Velocity statistics from spectral line data: effects of density-velocity correlations, magnetic field, and shear

In a previous work Lazarian and Pogosyan suggested a technique to extract velocity and density statistics, of interstellar turbulence, by means of analysing statistics of spectral line data cubes. In this paper we test that technique, by studying the effect of correlation between velocity and density fields, providing a systematic analysis of the uncertainties arising from the numerics, and exploring the effect of a linear shear. We make use of both compressible MHD simulations and synthetic data to emulate spectroscopic observations and test the technique. With the same synthetic spectroscopic data, we also studied anisotropies of the two point statistics and related those anisotropies with the magnetic field direction. This presents a new technique for magnetic field studies. The results show that the velocity and density spectral indices measured are consistent with the analytical predictions. We identified the dominant source of error with the limited number of data points along a given line of sight. We decrease this type of noise by increasing the number of points and by introducing Gaussian smoothing. We argue that in real observations the number of emitting elements is essentially infinite and that source of noise vanishes.Comment: 12 pages, 10 figures. Accepted for publication in MNRA

Vacuum tunneling in gravity

Topologically non-trivial vacuum structure in gravity models with Cartan variables (vielbein and contortion) is considered. We study the possibility of vacuum space-time tunneling in Einstein gravity assuming that the vielbein may play a fundamental role in quantum gravitational phenomena. It has been shown that in the case of RP3 space topology the tunneling between non-trivial topological vacuums can be realized by means of Eguchi-Hanson gravitational instanton. In Riemann-Cartan geometric approach to quantum gravity the vacuum tunneling can be provided by means of contortion quantum fluctuations. We define double self-duality condition for the contortion and give explicit self-dual configurations which can contribute to vacuum tunneling amplitude.Comment: 11 pages, 1 fig. is added, final versio

Cho and Pak reply to Lamm et al. comment on "A Convergent Series for the QED Effective Action"

Cho and Pak reply to Lamm et al. [hep-th/0007108] comment on "A Convergent Series for the Effective Action of QED" [hep-th/0006057].Comment: 1 pag

Cluster aggregation model for discontinuous percolation transition

The evolution of the Erd\H{o}s-R\'enyi (ER) network by adding edges can be viewed as a cluster aggregation process. Such ER processes can be described by a rate equation for the evolution of the cluster-size distribution with the connection kernel $K_{ij}\sim ij$, where $ij$ is the product of the sizes of two merging clusters. Here, we study more general cases in which $K_{ij}$ is sub-linear as $K_{ij}\sim (ij)^{\omega}$ with $0 \le \omega < 1/2$; we find that the percolation transition (PT) is discontinuous. Moreover, PT is also discontinuous when the ER dynamics evolves from proper initial conditions. The rate equation approach for such discontinuous PTs enables us to uncover the mechanism underlying the explosive PT under the Achlioptas process.Comment: 5 pages, 5 figure