Related papers: Scaling limits of weakly asymmetric interfaces
We modify the nonlinear shallow water equations, the Korteweg-de Vries equation, and the Whitham equation, to permit constant vorticity, and examine wave breaking, or the lack thereof. By wave breaking, we mean that the solution remains…
We consider a discrete model for anisotropic (2+1)-dimensional growth of an interface height function. Owing to a connection with q-Whittaker functions, this system enjoys many explicit integral formulas. By considering certain Gaussian…
We prove existence of weak solutions for a diffuse interface model for the flow of two viscous incompressible Newtonian fluids in a bounded domain in two and three space dimensions. In contrast to previous works, we study a new model…
We study the hydrodynamic and hydrostatic limits of the one-dimensional open symmetric inclusion process with slow boundary. Depending on the value of the parameter tuning the interaction rate of the bulk of the system with the boundary, we…
Many mathematical models of statistical physics in two dimensions are either known or conjectured to exhibit conformal invariance. Over the years, physicists proposed predictions of various exponents describing the behavior of these models.…
A fluctuating interfacial profile in one dimension is studied via Langevin simulations of the Edwards-Wilkinson equation with non-conserved noise and the Mullins-Herring equation with conserved noise. The profile is subject to either…
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…
This work discusses the homogenization analysis for diffusion processes on scale-free metric graphs, using weak variational formulations. The oscillations of the diffusion coefficient along the edges of a metric graph induce internal…
We discuss the sharp interface limit of a diffuse interface model for a two-phase flow of two partly miscible viscous Newtonian fluids of different densities, when a certain parameter \epsilon>0 related to the interface thickness tends to…
Singular or weak solutions of the incompressible Euler equations have been hypothesized to account for anomalous dissipation at very high Reynolds numbers and, in particular, to explain the d'Alembert paradox of non-vanishing drag. A…
This article investigates the properties of a few interacting particles trapped in a few wells and how these properties change under adiabatic tuning of interaction strength and inter-well tunneling. While some system properties are…
A simple two-species asymmetric exclusion model in one dimension with bulk and boundary exchanges of particles is investigated for the existence of spontaneous symmetry breaking. The model is a generalization of the bridge model for which…
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…
The dynamics of complex systems in nature often occurs in terms of punctuations, or avalanches, rather than following a smooth, gradual path. A comprehensive theory of avalanche dynamics in models of growth, interface depinning, and…
We consider weak solutions for a diffuse interface model of two non-Newtonian viscous, incompressible fluids of power-law type in the case of different densities in a bounded, sufficiently smooth domain. This leads to a coupled system of a…
We study the dynamics of an exactly solvable lattice model for inhomogeneous interface growth. The interface grows deterministically with constant velocity except along a defect line where the growth process is random. We obtain exact…
We examine the "naturalness" of the scaling of multiplicity and elliptic flow $v_2$ with rapidity in weakly and strongly coupled systems. We show that multiplicity scaling is relatively straight-forward to incorporate in existing ansatze…
We consider a one-dimensional, weakly asymmetric, boundary driven exclusion process on the interval $[0,N]\cap Z$ in the super-diffusive time scale $N^2 \epsilon^{-1}_N$, where $1\ll \epsilon^{-1}_N \ll N^{1/4}$. We assume that the external…
Wave front propagation with non-trivial bottom topography is studied within the formalism of hyperbolic long wave models. Evolution of non-smooth initial data is examined, and in particular the splitting of singular points and their short…
Using a matched asymptotic expansion we analyze the two-dimensional, near- critical reflection of a weakly nonlinear, internal gravity wave from a sloping boundary in a uniformly stratified fluid. Taking a distinguished limit in which the…