2022/02/22 by Ahmed Roman, Roman, Ahmed, Ruomin Zhu +3 · 2 citations
Earth and Planetary Sciences · Materials Science · Mathematics · Physics and Astronomy · #Cellular Automata and Lattice Gases (nlin.CG) #Condensed matter physics #Critical exponent #Dynamic scaling #Exponent #FOS: Physical sciences #Geometry #Lattice (music) #Material Dynamics and Properties #Mathematical physics #Mathematics #Pattern Formation and Solitons (nlin.PS) #Physics #Renormalization group #Scaling #Scaling law #Statistical physics #Theoretical and Computational Physics #Universality (dynamical systems) #nanoparticles nucleation surface interactions #nlin.CG #nlin.PS
paper · pdf · doi:10.48550/arxiv.2202.11224
published in arXiv (Cornell University) (Cornell University)
arxiv created 2022/02/22 · openalex publication_date 2022/02/22 · arxiv updated 2022/02/24 · openalex created_date 2022/04/03 · openalex updated_date 2026/08/06
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.