相关论文: The singular limit of a haptotaxis model with bist…
We extend the weak universality of KPZ in [Hairer-Quastel] to weakly asymmetric interface models with general growth mechanisms beyond polynomials. A key new ingredient is a pointwise bound on correlations of trigonometric functions of…
In this work a non-trivial effect of the interfacial curvature on the stability of accelerated interfaces, such as liquid rims, is uncovered. The new stability analysis, based on operator and boundary perturbation theories, reveals and…
Tissue growth underpins a wide array of biological and developmental processes, and numerical modeling of growing systems has been shown to be a useful tool for understanding these processes. However, the phenomena that can be captured are…
Ballistic deposition is a classical model for interface growth in which unit blocks fall down vertically at random on the different sites of $\mathbb{Z}$ and stick to the interface at the first point of contact, causing it to grow. We…
We consider a monostable time-delayed reaction-diffusion equation arising from population dynamics models. We let a small parameter tend to zero and investigate the behavior of the solutions. We construct accurate lower barriers --- by…
Using formal asymptotic methods we derive a free boundary problem representing one of the simplest mathematical descriptions of the growth and death of a tumour or other biological tissue. The mathematical model takes the form of a closed…
In this work, the sharp interface limit of the degenerate Cahn-Hilliard equation (in two space dimensions) with a polynomial double well free energy and a quadratic mobility is derived via a matched asymptotic analysis involving…
We study erratically moving spatial structures that are found in a driven interface in a random medium at the depinning threshold. We introduce a bond-disordered variant of the Sneppen model and study the effect of extremal dynamics on the…
The thin interface limit aims at minimizing the effects arising from a numerical interface thickness, inherent in diffuse interface models of solidification and microstructure evolution such as the phase field model. While the original…
The explicit form of the interface equation of motion derived assuming a minimal surface is extended to general bicontinuous interfaces that appear in the diffusion limited stage of the phase separation process of binary mixtures. The…
Understanding the interface dynamics in non-equilibrium quantum systems remains a challenge. We study the interface dynamics of strongly coupled immiscible binary superfluids by using holographic duality. The full nonlinear evolution of the…
We study the finite size fluctuations at the depinning transition for a one-dimensional elastic interface of size $L$ displacing in a disordered medium of transverse size $M=k L^\zeta$ with periodic boundary conditions, where $\zeta$ is the…
Plenty of research on elastic interfaces has been done on systems where the interface is pushed with a constant force. We studied the average velocity of an interface under a sinusoidal driving in the creep region, considering both…
We consider a discrete and a continuum model for the propagation of a curvature sensitive interface in a time independent random medium. In both cases we suppose that the medium contains obstacles that act on the propagation of the…
We study the near-the-interface behavior of a compact convex scalar curvature flow with a flat side. Under suitable initial conditions on the flat side, we show that the interface propagates with a finite and non-degenerate speed until the…
We discuss the sharp interface limit of the action functional associated to either the Glauber dynamics for Ising systems with Kac potentials or the Glauber+Kawasaki process. The corresponding limiting functionals, for which we provide…
We introduce a class of (2+1)-dimensional stochastic growth processes, that can be seen as irreversible random dynamics of discrete interfaces. "Irreversible" means that the interface has an average non-zero drift. Interface configurations…
The continuous-space symbiotic branching model describes the evolution of two interacting populations that can reproduce locally only in the simultaneous presence of each other. If started with complementary Heaviside initial conditions,…
A marginally outer trapped hypersurface is a generalization of minimal hypersurfaces originated from general relativity. We show a curvature estimate for stable marginally outer trapped hypersurfaces up to the free boundary satisfying a…
Instabilities of fluid-fluid interfaces are ubiquitous in passive soft matter. Adding activity to the interface or either fluid can dramatically change the stability of the interface. Using experiment and theory, we investigate the…