1,071 research outputs found
Criticality of the "critical state" of granular media: Dilatancy angle in the tetris model
The dilatancy angle describes the propensity of a granular medium to dilate
under an applied shear. Using a simple spin model (the ``tetris'' model) which
accounts for geometrical ``frustration'' effects, we study such a dilatancy
angle as a function of density. An exact mapping can be drawn with a directed
percolation process which proves that there exists a critical density
above which the system expands and below which it contracts under shear. When
applied to packings constructed by a random deposition under gravity, the
dilatancy angle is shown to be strongly anisotropic, and it constitutes an
efficient tool to characterize the texture of the medium.Comment: 7 pages RevTex, 8eps figure, to appear in Phys. Rev.
On the concept of complexity in random dynamical systems
We introduce a measure of complexity in terms of the average number of bits
per time unit necessary to specify the sequence generated by the system. In
random dynamical system, this indicator coincides with the rate K of divergence
of nearby trajectories evolving under two different noise realizations.
The meaning of K is discussed in the context of the information theory, and
it is shown that it can be determined from real experimental data. In presence
of strong dynamical intermittency, the value of K is very different from the
standard Lyapunov exponent computed considering two nearby trajectories
evolving under the same randomness. However, the former is much more relevant
than the latter from a physical point of view as illustrated by some numerical
computations for noisy maps and sandpile models.Comment: 35 pages, LaTe
Local Rigidity in Sandpile Models
We address the problem of the role of the concept of local rigidity in the
family of sandpile systems. We define rigidity as the ratio between the
critical energy and the amplitude of the external perturbation and we show, in
the framework of the Dynamically Driven Renormalization Group (DDRG), that any
finite value of the rigidity in a generalized sandpile model renormalizes to an
infinite value at the fixed point, i.e. on a large scale. The fixed point value
of the rigidity allows then for a non ambiguous distinction between
sandpile-like systems and diffusive systems. Numerical simulations support our
analytical results.Comment: to be published in Phys. Rev.
The dynamics of correlated novelties
One new thing often leads to another. Such correlated novelties are a
familiar part of daily life. They are also thought to be fundamental to the
evolution of biological systems, human society, and technology. By opening new
possibilities, one novelty can pave the way for others in a process that
Kauffman has called "expanding the adjacent possible". The dynamics of
correlated novelties, however, have yet to be quantified empirically or modeled
mathematically. Here we propose a simple mathematical model that mimics the
process of exploring a physical, biological or conceptual space that enlarges
whenever a novelty occurs. The model, a generalization of Polya's urn, predicts
statistical laws for the rate at which novelties happen (analogous to Heaps'
law) and for the probability distribution on the space explored (analogous to
Zipf's law), as well as signatures of the hypothesized process by which one
novelty sets the stage for another. We test these predictions on four data sets
of human activity: the edit events of Wikipedia pages, the emergence of tags in
annotation systems, the sequence of words in texts, and listening to new songs
in online music catalogues. By quantifying the dynamics of correlated
novelties, our results provide a starting point for a deeper understanding of
the ever-expanding adjacent possible and its role in biological, linguistic,
cultural, and technological evolution
Internal avalanches in models of granular media
We study the phenomenon of internal avalanching within the context of
recently introduced lattice models of granular media. The avalanche is produced
by pulling out a grain at the base of the packing and studying how many grains
have to rearrange before the packing is once more stable. We find that the
avalanches are long-ranged, decaying as a power-law. We study the distriution
of avalanches as a function of the density of the packing and find that the
avalanche distribution is a very sensitive structural probe of the system.Comment: 12 pages including 9 eps figures, LaTeX. To appear in Fractal
What is the temperature of a granular medium?
In this paper we discuss whether thermodynamical concepts and in particular
the notion of temperature could be relevant for the dynamics of granular
systems. We briefly review how a temperature-like quantity can be defined and
measured in granular media in very different regimes, namely the glassy-like,
the liquid-like and the granular gas. The common denominator will be given by
the Fluctuation-Dissipation Theorem, whose validity is explored by means of
both numerical and experimental techniques. It turns out that, although a
definition of a temperature is possible in all cases, its interpretation is far
from being obvious. We discuss the possible perspectives both from the
theoretical and, more importantly, from the experimental point of view
Splashing of liquids: interplay of surface roughness with surrounding gas
We investigate the interplay between substrate roughness and surrounding gas
pressure in controlling the dynamics of splashing when a liquid drop hits a dry
solid surface. We associate two distinct forms of splashing with each of these
control parameters: prompt splashing is due to surface roughness and corona
splashing is due to instabilities produced by the surrounding gas. The size
distribution of ejected droplets reveals the length scales of the underlying
droplet-creation process in both cases.Comment: 6 pages, 6 figure
Modeling the emergence of universality in color naming patterns
The empirical evidence that human color categorization exhibits some
universal patterns beyond superficial discrepancies across different cultures
is a major breakthrough in cognitive science. As observed in the World Color
Survey (WCS), indeed, any two groups of individuals develop quite different
categorization patterns, but some universal properties can be identified by a
statistical analysis over a large number of populations. Here, we reproduce the
WCS in a numerical model in which different populations develop independently
their own categorization systems by playing elementary language games. We find
that a simple perceptual constraint shared by all humans, namely the human Just
Noticeable Difference (JND), is sufficient to trigger the emergence of
universal patterns that unconstrained cultural interaction fails to produce. We
test the results of our experiment against real data by performing the same
statistical analysis proposed to quantify the universal tendencies shown in the
WCS [Kay P and Regier T. (2003) Proc. Natl. Acad. Sci. USA 100: 9085-9089], and
obtain an excellent quantitative agreement. This work confirms that synthetic
modeling has nowadays reached the maturity to contribute significantly to the
ongoing debate in cognitive science.Comment: Supplementery Information available here
http://www.pnas.org/content/107/6/2403/suppl/DCSupplementa
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