1,514,168 research outputs found
First passage time for random walks in heterogeneous networks
The first passage time (FPT) for random walks is a key indicator of how fast
information diffuses in a given system. Despite the role of FPT as a
fundamental feature in transport phenomena, its behavior, particularly in
heterogeneous networks, is not yet fully understood. Here, we study, both
analytically and numerically, the scaling behavior of the FPT distribution to a
given target node, averaged over all starting nodes. We find that random walks
arrive quickly at a local hub, and therefore, the FPT distribution shows a
crossover with respect to time from fast decay behavior (induced from the
attractive effect to the hub) to slow decay behavior (caused by the exploring
of the entire system). Moreover, the mean FPT is independent of the degree of
the target node in the case of compact exploration. These theoretical results
justify the necessity of using a random jump protocol (empirically used in
search engines) and provide guidelines for designing an effective network to
make information quickly accessible.Comment: 5 pages, 3 figure
Derivation, Properties, and Simulation of a Gas-Kinetic-Based, Non-Local Traffic Model
We derive macroscopic traffic equations from specific gas-kinetic equations,
dropping some of the assumptions and approximations made in previous papers.
The resulting partial differential equations for the vehicle density and
average velocity contain a non-local interaction term which is very favorable
for a fast and robust numerical integration, so that several thousand freeway
kilometers can be simulated in real-time. The model parameters can be easily
calibrated by means of empirical data. They are directly related to the
quantities characterizing individual driver-vehicle behavior, and their optimal
values have the expected order of magnitude. Therefore, they allow to
investigate the influences of varying street and weather conditions or freeway
control measures. Simulation results for realistic model parameters are in good
agreement with the diverse non-linear dynamical phenomena observed in freeway
traffic.Comment: For related work see
http://www.theo2.physik.uni-stuttgart.de/helbing.html and
http://www.theo2.physik.uni-stuttgart.de/treiber.htm
Spectral dimensions of hierarchical scale-free networks with shortcuts
The spectral dimension has been widely used to understand transport
properties on regular and fractal lattices. Nevertheless, it has been little
studied for complex networks such as scale-free and small world networks. Here
we study the spectral dimension and the return-to-origin probability of random
walks on hierarchical scale-free networks, which can be either fractals or
non-fractals depending on the weight of shortcuts. Applying the renormalization
group (RG) approach to the Gaussian model, we obtain the spectral dimension
exactly. While the spectral dimension varies between and for the
fractal case, it remains at , independent of the variation of network
structure for the non-fractal case. The crossover behavior between the two
cases is studied through the RG flow analysis. The analytic results are
confirmed by simulation results and their implications for the architecture of
complex systems are discussed.Comment: 10 pages, 3 figure
Clouds, Clumps, Cores & Comets - a Cosmic Chemical Connection?
We discuss the connection between the chemistry of dense interstellar clouds
and those characteristics of cometary matter that could be remnants of it. The
chemical evolution observed to occur in molecular clouds is summarized and a
model for dense core collapse that can plausibly account for the isotopic
fractionation of hydrogen, nitrogen, oxygen and carbon measured in primitive
solar system materials is presented.Comment: to be published in Advances in Geoscience
Top quark spin in ep collision
We discuss the degree of spin polarization of single top quarks produced via
fusion process in collision at TESLA+HERAp and CLIC+LHC energies
and 5.3 TeV. A description on how to combine the cross sections
of and processes is given.
-beam direction is taken to be the favorite top quark spin decomposition
axis in its rest frame and it is found to be comparable with the ones in
collision. It is argued that theoretical simplicity and experimental clearness
are the advantage of collision.Comment: 2 eps figure
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