2022/02/22 by Roman, Ahmed, Zhu, Ruomin, Nemenman, Ilya
#Cellular Automata and Lattice Gases (nlin.CG) #FOS: Physical sciences #Pattern Formation and Solitons (nlin.PS)
paper · doi:10.48550/arxiv.2202.11224
Motivated by recent experimental studies in microbiology, we suggest a modification of 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 a modification to the Family-Vicsek scaling, resulting in the dynamical exponent z = \fracα+γβ = 2. This modified scaling collapses the surface width vs time curves for various lattice sizes. This is a previously unobserved universality class of surface growth that could describe surface properties of a wide range of natural systems.