Twisting Null Geodesic Congruences, Scri, H-Space and Spin-Angular Momentum

The purpose of this work is to return, with a new observation and rather unconventional point of view, to the study of asymptotically flat solutions of Einstein equations. The essential observation is that from a given asymptotically flat space-time with a given Bondi shear, one can find (by integrating a partial differential equation) a class of asymptotically shear-free (but, in general, twistiing) null geodesic congruences. The class is uniquely given up to the arbitrary choice of a complex analytic world-line in a four-parameter complex space. Surprisingly this parameter space turns out to be the H-space that is associated with the real physical space-time under consideration. The main development in this work is the demonstration of how this complex world-line can be made both unique and also given a physical meaning. More specifically by forcing or requiring a certain term in the asymptotic Weyl tensor to vanish, the world-line is uniquely determined and becomes (by several arguments) identified as the `complex center-of-mass'. Roughly, its imaginary part becomes identified with the intrinsic spin-angular momentum while the real part yields the orbital angular momentum.Comment: 26 pages, authors were relisted alphabeticall

MonALISA : A Distributed Monitoring Service Architecture

The MonALISA (Monitoring Agents in A Large Integrated Services Architecture) system provides a distributed monitoring service. MonALISA is based on a scalable Dynamic Distributed Services Architecture which is designed to meet the needs of physics collaborations for monitoring global Grid systems, and is implemented using JINI/JAVA and WSDL/SOAP technologies. The scalability of the system derives from the use of multithreaded Station Servers to host a variety of loosely coupled self-describing dynamic services, the ability of each service to register itself and then to be discovered and used by any other services, or clients that require such information, and the ability of all services and clients subscribing to a set of events (state changes) in the system to be notified automatically. The framework integrates several existing monitoring tools and procedures to collect parameters describing computational nodes, applications and network performance. It has built-in SNMP support and network-performance monitoring algorithms that enable it to monitor end-to-end network performance as well as the performance and state of site facilities in a Grid. MonALISA is currently running around the clock on the US CMS test Grid as well as an increasing number of other sites. It is also being used to monitor the performance and optimize the interconnections among the reflectors in the VRVS system.Comment: Talk from the 2003 Computing in High Energy and Nuclear Physics (CHEP03), La Jolla, Ca, USA, March 2003, 8 pages, pdf. PSN MOET00

CR Structures and Asymptotically Flat Space-Times

We discuss the unique existence, arising by analogy to that in algebraically special space-times, of a CR structure realized on null infinity for any asymptotically flat Einstein or Einstein-Maxwell space-time.Comment: 6 page

Percolation and epidemics in a two-dimensional small world

Percolation on two-dimensional small-world networks has been proposed as a model for the spread of plant diseases. In this paper we give an analytic solution of this model using a combination of generating function methods and high-order series expansion. Our solution gives accurate predictions for quantities such as the position of the percolation threshold and the typical size of disease outbreaks as a function of the density of "shortcuts" in the small-world network. Our results agree with scaling hypotheses and numerical simulations for the same model.Comment: 7 pages, 3 figures, 2 table

A Cosmic Battery

We show that the Poynting-Robertson drag effect in an optically thin advection-dominated accretion flow around active gravitating objects generates strong azimuthal electric currents which give rise to astrophysically significant magnetic fields. Although the mechanism is most effective in accreting compact objects, it seems very promising to also account for the generation of stellar dipolar fields during the late protostellar collapse phase, when the star approaches the main sequence.Comment: 12 pages Latex, 1 postscript figure, to appear in the Astrophysical Journa

Bounds for the time to failure of hierarchical systems of fracture

For years limited Monte Carlo simulations have led to the suspicion that the time to failure of hierarchically organized load-transfer models of fracture is non-zero for sets of infinite size. This fact could have a profound significance in engineering practice and also in geophysics. Here, we develop an exact algebraic iterative method to compute the successive time intervals for individual breaking in systems of height $n$ in terms of the information calculated in the previous height $n-1$. As a byproduct of this method, rigorous lower and higher bounds for the time to failure of very large systems are easily obtained. The asymptotic behavior of the resulting lower bound leads to the evidence that the above mentioned suspicion is actually true.Comment: Final version. To appear in Phys. Rev. E, Feb 199

Testing formula satisfaction

We study the query complexity of testing for properties defined by read once formulae, as instances of massively parametrized properties, and prove several testability and non-testability results. First we prove the testability of any property accepted by a Boolean read-once formula involving any bounded arity gates, with a number of queries exponential in \epsilon and independent of all other parameters. When the gates are limited to being monotone, we prove that there is an estimation algorithm, that outputs an approximation of the distance of the input from satisfying the property. For formulae only involving And/Or gates, we provide a more efficient test whose query complexity is only quasi-polynomial in \epsilon. On the other hand we show that such testability results do not hold in general for formulae over non-Boolean alphabets; specifically we construct a property defined by a read-once arity 2 (non-Boolean) formula over alphabets of size 4, such that any 1/4-test for it requires a number of queries depending on the formula size

Maxwell Fields and Shear-Free Null Geodesic Congruences

We study and report on the class of vacuum Maxwell fields in Minkowski space that possess a non-degenerate, diverging, principle null vector field (null eigenvector field of the Maxwell tensor) that is tangent to a shear-free null geodesics congruence. These congruences can be either surface forming (the tangent vectors proportional to gradients) or not, i.e., the twisting congruences. In the non-twisting case, the associated Maxwell fields are precisely the Lienard-Wiechert fields, i.e., those Maxwell fields arising from an electric monopole moving on an arbitrary worldline. The null geodesic congruence is given by the generators of the light-cones with apex on the world-line. The twisting case is much richer, more interesting and far more complicated. In a twisting subcase, where our main interests lie, it can be given the following strange interpretation. If we allow the real Minkowski space to be complexified so that the real Minkowski coordinates x^a take complex values, i.e., x^a => z^a=x^a+iy^a with complex metric g=eta_abdz^adz^b, the real vacuum Maxwell equations can be extended into the complex and rewritten as curlW =iWdot, divW with W =E+iB. This subcase of Maxwell fields can then be extended into the complex so as to have as source, a complex analytic world-line, i.e., to now become complex Lienard-Wiechart fields. When viewed as real fields on the real Minkowski space, z^a=x^a, they possess a real principle null vector that is shear-free but twisting and diverging. The twist is a measure of how far the complex world-line is from the real 'slice'. Most Maxwell fields in this subcase are asymptotically flat with a time-varying set of electric and magnetic moments, all depending on the complex displacements and the complex velocities.Comment: 3

Probabilistic Approach to Time-Dependent Load-Transfer Models of Fracture

A probabilistic method for solving time-dependent load-transfer models of fracture is developed. It is applicable to any rule of load redistribution, i.e, local, hierarchical, etc. In the new method, the fluctuations are generated during the breaking process (annealed randomness) while in the usual method, the random lifetimes are fixed at the beginning (quenched disorder). Both approaches are equivalent.Comment: 13 pages, 4 figures. To appear in Phys.Rev.