Extreme power law in a driven many-particle system without threshold dynamics.
We study a one-dimensional system of spatially extended particles, which are attached to regularly spaced locations by means of elastic springs. The particles are assumed to be driven by Gaussian noise and to have dissipative, energy-conserving, or antidissipative (pinball-like) interactions, when the particle density exceeds a critical threshold. While each particle in separation shows a well-behaved behavior characterized by a Gaussian velocity distribution, the interaction of particles at high densities can cause an avalanchelike momentum and energy transfer, which can generate extreme (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 better understanding of crowd disasters. Our results suggest that these are most likely caused by passive momentum transfers, not by active pushing.
Computational Physics, Institut für Baustoffe, ETH Zurich, Wolfgang-Pauli-Strasse 27, 8093 Zurich, Switzerland.
Roman
R
Mani
ETH Zurich, Clausiusstrasse 50, 8092 Zurich, Switzerland.
Lucas
L
Böttcher
Computational Physics, Institut für Baustoffe, ETH Zurich, Wolfgang-Pauli-Strasse 27, 8093 Zurich, Switzerland.
Hans J
HJ
Herrmann
ETH Zurich, Clausiusstrasse 50, 8092 Zurich, Switzerland.
Dirk
D
Helbing