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  • Letter
  • Open Access

Universal power laws in two-dimensional diffusive search for randomly distributed targets

Rawan M. Nowier*, Nilaj Chakrabarty, and Peter Jung

  • Department of Physics and Astronomy and Quantitative Biology Institute, Ohio University, Athens, Ohio 45701, USA

  • *Contact author: rn757120@ohio.edu
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Phys. Rev. Research 7, L012005 – Published 8 January, 2025

DOI: https://doi.org/10.1103/PhysRevResearch.7.L012005

Abstract

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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Phys. Rev. Research 7, L012005– Published 8 January, 2025
  • Received 22 April 2024
  • Accepted 5 November 2024
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Published by the American Physical Society under the terms of the Creative Commons Attribution 4.0 International license. Further distribution of this work must maintain attribution to the author(s) and the published article's title, journal citation, and DOI.

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