1,289 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
Spectral Perturbation and Reconstructability of Complex Networks
In recent years, many network perturbation techniques, such as topological
perturbations and service perturbations, were employed to study and improve the
robustness of complex networks. However, there is no general way to evaluate
the network robustness. In this paper, we propose a new global measure for a
network, the reconstructability coefficient {\theta}, defined as the maximum
number of eigenvalues that can be removed, subject to the condition that the
adjacency matrix can be reconstructed exactly. Our main finding is that a
linear scaling law, E[{\theta}]=aN, seems universal, in that it holds for all
networks that we have studied.Comment: 9 pages, 10 figure
Restricted connections among distinguished players support cooperation
We study the evolution of cooperation within the spatial prisoner's dilemma
game on a square lattice where a fraction of players can spread their
strategy more easily than the rest due to a predetermined larger teaching
capability. In addition, players characterized with the larger teaching
capability are allowed to temporarily link with distant opponents of the same
kind with probability , thus introducing shortcut connections among the
distinguished. We show that these additional temporary connections are able to
sustain cooperation throughout the whole range of the temptation to defect.
Remarkably, we observe that as the temptation to defect increases the optimal
decreases, and moreover, only minute values of warrant the best
promotion of cooperation. Our study thus indicates that influential individuals
must be few and sparsely connected in order for cooperation to thrive in a
defection prone environment.Comment: 6 two-column pages, 6 figures; accepted for publication in Physical
Review
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.
Impact of aging on the evolution of cooperation in the spatial prisoner's dilemma game
Aging is always present, tailoring our interactions with others and
postulating a finite lifespan during which we are able to exercise them. We
consider the prisoner's dilemma game on a square lattice, and examine how
quenched age distributions and different aging protocols influence the
evolution of cooperation when taking the life experience and knowledge
accumulation into account as time passes. In agreement with previous studies,
we find that a quenched assignment of age to players, introducing heterogeneity
to the game, substantially promotes cooperative behavior. Introduction of aging
and subsequent death as a coevolutionary process may act detrimental on
cooperation but enhances it efficiently if the offspring of individuals that
have successfully passed their strategy is considered newborn. We study
resulting age distributions of players, and show that the heterogeneity is
vital yet insufficient for explaining the observed differences in cooperator
abundance on the spatial grid. The unexpected increment of cooperation levels
can be explained by a dynamical effect that has a highly selective impact on
the propagation of cooperator and defector states.Comment: 7 two-column pages, 5 figures; accepted for publication in Physical
Review
Experimental analysis of lateral impact on planar brittle material
The fragmentation of alumina and glass plates due to lateral impact is
studied. A few hundred plates have been fragmented at different impact
velocities and the produced fragments are analyzed. The method employed in this
work allows one to investigate some geometrical properties of the fragments,
besides the traditional size distribution usually studied in former
experiments. We found that, although both materials exhibit qualitative similar
fragment size distribution function, their geometrical properties appear to be
quite different. A schematic model for two-dimensional fragmentation is also
presented and its predictions are compared to our experimental results. The
comparison suggests that the analysis of the fragments' geometrical properties
constitutes a more stringent test of the theoretical models' assumptions than
the size distribution
Role of disorder in the size-scaling of material strength
We study the sample size dependence of the strength of disordered materials
with a flaw, by numerical simulations of lattice models for fracture. We find a
crossover between a regime controlled by the fluctuations due to disorder and
another controlled by stress-concentrations, ruled by continuum fracture
mechanics. The results are formulated in terms of a scaling law involving a
statistical fracture process zone. Its existence and scaling properties are
only revealed by sampling over many configurations of the disorder. The scaling
law is in good agreement with experimental results obtained from notched paper
samples.Comment: 4 pages 5 figure
Discrete element modelling of rock communition in a cone crusher using a bonded particle model
It is known that discrete element method modelling (DEM) of rock size reduction can be achieved by two approaches: the population balance model (PBM) and the bonded particle model (BPM). However, only PBM has been successfully used in DEM modelling cone crusher in the literature. The aim of this paper is to explore the feasibility of using the BPM to represent the size reduction of rock experienced within the cone crusher chamber. The feed rock particles were represented by isotropic dense random packing agglomerates. The simulation results were compared with the PBM simulation results, and it was shown that the BPM cone crusher model was able to satisfactorily replicate the performance of a cone crusher as well and it can provide more accurate prediction of the percentage of the fine products. In addition, the novel contribution here is that the rock feed material comprises particles of realistic shapes which break into more realistically shaped fragments compared with the fragments with defined shapes in the PBM model
Extreme value statistics and return intervals in long-range correlated uniform deviates
We study extremal statistics and return intervals in stationary long-range
correlated sequences for which the underlying probability density function is
bounded and uniform. The extremal statistics we consider e.g., maximum relative
to minimum are such that the reference point from which the maximum is measured
is itself a random quantity. We analytically calculate the limiting
distributions for independent and identically distributed random variables, and
use these as a reference point for correlated cases. The distributions are
different from that of the maximum itself i.e., a Weibull distribution,
reflecting the fact that the distribution of the reference point either
dominates over or convolves with the distribution of the maximum. The
functional form of the limiting distributions is unaffected by correlations,
although the convergence is slower. We show that our findings can be directly
generalized to a wide class of stochastic processes. We also analyze return
interval distributions, and compare them to recent conjectures of their
functional form
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
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