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The large-scale structure of the universe and quasi-Voronoi tessellation of shock fronts in forced Burgers turbulence in \(\mathbb{R}^d\). (English) Zbl 0895.60066

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 \(\mathbb{R}^d\) 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.

MSC:

60H15 Stochastic partial differential equations (aspects of stochastic analysis)
60G60 Random fields
60K40 Other physical applications of random processes
70K40 Forced motions for nonlinear problems in mechanics
76L05 Shock waves and blast waves in fluid mechanics
83F05 Relativistic cosmology
35Q53 KdV equations (Korteweg-de Vries equations)
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