Optics and Vision

Fry, Glenn A.

doi:10.1007/978-3-642-69425-7_9

Cited by 2 publications

(2 citation statements)

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“…(196), and ǫ ikl is the Levi-Civita tensor. Equation (199) is the condition for potential motion in Eulerian space [579]. The resulting density and velocity fields can be determined from…”

Section: Lagrangian Perturbation Theorymentioning

confidence: 99%

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Approximation methods for non-linear gravitational clustering

1995

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We discuss various analytical approximation methods for following the evolution of cosmological density perturbations into the strong (i.e. nonlinear) clustering regime. We start by giving a thorough treatment of linear gravitational instability in cosmological models and discussing the statistics of primordial density fluctuations produced in various scenarios of structure formation, and the role of non-baryonic dark matter. We critically review various methods for dealing with the non-linear evolution of density inhomogeneities, in the context of theories of the formation of galaxies and large-scale structure. These methods can be classified into five types: (i) simple extrapolations from linear theory, such as the high-peak model and the lognormal model; (ii) dynamical approximations, including the Zel'dovich approximation and its extensions; (iii) non-linear models based on purely geometric considerations, of which the main example is the Voronoi model; (iv) statistical solutions involving scaling arguments, such as the hierarchical closure ansatz for BBGKY, fractal models and the thermodynamic model of Saslaw; (v) numerical techniques based on particles and/or hydrodynamics. We compare the results of full dynamical evolution using particle codes and the various other approximation schemes. To put the models we discuss into perspective, we give a brief review of the observed properties of galaxy clustering and the statistical methods used to quantify it, such as correlation functions, power spectra, topology and spanning trees.

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“…(196), and ǫ ikl is the Levi-Civita tensor. Equation (199) is the condition for potential motion in Eulerian space [579]. The resulting density and velocity fields can be determined from…”

Section: Lagrangian Perturbation Theorymentioning

confidence: 99%

“…In the weakly nonlinear regime, equations (198) & (199) can be solved by expanding Ψ in a series Ψ = Ψ (1) + Ψ (2) +..; higher orders in Ψ (n) (n > 1) being related to lower orders via an iterative procedure [401,92,329]. In a spatially flat matter dominated Universe Ψ (n) are separable at every perturbative order…”

Section: Lagrangian Perturbation Theorymentioning

confidence: 99%