Gaussian memory in kinematic matrix theory for self-propellers.

Area of Science:

• Physics
• Statistical Mechanics
• Biophysics

Background:

• The kinematic matrix formalism efficiently analyzes self-propeller dynamics under uncorrelated noise.
• Real-world systems often exhibit correlated noise and significant inertia, limiting current models.

Purpose of the Study:

• To extend the kinematic matrix formalism to incorporate Gaussian correlated noises.
• To analyze the ensemble behaviors of inertial self-propellers under correlated noise.

Main Methods:

• Extension of the kinematic matrix formalism to handle Gaussian correlated noises.
• Application of the formalism to a 2D self-propeller model with velocity fluctuations and Ornstein-Uhlenbeck orientation evolution.
• Derivation of exact analytical results.

Main Results:

• The extended formalism successfully treats self-propellers with inertia and correlated noise.
• Identification of distinct dynamical regimes based on inertial, speed-fluctuation, and orientational diffusion time scales.
• Analysis of the emergent disorientation time scale.

Conclusions:

• The extended kinematic matrix formalism provides a powerful tool for studying complex self-propeller dynamics.
• Understanding these dynamical regimes is crucial for modeling biological and biomimetic active matter.
• The framework facilitates the analysis of systems with significant inertia and correlated noise.