The large-scale structure of the universe and quasi-Voronoi tessellation of shock fronts in forced Burgers turbulence in $\bold R\sp {d}

Burgers turbulence is an accepted formalism for the adhesion model of the large-scale distribution of matter in the universe. The paper uses variational methods to establish evolution of quasi-Voronoi (curved boundaries) tessellation structure of shock fronts for solutions of the inviscid nonhomogen...

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Bibliographic Details
Published in:The Annals of applied probability 1997-02, Vol.7 (1), p.200-228
Main Authors: Molchanov, S. A., Surgailis, D., Woyczynski, W. A.
Format: Article
Language:English
Subjects:
35Q53
60G60
60H15
60K40
70K40
76L05
83F05
Forced Burgers turbulence
large-scale structure of the Universe
quasi-Voronoi tessellations
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Summary:Burgers turbulence is an accepted formalism for the adhesion model of the large-scale distribution of matter in the universe. The paper uses variational methods to establish evolution of quasi-Voronoi (curved boundaries) tessellation structure of shock fronts for solutions of the inviscid nonhomogeneous Burgers equation in R^d in the presence of random forcing due to a degenerate potential. The mean rate of growth of the quasi-Voronoi cells is calculated and a scaled limit random tessellation structure is found. Time evolution of the probability that a cell contains a ball of a given radius is also determined.
ISSN:1050-5164
2168-8737
DOI:10.1214/aoap/1034625260