Related papers: Competition between growths governed by Bernoulli …
Material mixing induced by a Rayleigh-Taylor instability occurs ubiquitously in either nature or engineering when a light fluid pushes against a heavy fluid, accompanying with the formation and evolution of chaotic bubbles. Its general…
Given a branching random walk on a graph, we consider two kinds of truncations: by inhibiting the reproduction outside a subset of vertices and by allowing at most $m$ particles per site. We investigate the convergence of weak and strong…
We prove that Bernoulli bond percolation on any nonamenable, Gromov hyperbolic, quasi-transitive graph has a phase in which there are infinitely many infinite clusters, verifying a well-known conjecture of Benjamini and Schramm (1996) under…
This chapter investigates some mechanisms behind pattern formation driven by competitive-only or repelling interactions, and explores how these patterns are influenced by different types of particle movement. Despite competition and…
In this paper, we prove that Bernoulli percolation on bounded degree graphs with isoperimetric dimension $d>4$ undergoes a non-trivial phase transition (in the sense that $p_c<1$). As a corollary, we obtain that the critical point of…
The ecological invasion problem in which a weaker exotic species invades an ecosystem inhabited by two strongly competing native species is modelled by a three-species competition-diffusion system. It is known that for a certain range of…
We give an new proof of the well-known competitive exclusion principle in the chemostat model with $n$ species competing for a single resource, for any set of increasing growth functions. The proof is constructed by induction on the number…
For a positive integer $n$ let $\mathfrak{P}_n=\prod_{s_p(n)\ge p} p,$ where $p$ runs over all primes and $s_p(n)$ is the sum of the base $p$ digits of $n$. For all $n$ we prove that $\mathfrak{P}_n$ is divisible by all "small" primes with…
Let $G=(V,E)$ be a connected, locally finite, transitive graph, and consider Bernoulli bond percolation on $G$. In recent work, we conjectured that if $G$ is nonamenable then the matrix of critical connection probabilities…
This study extends the SIS epidemic model for single virus propagation over an arbitrary graph to an SI1SI2S epidemic model of two exclusive, competitive viruses over a two-layer network with generic structure, where network layers…
Using cyclic shear to drive a two dimensional granular system, we determine the structural characteristics for different inter-particle friction coefficients. These characteristics are the result of a competition between mechanical…
We study long-range Bernoulli percolation on $\mathbb{Z}^d$ in which each two vertices $x$ and $y$ are connected by an edge with probability $1-\exp(-\beta \|x-y\|^{-d-\alpha})$. It is a theorem of Noam Berger (CMP, 2002) that if…
We investigate the percolation properties of a planar reinforced network model. In this model, at every time step, every vertex chooses $k \ge 1$ incident edges, whose weight is then increased by 1. The choice of this $k$-tuple occurs…
We analysed some qualitative properties of the limit configuration of the solutions of a reaction-diffusion system of four competing species as the competition rate tends to infinity. Large interaction induces the spatial segregation of the…
We analyse the classical model of competition between three species studied by May and Leonard ({\it SIAM J Appl Math} \textbf{29} (1975) 243-256) with the approaches of singularity analysis and symmetry analysis to identify values of the…
By introducing a simple competition mechanism for bond insertion in random graphs, explosive percolation exhibits a sharp phase transition with rich critical phenomena. We investigate high-order connectivity in explosive percolation using…
RNA viruses exist in large intra-host populations which display great genotypic and phenotypic diversity. We analyze a model of viral competition between two different viral strains infecting a constantly replenished cell pool, in which we…
We investigate percolation on growing networks where the evolution of connected components resembles a non-equilibrium version of the multiplicative coalescent. The supercritical $\pi> \pi_c$ regime for a host of such models was conjectured…
In this paper we prove that, under the assumption of quasi-transitivity, if a branching random walk on ${{\mathbb{Z}}^d}$ survives locally (at arbitrarily large times there are individuals alive at the origin), then so does the same process…
Coexistence of competing species is, due to unavoidable fluctuations, always transient. In this Letter, we investigate the ultimate survival probabilities characterizing different species in cyclic competition. We show that they often obey…