Burgers dynamics for Poisson point process initial conditions
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arXiv
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| Format: | Preprint |
| Published: |
2025
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| _version_ | 1866917062858768384 |
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| author | Valageas, Patrick |
| author_facet | Valageas, Patrick |
| contents | 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. |
| format | Preprint |
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arxiv_https___arxiv_org_abs_2511_03647 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Burgers dynamics for Poisson point process initial conditions Valageas, Patrick Statistical Mechanics Cosmology and Nongalactic Astrophysics Fluid Dynamics 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. |
| title | Burgers dynamics for Poisson point process initial conditions |
| topic | Statistical Mechanics Cosmology and Nongalactic Astrophysics Fluid Dynamics |
| url | https://arxiv.org/abs/2511.03647 |