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 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 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

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.

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 $t$ 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 $t^{-1}$ 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

Exact Solution of an Evolutionary Model without Ageing

We introduce an age-structured asexual population model containing all the relevant features of evolutionary ageing theories. Beneficial as well as deleterious mutations, heredity and arbitrary fecundity are present and managed by natural selection. An exact solution without ageing is found. We show that fertility is associated with generalized forms of the Fibonacci sequence, while mutations and natural selection are merged into an integral equation which is solved by Fourier series. Average survival probabilities and Malthusian growth exponents are calculated indicating that the system may exhibit mutational meltdown. The relevance of the model in the context of fissile reproduction groups as many protozoa and coelenterates is discussed.Comment: LaTeX file, 15 pages, 2 ps figures, to appear in Phys. Rev.

Percolation and invasion percolation in the presence of mobile impurities

Abstract. We present a model for the solidification process of two immiscible fluids interacting repulsively with mobile impurities on a two-dimensional square lattice. In the space of the fluids and impurity concentrations, the phase diagram exhibits a critical curve separating a percolating from a non-percolating phase. Estimated values for the fractal dimension and the exponent β of the order parameter reveal that the critical exponents do not vary along this curve, i.e., they are independent of the impurity concentration. The universality class is that of the ordinary percolation. On the basis of the ideas of the dynamic epidemic and invasion percolation models, we also propose a model that may be relevant to cleaning porous media by fluid injection. An analysis of the acceptance profile, the fractal dimension and the gap exponent strongly indicate that this model belongs to the universality class of the ordinary invasion percolation