Related papers: Extinctions and Correlations for Uniformly Discret…
In this paper, we investigate the extinction behavior of nonnegative solutions to the Sobolev critical fast diffusion equation in bounded smooth domains with the Dirichlet zero boundary condition. Under the two-bubble energy threshold…
Universal phenomena far from equilibrium exhibit additional independent scaling exponents and functions as compared to thermal universal behavior. For the example of an ultracold Bose gas we simulate nonequilibrium transport processes in a…
We consider the extinction time of the contact process on increasing sequences of finite graphs obtained from a variety of random graph models. Under the assumption that the infection rate is above the critical value for the process on the…
We analyze networked heterogeneous nonlinear systems, with diffusive coupling and interconnected over a generic static directed graph. Due to the network's hetereogeneity, complete synchronization is impossible, in general, but an emergent…
Mathematical diffraction theory is concerned with the analysis of the diffraction image of a given structure and the corresponding inverse problem of structure determination. In recent years, the understanding of systems with continuous and…
Diffusion of electrons in two-dimensional disordered systems with spin-orbit interactions is investigated numerically. Asymptotic behaviors of the second moment of the wave packet and of the temporal auto-correlation function are examined.…
We introduce one dimensional sets to help describe and constrain the integral curves of an $n$ dimensional dynamical system. These curves provide more information about the system than the zero-dimensional sets (fixed points) do. In fact,…
From the exact single step evolution equation of the two-point correlation function of a particle distribution subjected to a stochastic displacement field $\bu(\bx)$, we derive different dynamical regimes when $\bu(\bx)$ is iterated to…
This paper considers synchronous discrete-time dynamical systems on graphs based on the threshold model. It is well known that after a finite number of rounds these systems either reach a fixed point or enter a 2-cycle. The problem of…
A directed percolation process with two symmetric particle species exhibiting exclusion in one dimension is investigated numerically. It is shown that if the species are coupled by branching ($A\to AB$, $B\to BA$) a continuous phase…
We obtain explicit expressions for the long range correlations in the ABC model and in diffusive models conditioned to produce an atypical current of particles.In both cases, the two-point correlation functions allow to detect the…
Many theories of physical interest, which admit a Hamiltonian description, exhibit symmetries under a particular class of non - strictly canonical transformation, known as dynamical similarities. The presence of such symmetries allows a…
We study a one-parameter generalization of the symmetric simple exclusion process on a one dimensional lattice. In addition to the usual dynamics (where particles can hop with equal rates to the left or to the right with an exclusion…
We consider generic finite range percolation models on $\mathbb{Z}^d$ under a high temperature assumption (exponential decay of connection probabilities and exponential ratio weak mixing). We prove that the rate of decay of point-to-point…
We study the existence and uniqueness of (locally) absolutely continuous trajectories of a dynamical system governed by a nonexpansive operator. The weak convergence of the orbits to a fixed point of the operator is investigated by relying…
Diffusion-coagulation can be simply described by a dynamic where particles perform a random walk on a lattice and coalesce with probability unity when meeting on the same site. Such processes display non-equilibrium properties with strong…
We investigate the homogeneous Dirichlet problem for the Fast Diffusion Equation $u_t=\Delta u^m$, posed in a smooth bounded domain $\Omega\subset \mathbb{R}^N$, in the exponent range $m_s=(N-2)_+/(N+2)<m<1$. It is known that bounded…
We consider consistent diffusion dynamics, leaving the celebrated Hua-Pickrell measures, depending on a complex parameter $s$, invariant. These, give rise to Feller-Markov processes on the infinite dimensional boundary $\Omega$ of the…
Extinction appears ubiquitously in many fields, including chemical reactions, population biology, evolution, and epidemiology. Even though extinction as a random process is a rare event, its occurrence is observed in large finite…
Using the theory of generalized hydrodynamics (GHD), we derive exact Euler-scale dynamical two-point correlation functions of conserved densities and currents in inhomogeneous, non-stationary states of many-body integrable systems with weak…