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 $v_0$, and by their translational and rotational diffusion coefficients, $D_t$ and $D_r$. 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 $\ell_p=v_0/D_r$ is large compared to the typical interaction length scale. While the low-density dynamics of ABP is characterized by a single P\'eclet number, $Pe=v_0^2/D_rD_t$, close to the glass transition the dynamics is found to depend on $Pe$ and $\ell_p$ 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 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