Related papers: Cut-off for sandpiles on tiling graphs
We obtain structural results on translational tilings of periodic functions in $\mathbb{Z}^d$ by finite tiles. In particular, we show that any level one tiling of a periodic set in $\mathbb{Z}^2$ must be weakly periodic (the disjoint union…
Given a finite collection of two-dimensional tile types, the field of study concerned with covering the plane with tiles of these types exclusively has a long history, having enjoyed great prominence in the last six to seven decades. Much…
To understand an aperiodic tiling (or a quasicrystal modeled on an aperiodic tiling), we construct a space of similar tilings, on which the group of translations acts naturally. This space is then an (abstract) dynamical system. Dynamical…
We show that the spontaneous breaking of center symmetry can be avoided on a $L^2\times 1^2$ lattice with the appropriate choice of twisted boundary conditions. In order for this to work it is crucial that the twisted boundary conditions…
We consider Activated Random Walks on arbitrary finite networks, with particles being inserted at random and absorbed at the boundary. Despite the non-reversibility of the dynamics and the lack of knowledge on the stationary distribution,…
Plaquette models are short range ferromagnetic spin models that play a key role in the dynamic facilitation approach to the liquid glass transition. In this paper we study the dynamics of the square plaquette model at the smallest of the…
We introduce a model for the dynamics of mud cracking in the limit of of extremely thin layers. In this model the growth of fracture proceeds by selecting the part of the material with the smallest (quenched) breaking threshold. In…
A one dimensional lattice model is formulated to study tapping dynamics and the long time steady distribution in granular media. The dynamics conserves the number of particles in the system, and density changes are associated to the…
Given a family of rotationally symmetric compact manifolds indexed by the dimension and a weight function, the goal of this paper is to investigate the cut-off phenomenon for the Brownian motions on this family. We provide a class of…
This paper considers non-backtracking random walks on random graphs generated according to the configuration model. The quantity of interest is the scaling of the mixing time of the random walk as the number of vertices of the random graph…
We investigate the dynamics of a phase-separating binary fluid, containing colloidal dumbbells anchored to the fluid-fluid interface. Extensive Lattice Boltzmann-Immersed Boundary method simulations reveal that the presence of soft…
In computational models of particle packings with periodic boundary conditions, it is assumed that the packing is attached to exact copies of itself in all possible directions. The periodicity of the boundary then requires that all of the…
We construct a family of trees on which a lazy simple random walk exhibits total variation cutoff. The main idea behind the construction is that hitting times of large sets should be concentrated around their means. For this sequence of…
The late-stage demixing following spinodal decomposition of a three-dimensional symmetric binary fluid mixture is studied numerically, using a thermodynamicaly consistent lattice Boltzmann method. We combine results from simulations with…
We study the topological dynamics by iterations of a piecewise continuous, non linear and locally contractive map in a real finite dimensional compact ball. We consider those maps satisfying the "separation property": different continuity…
In this paper, the Glauber dynamics for the Ising model on the complete multipartite graph $K_{np_1,\dots,np_m}$ is investigated where $0<p_i<1$ is the proportion of the vertices in the $i$th component. We show that the dynamics exhibits…
The mixing time of a random walk, with or without backtracking, on a random graph generated according to the configuration model on $n$ vertices, is known to be of order $\log n$. In this paper we investigate what happens when the random…
We consider the Glauber dynamics for model of polymer interacting with a substrate or wall. The state space is the set of one-dimensional nearest-neighbor paths on $\mathbb{Z}$ with nonnegative integer coordinates, starting at $0$ and…
We present a computational study of finite-time mixing of a line segment by cutting and shuffling. A family of one-dimensional interval exchange transformations is constructed as a model system in which to study these types of mixing…
The mixing time of the Glauber dynamics for spin systems on trees is closely related to reconstruction problem. Martinelli, Sinclair and Weitz established this correspondence for a class of spin systems with soft constraints bounding the…