Related papers: The bead model and limit behaviors of dimer models
Wire billiard is defined by a smooth embedded closed curve of non-vanishing curvature $k$ in $\mathbb{R}^n$ (a wire). For a class of curves, that we call nice wires, the wire billiard map is area preserving twist map of the cylinder. In…
In this work, we study long-time wave transport in correlated and uncorrelated disordered 2D arrays. When a separation of dimensions is applied to the model, we find that the predicted 1D random dimer phenomenology also appears in so-called…
The paper bounds the number of tessellations with T-shaped vertices on a fixed set of $k$ lines: tessellations are efficiently encoded, and algorithms retrieve them, proving injectivity. This yields existence of a completely random…
A mathematical model for wire rolling is developed, focusing on predicting the lateral spread. This provides, for the first time, an analytic model of lateral spread without any fitting parameters. The model is derived directly from the…
Critical models are, almost by definition, supposed to feature both slow decay of correlations for local observables while retaining some mixing even for macroscopic observables. A strong version of the latter property is that changing…
We establish sufficient conditions for existence of curves minimizing length as measured with respect to a degenerate metric on the plane while enclosing a specified amount of Euclidean area. Non-existence of minimizers can occur and…
We study the bead-spring model for a polymerized phantom membrane in the overdamped limit, which is the two-dimensional generalization of the well-known Rouse model for polymers. We derive the {\it exact} eigenmodes of the membrane dynamics…
A simple asperity model using random process theory is developed in the presence of adhesion. Using the DMT model for each individual asperity, and asymptotic results at large separations, a new adhesion parameter is found, on which the…
The present paper is concerned with diffusion processes running on tubular domains with conditions on nonreaching the boundary, respectively, reflecting at the boundary, and corresponding processes in the limit where the thin tubular…
We propose a simple model for a binary decision making process on a graph, motivated by modeling social decision making with cooperative individuals. The model is similar to a random field Ising model or fiber bundle model, but with key…
In this paper we investigate the geometry of a discrete Bayesian network whose graph is a tree all of whose variables are binary and the only observed variables are those labeling its leaves. We provide the full geometric description of…
Dilation is a puzzling phenomenon within Imprecise Probability theory: when it obtains, our uncertainty evaluation on event $A$ is vaguer after conditioning $A$ on $B$, whatever is event $B$ in a given partition $\mathcal{B}$. In this paper…
Single-particle continuum models such as the popular Bistritzer-MacDonald model have become powerful tools for predicting electronic phenomena of incommensurate 2D materials and the development of many-body models aimed to model…
We investigate one dimensional tight binding model in the presence of a correlated binary disorder. The disorder is due to the interaction of particles with heavy immobile other species. Off-diagonal disorder is created by means of a fast…
We study various mathematical aspects of discrete models on graphs, specifically the Dimer and the Ising models. We focus on proving gluing formulas for individual summands of the partition function. We also obtain partial results regarding…
We minimize a linear combination of the Willmore and the length functional among networks in $\mathbb{R}^d$ belonging to a given class determined by the number of curves, the order of the junctions and the angles between curves at the…
We study a disordered network of bistable bonds subjected to periodic strain. The model is inspired by experiments on crumpled sheets and it features behaviors associated with glasses, including a complex energy landscape, memories, and…
A knotted ribbon is one of physical aspect of a knot. A folded ribbon knot is a depiction of a knot obtained by folding a long and thin rectangular strip to become flat. The ribbonlength of a knot type can be defined as the minimum length…
In this paper we address the problem of continuous dependence on initial and boundary data for a one-dimensional debonding model describing a thin film peeled away from a substrate. The system underlying the process couples the weakly…
Consider a random graph process where vertices are chosen from the interval $[0,1]$, and edges are chosen independently at random, but so that, for a given vertex $x$, the probability that there is an edge to a vertex $y$ decreases as the…