A mathematical model for Neanderthal extinction

A simple mathematical homogeneous model of competition is used to describe Neanderthal extinction in Europe. It considers two interacting species, Neanderthals and Early Modern Men, in the same ecological niche. Using paleontological data we claim that the parameter of similarity, between both species, fluctuates between 0.992 and 0.997. An extension of the model including migration (diffusion) is also discussed nevertheless, extinction of Neanderthal seems unavoidable. Numerical analysis of travelling wave solution (fronts) comfirms the extinction. The wave-front-velocity is estimated from linear analysis and numerical simulations confirm this estimation. We conjecture a mathematical formulation for the principle of exclusion between competitive interacting species (Gause).Comment: 9 pages, 3 figures, latex, accepted in Journal of Theoretical Biolog

Comment on "quantum theory for mesosocopic electric circuits". Cond-mat/9907171 and cond-mat/9606206

In references cond-mat/9907171 and cond-mat/9606206 (Phys.Rev.B.53, 4927 (1996)) by You-Quan Li and Bin Chen, was considered a mesoscopic LC circuit with charge discreteness. So, it was proposed a finite difference Schroedinger equation for the charge time behavior. In this comment, we generalize the corresponding mesoscopic Hamiltonian in order to taken into account the dissipative effects (resistance R). Namely, a quantum term RI, proportional to the current, is added to the mesoscopic LC circuit equation. This is carried-out in analogy with the theory of Caldirola-Kanai for quantum one particle damping.Comment: 4 pages, 0 figures, late

Symbology from set theory applied to ecological systems: Gause's exclusion principle and applications

We introduce a symbolic representation like set theory to consider ecologic interactions between species (ECOSET). The ecologic exclusion principle (Gause) is put in a symbolic way and used as operational tool to consider more complex cases like interaction with sterile species (SIT technique), two species with two superposed sources (niche differentiation) and N+P species competing by N resources, etc. Displacement (regional or characters) is also considered by using this basic tool. Our symbolic notation gives us an operative and easy way to consider elementary process in ecology. Some experimental data (laboratory or field) for ecologic process are re-considered under the optic of this set-theory.Comment: 16 pages, 0 figure

Bose-Hubbard Hamiltonian from generalized commutation rules

In a first order approximation, the Bose-Hubbard Hamiltonian with on site interaction is obtained from the free Hamiltonian (U=0) and generalized commutation relation for the annihilation-creation operators. Similar generalized commutation relations were used for the first time in high energy physics. The spectrum of the system can be found formally by using the algebraic properties of the generalized operators.Comment: 8 pages, 0 figures, late

Is planetary chaos related to evolutionary (phenotypic) rates?

After Laskar, the Lyapunov time in the solar system is about five millions years (5.000.000 [years]). On the other hand, after Kimura, the evolutionary (phenotypic) rate, for hominids, is 1/5.000.000 [1/years]. Why are these two quantities so closely related? In this work, following a proposition by Finlayson and Hutchings et al, I found an inequality, which relates Lyapunov time and evolution rate. This inequality fits well with some known cases in biological evolution.Comment: 0 figure

Density of states of disordered systems with a finite correlation length

We consider a semiclassical formulation for the density of states (DOS) of disordered systems in any dimension. We show that this formulation becomes very accurate when the correlation length of the disorder potential is large. The disorder potential does not need to be smooth and is not limited to the perturbative regime, where the disorder is small. The DOS is expressed in terms of a convolution of the disorder distribution function and the non-disordered DOS. We apply this formalism to evaluate the broadening of Landau levels and to calculate the specific heat in disordered systems.Comment: 4 page

Chapman's model for ozone concentration: earth`s slowing rotation effect in the atmospheric past

Chapman's model for ozone concentration is studied. In this nonlinear model, the photodissociation coefficients for $O_{2}$ and $O_{3}$ are time-depending due to earth-rotation. From the Kapitsa's method, valid in the high frequency limit, we find the criterion for the existence of equilibrium solutions. These solutions are depending on the frequency, and require a rotation period $T$ which satisfies $TT_{2}$. Where the critical periods $T_{1}$ and $T_{2}$, with $T_{2}>T_{1}$, are a function of the parameters of the system (reaction rates and photodissociation coefficients). Conjectures respect to the retardation of the earth's rotation, due to friction, suggest that the criterion was not even verified in the atmospheric past.Comment: 12 page

Anderson's localization in a random metric: applications to cosmology

It is considered an equation for the Lyapunov exponent $$ in a random metric for a scalar propagating wave field. At first order in frequency this equation is solved explicitly. The localization length $L_{c}$ (reciprocal of Re($\gamma$)) is obtained as function of the metric-fluctuation-distance $\Delta R$ (function of disorder) and the frequency $\omega$ of the wave. Explicitly, low-frequencies propagate longer than high, that is $L_{c}\omega ^{2}=C^{te}$. Direct applications with cosmological quantities like background radiation microwave ($\lambda \sim 1/2\times 10^{-3}$ [m]) and the Universe-length (`localization length' $L_{c}\sim 1.6\times 10^{25}$ [m]) permits to evaluate the metric-fluctuations-distance as $\Delta R\sim 10^{-35}$ [m], a number at order of the Planck's length.Comment: 10 page

Discrete-charge quantum circuits in semiclassical approach

We discuss a new approach to describe mesoscopic systems, based on the ideas of quantum electrical circuits with charge discreteness. This approach has allowed us to propose a simple alternative descriptions of some mesoscopic systems, with interesting results for some mesoscopic systems. In his work, we show that the application of the Bohr-Sommerfeld quantization rules to the Quantum $LC$ circuit with discrete charge allows us to easily reproduce previous results

Bloch-like oscillations induced by charge discreteness in quantum mesoscopic rings

We study the effect of charge discreteness in a quantum mesoscopic ring wih inductance L. The ring is pierced by a time depending external magnetic field. When the external magnetic flux varies uniformly, the current induced in the ring oscillates with a frequency proportional to the charge discreteness and the flux variation. This phenomenon is very similar to the well known Bloch's oscillation in crystals. The similitude is related to the charge discreteness in the charge-current representation, which plays the same role as the constant lattice in crystals.Comment: 5 pages, 0 figures, Late