Blocking and Persistence in the Zero-Temperature Dynamics of Homogeneous and Disordered Ising Models

A ``persistence'' exponent theta has been extensively used to describe the nonequilibrium dynamics of spin systems following a deep quench: for zero-temperature homogeneous Ising models on the d-dimensional cubic lattice, the fraction p(t) of spins not flipped by time t decays to zero like t^[-theta(d)] for low d; for high d, p(t) may decay to p(infinity)>0, because of ``blocking'' (but perhaps still like a power). What are the effects of disorder or changes of lattice? We show that these can quite generally lead to blocking (and convergence to a metastable configuration) even for low d, and then present two examples --- one disordered and one homogeneous --- where p(t) decays exponentially to p(infinity).Comment: 8 pages (LaTeX); to appear in Physical Review Letter

Stress-intensity factors for small surface and corner cracks in plates

Three-dimensional finite-element and finite-alternating methods were used to obtain the stress-intensity factors for small surface and corner cracked plates subjected to remote tension and bending loads. The crack-depth-to-crack-length ratios (a/c) ranged from 0.2 to 1 and the crack-depth-to-plate-thickness ratios (a/t) ranged from 0.05 to 0.2. The performance of the finite-element alternating method was studied on these crack configurations. A study of the computational effort involved in the finite-element alternating method showed that several crack configurations could be analyzed with a single rectangular mesh idealization, whereas the conventional finite-element method requires a different mesh for each configuration. The stress-intensity factors obtained with the finite-element-alternating method agreed well (within 5 percent) with those calculated from the finite-element method with singularity elements

Sign-time distributions for interface growth

We apply the recently introduced distribution of sign-times (DST) to non-equilibrium interface growth dynamics. We are able to treat within a unified picture the persistence properties of a large class of relaxational and noisy linear growth processes, and prove the existence of a non-trivial scaling relation. A new critical dimension is found, relating to the persistence properties of these systems. We also illustrate, by means of numerical simulations, the different types of DST to be expected in both linear and non-linear growth mechanisms.Comment: 4 pages, 5 ps figs, replaced misprint in authors nam

Behaviour of spin-1/2 particle around a charged black hole

Dirac equation is separable in curved space-time and its solution was found for both spherically and axially symmetric geometry. But most of the works were done without considering the charge of the black hole. Here we consider the spherically symmetric charged black hole background namely Reissner-Nordstrom black hole. Due to presence of the charge of black-hole charge-charge interaction will be important for the cases of incoming charged particle (e.g. electron, proton etc.). Therefore both gravitational and electromagnetic gauge fields should be introduced. Naturally behaviour of the particle will be changed from that in Schwarzschild geometry. We compare both the solutions. In the case of Reissner-Nordstrom black hole there is a possibility of super-radiance unlike Schwarzschild case. We also check this branch of the solution.Comment: 8 Latex pages and 4 Figures; RevTex.style; Accepted for Publication in Classical and Quantum Gravit

Clustering and preferential attachment in growing networks

We study empirically the time evolution of scientific collaboration networks in physics and biology. In these networks, two scientists are considered connected if they have coauthored one or more papers together. We show that the probability of scientists collaborating increases with the number of other collaborators they have in common, and that the probability of a particular scientist acquiring new collaborators increases with the number of his or her past collaborators. These results provide experimental evidence in favor of previously conjectured mechanisms for clustering and power-law degree distributions in networks.Comment: 13 pages, 2 figure

The worldwide air transportation network: Anomalous centrality, community structure, and cities' global roles

We analyze the global structure of the world-wide air transportation network, a critical infrastructure with an enormous impact on local, national, and international economies. We find that the world-wide air transportation network is a scale-free small-world network. In contrast to the prediction of scale-free network models, however, we find that the most connected cities are not necessarily the most central, resulting in anomalous values of the centrality. We demonstrate that these anomalies arise because of the multi-community structure of the network. We identify the communities in the air transportation network and show that the community structure cannot be explained solely based on geographical constraints, and that geo-political considerations have to be taken into account. We identify each city's global role based on its pattern of inter- and intra-community connections, which enables us to obtain scale-specific representations of the network.Comment: Revised versio

Thermodynamics of spin systems on small-world hypergraphs

We study the thermodynamic properties of spin systems on small-world hypergraphs, obtained by superimposing sparse Poisson random graphs with p-spin interactions onto a one-dimensional Ising chain with nearest-neighbor interactions. We use replica-symmetric transfer-matrix techniques to derive a set of fixed-point equations describing the relevant order parameters and free energy, and solve them employing population dynamics. In the special case where the number of connections per site is of the order of the system size we are able to solve the model analytically. In the more general case where the number of connections is finite we determine the static and dynamic ferromagnetic-paramagnetic transitions using population dynamics. The results are tested against Monte-Carlo simulations.Comment: 14 pages, 7 figures; Added 2 figures. Extended result