Motility and swimming: universal description and generic trajectories

Area of Science:

• Physics of active matter
• Microscopic locomotion
• Nonlinear dynamics

Background:

• Autonomous locomotion is observed in biological cells and artificial microswimmers.
• Complex trajectories (straight, curved, random) are typically attributed to particle/medium asymmetry or external factors.
• Understanding the fundamental mechanisms governing microswimmer trajectories is crucial.

Purpose of the Study:

• To demonstrate that straight, circular, and helical trajectories can emerge naturally in active matter systems.
• To show these trajectories arise without requiring particle or medium asymmetry.
• To analyze the role of self-congruent solutions and spontaneous symmetry breaking.

Main Methods:

• General theoretical considerations without relying on specific model forms.
• Analysis of self-congruent solutions, where system states are identical under rotation and translation.
• Investigation of pitchfork bifurcations leading to spontaneous symmetry breaking.
• Development and analysis of a simple, exactly solvable nonlinear model of a phoretic particle.

Main Results:

• Straight, circular, and helical trajectories naturally emerge for particles in active concentration fields, independent of particle/medium asymmetry.
• These trajectories correspond to self-congruent solutions, indicating spontaneous symmetry breaking.
• A solvable model demonstrates transitions from non-motile to straight, circular, and helical motion via symmetry-breaking bifurcations.

Conclusions:

• Particle trajectory complexity in active systems is not solely dependent on asymmetry.
• Self-congruency and spontaneous symmetry breaking are key mechanisms driving diverse locomotion patterns.
• The observed trajectories are determined by model parameters, not external asymmetries.