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Related Experiment Video

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Visually Based Characterization of the Incipient Particle Motion in Regular Substrates: From Laminar to Turbulent Conditions

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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.

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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.