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Minimizing the profligacy of searches with reset
John C Sunil1, Richard A Blythe1, Martin R Evans1
1School of Physics and Astronomy, <a href="https://ror.org/01nrxwf90">University of Edinburgh</a>, Peter Guthrie Tait Road, Edinburgh EH9 3FD, Scotland, United Kingdom.
Physical Review. E
|December 18, 2024
Summary
We introduce search profligacy, balancing cost versus success probability. Optimal search strategies, particularly with stochastic resetting, reveal complex, non-intuitive parameter dependencies for efficient target finding.
Area of Science:
- Physics
- Statistical Mechanics
- Physical Chemistry
Background:
- Search processes are fundamental in nature and technology.
- Quantifying search efficiency is crucial for optimization.
- Stochastic resetting introduces a mechanism to influence search dynamics.
Purpose of the Study:
- To define and analyze "search profligacy" as a metric for search efficiency.
- To determine optimal search strategies under resetting conditions.
- To investigate the phase transitions associated with optimal resetting parameters.
Main Methods:
- Formulation of search profligacy as a cost-probability competition.
- Minimization of profligacy to derive optimal search strategies.
- Analysis of diffusion with stochastic resetting and its parameter dependence.
Main Results:
- Optimal resetting amount exhibits complex, non-trivial dependence on model parameters.
- Observed classical continuous and discontinuous phase transitions.
- Identified tricritical points and nonstandard transitions like reentrant behavior and overhangs.
Conclusions:
- Search profligacy provides a framework for optimizing search processes.
- Stochastic resetting introduces rich phase diagram behavior in optimal search.
- The study reveals novel transition phenomena in optimized diffusion processes.
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