Exponential clogging time for a one dimensional DLA

TL;DR

This paper introduces a simple model for DLA clogging on a cylinder and proves an exponential lower bound on the number of particles needed to cause clogging, providing insights into clogging phenomena.

Contribution

It establishes the first exponential lower bound for particle count before clogging in a DLA model on a cylinder, advancing understanding of clogging dynamics.

Findings

Exponential lower bound on clogging time established

Model applicable to artery clogging scenarios

Provides theoretical foundation for clogging analysis

Abstract

When considering DLA on a cylinder it is natural to ask how many particles it takes to clog the cylinder, e.g. modeling clogging of arteries. In this note we formulate a very simple DLA clogging model and establish an exponential lower bound on the number of particles arriving before clogging appears.