Nonlinear Field Equations for Aligning Self-Propelled Rods

2012/07/24 by Anton Peshkov, Igor S. Aranson, Eric Bertin +3 · 135 citations
Engineering · Mathematics · Medicine · Physics and Astronomy · #Aerospace Engineering and Energy Systems #Classical mechanics #Field (mathematics) #Mathematics #Medicine #Micro and Nano Robotics #Nonlinear system #Physics #Quantum mechanics #Rod #Structural Analysis and Optimization #cond-mat.soft #cond-mat.stat-mech

paper · pdf · doi:10.1103/physrevlett.109.268701

published in Physical Review Letters 109(26), 268701 (American Physical Society)

arxiv created 2012/07/24 · openalex publication_date 2012/12/27 · arxiv updated 2013/07/30 · openalex created_date 2025/10/10 · openalex updated_date 2026/08/05

Abstract

We derive a set of minimal and well-behaved nonlinear field equations describing the collective properties of self-propelled rods from a simple microscopic starting point, the Vicsek model with nematic alignment. Analysis of their linear and nonlinear dynamics shows good agreement with the original microscopic model. In particular, we derive an explicit expression for density-segregated, banded solutions, allowing us to develop a more complete analytic picture of the problem at the nonlinear level.

Citations

• Collective motion of self-propelled particles interacting without cohesion
• Active nematics on a substrate: Giant number fluctuations and long-time tails
• Enhanced Diffusion and Ordering of Self-Propelled Rods
• The Mechanics and Statistics of Active Matter

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