Dynamics of self-propelled particles under strong confinement.

Area of Science:

• Statistical mechanics
• Soft matter physics
• Active matter dynamics

Background:

• Self-propelled particles (SPPs) exhibit unique behaviors due to internal driving forces.
• Confinement significantly alters the dynamics and spatial distribution of active matter systems.
• Understanding particle behavior at boundaries is crucial for designing active matter devices.

Purpose of the Study:

• To develop a statistical theory for non-aligning, non-interacting SPPs in a 2D convex box.
• To investigate the influence of confinement strength and box geometry on particle distribution.
• To provide a theoretical framework for designing confinement geometries for specific particle distributions.

Main Methods:

• Development of a statistical theory based on particle trajectory persistence length.
• Analysis of steady-state particle density in relation to boundary curvature.
• Prediction of particle orientation distribution and pressure decay under confinement.

Main Results:

• In strongly confined systems (small box size relative to persistence length), bulk density is zero, and boundary density is proportional to local curvature.
• The theory allows for the inverse design of box shapes to achieve desired boundary density profiles.
• Predictions include orientation distributions at the boundary and exponential pressure decay with box size.

Conclusions:

• The developed statistical theory accurately describes SPP dynamics in confined geometries.
• Boundary curvature is a key factor determining particle accumulation in the strong confinement regime.
• The theory offers a versatile tool for controlling and predicting active matter behavior in engineered confinements.