On the Scaling Property of Power Grids

Compared with other natural or man-made networks, electric power grid assumes distinct electric topology with special small-world properties and electrical parameter settings. In this paper we study the scaling property of power grid in terms of both topology measures and electric parameters, with a number of realistic power grid test cases of different size. The examined measures and parameters include average node degree, average path length, algebraic connectivity, the bus type entropy that characterize relative locations of generation and load buses, generation capacity, total demand, and transmission capacity. Interpreting and testing the scaling property of power grid will help us better understand the intrinsic characteristics of electric energy delivery network of this critical infrastructure; and enable the development of an appropriate synthetic modeling that could be utilized to generate power grid test cases with accurate grid topology and electric parameters

The Large Scale Curvature of Networks

Understanding key structural properties of large scale networks are crucial for analyzing and optimizing their performance, and improving their reliability and security. Here we show that these networks possess a previously unnoticed feature, global curvature, which we argue has a major impact on core congestion: the load at the core of a network with N nodes scales as N^2 as compared to N^1.5 for a flat network. We substantiate this claim through analysis of a collection of real data networks across the globe as measured and documented by previous researchers.Comment: 4 pages, 5 figure

Linear Scaling Solution of the Coulomb problem using wavelets

The Coulomb problem for continuous charge distributions is a central problem in physics. Powerful methods, that scale linearly with system size and that allow us to use different resolutions in different regions of space are therefore highly desirable. Using wavelet based Multi Resolution Analysis we derive for the first time a method which has these properties. The power and accuracy of the method is illustrated by applying it to the calculation of of the electrostatic potential of a full three-dimensional all-electron Uranium dimer

On Compact Routing for the Internet

While there exist compact routing schemes designed for grids, trees, and Internet-like topologies that offer routing tables of sizes that scale logarithmically with the network size, we demonstrate in this paper that in view of recent results in compact routing research, such logarithmic scaling on Internet-like topologies is fundamentally impossible in the presence of topology dynamics or topology-independent (flat) addressing. We use analytic arguments to show that the number of routing control messages per topology change cannot scale better than linearly on Internet-like topologies. We also employ simulations to confirm that logarithmic routing table size scaling gets broken by topology-independent addressing, a cornerstone of popular locator-identifier split proposals aiming at improving routing scaling in the presence of network topology dynamics or host mobility. These pessimistic findings lead us to the conclusion that a fundamental re-examination of assumptions behind routing models and abstractions is needed in order to find a routing architecture that would be able to scale ``indefinitely.''Comment: This is a significantly revised, journal version of cs/050802

Asteroseismic fundamental properties of solar-type stars observed by the NASA Kepler Mission

We use asteroseismic data obtained by the NASA Kepler Mission to estimate the fundamental properties of more than 500 main-sequence and sub-giant stars. Data obtained during the first 10 months of Kepler science operations were used for this work, when these solar-type targets were observed for one month each in a survey mode. Stellar properties have been estimated using two global asteroseismic parameters and complementary photometric and spectroscopic data. Homogeneous sets of effective temperatures were available for the entire ensemble from complementary photometry; spectroscopic estimates of T_eff and [Fe/H] were available from a homogeneous analysis of ground-based data on a subset of 87 stars. [Abbreviated version... see paper for full abstract.]Comment: Accepted for publication in ApJS; 90 pages, 22 figures, 6 tables. Units on rho in tables now listed correctly as rho(Sun