Computational applications of nonextensive statistical mechanics

Computational applications of the nonextensive entropy _Sq$S_q$ and nonextensive statistical mechanics, a current generalization of the Boltzmann–Gibbs (BG) theory, are briefly reviewed. The corresponding bibliography is provided as well.     

Discrete-charge quantum circuits and electrical resistance

From the theory of quantum LC circuits with discrete charge, and semiclassical considerations, we obtain approximate energy eigenvalues, depending on the parameter . Next, we include electrical resistance for the quantum RLC circuit, obtaining a relation that strongly reminds us of the Landauer formula.     

Quantum RLC circuits: Charge discreteness and resonance

In a recent article [C.A. Utreras-Díaz, Phys. Lett. A 372 (2008) 5059], we have advanced a semiclassical theory of quantum circuits with discrete charge and electrical resistance. In this work, we present a few elementary applications of this theory. For the zero resistance inductive circuit, we obtain the Stark ladder energies in yet another way; for the circuit driven by a combination d.c. plus a.c. electromotive force (emf) we generalize earlier results by Chandía et al. [K. Chandía, J.C. Flores, E. Lazo, Phys. Lett. A 359 (2006) 693]. As a second application, we investigate the effect of electrical resistance and charge discreteness, in the resonance conditions of a series RLC quantum circuit.     

Chemical Equilibrium, Free Energy, and Entropy of Mixing

In this paper we describe an approach for teaching the relation between chemical equilibrium and free energy that is, according to our experience, very efficient and enlightening. This approach has a strong visual appeal and can be used at different levels, from simple presentation of the results as graphs of free energy versus reaction mixture composition, up to full derivation of formulas to find the equations of the curves.     

Ising spin glass on a D = 3 hierarchical lattice: Effects of tailed coupling distributions

Within a real-space renormalization-group framework, we approach the cubic lattice through a D = 3 diamond-like hierarchical lattice. The model is a standard, nearest-neighbor, Ising spin glass with coupling constants {J_ij} distributed according to the family of continuous probability distributions P_q(J_ij) ∝ 1/[1 + (q − 1)J_ij²/2J²]^{1/(q − 1)} (if 1 + (q − 1) J_ij²/2J² > 0, and zero otherwise; q ). Such distributions, which arise naturally in the treatment, within the recently proposed nonextensive thermostatistics, of anomalous diffusion, reproduce the usual, Gaussian case, for q → 1. Moreover, they present a second moment J_ij² proportional to (5 − 3q)⁻¹ for q < 5/3, diverging for q ≥ 5/3, but keeping a finite width at midheight. In the limit q → 3, P_q(J_ij) collapses with the abscissa, and so the width at midheight diverges. We compute the q-dependence of the spin-glass critical temperature T_c. We show numerically that T_c does not scale with J_ij^21/2 (contrary to the usual belief), but rather with the width at midheight of P_q(J_ij). Our results suggest that T_c vanishes as −1/q when q → −∞; furthermore, we verified that T_c diverges exponentially when q approaches 3 from below.     

Quenched bond-dilute Ising ferromagnet in square lattice: Thermodynamical properties

Within an effective field framework which substantially improves the Molecular Field Approximation, we calculate the phase diagram, magnetization, specific heat and susceptibility associated with the quenched bond-dilute Ising ferromagnet in square lattice. The results are qualitatively (and within certain extent quantitatively) satisfactory; in particular the effects, on the specific heat and susceptibility, of the (eventually) coexisting finite and infinite clusters are exhibited.     

Distribution of deoxynivalenol in wheat,wheat flour,bran, and gluten,and variability associated with the test procedure

Analytical data obtained on deoxynivalenol (DON) concentration in naturally contaminated wheat during processing in an industrial mill were statistically analyzed, and the distribution functions of DON concentration in lots of wheat, bran, wheat flour, and gluten were estimated. The analytical method had acceptable precision (HORRAT 0.25-0.32) for each test sample. The total variance combined sampling, sample preparation, and analytical variances were 0.188, 0.033, 0.42, and 0.0014 ppm2 for wheat, 1.93; flour, 0.99; bran, 4.68; and gluten, 0.29, respectively. The distribution function of DON contamination presented an asymmetric tail for high values of concentration in wheat grains and wheat flour; in bran it seemed to be bimodal with 2 separated peaks of different concentrations; in gluten the normal distribution function gave a reasonably good fit to empirical data. The function eta(c) = -In(-Inp), where p (c) is the cumulative distribution function was linear with c in the so-called extreme-value type I distribution and could be fitted by a cubic polynomial in c in the distributions determined for all the products. This variability and distributional information contributes to the design of better sampling plans in order to reduce the total variability and to estimate errors in the evaluation of DON concentration in lots of wheat and wheat products.     

Self-assembled films of poly(o-ethoxyaniline) complexed with sulfonated lignin

The interaction of poly(o-ethoxyaniline) (POEA) doped with HCl and sulfonated lignin (SL) was investigated using UV–Vis spectroscopy in order to probe the influence of pH and quantity of SL on the formation of a polyelectrolyte complex. The introduction of SL into the HCl doped POEA solution screens the positive charges of the protonated POEA allowing further protons to be pumped into the conducting polymers thus increasing its doping level. In addition, the strong interaction between these two electrolytes caused POEA to remain doped within a wide pH range. Layers were built from aqueous solutions of the complex formed by POEA and SL which were alternated with either pure POEA or sulfonated polystyrene in the form of layer-by-layer films. The resulting multilayer films remained doped even at pH 9.0, due to the strong complex formation, which prevents POEA from deprotonating. Surface potential measurements showed that the potential for the POEA+SL complex is more positive than for films with each layer investigated separately, thus confirming the strong interaction between POEA and SL.     

Complete assignment of 1H and 13C NMR data for three aryltetralin lignan lactones

We describe the complete 1H and 13C NMR analysis of three aryltetralin lignan lactones (polygamain, morelensin and 4,5-dimethoxymorelensin) using modern NMR techniques such as COSY, HMQC, HMBC, 2D-J-resolved and NOE experiments. The relative stereochemistry of these compounds, which is very important with regard to their biological activity, was completely determined.