The accuracy of parameters determined with the core-sampling method: application to Voronoi tessellations

The large-scale matter distribution represents a complex network of structure elements such as voids, clusters, filaments, and sheets. This network is spanned by a point distribution. The global properties of the point process can be measured by different statistical methods, which, however, do not describe directly the structure elements. The morphology of structure elements is an important property of the point distribution. Here we apply the core-sampling method to various Voronoi tessellations. Using the core-sampling method we identify one- and two-dimensional structure elements (filaments and sheets) in these Voronoi tessellations and reconstruct their mean separation along random straight lines. We compare the results of the core-sampling method with the a priori known structure elements of the Voronoi tessellations under consideration and find good agreement between the expected and found structure parameters, even in the presence of substantial noise. We conclude that the core-sampling method is a potentially powerful tool to investigate the distribution of such structure elements like filaments and walls of galaxies.Comment: 14 pages (Latex) with 6 figures, the complete paper with 8 figures is available at http://kosmos.aip.de/~got/projects.html {Characteristical scales in point distributions}, Astronomy and Astrophysics Supplement Series, accepte

The Cross Correlation between the Gravitational Potential and the Large Scale Matter Distribution

The large scale gravitational potential distribution and its influence on the large-scale matter clustering is considered on the basis of six simulations. It is found that the mean separation between zero levels of the potential along random straight lines coincides with the theoretical expectations, but it scatters largely. A strong link of the initial potential and the structure evolution is shown. It is found that the under-dense and over-dense regions correlate with regions of positive and negative gravitational potential at large redshifts. The over-dense regions arise due to a slow matter flow into the negative potential regions, where more pronounced non-linear structures appear. Such regions are related to the formation of huge super-large scale structures seen in the galaxy distribution.Comment: 14 pages LaTeX with 14 postscript figures included. To be publishes in Astron. Astroph. (accepted 17 July 1997

The Gauss-Legendre Sky Pixelization for the CMB polarization (GLESP-pol). Errors due to pixelization of the CMB sky

We present developing of method of the numerical analysis of polarization in the Gauss--Legendre Sky Pixelization (GLESP) scheme for the CMB maps. This incorporation of the polarization transforms in the pixelization scheme GLESP completes the creation of our new method for the numerical analysis of CMB maps. The comparison of GLESP and HEALPix calculations is done.Comment: 23 pages, 12 figure

Small-Scale Cosmic Microwave Background Fluctuations as a Probe of the Mass of Dark Matter Particles

The CMB anisotropy on arc second range is examined to test the power spectrum of perturbations in the small scale region and, in particular, to estimate the mass of dominant dark matter particles. It is shown that for the simplest evolutionary history with standard recombination, three and four beam observations could discriminate the mass of dark matter particles in the interval $0.5 KeV\leq M_{DM}\leq 4 KeV$ with an antenna beam (0.5 - 0.25) arc minute with amplitude $\approx 10^{-7}$.Comment: 29 page

The accuracy of parameters determined with the core-sampling method: application to Voronoi tessellations

. The large-scale matter distribution represents a complex network of structure elements such as voids, clusters, filaments, and sheets. This network is spanned by a point distribution. The global properties of the point process can be measured by different statistical methods, which, however, do not describe directly the structure elements. The morphology of structure elements is an important property of the point distribution. Here we apply the core-sampling method to various Voronoi tessellations. Using the core-sampling method we identify oneand two-dimensional structure elements (filaments and sheets) in these Voronoi tessellations and reconstruct their mean separation along random straight lines. We compare the results of the core-sampling method with the a priori known structure elements of the Voronoi tessellations under consideration and find good agreement between the expected and found structure parameters, even in the presence of substantial noise. We conclude that the cor..

The Cross Correlation between the Gravitational Potential and the Large Scale Matter Distribution

The large scale gravitational potential distribution and its influence on the large--scale matter clustering is considered on the basis of six simulations. It is found that the mean separation between zero levels of the potential along random straight lines coincides with the theoretical expectations, but it scatters largely. A strong link of the initial potential and the structure evolution is shown. It is found that the under--dense and over--dense regions correlate with regions of positive and negative gravitational potential at large redshifts. The over--dense regions arise due to a slow matter flow into the negative potential regions, where more pronounced non--linear structures appear. Such regions are related to the formation of huge super-large scale structures seen in the galaxy distribution. Key words: cosmology --- large scale structure --- structure formation 1