Related papers: A new look at the interfaces in percolation
We consider the random connection model in which an edge between two Poisson points at distance $r$ is present with probability $g(r)$. We conduct an extreme value analysis on this model, namely by investigating the longest edge with at…
Fluid interfaces, such as soap films, liquid droplets or lipid membranes, are known to give rise to several special geometries, whose complexity and beauty continue to fascinate us, as observers of the natural world, and challenge us as…
The motion of interfaces is an essential feature of microstructure evolution in crystalline materials. While atomic-scale descriptions provide mechanistic clarity, continuum descriptions are important for understanding microstructural…
A popular question in Bernoulli percolation models is if the probability of connection between two vertices in a transitive graph decays monotonically with the distance between these two vertices. For example, on the square lattice is an…
A new type of boundary dynamics is proposed to describe the interface that sweeps space to collect distributed material. Based upon geometrical consideration on a simple physical process representing a certain experiment, the dynamics is…
Percolation is the simplest fundamental model in statistical mechanics that exhibits phase transitions signaled by the emergence of a giant connected component. Despite its very simple rules, percolation theory has successfully been applied…
We consider critical oriented Bernoulli percolation on the square lattice $\mathbb{Z}^2$. We prove a Russo-Seymour-Welsh type result which allows us to derive several new results concerning the critical behavior: - We establish that the…
Percolation, describing critical behaviors of phase transition in a geometrical context, prompts wide investigations in natural and social networks as a fundamental model. The introduction of quantum-intrinsic interference and tunneling…
In 2006, the fourth author proposed a graph-theoretic model of interface dynamics called competitive erosion. Each vertex of the graph is occupied by a particle that can be either red or blue. New red and blue particles alternately get…
Some interfaces between two different topologically ordered systems can be gapped. In earlier work it has been shown that such gapped interfaces can themselves be effective one dimensional topological systems that possess localized…
The structure of liquid water in the proximity of an interface can deviate significantly from that of bulk water, with surface-induced structural perturbations typically converging to bulk values at about ~1 nm from the interface. While…
We study a subclass of the May-Leonard stochastic model with an arbitrary, even number of species, leading to the arising of two competing partnerships where individuals are indistinguishable. By carrying out a series of accurate numerical…
We study a lattice model where the coupling stochastically switches between repulsive (subtractive) and attractive (additive) at each site with probability p at every time instance. We observe that such kind of coupling stabilizes the local…
We study the effects of mobility on two crucial characteristics in multi-scale dynamic networks: percolation and connection times. Our analysis provides insights into the question, to what extent long-time averages are well-approximated by…
We study the phase transition phenomena for long-range oriented percolation and contact process. We studied a contact process in which the range of each vertex are independent, updated dynamically and given by some distribution $N$. We also…
An intrinsic feature of nearly all internal interfaces in crystalline systems (homo- and hetero-phase) is the presence of disconnections (topological line defects constrained to the interface that have both step and dislocation character).…
I consider p-Bernoulli bond percolation on graphs of vertex-transitive tilings of the hyperbolic plane with finite sided faces (or, equivalently, on transitive, nonamenable, planar graphs with one end) and on their duals. It is known…
We discuss duality properties of critical Boltzmann planar maps such that the degree of a typical face is in the domain of attraction of a stable distribution with parameter $\alpha\in(1,2]$. We consider the critical Bernoulli bond…
A set of discrete individual points located in an embedding continuum space can be seen as percolating or non-percolating, depending on the radius of the discs/spheres associated with each of them. This problem is relevant in theoretical…
Percolation with edge-passage probability p and first-passage percolation are studied for the n-cube B_n ={0,1}^n with nearest neighbor edges. For oriented and unoriented percolation, p=e/n and p=1/n are the respective critical…