Capture of a diffusive prey by multiple predators in confined space

Area of Science:

• Stochastic processes
• Mathematical physics
• Statistical mechanics

Background:

• The first passage time problem is crucial in stochastic processes.
• Previous research focused on open spaces, leaving confined systems understudied.
• Understanding target capture dynamics in confinement is essential for various scientific fields.

Purpose of the Study:

• To systematically study first passage times of diffusing targets captured by multiple searchers in confined environments.
• To analyze the characteristic capture timescale (τ) and its dependence on system parameters.
• To investigate the impact of confinement on target survival probability.

Main Methods:

• Development and application of a computational algorithm for accurate estimation of capture timescales (τ).
• Analysis of first passage times in one, two, and three spatial dimensions.
• Systematic investigation of τ as a function of the number of searchers (N), relative diffusivity (r), and system size.

Main Results:

• Target survival probability in confinement exhibits exponential decay at large times (∼e^{-t/τ}).
• The characteristic capture timescale (τ) was accurately estimated using the developed computational algorithm.
• τ deviates from the 1/N scaling observed for static targets, with variations dependent on relative diffusivity (r) and spatial dimensions.

Conclusions:

• Confinement significantly alters target capture dynamics compared to open spaces.
• The developed computational method provides accurate estimates for challenging capture timescale measurements.
• The study reveals complex scaling behaviors of capture times in multi-searcher, confined diffusion systems.