Related papers: Hydrodynamic Limit of Multiple SLE
The Riemann problem for the discrete conservation law $2 \dot{u}_n + u^2_{n+1} - u^2_{n-1} = 0$ is classified using Whitham modulation theory, a quasi-continuum approximation, and numerical simulations. A surprisingly elaborate set of…
This article considers some classes of models dealing with the dynamics of discrete curves subjected to stochastic deformations. It turns out that the problems of interest can be set in terms of interacting exclusion processes, the ultimate…
We analyze the evolution of a particle wave function when it propagates through free space in the longitudinal z-direction from a thin entrance slit to a detector behind a thin exit slit parallel to the horizontal y-axis. We consider an…
We consider the dispersive logarithmic Schr{\"o}dinger equation in a semi-classical scaling. We extend the results about the large time behaviour of the solution (dispersion faster than usual with an additional logarithmic factor,…
We derive the general solution of the unsteady Stokes equations for an unbounded fluid in spherical polar coordinates, in both time and frequency domains. The solution is an expansion in vector spherical harmonics and given as a sum of a…
We investigate the behavior of the slip length in Newtonian liquids subject to planar shear bounded by substrates with mixed boundary conditions. The upper wall, consisting of a homogenous surface of finite or vanishing slip, moves at a…
We continue our study of the emergence of Non-Equilibrium Steady States in quantum integrable models focusing on the expansion of a Lieb-Liniger gas for arbitrary repulsive interaction. As a first step towards the derivation of the…
Dynamical scaling arises naturally in various many-body systems far from equilibrium. After a short historical overview, the elements of possible extensions of dynamical scaling to a local scale-invariance will be introduced.…
Two-dimensional loop-erased random walks (LERWs) are random planar curves whose scaling limit is known to be a Schramm-Loewner evolution SLE_k with parameter k = 2. In this note, some properties of an SLE_k trace on doubly-connected domains…
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 coupled system of self-organized hydrodynamics and Navier-Stokes equations (SOH-NS), which models self-propelled particles in a viscous fluid, was recently derived by Degond et al. \cite{DMVY-2017-arXiv}, starting from a micro-macro…
We study the construction of invariant measures associated with higher order conservation laws of the intermediate long wave equation (ILW) and their convergence properties in the deep-water and shallow-water limits. By exploiting its…
We consider the whole-plane Shramm-Loewner evolution. Using exact solutions of fundamental equations for moments of derivative of conformal mappings we determine its average integral means beta-spectrum.
We consider the one-dimensional discrete linear Schrodinger (DLS) equation perturbed by a conservative stochastic dynamics, that changes the phase of each particles, conserving the total norm (or number of particles). The resulting total…
Using numerical results from ideal and viscous relativistic hydrodynamic simulations with three different equations of state, for Au+Au and Cu+Cu collisions at different centralities and initial energy densities, we explore the dependence…
A fourth-order nonlinear evolution equation is derived from a microscopic model for surface diffusion, namely, the continuum solid-on-solid model. We use the method developed by Varadhan for the computation of hydrodynamic scaling limit of…
In this paper we study a 2D Oldroyd free-boundary model which describes the evolution of a viscoelastic fluid. We prove existence of splash singularities, namely points where the boundary remains smooth but self-intersects. This paper…
We study the symmetric facilitated exclusion process (FEP) on the finite one-dimensional lattice $\lbrace 1,\dots ,N-1\rbrace$ when put in contact with boundary reservoirs, whose action is subject to an additional kinetic constraint in…
We prove several limit theorems that relate coalescent processes to continuous-state branching processes. Some of these theorems are stated in terms of the so-called generalized Fleming-Viot processes, which describe the evolution of a…
In this paper, we present the hydrodynamic limit of a multiscale system describing the dynamics of two populations of agents with alignment interactions and the effect of an internal variable. It consists of a kinetic equation coupled with…