According to many phenomenological and theoretical studies the distribution of family name frequencies in a population can be asymptotically described by a power law. We show that the Galton–Watson process corresponding to the dynamics of a growing population can be represented in Hilbert...

We study the spin-1 Blume–Capel model under a random crystal field in the tridimensional semi-infinite case. This has been done by using the real-space renormalization group approximation and specifically the Migdal–Kadanoff technique. Interesting results are obtained, which tell us that the...

Starting from the well-known field theory for directed percolation (DP), we describe an evolving population, near extinction, in an environment with its own nontrivial spatio-temporal dynamics. Here, we consider the special case where the environment follows a simple relaxational (Model A)...

The potential role of resummation techniques in the kinetic-theory approach to subgrid turbulence modeling is discussed.

A method is developed to calculate the critical line of two dimensional (2D) anisotropic Ising model including nearest-neighbor interactions. The method is based on the real-space renormalization group (RG) theory with increasing block sizes. The reduced temperatures, Ks (where K=JkBT and J, kB,...

The application of renormalization group (RG) theory to the asymptotic analysis of differential equations is considered. It is found that there is a class of small structural perturbations whose effects cannot be systematically treated using the Gell-Mann–Low RG approach applied in this...

A reduction procedure, suggested for classical systems some years ago, is extended to systems with quantum-phase transitions with the aim to generate exactly solvable models capturing fluctuation effects beyond the mean field approximation. For the reduced isotropic m-vector quantum models, an...

We review recent results obtained for the dynamics of incipient chaos. These results suggest a common picture underlying the three universal routes to chaos displayed by the prototypical logistic and circle maps. Namely, the period doubling, intermittency, and quasiperiodicity routes. In these...

The one-loop renormalization-group equations for Bose systems with quenched long-range correlated impurities are derived and analyzed with the help of three small expansion parameters. The classical-to-quantum crossover in a wide class of systems with long-range impurity correlations is...

We examine the pitchfork and tangent bifurcations in unimodal maps to illustrate a connection between renormalization group (RG) fixed points and entropy extremal properties. We observe that the exact RG solution for the tangent bifurcation is also applicable to the period-doubling cascade and...