Brownian self-driven particles on the surface of a sphere

Area of Science:

• Statistical Physics
• Soft Matter Physics
• Brownian Motion

Background:

• Brownian motion describes random particle movement.
• Self-propelled particles exhibit active movement.
• Spherical surfaces present unique dynamic constraints.

Purpose of the Study:

• To analyze the dynamics of overdamped Brownian self-propelled particles on a sphere.
• To elucidate the impact of self-propulsion on particle diffusion.
• To derive analytical expressions for particle displacement and probability distributions.

Main Methods:

• Calculating angular mean-square displacement (azimuthal and polar).
• Developing short- and long-time analytical expressions.
• Determining steady marginal angular probability density functions.

Main Results:

• Quantified the effect of self-propulsion on diffusion.
• Provided analytical expressions for angular mean-square displacement.
• Characterized the steady-state probability distributions of particle positions.

Conclusions:

• Self-propulsion significantly alters diffusion dynamics on spherical surfaces.
• Analytical models accurately describe particle behavior over different timescales.
• The study provides a framework for understanding active matter on curved substrates.