Velocity jump process with volume exclusions in a narrow channel

Area of Science:

• Physics
• Statistical Mechanics
• Transport Phenomena

Background:

• Particle collisions and interactions are fundamental in many physical systems.
• Understanding collective behavior in confined spaces is crucial for various scientific disciplines.
• Existing models often simplify interactions or spatial constraints.

Purpose of the Study:

• To analyze the impact of collisions in a system of N identical hard-core particles.
• To derive a nonlinear transport equation from a particle-level model.
• To investigate the effects of volume exclusion and channel confinement on particle motility.

Main Methods:

• Utilizing a velocity jump process for particle dynamics.
• Employing asymptotic expansion to derive a macroscopic transport equation.
• Comparing numerical solutions of the kinetic model with a stochastic particle system.

Main Results:

• The derived nonlinear transport equation accurately describes the system under low-occupied fractions.
• Numerical simulations show good agreement between the kinetic model and particle system for biased and unbiased velocity changes.
• Analysis reveals how volume exclusions and channel confinements significantly impact traveling speeds.

Conclusions:

• The study successfully models particle interactions and transport in a confined channel.
• The derived transport equation provides a valuable tool for understanding collective particle dynamics.
• Findings highlight the critical role of physical constraints and particle interactions in determining system behavior.