Random Search Walks Inside Absorbing Annuli
We revisit the problem of random search walks in the two-dimensional (2D) space between concentric absorbing annuli, in which a searcher performs random steps until finding either the inner or the outer ring. By considering step lengths drawn from a power-law distribution, we obtain the exact analyt...
Saved in:
| Main Authors: | , , , , |
|---|---|
| Format: | Article |
| Language: | English |
| Published: |
MDPI AG
2025-07-01
|
| Series: | Entropy |
| Subjects: | |
| Online Access: | https://www.mdpi.com/1099-4300/27/7/758 |
| Tags: |
Add Tag
No Tags, Be the first to tag this record!
|
| _version_ | 1849246592711786496 |
|---|---|
| author | Anderson S. Bibiano-Filho Jandson F. O. de Freitas Marcos G. E. da Luz Gandhimohan M. Viswanathan Ernesto P. Raposo |
| author_facet | Anderson S. Bibiano-Filho Jandson F. O. de Freitas Marcos G. E. da Luz Gandhimohan M. Viswanathan Ernesto P. Raposo |
| author_sort | Anderson S. Bibiano-Filho |
| collection | DOAJ |
| description | We revisit the problem of random search walks in the two-dimensional (2D) space between concentric absorbing annuli, in which a searcher performs random steps until finding either the inner or the outer ring. By considering step lengths drawn from a power-law distribution, we obtain the exact analytical result for the search efficiency <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mi>η</mi></semantics></math></inline-formula> in the ballistic limit, as well as an approximate expression for <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mi>η</mi></semantics></math></inline-formula> in the regime of searches starting far away from both rings, and the scaling behavior of <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mi>η</mi></semantics></math></inline-formula> for very small initial distances to the inner ring. Our numerical results show good overall agreement with the theoretical findings. We also analyze numerically the absorbing probabilities related to the encounter of the inner and outer rings and the associated Shannon entropy. The power-law exponent marking the crossing of such probabilities (equiprobability) and the maximum entropy condition grows logarithmically with the starting distance. Random search walks inside absorbing annuli are relevant, since they represent a mean-field approach to conventional random searches in 2D, which is still an open problem with important applications in various fields. |
| format | Article |
| id | doaj-art-d6b3edf16bc44fbbbe917dba627f806b |
| institution | Kabale University |
| issn | 1099-4300 |
| language | English |
| publishDate | 2025-07-01 |
| publisher | MDPI AG |
| record_format | Article |
| series | Entropy |
| spelling | doaj-art-d6b3edf16bc44fbbbe917dba627f806b2025-08-20T03:58:26ZengMDPI AGEntropy1099-43002025-07-0127775810.3390/e27070758Random Search Walks Inside Absorbing AnnuliAnderson S. Bibiano-Filho0Jandson F. O. de Freitas1Marcos G. E. da Luz2Gandhimohan M. Viswanathan3Ernesto P. Raposo4Laboratório de Física Teórica e Computacional, Departamento de Física, Universidade Federal de Pernambuco, Recife 50670-901, PE, BrazilDepartamento de Física, Universidade Federal de Viçosa, Viçosa 36570-900, MG, BrazilDepartamento de Física, Universidade Federal do Paraná, Curitiba 81531-980, PR, BrazilDepartment of Physics and National Institute of Science and Technology of Complex Systems, Federal University of Rio Grande do Norte, Natal 59078-970, RN, BrazilLaboratório de Física Teórica e Computacional, Departamento de Física, Universidade Federal de Pernambuco, Recife 50670-901, PE, BrazilWe revisit the problem of random search walks in the two-dimensional (2D) space between concentric absorbing annuli, in which a searcher performs random steps until finding either the inner or the outer ring. By considering step lengths drawn from a power-law distribution, we obtain the exact analytical result for the search efficiency <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mi>η</mi></semantics></math></inline-formula> in the ballistic limit, as well as an approximate expression for <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mi>η</mi></semantics></math></inline-formula> in the regime of searches starting far away from both rings, and the scaling behavior of <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mi>η</mi></semantics></math></inline-formula> for very small initial distances to the inner ring. Our numerical results show good overall agreement with the theoretical findings. We also analyze numerically the absorbing probabilities related to the encounter of the inner and outer rings and the associated Shannon entropy. The power-law exponent marking the crossing of such probabilities (equiprobability) and the maximum entropy condition grows logarithmically with the starting distance. Random search walks inside absorbing annuli are relevant, since they represent a mean-field approach to conventional random searches in 2D, which is still an open problem with important applications in various fields.https://www.mdpi.com/1099-4300/27/7/758random searchLévy walksphysics of foraging |
| spellingShingle | Anderson S. Bibiano-Filho Jandson F. O. de Freitas Marcos G. E. da Luz Gandhimohan M. Viswanathan Ernesto P. Raposo Random Search Walks Inside Absorbing Annuli Entropy random search Lévy walks physics of foraging |
| title | Random Search Walks Inside Absorbing Annuli |
| title_full | Random Search Walks Inside Absorbing Annuli |
| title_fullStr | Random Search Walks Inside Absorbing Annuli |
| title_full_unstemmed | Random Search Walks Inside Absorbing Annuli |
| title_short | Random Search Walks Inside Absorbing Annuli |
| title_sort | random search walks inside absorbing annuli |
| topic | random search Lévy walks physics of foraging |
| url | https://www.mdpi.com/1099-4300/27/7/758 |
| work_keys_str_mv | AT andersonsbibianofilho randomsearchwalksinsideabsorbingannuli AT jandsonfodefreitas randomsearchwalksinsideabsorbingannuli AT marcosgedaluz randomsearchwalksinsideabsorbingannuli AT gandhimohanmviswanathan randomsearchwalksinsideabsorbingannuli AT ernestopraposo randomsearchwalksinsideabsorbingannuli |