Spatially-Periodic Cluster Pattern of Coupled Forced Oscillators

TL;DR

This paper introduces a model explaining how particles under forced oscillation form periodic clusters, demonstrating instability of uniform distribution and emergence of stripe patterns through stability analysis and simulations.

Contribution

The study presents a new simple model for particle clustering under forced oscillation, incorporating effective viscosity and analyzing pattern formation.

Findings

Uniform distribution is unstable under the model.

Spatially-periodic patterns emerge in one dimension.

Stripe patterns form in two dimensions.

Abstract

We propose a simple model for periodic clustering of particles under forced oscillation. Effective viscosity is assumed to increase owing to neighboring particles by analogy with the Einstein viscosity law. The linear stability analysis and numerical simulations show that the uniform distribution is unstable, and spatially-periodic and stripe patterns appear respectively in one and two dimensions.