Clustering in anomalous files of independent particles

TL;DR

This paper investigates the clustering behavior of anomalous independent particles in a one-dimensional file, revealing a phase transition characterized by a critical clustering percentage and a logarithmic mean square displacement.

Contribution

It introduces a new model of anomalous independent particles exhibiting clustering and phase transition, connecting these phenomena to biological membrane rafts and channel regulation.

Findings

Particles form clusters with a critical percentage depending on alpha

Mean square displacement grows as log^2(t) over time

Clustering phase transition is numerically stable

Abstract

The dynamics of classical hard particles in a quasi one-dimensional channel were studied since the 1960s and used for explaining processes in chemistry, physics and biology and in applications. Here we show that in a previously un-described file made of anomalous, independent, particles (with jumping times taken from, {\psi}_{\alpha} (t) t^(-1-{\alpha}), 0<{\alpha}<1), particles form clusters. At steady state, the percentage of particles in clusters is about, \surd(1-{\alpha}^3), only for anomalous {\alpha}, characterizing the criticality of a phase transition. The asymptotic mean square displacement per particle in the file is about, log^2(t). We show numerically that this exciting phenomenon of a phase transition is very stable, and relate it with the mysterious phenomenon of rafts in biological membranes, and with regulation of biological channels.