304 research outputs found
The N-steps Invasion Percolation Model
A new kind of invasion percolation is introduced in order to take into
account the inertia of the invader fluid. The inertia strength is controlled by
the number N of pores (or steps) invaded after the perimeter rupture. The new
model belongs to a different class of universality with the fractal dimensions
of the percolating clusters depending on N. A blocking phenomenon takes place
in two dimensions. It imposes an upper bound value on N. For pore sizes larger
than the critical threshold, the acceptance profile exhibits a permanent tail.Comment: LaTeX file, 12 pages, 5 ps figures, to appear in Physica
Mode-Coupling Theory for Active Brownian Particles
We present a mode-coupling theory (MCT) for the high-density dynamics of
two-dimensional spherical active Brownian particles (ABP). The theory is based
on the integration-through-transients (ITT) formalism and hence provides a
starting point for the calculation of non-equilibrium averages in
active-Brownian particle systems. The ABP are characterized by a
self-propulsion velocity , and by their translational and rotational
diffusion coefficients, and . The theory treats both the
translational and the orientational degrees of freedom of ABP explicitly. This
allows to study the effect of self-propulsion of both weak and strong
persistence of the swimming direction, also at high densities where the
persistence length is large compared to the typical
interaction length scale. While the low-density dynamics of ABP is
characterized by a single P\'eclet number, , close to the
glass transition the dynamics is found to depend on and
separately. At fixed density, increasing the self-propulsion velocity causes
structural relaxatino to speed up, while decreasing the persistence length
slows down the relaxation. The theory predicts a non-trivial
idealized-glass-transition diagram in the three-dimensional parameter space of
density, self-propulsion velocity and rotational diffusivity. The active-MCT
glass is a nonergodic state where correlations of initial density fluctuations
never fully decay, but also an infinite memory of initial orientational
fluctuations is retained in the positions
The Branched Polymer Growth Model Revisited
The Branched Polymer Growth Model (BPGM) has been employed to study the
kinetic growth of ramified polymers in the presence of impurities. In this
article, the BPGM is revisited on the square lattice and a subtle modification
in its dynamics is proposed in order to adapt it to a scenario closer to
reality and experimentation. This new version of the model is denominated the
Adapted Branched Polymer Growth Model (ABPGM). It is shown that the ABPGM
preserves the functionalities of the monomers and so recovers the branching
probability b as an input parameter which effectively controls the relative
incidence of bifurcations. The critical locus separating infinite from finite
growth regimes of the ABPGM is obtained in the (b,c) space (where c is the
impurity concentration). Unlike the original model, the phase diagram of the
ABPGM exhibits a peculiar reentrance.Comment: 8 pages, 10 figures. To be published in PHYSICA
The Heumann-Hotzel model for aging revisited
Since its proposition in 1995, the Heumann-Hotzel model has remained as an
obscure model of biological aging. The main arguments used against it were its
apparent inability to describe populations with many age intervals and its
failure to prevent a population extinction when only deleterious mutations are
present. We find that with a simple and minor change in the model these
difficulties can be surmounted. Our numerical simulations show a plethora of
interesting features: the catastrophic senescence, the Gompertz law and that
postponing the reproduction increases the survival probability, as has already
been experimentally confirmed for the Drosophila fly.Comment: 11 pages, 5 figures, to be published in Phys. Rev.
The Optimized Model of Multiple Invasion Percolation
We study the optimized version of the multiple invasion percolation model.
Some topological aspects as the behavior of the acceptance profile,
coordination number and vertex type abundance were investigated and compared to
those of the ordinary invasion. Our results indicate that the clusters show a
very high degree of connectivity, spoiling the usual nodes-links-blobs
geometrical picture.Comment: LaTeX file, 6 pages, 2 ps figure
Statistics of football dynamics
We investigate the dynamics of football matches. Our goal is to characterize
statistically the temporal sequence of ball movements in this collective sport
game, searching for traits of complex behavior. Data were collected over a
variety of matches in South American, European and World championships
throughout 2005 and 2006. We show that the statistics of ball touches presents
power-law tails and can be described by -gamma distributions. To explain
such behavior we propose a model that provides information on the
characteristics of football dynamics. Furthermore, we discuss the statistics of
duration of out-of-play intervals, not directly related to the previous
scenario.Comment: 7 page
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