1,906 research outputs found
Glass transition and random walks on complex energy landscapes
We present a simple mathematical model of glassy dynamics seen as a random
walk in a directed, weighted network of minima taken as a representation of the
energy landscape. Our approach gives a broader perspective to previous studies
focusing on particular examples of energy landscapes obtained by sampling
energy minima and saddles of small systems. We point out how the relation
between the energies of the minima and their number of neighbors should be
studied in connection with the network's global topology, and show how the
tools developed in complex network theory can be put to use in this context
On the definition of temperature in dense granular media
In this Letter we report the measurement of a pseudo-temperature for
compacting granular media on the basis of the Fluctuation-Dissipation relations
in the aging dynamics of a model system. From the violation of the
Fluctuation-Dissipation Theorem an effective temperature emerges (a dynamical
temperature T_{dyn}) whose ratio with the equilibrium temperature T_d^{eq}
depends on the particle density. We compare the results for the
Fluctuation-Dissipation Ratio (FDR) T_{dyn}/T_d^{eq} at several densities with
the outcomes of Edwards' approach at the corresponding densities. It turns out
that the FDR and the so-called Edwards' ratio coincide at several densities
(very different ages of the system), opening in this way the door to
experimental checks as well as theoretical constructions.Comment: RevTex4 4 pages, 4 eps figure
Modeling the evolution of weighted networks
We present a general model for the growth of weighted networks in which the
structural growth is coupled with the edges' weight dynamical evolution. The
model is based on a simple weight-driven dynamics and a weights' reinforcement
mechanism coupled to the local network growth. That coupling can be generalized
in order to include the effect of additional randomness and non-linearities
which can be present in real-world networks. The model generates weighted
graphs exhibiting the statistical properties observed in several real-world
systems. In particular, the model yields a non-trivial time evolution of
vertices properties and scale-free behavior with exponents depending on the
microscopic parameters characterizing the coupling rules. Very interestingly,
the generated graphs spontaneously achieve a complex hierarchical architecture
characterized by clustering and connectivity correlations varying as a function
of the vertices' degree
Basins of attraction of metastable states of the spherical -spin model
We study the basins of attraction of metastable states in the spherical
-spin spin glass model, starting the relaxation dynamics at a given distance
from a thermalized condition. Weighting the initial condition with the
Boltzmann distribution we find a finite size for the basins. On the contrary, a
white weighting of the initial condition implies vanishing basins of
attraction. We make the corresponding of our results with the ones of a
recently constructed effective potential.Comment: LaTeX, 7 pages, 7 eps figure
Dynamical and bursty interactions in social networks
We present a modeling framework for dynamical and bursty contact networks
made of agents in social interaction. We consider agents' behavior at short
time scales, in which the contact network is formed by disconnected cliques of
different sizes. At each time a random agent can make a transition from being
isolated to being part of a group, or vice-versa. Different distributions of
contact times and inter-contact times between individuals are obtained by
considering transition probabilities with memory effects, i.e. the transition
probabilities for each agent depend both on its state (isolated or interacting)
and on the time elapsed since the last change of state. The model lends itself
to analytical and numerical investigations. The modeling framework can be
easily extended, and paves the way for systematic investigations of dynamical
processes occurring on rapidly evolving dynamical networks, such as the
propagation of an information, or spreading of diseases
Mean-field diffusive dynamics on weighted networks
Diffusion is a key element of a large set of phenomena occurring on natural
and social systems modeled in terms of complex weighted networks. Here, we
introduce a general formalism that allows to easily write down mean-field
equations for any diffusive dynamics on weighted networks. We also propose the
concept of annealed weighted networks, in which such equations become exact. We
show the validity of our approach addressing the problem of the random walk
process, pointing out a strong departure of the behavior observed in quenched
real scale-free networks from the mean-field predictions. Additionally, we show
how to employ our formalism for more complex dynamics. Our work sheds light on
mean-field theory on weighted networks and on its range of validity, and warns
about the reliability of mean-field results for complex dynamics.Comment: 8 pages, 3 figure
Metastable configurations of spin models on random graphs
One-flip stable configurations of an Ising-model on a random graph with
fluctuating connectivity are examined. In order to perform the quenched average
of the number of stable configurations we introduce a global order-parameter
function with two arguments. The analytical results are compared with numerical
simulations.Comment: 11 pages Revtex, minor changes, to appear in Phys. Rev.
Inter- and Intra-Chain Attractions in Solutions of Flexible Polyelectrolytes at Nonzero Concentration
Constant temperature molecular dynamics simulations were used to study
solutions of flexible polyelectrolyte chains at nonzero concentrations with
explicit counterions and unscreened coulombic interactions. Counterion
condensation, measured via the self-diffusion coefficient of the counterions,
is found to increase with polymer concentration, but contrary to the prediction
of Manning theory, the renormalized charge fraction on the chains decreases
with increasing Bjerrum length without showing any saturation. Scaling analysis
of the radius of gyration shows that the chains are extended at low polymer
concentrations and small Bjerrum lengths, while at sufficiently large Bjerrum
lengths, the chains shrink to produce compact structures with exponents smaller
than a gaussian chain, suggesting the presence of attractive intrachain
interactions. A careful study of the radial distribution function of the
center-of-mass of the polyelectrolyte chains shows clear evidence that
effective interchain attractive interactions also exist in solutions of
flexible polyelectrolytes, similar to what has been found for rodlike
polyelectrolytes. Our results suggest that the broad maximum observed in
scattering experiments is due to clustering of chains.Comment: 12 pages, REVTeX, 15 eps figure
Voter models on weighted networks
We study the dynamics of the voter and Moran processes running on top of
complex network substrates where each edge has a weight depending on the degree
of the nodes it connects. For each elementary dynamical step the first node is
chosen at random and the second is selected with probability proportional to
the weight of the connecting edge. We present a heterogeneous mean-field
approach allowing to identify conservation laws and to calculate exit
probabilities along with consensus times. In the specific case when the weight
is given by the product of nodes' degree raised to a power theta, we derive a
rich phase-diagram, with the consensus time exhibiting various scaling laws
depending on theta and on the exponent of the degree distribution gamma.
Numerical simulations give very good agreement for small values of |theta|. An
additional analytical treatment (heterogeneous pair approximation) improves the
agreement with numerics, but the theoretical understanding of the behavior in
the limit of large |theta| remains an open challenge.Comment: 21 double-spaced pages, 6 figure
Weighted Scale-free Networks in Euclidean Space Using Local Selection Rule
A spatial scale-free network is introduced and studied whose motivation has
been originated in the growing Internet as well as the Airport networks. We
argue that in these real-world networks a new node necessarily selects one of
its neighbouring local nodes for connection and is not controlled by the
preferential attachment as in the Barab\'asi-Albert (BA) model. This
observation has been mimicked in our model where the nodes pop-up at randomly
located positions in the Euclidean space and are connected to one end of the
nearest link. In spite of this crucial difference it is observed that the
leading behaviour of our network is like the BA model. Defining link weight as
an algebraic power of its Euclidean length, the weight distribution and the
non-linear dependence of the nodal strength on the degree are analytically
calculated. It is claimed that a power law decay of the link weights with time
ensures such a non-linear behavior. Switching off the Euclidean space from the
same model yields a much simpler definition of the Barab\'asi-Albert model
where numerical effort grows linearly with .Comment: 6 pages, 6 figure
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