相关论文: The singular limit of a haptotaxis model with bist…
We study a two-component reaction-diffusion system in which one of the reaction terms becomes singularly large. Assuming that the initial data are nonnegative and mutually segregated, we prove that the solution converges to that of the heat…
We consider an infinite-dimensional stochastic clustering model on $\mathbb{R}$. In discrete time, each point of a unit-intensity simple point process moves halfway toward either of its left or right neighbors, chosen uniformly at random.…
We study variational models for dislocations in three dimensions in the line-tension scaling. We present a unified approach which allows to treat energies with subquadratic growth at infinity and other regularizations of the singularity…
Molecular simulations employing empiric force fields have provided valuable knowledge about the ice growth process in the last decade. The development of novel computational techniques allows us to study this process, which requires long…
In this paper we study singular limits of congestion-averse growth models, connecting different models describing the effect of congestion. These models arise in particular in the context of tissue growth. The main ingredient of our…
In fluid dynamics, an interface splash singularity occurs when a locally smooth interface self-intersects in finite time. By means of elementary arguments, we prove that such a singularity cannot occur in finite time for vortex sheet…
In this work, a mathematical model based on interface energy is proposed within the framework of surface continuum mechanics to study the dynamics of encapsulated bubbles. The interface model naturally induces a residual stress field into…
The movement of a purely elastic interface driven on a disordered energy potential is characterized by a depinning transition: when the pulling force S is larger than some critical value S_1 the system is in a flowing regime and moves at a…
We study interfaces in an Allen-Cahn equation, separating two metastable states. Our focus is on a directional quenching scenario, where a parameter renders the system bistable in a half plane and monostable in its complement, with the…
In this paper, we consider the mean curvature flow with driving force on fixed extreme points in the plane. We give a general local existence and uniqueness result of this problem with $C^2$ initial curve. For a special family of initial…
We study effects of turbulent mixing on the random growth of an interface in the problem of the deposition of a substance on a substrate. The growth is modelled by the well-known Kardar--Parisi--Zhang model. The turbulent advecting velocity…
We introduce a formula for translating any upper bound on the percolation threshold of a lattice \g into a lower bound on the exponential growth rate of lattice animals $a(G)$ and vice-versa. We exploit this to improve on the best known…
A non-equilibrium theory of isothermal and diffusionless evolution of incoherent interfaces within a plastically deforming solid is developed. The irreversible dynamics of the interface are driven by its normal motion, incoherency (slip and…
Tissue growth kinetics and interface dynamics depend on the properties of the tissue environment and cell-cell interactions. In cellular environments, substrate heterogeneity and geometry arise from a variety factors, such as the structure…
We study the forced fluid invasion of an air-filled model porous medium at constant flow rate, in 1+1 dimensions, both experimentally and theoretically. We focus on the non-local character of the interface dynamics, due to liquid…
We investigate the behavior, as a small parameter tends to zero, of a nonlocal Allen-Cahn equation. Given a rather general initial data, we perform a rigorous analysis of both the generation and the motion of interface, and obtain a new…
We consider the limit of a linear kinetic equation, with reflection-transmission-absorption at an interface, with a degenerate scattering kernel. The equation arise from a microscopic chain of oscillators in contact with a heat bath. In the…
Space-time varying media with moving interfaces unlock new ways to manipulate electromagnetic waves. Yet, analytical solutions have been mostly limited to interfaces moving at constant velocity or constant proper acceleration. Here, we…
We model the performance of an ideal closed chain of L processing elements that work in parallel in an asynchronous manner. Their state updates follow a generic conservative algorithm. The conservative update rule determines the growth of a…
We consider a one-dimensional diffusion process with coefficients that are periodic outside of a finite 'interface region'. The question investigated in this article is the limiting long time / large scale behaviour of such a process under…