相关论文: Sharp interface limit of the Fisher-KPP equation w…

In this paper we consider a family of active scalars with a velocity field given by $u = \Lambda^{-1+\alpha}\nabla^{\perp} \theta$, for $\alpha \in (0,1)$. This family of equations is a more singular version of the two-dimensional Surface…

We characterize all compact embedded stable minimal capillary surfaces with capillary angle close to either $0$ or $\pi$ that are supported on a complete embedded minimal surface with finite total curvature that is not an affine plane.…

We consider the symmetric simple exclusion process evolving on the interval of length $n-1$ in contact with reservoirs of density $\rho \in (0,1)$ at the boundary. We use Yau's relative entropy method to show that if the initial measure is…

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)].…

We analyze a two-dimensional phase field model designed to describe the dynamics of crystalline grains. The phenomenological free energy is a functional of two order parameters. The first one reflects the orientational order while the…

The critical temperature of thin Fe layers on Ir(100) is measured through M\"o{\ss}bauer spectroscopy as a function of the layer thickness. From a phenomenological finite-size scaling analysis, we find an effective shift exponent lambda =…

We consider the Fisher-KPP equation with a non-local interaction term. Hamel and Ryzhik showed that in solutions of this equation, the front location at a large time $t$ is $\sqrt 2 t +o(t)$. We study the asymptotics of the second order…

This paper investigates the connection between the effective, large scale behavior of Allen-Cahn energy functionals in periodic media and the sharp interface limit of the associated $L^{2}$ gradient flows. By introducing a Percival-type…

The motion and deformation of a droplet suspended in an unbounded fluid with an arbitrary, but Stokesian, imposed flow is investigated when there is a slip at the interface between the two liquids. The boundary condition at the interface is…

We consider the wave equation $\varepsilon^2(-\partial_t^2 + \Delta)u + f(u) = 0$ for $0<\varepsilon\ll 1$, where $f$ is the derivative of a balanced, double-well potential, the model case being $f(u) = u-u^3$. For equations of this form,…

We consider the following model of degenerate and singular oscillatory integral operators: \begin{equation*} Tf(x)=\int_{\mathbb{R}} e^{i\lambda S(x,y)}K(x,y)\psi(x,y)f(y)dy, \end{equation*} where the phase functions are homogeneous…

We consider Fisher-KPP equation with advection: $u_t=u_{xx}-\beta u_x+f(u)$ for $x\in (g(t),h(t))$, where $g(t)$ and $h(t)$ are two free boundaries satisfying Stefan conditions. This equation is used to describe the population dynamics in…

We provide an asymptotic analysis of a non-local Fisher-KPP type equation in periodic media and with a non-local stable operator of order $\alpha$ $\in$ (0, 2). We perform a long time-long range scaling in order to prove that the stable…

We analyze the continuum limit of a thresholding algorithm for motion by mean curvature of one dimensional interfaces in various space-time discrete regimes. The algorithm can be viewed as a time-splitting scheme for the Allen-Cahn equation…

We consider a two-phase flow of two incompressible, viscous and immiscible fluids which are separated by a sharp interface in the case of a simple phase transition. In this model the interface is no longer material and its evolution is…

We investigate the influence of a general non-local advection term of the form K * u to propagation in the one-dimensional Fisher-KPP equation. This model is a generalization of the Keller-Segel-Fisher system. When K $\in$ L 1 (R), we…

The depinning transition of elastic interfaces with an elastic interaction kernel decaying as $1/r^{d+\sigma}$ is characterized by critical exponents which continuously vary with $\sigma$. These exponents are expected to be unique and…

A difficulty in the classical hydrodynamic analysis of moving contact-line problems, associated with the no-slip wall boundary condition resulting in an unbalanced divergence of the viscous stresses, is reexamined with a smoothed,…

Invasion waves are a fundamental building block of theoretical ecology. In this study we aim to take the first steps to link propagation failure and fast acceleration of traveling waves to critical transitions (or tipping points). The…

We study nonlinear stability of pulled fronts in scalar parabolic equations on the real line of arbitrary order, under conceptual assumptions on existence and spectral stability of fronts. In this general setting, we establish sharp…