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  • Letter
  • Open Access

Ballistic deposition with memory: A new universality class of surface growth with a new scaling law

Ahmed Roman1, Ruomin Zhu2, and Ilya Nemenman1,3,4

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Phys. Rev. Research 6, L032053 – Published 5 September, 2024

DOI: https://doi.org/10.1103/PhysRevResearch.6.L032053

Abstract

Motivated by recent experimental studies in microbiology, we suggest modifying the classic ballistic deposition model of surface growth, where the memory of a deposition at a site induces more depositions at that site or its neighbors. By studying the statistics of surfaces in this model, we obtain three independent critical exponents: the growth exponent β=5/4, the roughening exponent α=2, and the new (size) exponent γ=1/2. The model requires modifying the Family-Vicsek scaling, resulting in the dynamical exponent z=α+γβ=2. This modified scaling collapses the surface width vs time curves for various lattice sizes. This previously unobserved universality class of surface growth could describe the surface properties of a wide range of natural systems.

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Phys. Rev. Research 6, L032053– Published 5 September, 2024
  • Received 7 March 2022
  • Revised 23 April 2024
  • Accepted 25 June 2024
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