相关论文: The singular limit of a haptotaxis model with bist…

Interfaces in a model with a single, real nonconserved order parameter and purely dissipative evolution equation are considered. We show that a systematic perturbative approach, called the expansion in width and developed for curved domain…

We study the hydrodynamics of the A-B interface with finite curvature. The interface tension is shown to enhance both the transition velocity and the amplitudes of second sound. In addition, the magnetic signals emitted by the growing…

The growth of several biological tissues is known to be controlled in part by local geometrical features, such as the curvature of the tissue interface. This control leads to changes in tissue shape that in turn can affect the tissue's…

We briefly review the properties of radially growing interfaces and their connection to biological growth. We focus on simplified models which result from the abstraction of only considering domain growth and not the interface curvature.…

We investigate the singular limit, as $\ep \to 0$, of the Fisher equation $\partial_t u=\ep \Delta u + \ep ^{-1}u(1-u)$ in the whole space. We consider initial data with compact support plus perturbations with {\it slow exponential decay}.…

We consider a family of axisymmetric curves evolving by its mean curvature with driving force in the half space. We impose a boundary condition that the curves are perpendicular to the boundary for $t>0$, however, the initial curve…

We consider driven dimer models on the square and honeycomb graphs, starting from a stationary Gibbs measure. Each model can be thought of as a two dimensional stochastic growth model of an interface, belonging to the anisotropic KPZ…

The response of spatially extended systems to a force leading their steady state out of equilibrium is strongly affected by the presence of disorder. We focus on the mean velocity induced by a constant force applied on one-dimensional…

We study the competition interface between two growing clusters in a growth model associated to last-passage percolation. When the initial unoccupied set is approximately a cone, we show that this interface has an asymptotic direction with…

We study the singular limit of a spatially inhomogeneous and anisotropic reaction-diffusion equation. We use a Finsler metric related to the anisotropic diffusion term and work in relative geometry. We prove a weak comparison principle and…

We find analytical solutions to the Cahn-Hilliard equation for the dynamics of an interface in a system with a conserved order parameter (Model B). We show that, although steady-state solutions of Model B are unphysical in the far-field,…

The dynamics of an elastic interface profile h(x,t) under a driving force increasing at rate c, a restored force -epsilon h, and disorder is investigated. Using perturbation theory and functional renormalization group the phase diagram and…

We study the pinning phase transition for discrete surface dynamics in random environments. A renormalization procedure is devised to prove that the interface moves with positive velocity under a finite size condition. This condition is…

We consider a discrete-time model for random interface growth which admits exact formulas and converges to the Polynuclear growth model in a particular limit. The height of the interface is initially flat and the evolution involves the…

The growth of bacterial flagellar filaments is a self-assembly process where flagellin molecules are transported through the narrow core of the flagellum and are added at the distal end. To model this situation, we generalize a growth…

Interfaces in tissues are ubiquitous, both between tissue and environment as well as between populations of different cell types. The propagation of an interface can be driven mechanically. % e.g. by a difference in the respective…

We investigate some unstable behavior of the interface given by two incompressible fluids of different densities evolving by the regular Stokes law with gravity force. In the unstable scenario, where the denser fluid lies above the lighter…

We provide a theoretical framework to analyze the properties of frontal collisions of two growing interfaces considering different short range interactions between them. Due to their roughness, the collision events spread in time and form…

In this note, we consider a nonlinear diffusion equation with a bistable reaction term arising in population dynamics. Given a rather general initial data, we investigate its behavior for small times as the reaction coefficient tends to…

Using a hydrodynamic lattice-gas model, we study interface growth in a binary fluid with various concentrations of surfactant. We find that the interface is smoothed by small concentrations of surfactant, while microemulsion droplets form…