Related papers: Diffusion disorder in the contact process
We first study crossing statistics in random connection models (RCM) built on marked Poisson point processes on $\mathbb R^d$. Under general assumptions, we show exponential tail bounds for the number of crossings of a box contained in the…
Recently it has been demonstrated that the connectivity transition from microscopic connectivity to macroscopic connectedness, known as percolation, is generically announced by a cascade of microtransitions of the percolation order…
We determine the phase diagrams of conservative diffusive contact processes by means of numerical simulations. These models are versions of the ordinary diffusive single-creation, pair-creation and triplet-creation contact processes in…
We derive general properties of anomalous diffusion and nonexponential relaxation from the theory of tempered \alpha-stable processes. Its most important application is to overcome the infinite-moment difficulty for the \alpha-stable random…
We study a dissipative version of the contact process, with mean-field interaction, which admits a simple epidemiological interpretation. The propagation of chaos and the corresponding normal fluctuations reveal that the noise present in…
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…
Critical transitions are of great interest to scientists in many fields. Most knowledge about these transitions comes from systems exhibiting the multistability of spatially uniform states. In spatially extended and, particularly, in…
We study the one-dimensional diffusion process which takes place between two reflecting boundaries and which is acted upon by a time-dependent and spatially-constant force. The assumed force possesses both the harmonically oscillating and…
We study the effects of quenched disorder in a class of quantum chains with (p+1)-multispin interactions exhibiting a free fermionic spectrum, paying special attention to the case p=2. Depending if disorder couples to (i) all the couplings…
Crossover behaviors from the pair contact process with diffusion (PCPD) and the driven PCPD (DPCPD) to the directed percolation (DP) are studied in one dimension by introducing a single particle annihilation/branching dynamics. The…
A stochastic cellular automaton exhibiting parity conserving class transition has been investigated in the presence of quenched spatial disorder by large scale simulations. Numerical evidence has been found that weak disorder causes…
We investigate the diffusive properties of energy fluctuations in a one-dimensional diatomic chain of hard-point particles interacting through a square--well potential. The evolution of initially localized infinitesimal and finite…
The theory of continuous phase transitions predicts the universal collective properties of a physical system near a critical point, which for instance manifest in characteristic power-law behaviours of physical observables. The…
In this work we study global well-posedness and large time behaviour for a typical reaction--diffusion system, which include degenerate diffusion, and whose non-linearities arise from chemical reactions. We show that there is an {\it…
We consider the directed percolation process as a prototype of systems displaying a nonequilibrium phase transition into an absorbing state. The model is in a critical state when the activation probability is adjusted at some precise value…
We study a nonlocal adhesion model for two interacting tumor cell phenotypes, combining diffusion, pairwise interactions, and random phenotypic switching. The system admits a microscopic diffusion--jump particle description whose mean-field…
We introduce an exponential random graph model for networks with a fixed degree distribution and with a tunable degree-degree correlation. We then investigate the nature of a percolation transition in the correlated network with the Poisson…
We establish the sharpness of the percolation phase transition for a class of infinite-range weighted random connection models. The vertex set is given by a marked Poisson point process on $\mathbb{R}^d$ with intensity $\lambda>0$, where…
We study the nonequilibrium phase transition in a model of aggregation of masses allowing for diffusion, aggregation on contact and fragmentation. The model undergoes a dynamical phase transition in all dimensions. The steady state mass…
The role of quantum fluctuations in modifying the critical behavior of non-equilibrium phase transitions is a fundamental but unsolved question. In this study, we examine the absorbing state phase transition of a 1D chain of qubits…