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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.
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.
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