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Dissipative Lévy random searches: universal behavior at low target density.

P J Ribeiro-Neto¹, E P Raposo, H A Araújo

¹Laboratório de Física Teórica e Computacional, Departamento de Física, Universidade Federal de Pernambuco, 50670-901 Recife-PE, Brazil.

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

|February 2, 2013

Summary

This study explores survival in low target-density scenarios, revealing a second-order phase transition in one-dimensional random searches. Surprisingly, critical exponents are identical across various energy cost functions, indicating a single universality class.

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Area of Science:

Statistical Physics
Theoretical Ecology
Mathematical Biology

Background:

Survival probability is crucial in ecological and biological systems.
Understanding random search dynamics is key to predicting organism movement and resource acquisition.
The impact of locomotion costs on search efficiency is an ongoing area of research.

Purpose of the Study:

To investigate survival probabilities in the low target-density limit.
To identify and characterize phase transitions in one-dimensional random search processes.
To determine the universality of critical exponents associated with locomotion energy costs.

Main Methods:

Analytical calculations were employed to model the random search process.
Numerical simulations were conducted to validate the analytical findings.
The study focused on scenarios where energy cost is a function of distance traveled.

Main Results:

A second-order phase transition was identified in the one-dimensional random search.
Identical critical exponents were found for a range of arbitrary energy cost functions.
This suggests a robust universality class governing the search process.

Conclusions:

The findings reveal a universal behavior in one-dimensional random searches, irrespective of specific energy cost functions.
This universality simplifies the understanding of survival dynamics in sparse environments.
The identified universality class has implications for modeling various biological and physical search processes.