Active search for a reactive target in thermal environments.

Area of Science:

• Statistical physics
• Active matter physics
• Biophysics

Background:

• Active particles exhibit complex behaviors in thermal environments.
• Understanding search strategies is crucial in various physical and biological systems.
• Run-and-tumble particles are a common model for active matter.

Purpose of the Study:

• To analytically determine the mean searching time (MST) for a run-and-tumble particle.
• To identify optimal self-propulsion velocities that minimize MST.
• To investigate the influence of diffusion and target absorption strength on search efficiency.

Main Methods:

• Solving the Fokker-Planck equation for a uniform initial distribution.
• Analytical calculation of mean searching time.
• Application of the Landau approach to analyze phase transitions.

Main Results:

• An optimal self-propulsion velocity exists that minimizes MST.
• High diffusion constants favor purely diffusive Brownian motion over active motion.
• Phase diagrams reveal distinct passive-efficient and active-efficient regions.
• Transition of optimal velocity can be continuous or discontinuous based on absorption strength.

Conclusions:

• The study provides a comprehensive analysis of active particle search strategies.
• Optimal search dynamics depend on particle activity, diffusion, and target properties.
• The findings offer insights into efficient search mechanisms in complex environments.