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Related Experiment Video

Updated: Dec 7, 2025

Visually Based Characterization of the Incipient Particle Motion in Regular Substrates: From Laminar to Turbulent Conditions
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Large-Scale Dynamics of Self-propelled Particles Moving Through Obstacles: Model Derivation and Pattern Formation.

P Aceves-Sanchez1, P Degond2, E E Keaveny2

  • 1Department of Mathematics, North Carolina State University, Raleigh, NC, 27695, USA.

Bulletin of Mathematical Biology
|September 26, 2020
PubMed
Summary
This summary is machine-generated.

We modeled the interaction between self-propelled particles (SPPs) and obstacles, revealing distinct large-scale patterns like traveling bands and clusters. These findings inform a partial differential equations model predicting pattern formation based on interaction strength.

Keywords:
Gradient flowHydrodynamic limitNon-local interactionsPattern formationSelf-propelled particlesStability analysis

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Area of Science:

  • Physics
  • Complex Systems
  • Statistical Mechanics

Background:

  • Self-propelled particles (SPPs) exhibit emergent collective behaviors.
  • Interactions with obstacles can significantly alter SPP dynamics and pattern formation.

Purpose of the Study:

  • To model and analyze the large-scale patterns arising from SPP-obstacle interactions.
  • To develop a macroscopic model for predicting pattern formation and characteristics.

Main Methods:

  • Simulations using an individual-based model.
  • Derivation of a macroscopic partial differential equations model.
  • Linear stability analysis of the derived equations.

Main Results:

  • Identified three distinct large-scale patterns: traveling bands, trails, and moving clusters.
  • Developed a coupled system of nonlinear, non-local partial differential equations.
  • Linear stability analysis predicts pattern formation for strong interactions and allows prediction of pattern size.

Conclusions:

  • Obstacle interactions induce short-ranged SPP aggregation.
  • The macroscopic model provides insights into pattern formation mechanisms and parameters.