6,353 research outputs found
Features and heterogeneities in growing network models
Many complex networks from the World-Wide-Web to biological networks are
growing taking into account the heterogeneous features of the nodes. The
feature of a node might be a discrete quantity such as a classification of a
URL document as personal page, thematic website, news, blog, search engine,
social network, ect. or the classification of a gene in a functional module.
Moreover the feature of a node can be a continuous variable such as the
position of a node in the embedding space. In order to account for these
properties, in this paper we provide a generalization of growing network models
with preferential attachment that includes the effect of heterogeneous features
of the nodes. The main effect of heterogeneity is the emergence of an
"effective fitness" for each class of nodes, determining the rate at which
nodes acquire new links. The degree distribution exhibits a multiscaling
behaviour analogous to the the fitness model. This property is robust with
respect to variations in the model, as long as links are assigned through
effective preferential attachment. Beyond the degree distribution, in this
paper we give a full characterization of the other relevant properties of the
model. We evaluate the clustering coefficient and show that it disappears for
large network size, a property shared with the Barab\'asi-Albert model.
Negative degree correlations are also present in the studied class of models,
along with non-trivial mixing patterns among features. We therefore conclude
that both small clustering coefficients and disassortative mixing are outcomes
of the preferential attachment mechanism in general growing networks.Comment: 16 pages, 6 figures, revte
Static triplet correlations in glass-forming liquids: A molecular dynamics study
We present a numerical evaluation of the three-point static correlations
functions of the Kob-Andersen Lennard-Jones binary mixture and of its purely
repulsive, Weeks-Chandler-Andersen variant. In the glassy regime, the two
models possess a similar pair structure, yet their dynamics differ markedly.
The static triplet correlation functions S^(3) indicate that the local ordering
is more pronounced in the Lennard-Jones model, an observation consistent with
its slower dynamics. A comparison of the direct triplet correlation functions
c^(3) reveals that these structural differences are due, to a good extent, to
an amplification of the small discrepancies observed at the pair level. We
demonstrate the existence of a broad, positive peak at small wave-vectors and
angles in c^(3). In this portion of k-space, slight, systematic differences
between the models are observed, revealing "genuine" three-body contributions
to the triplet structure. The possible role of the low-k features of c^(3) and
the implications of our results for dynamic theories of the glass transition
are discussed.Comment: 9 pages, 8 figures, contribution to the JCP Special Issue on the
Glass Transitio
Spatial correlations in the relaxation of the Kob-Andersen model
We describe spatio-temporal correlations and heterogeneities in a kinetically
constrained glassy model, the Kob-Andersen model. The kinetic constraints of
the model alone induce the existence of dynamic correlation lengths, that
increase as the density increases, in a way compatible with a
double-exponential law. We characterize in detail the trapping time correlation
length, the cooperativity length, and the distribution of persistent clusters
of particles. This last quantity is related to the typical size of blocked
clusters that slow down the dynamics for a given density.Comment: 7 pages, 6 figures, published version (title has changed
On the Nature and Shape of Tubulin Trails: Implications on Microtubule Self-Organization
Microtubules, major elements of the cell skeleton are, most of the time, well
organized in vivo, but they can also show self-organizing behaviors in time
and/or space in purified solutions in vitro. Theoretical studies and models
based on the concepts of collective dynamics in complex systems,
reaction-diffusion processes and emergent phenomena were proposed to explain
some of these behaviors. In the particular case of microtubule spatial
self-organization, it has been advanced that microtubules could behave like
ants, self-organizing by 'talking to each other' by way of hypothetic (because
never observed) concentrated chemical trails of tubulin that are expected to be
released by their disassembling ends. Deterministic models based on this idea
yielded indeed like-looking spatio-temporal self-organizing behaviors.
Nevertheless the question remains of whether microscopic tubulin trails
produced by individual or bundles of several microtubules are intense enough to
allow microtubule self-organization at a macroscopic level. In the present
work, by simulating the diffusion of tubulin in microtubule solutions at the
microscopic scale, we measure the shape and intensity of tubulin trails and
discuss about the assumption of microtubule self-organization due to the
production of chemical trails by disassembling microtubules. We show that the
tubulin trails produced by individual microtubules or small microtubule arrays
are very weak and not elongated even at very high reactive rates. Although the
variations of concentration due to such trails are not significant compared to
natural fluctuations of the concentration of tubuline in the chemical
environment, the study shows that heterogeneities of biochemical composition
can form due to microtubule disassembly. They could become significant when
produced by numerous microtubule ends located in the same place. Their possible
formation could play a role in certain conditions of reaction. In particular,
it gives a mesoscopic basis to explain the collective dynamics observed in
excitable microtubule solutions showing the propagation of concentration waves
of microtubules at the millimeter scale, although we doubt that individual
microtubules or bundles can behave like molecular ants
Localization transition, Lifschitz tails and rare-region effects in network models
Effects of heterogeneity in the suspected-infected-susceptible model on
networks are investigated using quenched mean-field theory. The emergence of
localization is described by the distributions of the inverse participation
ratio and compared with the rare-region effects appearing in simulations and in
the Lifschitz tails. The latter, in the linear approximation, is related to the
spectral density of the Laplacian matrix and to the time dependent order
parameter. I show that these approximations indicate correctly Griffiths Phases
both on regular one-dimensional lattices and on small world networks exhibiting
purely topological disorder. I discuss the localization transition that occurs
on scale-free networks at degree exponent.Comment: 9 pages, 9 figures, accepted version in PR
Seismic scattering and absorption mapping from intermediate-depth earthquakes reveals complex tectonic interactions acting in the Vrancea region and surroundings (Romania)
The present study was performed during a stay at the University of Münster financed by a grant awarded by the German Academic Exchange Service (DAAD) in 2014. Data used in the present study were provided by the National Institute for Earth Physics (Romania) and processed within the National Data Centre in Magurele. Seismic Analysis Code (SAC) (Goldstein and Snoke, 2005) and GMT (Wessel et al., 2013) codes were used. We thank the College of Physical Sciences (University of Aberdeen) and the Santander Mobility Award for providing travel grant to LDS to complete this manuscript. We are grateful as well to the anonymous reviewer for his useful remarks which helped us to improve the paper.Peer reviewedPostprin
Physical Pictures of Transport in Heterogeneous Media: Advection-Dispersion, Random Walk and Fractional Derivative Formulations
The basic conceptual picture and theoretical basis for development of
transport equations in porous media are examined. The general form of the
governing equations is derived for conservative chemical transport in
heterogeneous geological formations, for single realizations and for ensemble
averages of the domain. The application of these transport equations is focused
on accounting for the appearance of non-Fickian (anomalous) transport behavior.
The general ensemble-averaged transport equation is shown to be equivalent to a
continuous time random walk (CTRW) and reduces to the conventional forms of the
advection-dispersion equation (ADE) under highly restrictive conditions.
Fractional derivative formulations of the transport equations, both temporal
and spatial, emerge as special cases of the CTRW. In particular, the use in
this context of L{\'e}vy flights is critically examined. In order to determine
chemical transport in field-scale situations, the CTRW approach is generalized
to non-stationary systems. We outline a practical numerical scheme, similar to
those used with extended geological models, to account for the often important
effects of unresolved heterogeneities.Comment: 14 pages, REVTeX4, accepted to Wat. Res. Res; reference adde
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