16,905 research outputs found
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 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
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