Related papers: A new look at the interfaces in percolation
Accurate representation of interfaces and flux exchange is vital for coupled multiphysics simulations across a broad range of applications. Currently, coupling approaches are limited by the underlying discretization or to specific physical…
The problem of continuum percolation in dispersions of rods is reformulated in terms of weighted random geometric graphs. Nodes (or sites or vertices) in the graph represent spatial locations occupied by the centers of the rods. The…
We provide a new proof of the sharpness of the phase transition for nearest-neighbour Bernoulli percolation. More precisely, we show that - for $p<p_c$, the probability that the origin is connected by an open path to distance $n$ decays…
Consider the Ising model at low-temperatures and positive external field $\lambda$ on an $N\times N$ box with Dobrushin boundary conditions that are plus on the north, east, and west boundaries and minus on the south boundary. If $\lambda =…
The bulk-edge correspondence is a condensed matter theorem that relates the conductance of a Hall insulator in a half-plane to that of its (straight) boundary. In this work, we extend this result to domains with curved boundaries. Under…
We consider a kinetic model of two species of particles interacting with a reservoir at fixed temperature, described by two coupled Vlasov-Fokker-Plank equations. We prove that in the diffusive limit the evolution is described by a…
We introduce a class of random graphs with a community structure, which we call the hierarchical configuration model. On the inter-community level, the graph is a configuration model, and on the intra-community level, every vertex in the…
We study interfaces in an Allen-Cahn equation, separating two metastable states. Our focus is on a directional quenching scenario, where a parameter renders the system bistable in a half plane and monostable in its complement, with the…
Percolation is the paradigm for random connectivity and has been one of the most applied statistical models. With simple geometrical rules a transition is obtained which is related to magnetic models. This transition is, in all dimensions,…
Global physical properties of random media change qualitatively at a percolation threshold, where isolated clusters merge to form one infinite connected component. The precise knowledge of percolation thresholds is thus of paramount…
We study the dynamics of the travelling interface arising from a bistable piece-wise linear one-way coupled map lattice. We show how the dynamics of the interfacial sites, separating the two superstable phases of the local map, is finite…
A novel type of shallow interface state in junctions of two semiconductors without band inversion is identified within the envelope function approximation, using the two-band model. It occurs in abrupt junctions when the interband velocity…
Complex natural or engineered systems comprise multiple characteristic scales, multiple spatiotemporal domains, and even multiple physical closure laws. To address such challenges, we introduce an interface learning paradigm and put forth a…
We study the independent alignment percolation model on $\mathbb{Z}^d$ introduced by Beaton, Grimmett and Holmes [arXiv:1908.07203]. It is a model for random intersecting line segments defined as follows. First the sites of $\mathbb{Z}^d$…
The percolation threshold for flow or conduction through voids surrounding randomly placed spheres is rigorously calculated. With large scale Monte Carlo simulations, we give a rigorous continuum treatment to the geometry of the…
Recently, new results on percolation of interdependent networks have shown that the percolation transition can be first order. In this paper we show that, when considering antagonistic interactions between interacting networks, the…
We consider a diffusion process with coefficients that are periodic outside of an "interface region" of finite thickness. The question investigated in this article is the limiting long time/large scale behavior of such a process under…
Topographical and diffuse interface reconfigurations occur with a change in the solidification rate. In this article we pursue the hypothesis that the interface configuration during solidification is determined by the rate of entropy…
We study random bubble lattices which can be produced by processes such as first order phase transitions, and derive characteristics that are important for understanding the percolation of distinct varieties of bubbles. The results are…
We consider a diffusion process with coefficients that are periodic outside of an 'interface region' of finite thickness. The question investigated in the articles [1,2] is the limiting long time / large scale behaviour of such a process…