Gaussian Memory in Kinematic Matrix Theory for Self-Propellers

TL;DR

This paper extends the kinematic matrix formalism to include Gaussian correlated noise, enabling analysis of more realistic self-propeller models with inertia and complex noise influences.

Contribution

The authors develop an extension of the kinematic matrix formalism to handle Gaussian correlated noise, broadening its applicability to real-world self-propellers with inertia.

Findings

Identified multiple dynamical regimes based on inertial and noise parameters.

Derived exact results for ensemble behaviors of 2D self-propellers.

Analyzed the impact of Ornstein-Uhlenbeck noise on orientation and velocity.

Abstract

We extend the kinematic matrix ("kinematrix") formalism [Phys. Rev. E 89, 062304 (2014)], which via simple matrix algebra accesses ensemble properties of self-propellers influenced by uncorrelated noise, to treat Gaussian correlated noises. This extension brings into reach many real-world biological and biomimetic self-propellers for which inertia is significant. Applying the formalism, we analyze in detail ensemble behaviors of a 2D self-propeller with velocity fluctuations and orientation evolution driven by an Ornstein-Uhlenbeck process. On the basis of exact results, a variety of dynamical regimes determined by the inertial, speed-fluctuation, orientational diffusion, and emergent disorientation time scales are delineated and discussed.