Ballistic deposition patterns beneath a growing KPZ interface

Details Ballistic deposition patterns beneath a growing KPZ interface Ballistic deposition patterns beneath a growing KPZ interface

2010-06-23

arxiv.org/abs/1006.4576v2

Phys. Rev. E 82, 061107 (2010)

Physics

Condensed Matter

Statistical Mechanics

10 pages, 5 figures. Minor edits: typo corrected, added explanation of two acronyms. The text is essentially equivalent to ver

Scientific paper

10.1103/PhysRevE.82.061107

We consider a (1+1)-dimensional ballistic deposition process with next-nearest neighbor interaction, which belongs to the KPZ universality class, and introduce for this discrete model a variational formulation similar to that for the randomly forced continuous Burgers equation. This allows to identify the characteristic structures in the bulk of a growing aggregate ("clusters" and "crevices") with minimizers and shocks in the Burgers turbulence, and to introduce a new kind of equipped Airy process for ballistic growth. We dub it the "hairy Airy process" and investigate its statistics numerically. We also identify scaling laws that characterize the ballistic deposition patterns in the bulk: the law of "thinning" of the forest of clusters with increasing height, the law of transversal fluctuations of cluster boundaries, and the size distribution of clusters. The corresponding critical exponents are determined exactly based on the analogy with the Burgers turbulence and simple scaling considerations.

Affiliated with

Also associated with

No associations

Rating

Ballistic deposition patterns beneath a growing KPZ interface does not yet have a rating. At this time, there are no reviews or comments for this scientific paper.

If you have personal experience with Ballistic deposition patterns beneath a growing KPZ interface, we encourage you to share that experience with our LandOfFree.com community. Your opinion is very important and Ballistic deposition patterns beneath a growing KPZ interface will most certainly appreciate the feedback.

Rate now

Comments { 0 }

Profile ID: LFWR-SCP-O-278288