Inertial and confined dynamics of a constant-speed active particle in three dimensions

Area of Science:

• Physics
• Statistical Mechanics
• Soft Matter Physics

Background:

• Self-propelled particles exhibit complex dynamics in various environments.
• Understanding three-dimensional motion and reorientation is crucial for active matter research.
• Existing models often simplify orientational dynamics, limiting their applicability.

Purpose of the Study:

• To develop and analyze a novel model for a 3D self-propelled particle.
• To investigate the effects of rotational Langevin dynamics on particle motion.
• To characterize the system's nonequilibrium properties and response to confinement.

Main Methods:

• Formulation of a 3D rotational Langevin equation with Ornstein-Uhlenbeck-like statistics.
• Analytical derivation of dynamics for underdamped and overdamped regimes.
• Calculation of mean-squared displacement, velocity-propulsion alignment, and entropy production rate (EPR).

Main Results:

• Underdamped dynamics show a ballistic-to-diffusive crossover independent of initial velocity.
• Finite velocity-propulsion misalignment suppresses EPR, distinguishing the model.
• Overdamped particles in confinement exhibit spherical diffusion governed by propulsion, friction, and trap stiffness.

Conclusions:

• The model provides a comprehensive framework for 3D active particle dynamics.
• The study highlights the impact of orientational noise and confinement on system behavior.
• Numerical simulations validate theoretical predictions for confined active systems.