Pattern Formation and a Clustering Transition in Power-Law Sequential Adsorption

TL;DR

This paper introduces a new model for particle adsorption that reveals a clustering transition, differentiating between weakly and strongly correlated particle distributions with fractal characteristics.

Contribution

The paper presents a novel model capturing clustering transitions in particle adsorption, highlighting fractal structures and broad applicability to various natural phenomena.

Findings

Identification of a clustering transition separating different correlation phases

Demonstration of fractal nature in both phases

Relevance to diverse clustering phenomena

Abstract

A new model that describes adsorption and clustering of particles on a surface is introduced. A {\it clustering} transition is found which separates between a phase of weakly correlated particle distributions and a phase of strongly correlated distributions in which the particles form localized fractal clusters. The order parameter of the transition is identified and the fractal nature of both phases is examined. The model is relevant to a large class of clustering phenomena such as aggregation and growth on surfaces, population distribution in cities, plant and bacterial colonies as well as gravitational clustering.