Universal power laws in two-dimensional diffusive search for randomly distributed targets
We consider a two-dimensional diffusional search of randomly distributed targets characterized by their density and size. We derive analytical expressions for the binding rates averaged over ensembles of randomly distributed targets and initial positions of the searcher and test them through direct...
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| Main Authors: | , , |
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| Format: | Article |
| Language: | English |
| Published: |
American Physical Society
2025-01-01
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| Series: | Physical Review Research |
| Online Access: | http://doi.org/10.1103/PhysRevResearch.7.L012005 |
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| Summary: | We consider a two-dimensional diffusional search of randomly distributed targets characterized by their density and size. We derive analytical expressions for the binding rates averaged over ensembles of randomly distributed targets and initial positions of the searcher and test them through direct numerical simulations. These results suggest that the binding rates follow power laws over a wide range of target densities, with an exponent of about 1.1 for low densities and an exponent of 3/2 for larger densities. The transition between the two power laws depends on the size of the targets and searchers. We further predict linear dependence of the binding rate on the size of searchers and targets for small target densities. |
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| ISSN: | 2643-1564 |