Accumulation on the boundary for one-dimensional stochastic particle system

TL;DR

This paper analyzes a one-dimensional stochastic particle system where particles disappear upon reaching a boundary, causing the boundary to move, with applications in traffic, biology, and material growth.

Contribution

It introduces a model linking particle dynamics with boundary growth, providing insights into the correlation between them and potential applications.

Findings

Derived the relationship between particle interactions and boundary movement

Identified conditions affecting the boundary growth rate

Connected the model to real-world phenomena like traffic jams and biological growth

Abstract

We consider infinite particle system on the positive half-line moving independently of each other. When a particle hits the boundary it immediately disappears, and the boundary moves to the right on some fixed quantity (particle size). We study the speed of the boundary movement (growth). Possible applications - dynamics of the traffic jam growth, growth of thrombus, epitaxy. Nontrivial mathematics is related to the correlation between particle dynamics and boundary growth.