1,177 research outputs found
Do Athermal Amorphous Solids Exist?
We study the elastic theory of amorphous solids made of particles with finite
range interactions in the thermodynamic limit. For the elastic theory to exist
one requires all the elastic coefficients, linear and nonlinear, to attain a
finite thermodynamic limit. We show that for such systems the existence of
non-affine mechanical responses results in anomalous fluctuations of all the
nonlinear coefficients of the elastic theory. While the shear modulus exists,
the first nonlinear coefficient B_2 has anomalous fluctuations and the second
nonlinear coefficient B_3 and all the higher order coefficients (which are
non-zero by symmetry) diverge in the thermodynamic limit. These results put a
question mark on the existence of elasticity (or solidity) of amorphous solids
at finite strains, even at zero temperature. We discuss the physical meaning of
these results and propose that in these systems elasticity can never be
decoupled from plasticity: the nonlinear response must be very substantially
plastic.Comment: 11 pages, 11 figure
Time-Varying Priority Queuing Models for Human Dynamics
Queuing models provide insight into the temporal inhomogeneity of human
dynamics, characterized by the broad distribution of waiting times of
individuals performing tasks. We study the queuing model of an agent trying to
execute a task of interest, the priority of which may vary with time due to the
agent's "state of mind." However, its execution is disrupted by other tasks of
random priorities. By considering the priority of the task of interest either
decreasing or increasing algebraically in time, we analytically obtain and
numerically confirm the bimodal and unimodal waiting time distributions with
power-law decaying tails, respectively. These results are also compared to the
updating time distribution of papers in the arXiv.org and the processing time
distribution of papers in Physical Review journals. Our analysis helps to
understand human task execution in a more realistic scenario.Comment: 8 pages, 6 figure
Renormalization group theory for finite-size scaling in extreme statistics
We present a renormalization group (RG) approach to explain universal
features of extreme statistics, applied here to independent, identically
distributed variables. The outlines of the theory have been described in a
previous Letter, the main result being that finite-size shape corrections to
the limit distribution can be obtained from a linearization of the RG
transformation near a fixed point, leading to the computation of stable
perturbations as eigenfunctions. Here we show details of the RG theory which
exhibit remarkable similarities to the RG known in statistical physics. Besides
the fixed points explaining universality, and the least stable eigendirections
accounting for convergence rates and shape corrections, the similarities
include marginally stable perturbations which turn out to be generic for the
Fisher-Tippett-Gumbel class. Distribution functions containing unstable
perturbations are also considered. We find that, after a transitory divergence,
they return to the universal fixed line at the same or at a different point
depending on the type of perturbation.Comment: 15 pages, 8 figures, to appear in Phys. Rev.
Coevolution of dynamical states and interactions in dynamic networks
We explore the coupled dynamics of the internal states of a set of
interacting elements and the network of interactions among them. Interactions
are modeled by a spatial game and the network of interaction links evolves
adapting to the outcome of the game. As an example we consider a model of
cooperation, where the adaptation is shown to facilitate the formation of a
hierarchical interaction network that sustains a highly cooperative stationary
state. The resulting network has the characteristics of a small world network
when a mechanism of local neighbor selection is introduced in the adaptive
network dynamics. The highly connected nodes in the hierarchical structure of
the network play a leading role in the stability of the network. Perturbations
acting on the state of these special nodes trigger global avalanches leading to
complete network reorganization.Comment: 4 pages, 5 figures, for related material visit
http:www.imedea.uib.es/physdept
Noise-guided evolution within cyclical interactions
We study a stochastic predator-prey model on a square lattice, where each of
the six species has two superior and two inferior partners. The invasion
probabilities between species depend on the predator-prey pair and are
supplemented by Gaussian noise. Conditions are identified that warrant the
largest impact of noise on the evolutionary process, and the results of Monte
Carlo simulations are qualitatively reproduced by a four-point cluster
dynamical mean-field approximation. The observed noise-guided evolution is
deeply routed in short-range spatial correlations, which is supported by
simulations on other host lattice topologies. Our findings are conceptually
related to the coherence resonance phenomenon in dynamical systems via the
mechanism of threshold duality. We also show that the introduced concept of
noise-guided evolution via the exploitation of threshold duality is not limited
to predator-prey cyclical interactions, but may apply to models of evolutionary
game theory as well, thus indicating its applicability in several different
fields of research.Comment: to be published in New J. Phy
Extreme value distributions and Renormalization Group
In the classical theorems of extreme value theory the limits of suitably
rescaled maxima of sequences of independent, identically distributed random
variables are studied. So far, only affine rescalings have been considered. We
show, however, that more general rescalings are natural and lead to new limit
distributions, apart from the Gumbel, Weibull, and Fr\'echet families. The
problem is approached using the language of Renormalization Group
transformations in the space of probability densities. The limit distributions
are fixed points of the transformation and the study of the differential around
them allows a local analysis of the domains of attraction and the computation
of finite-size corrections.Comment: 16 pages, 5 figures. Final versio
The distance upon contact: Determination from roughness profile
The point at which two random rough surfaces make contact takes place at the
contact of the highest asperities. The distance upon contact d_0 in the limit
of zero load has crucial importance for determination of dispersive forces.
Using gold films as an example we demonstrate that for two parallel plates d_0
is a function of the nominal size of the contact area L and give a simple
expression for d_0(L) via the surface roughness characteristics. In the case of
a sphere of fixed radius R and a plate the scale dependence manifests itself as
an additional uncertainty \delta d(L) in the separation, where the scale L is
related with the separation d via the effective area of interaction L^2\sim\pi
Rd. This uncertainty depends on the roughness of interacting bodies and
disappears in the limit L\to \infty.Comment: 5 pages, 4 figures, to be published in PR
Cooperation enhanced by inhomogeneous activity of teaching for evolutionary Prisoner's Dilemma games
Evolutionary Prisoner's Dilemma games with quenched inhomogeneities in the
spatial dynamical rules are considered. The players following one of the two
pure strategies (cooperation or defection) are distributed on a two-dimensional
lattice. The rate of strategy adoption from a randomly chosen neighbors are
controlled by the payoff difference and a two-value pre-factor
characterizing the players whom the strategy learned from. The reduced teaching
activity of players is distributed randomly with concentrations at the
beginning and fixed further on. Numerical and analytical calculations are
performed to study the concentration of cooperators as a function of and
for different noise levels and connectivity structures. Significant
increase of cooperation is found within a wide range of parameters for this
dynamics. The results highlight the importance of asymmetry characterizing the
exchange of master-follower role during the strategy adoptions.Comment: 4 pages, 5 figures, corrected typo
Extreme fluctuations in noisy task-completion landscapes on scale-free networks
We study the statistics and scaling of extreme fluctuations in noisy
task-completion landscapes, such as those emerging in synchronized
distributed-computing networks, or generic causally-constrained queuing
networks, with scale-free topology. In these networks the average size of the
fluctuations becomes finite (synchronized state) and the extreme fluctuations
typically diverge only logarithmically in the large system-size limit ensuring
synchronization in a practical sense. Provided that local fluctuations in the
network are short-tailed, the statistics of the extremes are governed by the
Gumbel distribution. We present large-scale simulation results using the exact
algorithmic rules, supported by mean-field arguments based on a coarse-grained
description.Comment: 16 pages, 6 figures, revte
Coevolutionary Dynamics: From Finite to Infinite Populations
Traditionally, frequency dependent evolutionary dynamics is described by
deterministic replicator dynamics assuming implicitly infinite population
sizes. Only recently have stochastic processes been introduced to study
evolutionary dynamics in finite populations. However, the relationship between
deterministic and stochastic approaches remained unclear. Here we solve this
problem by explicitly considering large populations. In particular, we identify
different microscopic stochastic processes that lead to the standard or the
adjusted replicator dynamics. Moreover, differences on the individual level can
lead to qualitatively different dynamics in asymmetric conflicts and, depending
on the population size, can even invert the direction of the evolutionary
process.Comment: 4 pages (2 figs included). Published in Phys. Rev. Lett., December
200
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