We use the BBGKY hierarchy equations to calculate, perturbatively, the lowest order nonlinear correction to the two point correlation and the pair velocity for Gaussian initial conditions in a critical density matter dominated cosmological model. We compare our results with the results obtained using the hydrodynamic equations which neglect pressure and we nd that the two match, indicating that...

We investigate correlation functions in a periodic box-ball system. For the second and the third nearest neighbor correlation functions, we give explicit formulae obtained by combinatorial methods. A recursion formula for a specific N -point functions is also presented.

We consider a situation where the density and peculiar velocities in real space are linear, and we calculate ξs the two-point correlation function in redshift space, incorporating all non-linear effects which arise as a consequence of the map from real to redshift space. Our result is non-perturbative and it includes the effects of possible multi-streaming in redshift space. We find that the de...

Rich clusters of galaxies are observed to be strongly correlated at distances where the correlations of individual galaxies appear to be negligible. ' For example, the two-point correlation function for Abell clusters (richness R & 1) is unity at about 25k ' Mpc, where h is the Hubble constant and Mpc denotes megaparsecs, while the two-point correlation function for galaxies is unity at about 5...

Heterogeneous materials abound in nature and man-made situations. Examples include porous media, biological materials, and composite materials. Diverse and interesting properties exhibited by these materials result from their complex microstructures, which also make it difficult to model the materials. Yeong and Torquato [Phys. Rev. E 57, 495 (1998)] introduced a stochastic optimization techniq...

The Two-Point Angular Correlation Function is a standard analysis tool used to study angular anisotropies. Since BATSE’s sky exposure (the angular sampling of gamma-ray bursts) is anisotropic, the TPACF should at some point identify anisotropies in BATSE burst catalogs due to sky exposure. The effects of BATSE sky exposure are thus explored here for BATSE 3B and 4B catalogs. Sky-exposure effect...

In this paper, we prove a general theorem dealing with |C,α ,γ ,β ;σ |k summability factors by using a general class of power increasing sequences instead of an almost increasing sequence. This theorem also includes several known and new results.