相关论文: Aspects of Scaling in Gravitational Clustering
The stable clustering hypothesis is a key analytical anchor on the nonlinear dynamics of gravitational clustering in cosmology. It states that on sufficiently small scales the mean pair velocity approaches zero, or equivalently, that the…
The power spectrum P(k)\propto k^n with n=-2 is close to the shape of the measured galaxy spectrum on small scales. Unfortunately this spectrum has proven rather difficult to simulate. Further, 2-dimensional simulations have suggested a…
Hamilton et al. (1991) proposed a simple formula relating the nonlinear autocorrelation function of the mass distribution to the primordial spectrum of density fluctuations for gravitational clustering in an $\Omega=1$ universe. High…
We study non-linear gravitational clustering from cold gaussian power-law initial conditions in a family of scale-free EdS models, characterized by a free parameter $\kappa$ fixing the ratio between the mass driving the expansion and the…
The nonlinear clustering of dark matter particles in an expanding universe is usually studied by N-body simulations. One can gain some insight into this complex problem if simple relations between physical quantities in the linear and…
An analytical understanding of the strongly nonlinear regime of gravitational collapse has been difficult to achieve. The only insight has been the stable clustering hypothesis, which assumes that the number of neighbors for objects…
We study clustering in a stochastic system of particles sliding down a fluctuating surface in one and two dimensions. In steady state, the density-density correlation function is a scaling function of separation and system size.This scaling…
We present the results of a large library of cosmological N-body simulations, using power-law initial spectra. The nonlinear evolution of the matter power spectra is compared with the predictions of existing analytic scaling formulae based…
The determination of the resolution of cosmological N-body simulations, i.e., the range of scales in which quantities measured in them represent accurately the continuum limit, is an important open question. We address it here using…
The stable clustering hypothesis is a fundamental assumption about the nonlinear clustering of matter in cosmology. It states that the mean physical separation of particles is a constant on sufficiently small scales. While many authors have…
We study gravitational clustering of mass points in three dimensions with random initial positions and periodic boundary conditions (no expansion) by numerical simulations. Correlation properties are well defined in the system and a sort of…
Two-dimensional cluster-cluster aggregation is studied when clusters move both diffusively and sediment with a size dependent velocity. Sedimentation breaks the rotational symmetry and the ensuing clusters are not self-similar fractals: the…
We measure the scaling properties of the probability distribution of the smoothed density field in $N$-body simulations of expanding universes with scale-free initial power-spectra, with particular attention to the predictions of the stable…
An extended polymer collapses to form a globule when subjected to a quench below the collapse transition temperature. The process begins with the formation of clusters of monomers or ``pearls''. The nascent clusters merge, resulting in…
Self-gravitating systems have acquired growing interest in statistical mechanics, due to the peculiarities of the 1/r potential. Indeed, the usual approach of statistical mechanics cannot be applied to a system of many point particles…
We present a continuation of an analysis that aims to quantify resolution of $N$-body simulations by exploiting large (up to $N=4096^3$) simulations of scale-free cosmologies run using Abacus. Here we focus on radial pairwise velocities of…
We show that a scaling approach successfully characterizes clustering and intermittency in space and time, in systems of noninteracting particles driven by fluctuating surfaces. We study both the steady state and the approach to it, for…
The potential is a constant to linear order in cosmological gravitational clustering. In this Letter we present results of testing the conjecture, proposed by Pauls and Melott (1995), that the effect of nonlinear evolution on the potential…
Spectral clustering refers to a family of unsupervised learning algorithms that compute a spectral embedding of the original data based on the eigenvectors of a similarity graph. This non-linear transformation of the data is both the key of…
The first objects to arise in a cold dark matter universe present a daunting challenge for models of structure formation. In the ultra small-scale limit, CDM structures form nearly simultaneously across a wide range of scales. Hierarchical…