2025/11/05 by Patrick Valageas, Valageas, Patrick
Mathematics · Physics and Astronomy · #Cosmology and Nongalactic Astrophysics (astro-ph.CO) #FOS: Physical sciences #Fluid Dynamics (physics.flu-dyn) #Point processes and geometric inequalities #Random Matrices and Applications #Statistical Mechanics (cond-mat.stat-mech) #Statistical Mechanics and Entropy
paper · pdf · doi:10.48550/arxiv.2511.03647
openalex publication_date 2025/11/05 · openalex created_date 2025/11/07 · openalex updated_date 2026/07/28
We investigate the statistical properties of one-dimensional Burgers dynamics evolving from stochastic initial conditions defined by a Poisson point process for the velocity potential, with a power-law intensity. Thanks to the geometrical interpretation of the solution in the inviscid limit, in terms of first-contact parabolas, we obtain explicit results for the multiplicity functions of shocks and voids, and for velocity and density one- and two-point correlation functions and power spectra. These initial conditions gives rise to self-similar dynamics with probability distributions that display power-law tails. In the limit where the exponent α of the Poisson process that defines the initial conditions goes to infinity, the power-law tails steepen to Gaussian falloffs and we recover the spatial distributions obtained in the classical study by Kida (1979) of Gaussian initial conditions with vanishing large-scale power.