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Effect of partial absorption on diffusion with resetting.

Justin Whitehouse¹, Martin R Evans, Satya N Majumdar

¹SUPA, School of Physics and Astronomy, University of Edinburgh, Mayfield Road, Edinburgh EH9 3JZ, United Kingdom.

Physical Review. E, Statistical, Nonlinear, and Soft Matter Physics

|March 19, 2013

Summary

This summary is machine-generated.

Partial absorption affects diffusive particle searchers. Mean absorption time increases, and survival probability is modified by target absorption properties, impacting search efficiency.

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Area of Science:

Statistical Physics
Stochastic Processes
Mathematical Biology

Background:

Diffusive particle motion is fundamental in many physical and biological systems.
First-passage time problems analyze the time taken for a process to reach a certain state.
Partial absorption at a target influences the dynamics of diffusive searchers.

Purpose of the Study:

To investigate the impact of partial absorption on a stochastically resetting diffusive particle.
To analyze how target absorption properties affect mean absorption time and survival probabilities.
To extend these findings to multiparticle systems searching for a single target.

Main Methods:

Modeling a diffusive particle with stochastic position resetting and finite absorption rate.
Analyzing first-passage time properties, specifically the mean time to absorption (MTA).
Extending the model to multiparticle systems with uniform initial distribution and calculating average and typical survival probabilities.

Main Results:

The mean time to absorption (MTA) is increased by a term proportional to the inverse of the absorption velocity (1/a).
Average survival probability is modified by a multiplicative factor dependent on 1/a.
The decay rate of typical survival probability is decreased by an additive term proportional to 1/a.

Conclusions:

Partial absorption significantly alters the dynamics of diffusive searchers, increasing search times.
The degree of target absorption (characterized by 'a') critically influences search efficiency in both single and multiparticle systems.
These findings have implications for understanding search strategies in biological and physical contexts.