Gaussian theory for spatially distributed self-propelled particles.

Area of Science:

• Physics
• Statistical Mechanics
• Complex Systems

Background:

• Deriving continuum equations from microscopic models of interacting self-propelled particles necessitates approximations.
• The conventional truncation method involves zeroing Fourier modes of the orientation distribution.

Purpose of the Study:

• To propose and validate a novel Gaussian approximation (GA) method for deriving continuum equations for interacting self-propelled particles.
• To compare the GA with simulations and assess its accuracy against existing approximation methods.

Main Methods:

• Justifying the suitability of a wrapped Gaussian distribution for individual particle directions via microscopic simulations.
• Numerically integrating the continuum equations derived using the GA.
• Comparing GA results with direct particle simulations, focusing on global polarization and spatiotemporal structures.

Main Results:

• The GA accurately models the distribution of particle directions as a wrapped Gaussian.
• Global polarization in the GA exhibits hysteresis dependent on noise intensity, mirroring simulation results.
• The GA shows excellent agreement with simulations for low noise intensities and qualitative agreement over a wider range.

Conclusions:

• The Gaussian approximation (GA) provides a valid and accurate method for deriving continuum equations for self-propelled particles.
• The GA is a strong candidate for describing spatially distributed self-propelled particles, outperforming other approximations at low noise levels.