927 research outputs found
Communication Bottlenecks in Scale-Free Networks
We consider the effects of network topology on the optimality of packet
routing quantified by , the rate of packet insertion beyond which
congestion and queue growth occurs. The key result of this paper is to show
that for any network, there exists an absolute upper bound, expressed in terms
of vertex separators, for the scaling of with network size ,
irrespective of the routing algorithm used. We then derive an estimate to this
upper bound for scale-free networks, and introduce a novel static routing
protocol which is superior to shortest path routing under intense packet
insertion rates.Comment: 5 pages, 3 figure
Resilience of Complex Networks to Random Breakdown
Using Monte Carlo simulations we calculate , the fraction of nodes which
are randomly removed before global connectivity is lost, for networks with
scale-free and bimodal degree distributions. Our results differ with the
results predicted by an equation for proposed by Cohen, et al. We discuss
the reasons for this disagreement and clarify the domain for which the proposed
equation is valid
Sensitivity of Helioseismic Measurements of Normal-mode Coupling to Flows and Sound-speed Perturbations
In this article, we derive and compute the sensitivity of measurements of
coupling between normal modes of oscillation in the Sun to underlying flows.
The theory is based on first-Born perturbation theory, and the analysis is
carried out using the formalism described by \citet{lavely92}. Albeit tedious,
we detail the derivation and compute the sensitivity of specific pairs of
coupled normal modes to anomalies in the interior. Indeed, these kernels are
critical for the accurate inference of convective flow amplitudes and
large-scale circulations in the solar interior. We resolve some inconsistencies
in the derivation of \citet{lavely92} and reformulate the fluid-continuity
condition. We also derive and compute sound-speed kernels, paving the way for
inverting for thermal anomalies alongside flows.Comment: 24 pages, 8 Figures; MNRA
Probability density function of turbulent velocity fluctuation
The probability density function (PDF) of velocity fluctuations is studied
experimentally for grid turbulence in a systematical manner. At small distances
from the grid, where the turbulence is still developing, the PDF is
sub-Gaussian. At intermediate distances, where the turbulence is fully
developed, the PDF is Gaussian. At large distances, where the turbulence has
decayed, the PDF is hyper-Gaussian. The Fourier transforms of the velocity
fluctuations always have Gaussian PDFs. At intermediate distances from the
grid, the Fourier transforms are statistically independent of each other. This
is the necessary and sufficient condition for Gaussianity of the velocity
fluctuations. At small and large distances, the Fourier transforms are
dependent.Comment: 7 pages, 8 figures in a PS file, to appear in Physical Review
Beyond scaling and locality in turbulence
An analytic perturbation theory is suggested in order to find finite-size
corrections to the scaling power laws. In the frame of this theory it is shown
that the first order finite-size correction to the scaling power laws has
following form , where
is a finite-size scale (in particular for turbulence, it can be the Kolmogorov
dissipation scale). Using data of laboratory experiments and numerical
simulations it is shown shown that a degenerate case with can
describe turbulence statistics in the near-dissipation range , where
the ordinary (power-law) scaling does not apply. For moderate Reynolds numbers
the degenerate scaling range covers almost the entire range of scales of
velocity structure functions (the log-corrections apply to finite Reynolds
number). Interplay between local and non-local regimes has been considered as a
possible hydrodynamic mechanism providing the basis for the degenerate scaling
of structure functions and extended self-similarity. These results have been
also expanded on passive scalar mixing in turbulence. Overlapping phenomenon
between local and non-local regimes and a relation between position of maximum
of the generalized energy input rate and the actual crossover scale between
these regimes are briefly discussed.Comment: extended versio
Wall-bounded turbulent flows at high Reynolds numbers: Recent advances and key issues
Wall-bounded turbulent flows at high Reynolds numbers have become an increasingly active area of
research in recent years. Many challenges remain in theory, scaling, physical understanding,
experimental techniques, and numerical simulations. In this paper we distill the salient advances of
recent origin, particularly those that challenge textbook orthodoxy. Some of the outstanding
questions, such as the extent of the logarithmic overlap layer, the universality or otherwise of the
principal model parameters such as the von Kármán “constant,” the parametrization of roughness
effects, and the scaling of mean flow and Reynolds stresses, are highlighted. Research avenues that
may provide answers to these questions, notably the improvement of measuring techniques and the
construction of new facilities, are identified. We also highlight aspects where differences of opinion
persist, with the expectation that this discussion might mark the beginning of their resolution
Biological Principles in Self-Organization of Young Brain - Viewed from Kohonen Model
Variants of the Kohonen model are proposed to study biological principles of
self-organization in a model of young brain. We suggest a function to measure
aquired knowledge and use it to auto-adapt the topology of neuronal
connectivity, yielding substantial organizational improvement relative to the
standard model. In the early phase of organization with most intense learning,
we observe that neural connectivity is of Small World type, which is very
efficient to organize neurons in response to stimuli. In analogy to human brain
where pruning of neural connectivity (and neuron cell death) occurs in early
life, this feature is present also in our model, which is found to stabilize
neuronal response to stimuli
Vortex tubes in velocity fields of laboratory isotropic turbulence: dependence on the Reynolds number
The streamwise and transverse velocities are measured simultaneously in
isotropic grid turbulence at relatively high Reynolds numbers, Re(lambda) =
110-330. Using a conditional averaging technique, we extract typical
intermittency patterns, which are consistent with velocity profiles of a model
for a vortex tube, i.e., Burgers vortex. The radii of the vortex tubes are
several of the Kolmogorov length regardless of the Reynolds number. Using the
distribution of an interval between successive enhancements of a small-scale
velocity increment, we study the spatial distribution of vortex tubes. The
vortex tubes tend to cluster together. This tendency is increasingly
significant with the Reynolds number. Using statistics of velocity increments,
we also study the energetical importance of vortex tubes as a function of the
scale. The vortex tubes are important over the background flow at small scales
especially below the Taylor microscale. At a fixed scale, the importance is
increasingly significant with the Reynolds number.Comment: 8 pages, 3 PS files for 8 figures, to appear in Physical Review
A Minimalist Turbulent Boundary Layer Model
We introduce an elementary model of a turbulent boundary layer over a flat
surface, given as a vertical random distribution of spanwise Lamb-Oseen vortex
configurations placed over a non-slip boundary condition line. We are able to
reproduce several important features of realistic flows, such as the viscous
and logarithmic boundary sublayers, and the general behavior of the first
statistical moments (turbulent intensity, skewness and flatness) of the
streamwise velocity fluctuations. As an application, we advance some heuristic
considerations on the boundary layer underlying kinematics that could be
associated with the phenomenon of drag reduction by polymers, finding a
suggestive support from its experimental signatures.Comment: 5 pages, 10 figure
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