A model for cascading failures in complex networks

Large but rare cascades triggered by small initial shocks are present in most of the infrastructure networks. Here we present a simple model for cascading failures based on the dynamical redistribution of the flow on the network. We show that the breakdown of a single node is sufficient to collapse the efficiency of the entire system if the node is among the ones with largest load. This is particularly important for real-world networks with an highly hetereogeneous distribution of loads as the Internet and electrical power grids.Comment: 4 pages, 4 figure

Minimum Energy Configurations in the NN-Body Problem and the Celestial Mechanics of Granular Systems

Minimum energy configurations in celestial mechanics are investigated. It is shown that this is not a well defined problem for point-mass celestial mechanics but well-posed for finite density distributions. This naturally leads to a granular mechanics extension of usual celestial mechanics questions such as relative equilibria and stability. This paper specifically studies and finds all relative equilibria and minimum energy configurations for $N=1,2,3$ and develops hypotheses on the relative equilibria and minimum energy configurations for $N\gg 1$ bodies.Comment: Accepted for publication in Celestial Mechanics and Dynamical Astronom

Book Reviews

Review of Prehistory, by Derek Roe; Aspects of Prehistory, by Grahame Clark; World Prehistory, by Grahame Clark; Introductory Readings in Archaeology, by Brian M. Fagan, ed.; The Origins of Civilization, by Carroll L. Riley; The Archaeology of Early Man, by J. M. Coles and E. S. Higgs; Shipwrecks and Archaeology, by Peter Throckmorton; A History of Dyed Textiles, by Stuart Robinson; Food in Antiquity, by Don and Patricia Brothwell; World Archaeology, Vol. 1, nos. 1, 2, 3, by Roy Hodson and Colin Platt, eds.; The Structure and Growth of Australia's Aboriginal Population, by F. Lancaster Jones; Attitudes and Social Conditions, by Ronald Taft, John L. M. Dawson, and Pamela Beasley; Aboriginal Settlements, by J. P. M. Long; The Destruction of Aboriginal Society, by C. D. Rowley; Aboriginal Advancement to Integration, by H. P. Schapper

Generalized Uncertainty Principle, Modified Dispersion Relations and Early Universe Thermodynamics

In this paper, we study the effects of Generalized Uncertainty Principle(GUP) and Modified Dispersion Relations(MDRs) on the thermodynamics of ultra-relativistic particles in early universe. We show that limitations imposed by GUP and particle horizon on the measurement processes, lead to certain modifications of early universe thermodynamics.Comment: 21 Pages, 3 eps Figure, Revised Versio

Cascade-based attacks on complex networks

We live in a modern world supported by large, complex networks. Examples range from financial markets to communication and transportation systems. In many realistic situations the flow of physical quantities in the network, as characterized by the loads on nodes, is important. We show that for such networks where loads can redistribute among the nodes, intentional attacks can lead to a cascade of overload failures, which can in turn cause the entire or a substantial part of the network to collapse. This is relevant for real-world networks that possess a highly heterogeneous distribution of loads, such as the Internet and power grids. We demonstrate that the heterogeneity of these networks makes them particularly vulnerable to attacks in that a large-scale cascade may be triggered by disabling a single key node. This brings obvious concerns on the security of such systems.Comment: 4 pages, 4 figures, Revte

Lorentz invariance violation in top-down scenarios of ultrahigh energy cosmic ray creation

The violation of Lorentz invariance (LI) has been invoked in a number of ways to explain issues dealing with ultrahigh energy cosmic ray (UHECR) production and propagation. These treatments, however, have mostly been limited to examples in the proton-neutron system and photon-electron system. In this paper we show how a broader violation of Lorentz invariance would allow for a series of previously forbidden decays to occur, and how that could lead to UHECR primaries being heavy baryonic states or Higgs bosons.Comment: Replaced with heavily revised (see new Abstract) version accepted by Phys. Rev. D. 6 page

Near-Horizon Conformal Symmetry and Black Hole Entropy in Any Dimension

Recently, Carlip proposed a derivation of the entropy of the two-dimensional dilatonic black hole by investigating the Virasoro algebra associated with a newly introduced near-horizon conformal symmetry. We point out not only that the algebra of these conformal transformations is not well defined on the horizon, but also that the correct use of the eigenvalue of the operator $L_0$ yields vanishing entropy. It has been shown that these problems can be resolved by choosing a different basis of the conformal transformations which is regular even at the horizon. We also show the generalization of Carlip's derivation to any higher dimensional case in pure Einstein gravity. The entropy obtained is proportional to the area of the event horizon, but it also depends linearly on the product of the surface gravity and the parameter length of a horizon segment in consideration. We finally point out that this derivation of black hole entropy is quite different from the ones proposed so far, and several features of this method and some open issues are also discussed.Comment: 14 pages, no figur

A Study of Phase Transition in Black Hole Thermodynamics

This paper deals with five-dimensional black hole solutions in (a) Einstein-Maxwell-Gauss-Bonnet theory with a cosmological constant and (b)Einstein-Yang-Mills-Gauss-Bonnet theory for spherically symmetric space time. In both the cases the possibility of phase transition is examined and it is analyzed whether the phase transition is a Hawking-Page type phase transition or not.Comment: 16 figure

TeV Astrophysics Constraints on Planck Scale Lorentz Violation

We analyze observational constraints from TeV astrophysics on Lorentz violating nonlinear dispersion for photons and electrons without assuming any a priori equality between the photon and electron parameters. The constraints arise from thresholds for vacuum Cerenkov radiation, photon decay and photo-production of electron-positron pairs. We show that the parameter plane for cubic momentum terms in the dispersion relations is constrained to an order unity region in Planck units. We find that the threshold configuration can occur with an asymmetric distribution of momentum for pair creation, and with a hard photon for vacuum Cerenkov radiation.Comment: 4 pages, RevTeX4, 1 figure. Some references and a footnote added, improved discussion on the photon annihilation and GZK cutoff. Minor changes of wording. Main results unchanged. Version to appear as a Rapid Communication in PR