Emergence of particle clusters in a one-dimensional model: connection to condensation processes

TL;DR

This paper investigates a one-dimensional particle model with attractive interactions, revealing the emergence of multiple correlated clusters and fractal structures, which relate to condensation phenomena in mass transport systems.

Contribution

It introduces a hydrodynamic limit where interaction strength scales with system size, leading to novel cluster formation and self-similar structures in the model.

Findings

Multiple particle clusters form with finite mass fractions.

Clusters exhibit spatial correlations and fractal patterns.

Results connect to condensation phenomena in mass transport models.

Abstract

We discuss a simple model of particles hopping in one dimension with attractive interactions. Taking a hydrodynamic limit in which the interaction strength increases with the system size, we observe the formation of multiple clusters of particles, each containing a finite fraction of the all the particles in the system. These clusters are correlated in space, and the system has a self-similar (fractal) structure. These results are related to condensation phenomena in mass transport models and to a recent mathematical analysis of the hydrodynamic limit in a related model.