Crazy 1d billiards: Behavior of spring-fixated, noisy colliding particles

TL;DR

This paper investigates a one-dimensional system of particles attached to fixed points by springs, driven by noise, revealing how high-density interactions can cause avalanche-like energy transfers and power-law behaviors, with implications for crowd dynamics.

Contribution

It introduces a novel model of noisy, spring-fixated particles exhibiting complex high-density interactions and power-law phenomena, relevant for understanding crowd disasters.

Findings

Velocity distributions are Gaussian at individual particle level.

High-density interactions lead to avalanche-like energy transfers.

Velocity variance peaks near system boundaries.

Abstract

We study a one-dimensional system of spatially extended particles, which are fixated to regularly spaced locations by means of elastic springs. The particles are assumed to be driven by a Gaussian noise and to have dissipative, energy-conserving or anti-dissipative (flipper-like) interactions, when the particle density exceeds a critical threshold. While each particle in separation shows a wellbehaved behavior characterized by a Gaussian velocity distribution, the interaction of particles at high densities can cause an avalanche-like momentum and energy transfer, which can generate steep power laws without a well-defined variance and mean value. Specifically, the velocity variance increases dramatically towards the free boundaries of the driven-many-particle system. The model might also have some relevance for a better understanding of crowd disasters. Our results suggest that these are most likely caused by passive momentum transfers, and not by active pushing.