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Structure of the active Fokker-Planck equation.
Pedro Herrera1, Mario Sandoval1
1Department of Physics, Complex Systems, Universidad Autonoma Metropolitana-Iztapalapa, Mexico City 09340, Mexico.
Physical Review. E
|February 17, 2024
Summary
This study on the active Fokker-Planck equation reveals dual velocity distribution behaviors: bimodal under specific conditions and Gaussian otherwise. These findings impact understanding of active matter transport properties.
Area of Science:
- Physics
- Statistical Mechanics
- Active Matter
Background:
- The active Fokker-Planck equation models systems with self-propelled particles.
- Understanding particle velocity distributions is crucial for predicting transport properties.
Purpose of the Study:
- To solve the steady noninteractive active Fokker-Planck equation in one and two dimensions.
- To analyze the resulting velocity distribution functions and their dependence on system parameters.
- To investigate the impact of these distributions on transport properties like mean-square speed.
Main Methods:
- Analytical solution of the steady noninteractive active Fokker-Planck equation.
- Analysis of limiting cases for velocity distribution functions.
- Calculation of transport properties based on derived velocity distributions.
Main Results:
- The velocity distribution exhibits a dual behavior: bimodal when inertial relaxation time is less than orientation time, and Gaussian in the inverse case.
- A novel mathematical identity involving Bessel functions of the first kind and bimodal exponential functions was discovered.
Conclusions:
- The active Fokker-Planck equation demonstrates rich emergent behavior in particle velocity distributions.
- The findings provide insights into the transport characteristics of active matter systems.
- The discovered mathematical identity may find applications in related theoretical frameworks.
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