Singular perturbation analysis of a reduced model for collective motion: A renormalization group approach

Details Singular perturbation analysis of a reduced model for collective motion: A renormalization group approach Singular perturbation analysis of a reduced model for collective motion: A renormalization group approach

2011-02-02

arxiv.org/abs/1102.0407v1

Physical Review E 83, 031127 (2011)

Physics

Condensed Matter

Soft Condensed Matter

Scientific paper

10.1103/PhysRevE.83.031127

In a system of noisy self-propelled particles with interactions that favor directional alignment, collective motion will appear if the density of particles is beyond a critical density. Starting with a reduced model for collective motion, we determine how the critical density depends on the form of the initial perturbation. Specifically, we employ a renormalization-group improved perturbative method to analyze the model equations, and show analytically, up to first order in the perturbation parameter, how the critical density is modified by the strength of the initial angular perturbation in the system.

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