66 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
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
Time evolution of the Partridge-Barton Model
The time evolution of the Partridge-Barton model in the presence of the
pleiotropic constraint and deleterious somatic mutations is exactly solved for
arbitrary fecundity in the context of a matricial formalism. Analytical
expressions for the time dependence of the mean survival probabilities are
derived. Using the fact that the asymptotic behavior for large time is
controlled by the largest matrix eigenvalue, we obtain the steady state values
for the mean survival probabilities and the Malthusian growth exponent. The
mean age of the population exhibits a power law decayment. Some Monte
Carlo simulations were also performed and they corroborated our theoretical
results.Comment: 10 pages, Latex, 1 postscript figure, published in Phys. Rev. E 61,
5664 (2000
Characterizing and modeling preferential flow using magnetic resonance imaging and multifractal theory.
bitstream/item/89956/1/Proci-07.00331.PD
Critical behavior for mixed site-bond directed percolation
We study mixed site-bond directed percolation on 2D and 3D lattices by using
time-dependent simulations. Our results are compared with rigorous bounds
recently obtained by Liggett and by Katori and Tsukahara. The critical
fractions and of sites and bonds are extremely well
approximated by a relationship reported earlier for isotropic percolation,
, where and are the critical fractions in
pure site and bond directed percolation.Comment: 10 pages, figures available on request from [email protected]
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