On the Tomography of Networks and Multicast Trees

In this paper we model the tomography of scale free networks by studying the structure of layers around an arbitrary network node. We find, both analytically and empirically, that the distance distribution of all nodes from a specific network node consists of two regimes. The first is characterized by rapid growth, and the second decays exponentially. We also show that the nodes degree distribution at each layer is a power law with an exponential cut-off. We obtain similar results for the layers surrounding the root of multicast trees cut from such networks, as well as the Internet. All of our results were obtained both analytically and on empirical Interenet data

Meissner response of a bulk superconductor with an embedded sheet of reduced penetration depth

We calculate the change in susceptibility resulting from a thin sheet with reduced penetration depth embedded perpendicular to the surface of an isotropic superconductor, in a geometry applicable to scanning Superconducting QUantum Interference Device (SQUID) microscopy, by numerically solving Maxwell's and London's equations using the finite element method. The predicted stripes in susceptibility agree well in shape with the observations of Kalisky et al. of enhanced susceptibility above twin planes in the underdoped pnictide superconductor Ba(Fe1-xCox)2As2 (Ba-122). By comparing the predicted stripe amplitudes with experiment and using the London relation between penetration depth and superfluid density, we estimate the enhanced Cooper pair density on the twin planes, and the barrier force for a vortex to cross a twin plane. Fits to the observed temperature dependence of the stripe amplitude suggest that the twin planes have a higher critical temperature than the bulk, although stripes are not observed above the bulk critical temperature.Comment: 16 pages, 9 figure

Photoinduced nucleation of carbon disulfide

The action of light on undersaturated and supersaturated vapors of carbon disulfide has been investigated using a batch photochemical reactor and a thermal diffusion cloud chamber, respectively. Photoinduced nucleation was observed in each case. In the batch reactor enough sulfur was produced to nucleate and grow a sulfur aerosol. A model for the photoinduced nucleation of supersaturated carbon disulfide is proposed based upon the photochemical production and subsequent nucleation of sulfur. The model predictions compare well with observed nucleation delay time and nucleation rate data. A variation of the model utilizing diradical polymerization instead of nucleation is used to explain photoinduced nucleation results in the literature involving dilute solutions of carbon disulfide in supersaturated ethanol vapor

Localization transition on complex networks via spectral statistics

The spectral statistics of complex networks are numerically studied. The features of the Anderson metal-insulator transition are found to be similar for a wide range of different networks. A metal-insulator transition as a function of the disorder can be observed for different classes of complex networks for which the average connectivity is small. The critical index of the transition corresponds to the mean field expectation. When the connectivity is higher, the amount of disorder needed to reach a certain degree of localization is proportional to the average connectivity, though a precise transition cannot be identified. The absence of a clear transition at high connectivity is probably due to the very compact structure of the highly connected networks, resulting in a small diameter even for a large number of sites.Comment: 6 pages, expanded introduction and referencess (to appear in PRE

Appropriateness of correlated first order auto-regressive processes for modeling daily temperature records

The present study investigates linear and volatile (nonlinear) correlations of first-order autoregressive process with uncorrelated AR (1) and long-range correlated CAR (1) Gaussian innovations as a function of the process parameter ($\theta$). In the light of recent findings \cite{jano}, we discuss the choice of CAR (1) in modeling daily temperature records. We demonstrate that while CAR (1) is able to capture linear correlations it is unable to capture nonlinear (volatile) correlations in daily temperature records.Comment: Accepted for publication in Physica