M. Argollo de Menezes

Shortest paths on systems with power-law distributed long-range connections

We discuss shortest-path lengths l(r) on periodic rings of size L supplemented with an average of pL randomly located long-range links whose lengths are distributed according to P(l) approximately l(-mu). Using rescaling arguments and numerical simulation on systems of up to 10(7) sites, we show that a characteristic length xi exists such that l(r) approximately r for r<xi but l(r) approximately r(theta(s)(mu)) for r>>xi. For small p we find that the shortest-path length satisfies the scaling relation l(r,mu,p)/xi=f(mu,r/xi). Three regions with different asymptotic behaviors are found, respectively: (a) mu>2 where theta(s)=1, (b) 1<mu<2 where 0<theta(s)(mu)<1/2, and (c) mu<1 where l(r) behaves logarithmically, i.e., theta(s)=0. The characteristic length xi is of the form xi approximately p(-nu) with nu=1/(2-mu) in region (b), but depends on L as well in region (c). A directed model of shortest paths is solved and compared with numerical results.

GENERALIZED SIMULATED ANNEALING METHOD IN THE ANALYSIS OF ATOM-ATOM INTERACTION

Abstract The techniques of generalized simulated annealing are here presented in a way to fit the external turning points of a diatomic molecule potential energy curve. In order to evaluate the advantages of this method the long-range part of the potential energy curve for the A 1 Σ + u electronic state of the 6 Li 2 molecule is treated using the multipolar expansion and the asymptotic exchange energy considering the gradual change from a Hunds case a towards Hunds case c. The results are carefully compared with previous determinations using conventional fitting methods of molecular spectroscopy.

Detrended fluctuation analysis of a systolic blood pressure control loop

We use detrended fluctuation analysis (DFA) to study the dynamics of blood pressure oscillations and its feedback control in rats by analyzing systolic pressure time series before and after a surgical procedure that interrupts its control loop. We found, for each situation, a crossover between two scaling regions characterized by exponents that reflect the nature of the feedback control and its range of operation. In addition, we found evidence of adaptation in the dynamics of blood pressure regulation a few days after surgical disruption of its main feedback circuit. Based on the paradigm of antagonistic, bipartite (vagal and sympathetic) action of the central nerve system, we propose a simple model for pressure homeostasis as the balance between two nonlinear opposing forces, successfully reproducing the crossover observed in the DFA of actual pressure signals.

Using entropy-based methods to study general constrained parameter optimization problems

We propose the use of physics techniques for entropy determination on constrained parameter optimization problems. The main feature of such techniques, the construction of an unbiased walk on energy space, suggests their use on the quest for optimal solutions of an optimization problem. Moreover, the entropy, and its associated density of states, give us information concerning the feasibility of solutions.

Why trees live longer

Through simulations of the bit string model for biological aging, we reproduced the observed feature of trees and some species of fish of high maximum lifespans if fertility increases with age. Our results provide an additional evidence for the importance of the mutation accumulation theory from biological aging.

Magnetotransport in nanostructures: The role of inhomogeneous currents

In the study of electronic transport in nanostructures, electric current is commonly considered homogeneous along the sample. We use a method to calculate the magnetoresistance of magnetic nanostructures where the current density may vary in space. The current distribution is numerically calculated by combining micromagnetic simulations with an associated resistor network and by solving the latter with a relaxation method. As an example, we consider a Permalloy disk exhibiting a vortex-like magnetization profile. We find that the current density is inhomogeneous along the disk, and that during the core magnetization reversal it is concentrated toward the center of the vortex and is repelled by the antivortex. We then consider the effects of the inhomogeneous current density on spin-torque transfer. The numerical value of the critical current density necessary to produce a vortex core reversal is smaller than the one that does not take the inhomogeneity into account.

THE ONSET OF MACKEY–GLASS LEUKEMIA AT THE EDGE OF CHAOS

In this paper, we revisit the Mackey–Glass model for blood-forming process which was proposed to describe the spontaneous fluctuations of the blood cell counts in normal individuals and the first stage of chronic myelocytic (or granylocytic) leukemia (CML). We obtain the bifurcation diagram as a function of the time delay parameter and show that the onset of leukemia is related to instabilities associated to the presence of periodic windows in the midst of a chaotic regime. We also introduce a very simple modification in the death rate parameter in order to simulate the accumulation of cells and the progressive increase of the minima counts experimentally observed in the final stage of the disease in CML patients. The bifurcation diagram as a function of the death rate parameter is also obtained and we discuss the effects of treatments like leukapheresis.

Strategies of Reproduction and Longevity

In this work we try to verify whether the increased lifespan of trees and some lobsters, like Homarus, whose fertility increases with advancing age, can be explained by the mutation accumulation theory of biological ageing. Computer simulations of the Penna model seems to support this hypothesis, showing that it is a robust strategy of reproduction.

Entropy-based analysis of the number partitioning problem.

In this paper we apply the multicanonical method of statistical physics on the number partitioning problem (NPP). This problem is a basic NP-hard problem from computer science, and can be formulated as a spin-glass problem. We compute the spectral degeneracy, which gives us information about the number of solutions for a given cost E and cardinality difference m. We also study an extension of this problem for Q partitions. We show that a fundamental difference on the spectral degeneracy of the generalized (Q>2) NPP exists, which could explain why it is so difficult to find good solutions for this case.

Beyond the Hubbard-I solution with a one-pole self-energy at half-filling within the moment approach

We have postulated a single pole for the self-energy, Σ(k,ω), looking for the consequences on the one-particle Green function, G(k,ω) in the Hubbard model. We find that G(k,ω) satisfies the first two sum rules or moments of Nolting (Z. Physik 255 (1972) 25) for any values of the two unknown k parameters of Σ(k,ω). In order to find these two parameters we have used the third and four sum rules of Nolting. G(k,ω) turns out to be identical to the one of Nolting (Z. Physik 255 (1972) 25), which is beyond a Hubbard-I solution since satisfies four sum rules. With our proposal we have been able to obtain an expansion in powers of U for the self-energy (here to second order in U). We present numerical results at half-filling for (1) the static spin susceptibility, χ(T) vs. T/t and (2) the band narrowing parameter, B(T) vs. T/t. The two-pole ansatz of Nolting for the one-particle Green function is equivalent to a single pole ansatz for the self-energy which remains the fundamental quantity for more elaborated calculations when, for example, lifetime effects are included.