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

Roman Mani; Lucas Böttcher; Hans J. Herrmann; Dirk Helbing

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arXiv · 1404.7460

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

Roman Mani·Lucas Böttcher·Hans J. Herrmann·Dirk Helbing

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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.

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Roman Mani, Lucas Böttcher, Hans J. Herrmann, Dirk Helbing. 2014-03-31. Crazy 1d billiards: Behavior of spring-fixated, noisy colliding particles. https://arxiv.org/abs/1404.7460

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