Active motions of Brownian particles in a generalized energy-depot model

TL;DR

This paper introduces a generalized energy-depot model for active Brownian particles, capturing diverse motion patterns including oscillations and stepping behaviors, with implications for biological systems and nano-robot control.

Contribution

It develops a flexible energy conversion framework dependent on position and velocity, revealing new active motion phenomena and noise effects in a unified model.

Findings

Particles exhibit diverse motion patterns like braking and stepping.

Spontaneous oscillations with negative stiffness are observed.

Noise induces random walk-like behavior in stepping motion.

Abstract

We present a generalized energy-depot model in which the conversion rate of the internal energy into motion can be dependent on the position and the velocity of a particle. When the conversion rate is a general function of the velocity, the active particle exhibits diverse patterns of motion including a braking mechanism and a stepping motion. The phase trajectories of the motion are investigated in a systematic way. With a particular form of the conversion rate dependent on the position and velocity, the particle shows a spontaneous oscillation characterizing a negative stiffness. These types of active behaviors are compared with the similar phenomena observed in biology such as the stepping motion of molecular motors and the amplification in hearing mechanism. Hence, our model can provide a generic understanding of the active motion related to the energy conversion and also a new control mechanism for nano-robots. We also investigate the noise effect, especially on the stepping motion and observe the random walk-like behavior as expected.