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

Fitness-dependent topological properties of the World Trade Web

Among the proposed network models, the hidden variable (or good get richer) one is particularly interesting, even if an explicit empirical test of its hypotheses has not yet been performed on a real network. Here we provide the first empirical test of this mechanism on the world trade web, the network defined by the trade relationships between world countries. We find that the power-law distributed gross domestic product can be successfully identified with the hidden variable (or fitness) determining the topology of the world trade web: all previously studied properties up to third-order correlation structure (degree distribution, degree correlations and hierarchy) are found to be in excellent agreement with the predictions of the model. The choice of the connection probability is such that all realizations of the network with the same degree sequence are equiprobable.Comment: 4 Pages, 4 Figures. Final version accepted for publication on Physical Review Letter

Anomalous ordering in inhomogeneously strained materials

We study a continuous quasi-two-dimensional order-disorder phase transition that occurs in a simple model of a material that is inhomogeneously strained due to the presence of dislocation lines. Performing Monte Carlo simulations of different system sizes and using finite size scaling, we measure critical exponents describing the transition of beta=0.18\pm0.02, gamma=1.0\pm0.1, and alpha=0.10\pm0.02. Comparable exponents have been reported in a variety of physical systems. These systems undergo a range of different types of phase transitions, including structural transitions, exciton percolation, and magnetic ordering. In particular, similar exponents have been found to describe the development of magnetic order at the onset of the pseudogap transition in high-temperature superconductors. Their common universal critical exponents suggest that the essential physics of the transition in all of these physical systems is the same as in our model. We argue that the nature of the transition in our model is related to surface transitions, although our model has no free surface.Comment: 5 pages, 3 figure

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

Finite-Size Scaling Critical Behavior of Randomly Pinned Spin-Density Waves

We have performed Monte Carlo studies of the 3D $XY$ model with random uniaxial anisotropy, which is a model for randomly pinned spin-density waves. We study $L \times L \times L$ simple cubic lattices, using $L$ values in the range 16 to 64, and with random anisotropy strengths of $D / 2 J$ = 1, 2, 3, 6 and $\infty$. There is a well-defined finite temperature critical point, $T_c$, for each these values of $D / 2 J$. We present results for the angle-averaged magnetic structure factor, $S (k)$ at $T_c$ for $L = 64$. We also use finite-size scaling analysis to study scaling functions for the critical behavior of the specific heat, the magnetization and the longitudinal magnetic susceptibility. Good data collapse of the scaling functions over a wide range of $T$ is seen for $D / 2 J$ = 6 and $\infty$. For our finite values of $D / 2 J$ the scaled magnetization function increases with $L$ below $T_c$, and appears to approach an $L$-independent limit for large $L$. This suggests that the system is ferromagnetic below $T_c$.Comment: 21 pages in single column format, 20 .eps files, revised and expanded, errors corrected, submitted to PR

Liquid-liquid transition in supercooled silicon determined by first-principles simulation

First principles molecular dynamics simulations reveal a liquid-liquid phase transition in supercooled elemental silicon. Two phases coexist below $T_c\approx 1232K$. The low density phase is nearly tetra-coordinated, with a pseudogap at the Fermi surface, while the high density phase is more highly coordinated and metallic in nature. The transition is observed through the formation of van der Waals loops in pressure-volume isotherms below $T_c$.Comment: 9 pages 4 figure

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

Tensorial Spin-s Harmonics

We show how to define and go from the spin-s spherical harmonics to the tensorial spin-s harmonics. These quantities, which are functions on the sphere taking values as Euclidean tensors, turn out to be extremely useful for many calculations in General Relativity. In the calculations, products of these functions, with their needed decompositions which are given here, often arise naturally

Scaling in the structure of directory trees in a computer cluster

We describe the topological structure and the underlying organization principles of the directories created by users of a computer cluster when storing his/her own files. We analyze degree distributions, average distance between files, distribution of communities and allometric scaling exponents of the directory trees. We find that users create trees with a broad, scale-free degree distribution. The structure of the directories is well captured by a growth model with a single parameter. The degree distribution of the different trees has a non-universal exponent associated with different values of the parameter of the model. However, the distribution of community sizes has a universal exponent analytically obtained from our model.Comment: refined data analysis and modeling, completely reorganized version, 4 pages, 2 figure

Growth and form of the mound in Gale Crater, Mars: Slope wind enhanced erosion and transport

Ancient sediments provide archives of climate and habitability on Mars. Gale Crater, the landing site for the Mars Science Laboratory (MSL), hosts a 5-km-high sedimentary mound (Mount Sharp/Aeolis Mons). Hypotheses for mound formation include evaporitic, lacustrine, fluviodeltaic, and aeolian processes, but the origin and original extent of Gale’s mound is unknown. Here we show new measurements of sedimentary strata within the mound that indicate ∼3° outward dips oriented radially away from the mound center, inconsistent with the first three hypotheses. Moreover, although mounds are widely considered to be erosional remnants of a once crater-filling unit, we find that the Gale mound’s current form is close to its maximal extent. Instead we propose that the mound’s structure, stratigraphy, and current shape can be explained by growth in place near the center of the crater mediated by wind-topography feedbacks. Our model shows how sediment can initially accrete near the crater center far from crater-wall katabatic winds, until the increasing relief of the resulting mound generates mound-flank slope winds strong enough to erode the mound. The slope wind enhanced erosion and transport (SWEET) hypothesis indicates mound formation dominantly by aeolian deposition with limited organic carbon preservation potential, and a relatively limited role for lacustrine and fluvial activity. Morphodynamic feedbacks between wind and topography are widely applicable to a range of sedimentary and ice mounds across the Martian surface, and possibly other planets