Large-Scale Dynamics of Self-propelled Particles Moving Through Obstacles: Model Derivation and Pattern Formation

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.