2,349 research outputs found
The structure of borders in a small world
Geographic borders are not only essential for the effective functioning of
government, the distribution of administrative responsibilities and the
allocation of public resources, they also influence the interregional flow of
information, cross-border trade operations, the diffusion of innovation and
technology, and the spatial spread of infectious diseases. However, as growing
interactions and mobility across long distances, cultural, and political
borders continue to amplify the small world effect and effectively decrease the
relative importance of local interactions, it is difficult to assess the
location and structure of effective borders that may play the most significant
role in mobility-driven processes. The paradigm of spatially coherent
communities may no longer be a plausible one, and it is unclear what structures
emerge from the interplay of interactions and activities across spatial scales.
Here we analyse a multi-scale proxy network for human mobility that
incorporates travel across a few to a few thousand kilometres. We determine an
effective system of geographically continuous borders implicitly encoded in
multi-scale mobility patterns. We find that effective large scale boundaries
define spatially coherent subdivisions and only partially coincide with
administrative borders. We find that spatial coherence is partially lost if
only long range traffic is taken into account and show that prevalent models
for multi-scale mobility networks cannot account for the observed patterns.
These results will allow for new types of quantitative, comparative analyses of
multi-scale interaction networks in general and may provide insight into a
multitude of spatiotemporal phenomena generated by human activity.Comment: 9 page
Accelerating random walks by disorder
We investigate the dynamic impact of heterogeneous environments on
superdiffusive random walks known as L\'evy flights. We devote particular
attention to the relative weight of source and target locations on the rates
for spatial displacements of the random walk. Unlike ordinary random walks
which are slowed down for all values of the relative weight of source and
target, non-local superdiffusive processes show distinct regimes of attenuation
and acceleration for increased source and target weight, respectively.
Consequently, spatial inhomogeneities can facilitate the spread of
superdiffusive processes, in contrast to common belief that external disorder
generally slows down stochastic processes. Our results are based on a novel
type of fractional Fokker-Planck equation which we investigate numerically and
by perturbation theory for weak disorder.Comment: 8 pages, 5 figure
Levy flights and Levy -Schroedinger semigroups
We analyze two different confining mechanisms for L\'{e}vy flights in the
presence of external potentials. One of them is due to a conservative force in
the corresponding Langevin equation. Another is implemented by
Levy-Schroedinger semigroups which induce so-called topological Levy processes
(Levy flights with locally modified jump rates in the master equation). Given a
stationary probability function (pdf) associated with the Langevin-based
fractional Fokker-Planck equation, we demonstrate that generically there exists
a topological L\'{e}vy process with the very same invariant pdf and in the
reverse.Comment: To appear in Cent. Eur. J. Phys. (2010
Video Pandemics: Worldwide Viral Spreading of Psy's Gangnam Style Video
Viral videos can reach global penetration traveling through international
channels of communication similarly to real diseases starting from a
well-localized source. In past centuries, disease fronts propagated in a
concentric spatial fashion from the the source of the outbreak via the short
range human contact network. The emergence of long-distance air-travel changed
these ancient patterns. However, recently, Brockmann and Helbing have shown
that concentric propagation waves can be reinstated if propagation time and
distance is measured in the flight-time and travel volume weighted underlying
air-travel network. Here, we adopt this method for the analysis of viral meme
propagation in Twitter messages, and define a similar weighted network distance
in the communication network connecting countries and states of the World. We
recover a wave-like behavior on average and assess the randomizing effect of
non-locality of spreading. We show that similar result can be recovered from
Google Trends data as well.Comment: 10 page
STEPS - an approach for human mobility modeling
In this paper we introduce Spatio-TEmporal Parametric Stepping (STEPS) - a simple parametric mobility model which can cover a large spectrum of human mobility patterns. STEPS makes abstraction of spatio-temporal preferences in human mobility by using a power law to rule the nodes movement. Nodes in STEPS have preferential attachment to favorite locations where they spend most of their time. Via simulations, we show that STEPS is able, not only to express the peer to peer properties such as inter-ontact/contact time and to reflect accurately realistic routing performance, but also to express the structural properties of the underlying interaction graph such as small-world phenomenon. Moreover, STEPS is easy to implement, exible to configure and also theoretically tractable
Neutron star properties and the equation of state of neutron-rich matter
We calculate total masses and radii of neutron stars (NS) for pure neutron
matter and nuclear matter in beta-equilibrium. We apply a relativistic nuclear
matter equation of state (EOS) derived from Dirac-Brueckner-Hartree-Fock (DBHF)
calculations. We use realistic nucleon-nucleon (NN) interactions defined in the
framework of the meson exchange potential models. Our results are compared with
other theoretical predictions and recent observational data. Suggestions for
further study are discussed.Comment: 13 pages, 9 figures, 1 table; Revised version, accepted for
publication in Physical Review
Levy Flights in Inhomogeneous Media
We investigate the impact of external periodic potentials on superdiffusive
random walks known as Levy flights and show that even strongly superdiffusive
transport is substantially affected by the external field. Unlike ordinary
random walks, Levy flights are surprisingly sensitive to the shape of the
potential while their asymptotic behavior ceases to depend on the Levy index
. Our analysis is based on a novel generalization of the Fokker-Planck
equation suitable for systems in thermal equilibrium. Thus, the results
presented are applicable to the large class of situations in which
superdiffusion is caused by topological complexity, such as diffusion on folded
polymers and scale-free networks.Comment: 4 pages, 4 figure
Particle Dispersion on Rapidly Folding Random Hetero-Polymers
We investigate the dynamics of a particle moving randomly along a disordered
hetero-polymer subjected to rapid conformational changes which induce
superdiffusive motion in chemical coordinates. We study the antagonistic
interplay between the enhanced diffusion and the quenched disorder. The
dispersion speed exhibits universal behavior independent of the folding
statistics. On the other hand it is strongly affected by the structure of the
disordered potential. The results may serve as a reference point for a number
of translocation phenomena observed in biological cells, such as protein
dynamics on DNA strands.Comment: 4 pages, 4 figure
Momentum-Dependent Mean Field Based Upon the Dirac-Brueckner Approach for Nuclear Matter
A momentum-dependent mean field potential, suitable for application in the
transport-model description of nucleus-nucleus collisions, is derived in a
microscopic way. The derivation is based upon the Bonn meson-exchange model for
the nucleon-nucleon interaction and the Dirac-Brueckner approach for nuclear
matter. The properties of the microscopic mean field are examined and compared
with phenomenological parametrizations which are commonly used in
transport-model calculations.Comment: 15 pages text (RevTex) and 4 figures (postscript in a separate
uuencoded file), UI-NTH-930
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