Gravitational force in an infinite one-dimensional Poisson distribution

Autor: Andrea Gabrielli, Michael Joyce
Přispěvatelé: Gabrielli, A., Joyce, M., Laboratoire de Physique Nucléaire et de Hautes Énergies (LPNHE), Université Pierre et Marie Curie - Paris 6 (UPMC)-Institut National de Physique Nucléaire et de Physique des Particules du CNRS (IN2P3)-Université Paris Diderot - Paris 7 (UPD7)-Centre National de la Recherche Scientifique (CNRS)
Rok vydání: 2010
Předmět:
Distribution (number theory)
Other topics in statistical physics
[SDU.ASTR.CO]Sciences of the Universe [physics]/Astrophysics [astro-ph]/Cosmology and Extra-Galactic Astrophysics [astro-ph.CO]
FOS: Physical sciences
Numerical simulations of chaotic systems
Probability density function
Poisson distribution
01 natural sciences
010305 fluids & plasmas
Classical statistical mechanics
[PHYS.ASTR.CO]Physics [physics]/Astrophysics [astro-ph]/Cosmology and Extra-Galactic Astrophysics [astro-ph.CO]
Renormalization
thermodynamics
symbols.namesake
Gravitational field
0103 physical sciences
Zero-inflated model
Limit (mathematics)
[PHYS.COND.CM-SM]Physics [physics]/Condensed Matter [cond-mat]/Statistical Mechanics [cond-mat.stat-mech]
010306 general physics
Condensed Matter - Statistical Mechanics
Mathematics
Statistical Mechanics (cond-mat.stat-mech)
Mathematical analysis
16. Peace & justice
Exponential function
and nonlinear dynamical systems
symbols
Zdroj: Physical Review E : Statistical, Nonlinear, and Soft Matter Physics
Physical Review E : Statistical, Nonlinear, and Soft Matter Physics, American Physical Society, 2010, 81, pp.21102. ⟨10.1103/PHYSREVE.81.021102⟩
Physical Review E : Statistical, Nonlinear, and Soft Matter Physics, 2010, 81, pp.21102. ⟨10.1103/PHYSREVE.81.021102⟩
Physical review. E, Statistical, nonlinear, and soft matter physics
81 (2010): 021102. doi:10.1103/PhysRevE.81.021102
info:cnr-pdr/source/autori:A. Gabrielli (1,2); M. Joyce (3,4)/titolo:Gravitational force in an infinite one-dimensional Poisson distribution/doi:10.1103%2FPhysRevE.81.021102/rivista:Physical review. E, Statistical, nonlinear, and soft matter physics (Print)/anno:2010/pagina_da:021102/pagina_a:/intervallo_pagine:021102/volume:81
ISSN: 1550-2376
1539-3755
Popis: We consider the statistical properties of the gravitational field F in an infinite one-dimensional homogeneous Poisson distribution of particles, using an exponential cut-off of the pair interaction to control and study the divergences which arise. Deriving an exact analytic expression for the probability density function (PDF) P(F), we show that it is badly defined in the limit in which the well known Holtzmark distribution is obtained in the analogous three-dimensional case. A well defined P(F) may, however, be obtained in the infinite range limit by an appropriate renormalization of the coupling strength, giving a Gaussian form. Calculating the spatial correlation properties we show that this latter procedure has a trivial physical meaning. Finally we calculate the PDF and correlation properties of differences of forces (at separate spatial points), which are well defined without any renormalization. We explain that the convergence of these quantities is in fact sufficient to allow a physically meaningful infinite system limit to be defined for the clustering dynamics from Poissonian initial conditions.
9 pages, minor changes, final version published in Phys. Rev. E
Databáze: OpenAIRE
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