Related papers: Avoiding a Spanning Cluster in Percolation Models
Intercellular exchange networks are essential for the adaptive capabilities of populations of cells. While diffusional exchanges have traditionally been difficult to map, recent advances in nanotechnology enable precise probing of exchange…
A central goal of protein-folding theory is to predict the stochastic dynamics of transition paths --- the rare trajectories that transit between the folded and unfolded ensembles --- using only thermodynamic information, such as a…
Non-Hermitian systems distinguish themselves from Hermitian systems by exhibiting a phase transition point called an exceptional point (EP), which is the point at which two eigenstates coalesce under a system parameter variation. Many…
The existence of the {\em typical set} is key for data compression strategies and for the emergence of robust statistical observables in macroscopic physical systems. Standard approaches derive its existence from a restricted set of…
In line with Pomeau's conjecture about the relevance of directed percolation (DP) to turbulence onset/decay in wall-bounded flows, we propose a minimal stochastic model dedicated to the interpretation of the spatially intermittent regimes…
A key feature of the classical Fluctuation Dissipation theorem is its ability to approximate the average response of a dynamical system to a sufficiently small external perturbation from an appropriate time correlation function of the…
We have studied the kinetics of cluster formation for dynamical systems of dimensions up to $n=8$ interacting through elastic collisions or coalescence. These systems could serve as possible models for gas kinetics, polymerization and…
We present an application of the theory of stochastic processes to model and categorize non-equilibrium physical phenomena. The concepts of uniformly continuous probability measures and modular evolution lead to a systematic hierarchical…
We propose a statistical model defined on the three-dimensional diamond network where the splitting of randomly selected nodes leads to a spatially disordered network, with decreasing degree of connectivity. The terminal state, that is…
We consider the modeling of the dynamics of the chemostat at its very source. The chemostat is classically represented as a system of ordinary differential equations. Our goal is to establish a stochastic model that is valid at the scale…
We study the percolation properties of the growing clusters model. In this model, a number of seeds placed on random locations on a lattice are allowed to grow with a constant velocity to form clusters. When two or more clusters eventually…
In this paper we consider a diffusion process obtained as a small random perturbation of a dynamical system attracted to a stable equilibrium point. The drift and the diffusive perturbation are assumed to evolve slowly in time. We describe…
We study a two-dimensional kinetic Ising model with Swendsen-Wang dynamics, replacing the usual percolation on top of Ising clusters by explosive percolation. The model exhibits a reversible first-order phase transition with hysteresis.…
In this paper we analyze some aspects of {\em exponential flights}, a stochastic process that governs the evolution of many random transport phenomena, such as neutron propagation, chemical/biological species migration, or electron motion.…
Tumors initiate when a population of proliferating cells accumulates a certain number and type of genetic and/or epigenetic alterations. The population dynamics of such sequential acquisition of (epi)genetic alterations has been the topic…
Diffusion models do not recover semantic structure uniformly over time. Instead, samples transition from semantic ambiguity to class commitment within a narrow regime. Recent theoretical work attributes this transition to dynamical…
Edges, binding together nodes within networks, have the potential to induce dramatic transitions when specific collective failure behaviors emerge. These changes, initially unfolding covertly and then erupting abruptly, pose substantial,…
The most intriguing properties of non-Hermitian systems are found near the exceptional points (EPs) at which the Hamiltonian matrix becomes defective. Due to the complex topological structure of the energy Riemann surfaces close to an EP…
In this paper we introduce a contact process in an evolving random environment (CPERE) on a connected and transitive graph with bounded degree, where we assume that this environment is described through an ergodic spin systems with finite…
The selection of an equilibrium state by maximising the entropy of a system, subject to certain constraints, is often powerfully motivated as an exercise in logical inference, a procedure where conclusions are reached on the basis of…