Related papers: Fixation for coarsening dynamics in 2D slabs
The leading order "temperature" of a dense two dimensional granular material fluidised by external vibrations is determined. An asymptotic solution is obtained where the particles are considered to be elastic in the leading approximation.…
We present a comparative study of the fate of an Ising ferromagnet on the square lattice with periodic boundary conditions evolving under three different zero-temperature dynamics. The first one is Glauber dynamics, the two other dynamics…
A ``persistence'' exponent theta has been extensively used to describe the nonequilibrium dynamics of spin systems following a deep quench: for zero-temperature homogeneous Ising models on the d-dimensional cubic lattice, the fraction p(t)…
We derive constraints on the existence of walls for Bridgeland stability conditions for general projective surfaces. We show that in suitable planes of stability conditions the walls are bounded and derive conditions for when the number of…
Liquid wetting of a surface is omnipresent in nature and the advance of micro-fabrication and assembly techniques in recent years offers increasing ability to control this phenomenon. Here, we identify how surface roughness influences the…
The dynamics of a flexible filament sedimenting in a viscous fluid are explored analytically and numerically. Compared to the well-studied case of sedimenting rigid rods, the introduction of filament compliance is shown to cause a…
We investigate the final state of zero-temperature Ising ferromagnets which are endowed with single-spin flip Glauber dynamics. Surprisingly, the ground state is generally not reached for zero initial magnetization. In two dimensions, the…
In this paper, we investigate the asymptotic stability threshold problem for the 2-D Navier-Stokes equations in a finite channel with no-slip boundary conditions, around monotone shear flow $(U(t,y),0)$. We establish that the flow is…
Partially molten materials resist shearing and compaction. This resistance is described by a fourth-rank effective viscosity tensor. When the tensor is isotropic, two scalars determine the resistance: an effective shear and an effective…
We study the coarsening model (zero-temperature Ising Glauber dynamics) on $\mathbb{Z}^d$ (for $d \geq 2$) with an asymmetric tie-breaking rule. This is a Markov process on the state space $\{-1,+1\}^{\mathbb{Z}^d}$ of "spin configurations"…
For the contact of two finite portions of interacting rigid crystalline surfaces, we compute the dependence of the pinning energy barrier on the misfit angle and contact area. The resulting data are used to investigate the distribution of…
We study the influence of surface roughness on the adhesion of elastic solids. Most real surfaces have roughness on many different length scales, and this fact is taken into account in our analysis. We consider in detail the case when the…
This paper is dedicated to the solidification of a water drop impacting a cold solid surface. In a first part, we establish a 1D solidification model, derived from the Stefan problem, that aims at predicting the freezing dynamic of a liquid…
The critical properties of an infinitely long Ising strip with finite width L joined periodically or antiperiodically are investigated by analyzing the distribution of partition function zeros. For periodic boundary condition, the the…
We address the question of existence of nonconstant stable stationary solution to the heat equation on a class of convex domains subject to nonlinear boundary flux involving a positive parameter. Such solutions which were known to exist in…
We recently showed that the two-dimensional Ising spin glass allows for a line of renormalization group fixed points which explains properties observed in numerical studies. We observe that this exact result corresponds to enhancement to a…
Using the notion of Gamma-convergence, we discuss the limiting behavior of the 3d nonlinear elastic energy for thin elliptic shells, as their thickness h converges to zero, under the assumption that the elastic energy of deformations scales…
The dynamics of a system composed of inelastic hard spheres or disks that are confined between two parallel vertically vibrating walls is studied (the vertical direction is defined as the direction perpendicular to the walls). The distance…
We consider thin fluid films placed on thermally conductive substrates and exposed to time-dependent spatially uniform heat source. The evolution of the films is considered within the long-wave framework in the regime such that both…
Periodic travelling waves at the free surface of an incompressible inviscid fluid in two dimensions under gravity are numerically computed for an arbitrary vorticity distribution. The fluid domain over one period is conformally mapped from…