Nonequilibrium Phase Transition in Non-Local and Nonlinear Diffusion Model

TL;DR

This paper investigates a one-dimensional nonlocal nonlinear diffusion model, revealing a dynamical phase transition with universal critical behavior, achieved through self-organization and symmetry transformations, applicable to aggregation and cooperation phenomena.

Contribution

It provides analytical and numerical insights into the critical dynamics of a nonlocal nonlinear diffusion equation, highlighting a novel self-organized phase transition mechanism.

Findings

Identification of a dynamical phase transition in the model

Demonstration of universality in critical behavior

Characterization of self-organized critical state

Abstract

We present the results of analytical and numerical studies of a one-dimensional nonlocal and nonlinear diffusion equation describing non-equilibrium processes ranging from aggregation phenomena to cooperation of individuals. We study a dynamical phase transition that is obtained on tuning the initial conditions and demonstrate universality and characterize the critical behavior. The critical state is shown to be reached in a self-organized manner on dynamically evolving the diffusion equation subjected to a mirror symmmetry transformation.