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Published on: February 22, 2018
Ballistic deposition patterns beneath a growing Kardar-Parisi-Zhang interface
Konstantin Khanin1, Sergei Nechaev, Gleb Oshanin
1Department of Mathematics, University of Toronto, 100 St. George Street, Toronto, Ontario, Canada.
Physical Review. E, Statistical, Nonlinear, and Soft Matter Physics
|January 15, 2011
Summary
This study analyzes ballistic deposition, revealing how cluster density decreases with height. It connects this to Burgers turbulence, finding a power-law relationship and superdiffusive interfaces.
Area of Science:
- Statistical Physics
- Surface Growth Phenomena
- Complex Systems
Background:
- Ballistic deposition models growth processes.
- The Kardar-Parisi-Zhang (KPZ) universality class describes dynamic scaling in many systems.
- Understanding bulk structures in growing aggregates is crucial.
Purpose of the Study:
- To analyze the bulk structures in a (1+1)-dimensional ballistic deposition process.
- To investigate the relationship between clusters, crevices, and Burgers turbulence.
- To determine scaling laws for cluster density, interface fluctuations, and cluster sizes.
Main Methods:
- Utilizing a variational formulation for the discrete stochastic equation.
- Drawing parallels with randomly forced continuous Burgers equation analysis.
- Introducing and numerically analyzing the 'hairy' Airy process.
Main Results:
- Identified clusters and crevices as minimizers and shocks in Burgers turbulence.
- Found cluster density c(h) follows c(h) ~ h^(-2/3).
- Determined superdiffusive intercluster interfaces with an exponent twice the KPZ surface exponent.
Conclusions:
- The (1+1)-dimensional ballistic deposition process exhibits distinct bulk structures governed by competition.
- The connection to Burgers turbulence provides a powerful analytical framework.
- New scaling laws and the 'hairy' Airy process offer insights into complex growth dynamics.
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