Optimal Random Deposition of Interacting Particles

Adrian Baule
Phys. Rev. Lett. 122, 130602 – Published 5 April 2019
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Abstract

Irreversible random sequential deposition of interacting particles is widely used to model aggregation phenomena in physical, chemical, and biophysical systems. We show that in one dimension the exact time-dependent solution of such processes can be found for arbitrary interaction potentials with finite range. The exact solution allows us to rigorously prove characteristic features of the deposition kinetics, which have previously only been accessible by simulations. We show in particular that a unique interaction potential exists that leads to a maximally dense line coverage for a given interaction range. Remarkably, this potential is singular and can only be expressed as a mathematical limit. The relevance of these results for models of nucleosome packing on DNA is discussed. The results highlight how the generation of an optimally dense packing requires a highly coordinated packing dynamics, which can be effectively tuned by the interaction potential even in the presence of intrinsic randomness.

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  • Received 28 June 2018
  • Revised 7 February 2019

DOI:https://doi.org/10.1103/PhysRevLett.122.130602

© 2019 American Physical Society

Physics Subject Headings (PhySH)

Statistical Physics & Thermodynamics

Authors & Affiliations

Adrian Baule*

  • School of Mathematical Sciences, Queen Mary University of London, London E1 4NS, United Kingdom

  • *a.baule@qmul.ac.uk

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Issue

Vol. 122, Iss. 13 — 5 April 2019

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