two reaction-diffusion PDEs. This system was introduced as a phase-field model of (crawling) motion of eukaryotic cells…
The motion of a eukaryotic cell presents a variety of interesting and challenging problems from both a modeling and a computational perspective. The processes span many spatial scales (from molecular to tissue) as well as disparate time…
Drifting pattern domains (DPDs), moving localized patches of traveling waves embedded in a stationary (Turing) pattern background and vice versa, are observed in simulations of a reaction-diffusion model with nonlocal coupling. Within this…
Conformal field theories can exchange energy through a boundary interface. Imposing conformal boundary conditions for static interfaces implies energy conservation at the interface. Recently, the reflective and transmitive properties of…
This paper reviews (and expands) some recent results on the modeling of aggregation-diffusion phenomena at various scales, focusing on the emergence of collective dynamics as a result of the competition between attractive and repulsive…
We study the dynamics of an interface (active domain) between different absorbing regions in models with two absorbing states in one dimension; probabilistic cellular automata models and interacting monomer-dimer models. These models…
Propagating interfaces are ubiquitous in nature, underlying instabilities and pattern formation in biology and material science. Physical principles governing interface growth are well understood in passive settings; however, our…
Pinning and depinning of wavefronts are ubiquitous features of spatially discrete systems describing a host of phenomena in physics, biology, etc. A large class of discrete systems is described by overdamped chains of nonlinear oscillators…
We consider the slow nonlinear diffusion equation subject to a constant absorption rate and construct local self-similar solutions for reversing (and anti-reversing) interfaces, where an initially advancing (receding) interface gives way to…
A long-standing goal of materials science is to understand, predict and control the evolution of microstructures in crystalline materials. Most microstructure evolution is controlled by interface motion; hence, the establishment of rigorous…
The lateral diffusion and trapping of protein receptors within the postsynaptic membrane of a neuron plays a key role in determining the strength of synaptic connections and their regulation during learning and memory. In this paper we…