1,878 research outputs found
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
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
Mutual selection in time-varying networks
Copyright @ 2013 American Physical SocietyTime-varying networks play an important role in the investigation of the stochastic processes that occur on complex networks. The ability to formulate the development of the network topology on the same time scale as the evolution of the random process is important for a variety of applications, including the spreading of diseases. Past contributions have investigated random processes on time-varying networks with a purely random attachment mechanism. The possibility of extending these findings towards a time-varying network that is driven by mutual attractiveness is explored in this paper. Mutual attractiveness models are characterized by a linking function that describes the probability of the existence of an edge, which depends mutually on the attractiveness of the nodes on both ends of that edge. This class of attachment mechanisms has been considered before in the fitness-based complex networks literature but not on time-varying networks. Also, the impact of mutual selection is investigated alongside opinion formation and epidemic outbreaks. We find closed-form solutions for the quantities of interest using a factorizable linking function. The voter model exhibits an unanticipated behavior as the network never reaches consensus in the case of mutual selection but stays forever in its initial macroscopic configuration, which is a further piece of evidence that time-varying networks differ markedly from their static counterpart with respect to random processes that take place on them. We also find that epidemic outbreaks are accelerated by uncorrelated mutual selection compared to previously considered random attachment
Continuum limit of amorphous elastic bodies (III): Three dimensional systems
Extending recent numerical studies on two dimensional amorphous bodies, we
characterize the approach of elastic continuum limit in three dimensional
(weakly polydisperse) Lennard-Jones systems. While performing a systematic
finite-size analysis (for two different quench protocols) we investigate the
non-affine displacement field under external strain, the linear response to an
external delta force and the low-frequency harmonic eigenmodes and their
density distribution. Qualitatively similar behavior is found as in two
dimensions. We demonstrate that the classical elasticity description breaks
down below an intermediate length scale , which in our system is
approximately 23 molecular sizes. This length characterizes the correlations of
the non-affine displacement field, the self-averaging of external noise with
distance from the source and gives the lower wave length bound for the
applicability of the classical eigenfrequency calculations. We trace back the
"Boson-peak" of the density of eigenfrequencies (obtained from the velocity
auto-correlation function) to the inhomogeneities on wave lengths smaller than
.Comment: 27 pages, 11 figures, submitted to Phys. Rev.
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
Gender homophily from spatial behavior in a primary school: a sociometric study
We investigate gender homophily in the spatial proximity of children (6 to 12
years old) in a French primary school, using time-resolved data on face-to-face
proximity recorded by means of wearable sensors. For strong ties, i.e., for
pairs of children who interact more than a defined threshold, we find
statistical evidence of gender preference that increases with grade. For weak
ties, conversely, gender homophily is negatively correlated with grade for
girls, and positively correlated with grade for boys. This different evolution
with grade of weak and strong ties exposes a contrasted picture of gender
homophily
Dynamical Monte Carlo Study of Equilibrium Polymers (II): The Role of Rings
We investigate by means of a number of different dynamical Monte Carlo
simulation methods the self-assembly of equilibrium polymers in dilute,
semidilute and concentrated solutions under good-solvent conditions. In our
simulations, both linear chains and closed loops compete for the monomers,
expanding on earlier work in which loop formation was disallowed. Our findings
show that the conformational properties of the linear chains, as well as the
shape of their size distribution function, are not altered by the formation of
rings. Rings only seem to deplete material from the solution available to the
linear chains. In agreement with scaling theory, the rings obey an algebraic
size distribution, whereas the linear chains conform to a Schultz--Zimm type of
distribution in dilute solution, and to an exponentional distribution in
semidilute and concentrated solution. A diagram presenting different states of
aggregation, including monomer-, ring- and chain-dominated regimes, is given
First-order transition in small-world networks
The small-world transition is a first-order transition at zero density of
shortcuts, whereby the normalized shortest-path distance undergoes a
discontinuity in the thermodynamic limit. On finite systems the apparent
transition is shifted by . Equivalently a ``persistence
size'' can be defined in connection with finite-size
effects. Assuming , simple rescaling arguments imply that
. We confirm this result by extensive numerical simulation in one to
four dimensions, and argue that implies that this transition is
first-order.Comment: 4 pages, 3 figures, To appear in Europhysics Letter
Compaction dynamics of a granular media under vertical tapping
We report new experimental results on granular compaction under consecutive
vertical taps. The evolution of the mean volume fraction and of the mean
potential energy of a granular packing presents a slow densification until a
final steady-state, and is reminiscent to usual relaxation in glasses via a
stretched exponential law. The intensity of the taps seems to rule the
characteristic time of the relaxation according to an Arrhenius's type relation
>. Finally, the analysis of the vertical volume fraction profile reveals an
almost homogeneous densification in the packing.Comment: 7 pages, 4 figures, to appear in Europhysics Letter
Driven activation versus thermal activation
Activated dynamics in a glassy system undergoing steady shear deformation is
studied by numerical simulations. Our results show that the external driving
force has a strong influence on the barrier crossing rate, even though the
reaction coordinate is only weakly coupled to the nonequilibrium system. This
"driven activation" can be quantified by introducing in the Arrhenius
expression an effective temperature, which is close to the one determined from
the fluctuation-dissipation relation. This conclusion is supported by
analytical results for a simplified model system.Comment: 5 pages, 3 figure
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