Optimal Tradeoff Between Exposed and Hidden Nodes in Large Wireless Networks

Wireless networks equipped with the CSMA protocol are subject to collisions due to interference. For a given interference range we investigate the tradeoff between collisions (hidden nodes) and unused capacity (exposed nodes). We show that the sensing range that maximizes throughput critically depends on the activation rate of nodes. For infinite line networks, we prove the existence of a threshold: When the activation rate is below this threshold the optimal sensing range is small (to maximize spatial reuse). When the activation rate is above the threshold the optimal sensing range is just large enough to preclude all collisions. Simulations suggest that this threshold policy extends to more complex linear and non-linear topologies

Non-Abelian Giant Gravitons

We argue that the giant graviton configurations known from the literature have a complementary, microscopical description in terms of multiple gravitational waves undergoing a dielectric (or magnetic moment) effect. We present a non-Abelian effective action for these gravitational waves with dielectric couplings and show that stable dielectric solutions exist. These solutions agree in the large $N$ limit with the giant graviton configurations in the literature.Comment: 8 pages. Contribution to the proceedings of the RTN workshop in Leuven, Belgium, September 200

On the computation of the Benjamin-Feir Index

Recently it has been shown theoretically, numerically and experimentally that the statistical properties (probability density function of wave amplitude and wave height)of long crested surface gravity waves depend not only on steepness but also on the Benjamin-Feir Index (BFI), which is the ratio between wave steepness and spectral bandwidth. The computation of this index requires the estimation of a number of parameters such as the spectral bandwidth and the peak frequency. For a given time series or a wave spectrum those parameters can be calculated using different methods, thus leading to different numerical values of the BFI. We analyze different approaches for computing the BFI and, based on numerical experiments with simulated spectra, we outline a unique robust methodology for its computation

The Influence of Network Topology on Sound Propagation in Granular Materials

Granular materials, whose features range from the particle scale to the force-chain scale to the bulk scale, are usually modeled as either particulate or continuum materials. In contrast with either of these approaches, network representations are natural for the simultaneous examination of microscopic, mesoscopic, and macroscopic features. In this paper, we treat granular materials as spatially-embedded networks in which the nodes (particles) are connected by weighted edges obtained from contact forces. We test a variety of network measures for their utility in helping to describe sound propagation in granular networks and find that network diagnostics can be used to probe particle-, curve-, domain-, and system-scale structures in granular media. In particular, diagnostics of meso-scale network structure are reproducible across experiments, are correlated with sound propagation in this medium, and can be used to identify potentially interesting size scales. We also demonstrate that the sensitivity of network diagnostics depends on the phase of sound propagation. In the injection phase, the signal propagates systemically, as indicated by correlations with the network diagnostic of global efficiency. In the scattering phase, however, the signal is better predicted by meso-scale community structure, suggesting that the acoustic signal scatters over local geographic neighborhoods. Collectively, our results demonstrate how the force network of a granular system is imprinted on transmitted waves.Comment: 19 pages, 9 figures, and 3 table

Localization of Multi-Dimensional Wigner Distributions

A well known result of P. Flandrin states that a Gaussian uniquely maximizes the integral of the Wigner distribution over every centered disc in the phase plane. While there is no difficulty in generalizing this result to higher-dimensional poly-discs, the generalization to balls is less obvious. In this note we provide such a generalization.Comment: Minor corrections, to appear in the Journal of Mathematical Physic

Epidemic analysis of the second-order transition in the Ziff-Gulari-Barshad surface-reaction model

We study the dynamic behavior of the Ziff-Gulari-Barshad (ZGB) irreversible surface-reaction model around its kinetic second-order phase transition, using both epidemic and poisoning-time analyses. We find that the critical point is given by p_1 = 0.3873682 \pm 0.0000015, which is lower than the previous value. We also obtain precise values of the dynamical critical exponents z, \delta, and \eta which provide further numerical evidence that this transition is in the same universality class as directed percolation.Comment: REVTEX, 4 pages, 5 figures, Submitted to Physical Review

Correlated Initial Conditions in Directed Percolation

We investigate the influence of correlated initial conditions on the temporal evolution of a (d+1)-dimensional critical directed percolation process. Generating initial states with correlations ~r^(sigma-d) we observe that the density of active sites in Monte-Carlo simulations evolves as rho(t)~t^kappa. The exponent kappa depends continuously on sigma and varies in the range -beta/nu_{||}<=kappa<=eta. Our numerical results are confirmed by an exact field-theoretical renormalization group calculation.Comment: 10 pages, RevTeX, including 5 encapsulated postscript figure