Quasi-equilibrium volume changes of polyaniline films upon redox switching. Formal potential distribution and configurational modeling

The quasi-equilibrium electrochemomechanical behavior of relatively thick polyaniline films in sulfuric acid is investigated through experimental measurements and theoretical modeling. The leucoemeraldine (LE)-emeraldine (EM) conversion, or redox switching, is studied. The dependence of film volume and electrochemical charge is determined as a function of applied potential. It is observed that the film volume follows the charge, showing an expansion during the second half of the LE-EM oxidation. The model postulates the existence of a stable intermediate, protoemeraldine (PE), with a formal potential distribution for the PE-EM reaction. The volume change is modeled statistically considering contributions from mixing, polymer deformation, and electrostatic charge. The model shows very good agreement with the experiments, indicating that, in the conditions studied, the deformation contribution dominates the volume changes as a result of the conformational modifications undergone by the polymer in the PE-EM oxidation.     

Particle scattering in loop quantum gravity

We devise a technique for defining and computing -point functions in the context of a background-independent gravitational quantum field theory. We construct a tentative implementation of this technique in a perturbatively finite model defined using spin foam techniques in the context of loop quantum gravity.     

Magnetoelastic instability in molecular antiferromagnetic rings

Lattice stability in a model of an antiferromagnetic ring coupled to adiabatic phonons is investigated for different values of the spin and numbers of magnetic sites. The magnetoelastic transition is shown to be heavily affected by the spin value, displaying a qualitative difference in the nature of the instability for spin one-half. Among the different synthesized materials, Cu8 seems to be the best candidate to observe lattice dimerization in these systems. Our analysis excludes stable lattice distortions in higher spin rings. The effects of thermal fluctuations are studied in the Cu8 model, where a characteristic crossover temperature is estimated.     

Correlations in a Mozart's music score (K-73x) with palindromic and upside-down structure

In this work, we study long-range correlations in a “Scherzo-Duetto di Mozart” score (K-73x) for two violins. This is a fascinating piece, as the second violin part is upside down on the same sheet below the first violin, and some parts are like a palindrome. Given such ingenious structure, it is expected the existence of long-range correlations in the score structure. In order to quantify long-range correlations, we considered the music score as a sequence of integer numbers, each of them corresponding to last common denominator units of note. By using detrended fluctuation analysis (DFA), correlations are quantified by means of the scaling exponent that reflects the type of correlations for a given distance between neighbors note. The following conclusions can be drawn from the analysis: (a) For about 10-25 neighbor note distances, correlations are similar to 1/f-noise. This is an interesting finding since it has been shown that pleasant sounds for humans display a behavior similar to 1/f noise. (b) As the neighbor note distance increases, the long-range correlations decays continuously. For some score sections, the music score behaves like non-correlated (i.e., purely random) noise. Summing up, the results show that the studied Mozart's score contains a certain degree of correlation for relatively small note distances, and becomes close to non-correlated behavior for long note distances. We considered also the sequence constructed by considering the distance between the simultaneously played notes of the two violins. Interestingly, for relatively small neighbor note distances, a scaling behavior similar to that found for individual violins is also displayed. In some sense, this is an expression of the specific structure (palindromes plus upside down construction) used by Mozart in the composition of this music score. Although we focused on a particular high-art music score, our results suggest that modern methods borrowed from statistical physics can be useful for the systematic study of music composition techniques.     

One‐pot Preparation,Spectroscopic and Structural Characterization of Mercury(II) Complexes of Bulky Diimines with Halides and Pseudohalides

The preparation and characterization of two novel HgCl₂ and Hg(SCN)₂ complexes with bis[N‐(2‐tert‐butylphenyl)imine]acenaphthene is here described. One‐pot reaction techniques were used, leading to high yields of 75 % and 81 %, respectively. The complexes were characterized by microanalysis, i.r. and ¹HNMR spectroscopy, and by single crystal X‐ray diffraction. The structures of the complexes present similar characteristics, the most outstanding being the formation of dimers via intermolecular interaction. Whereas the HgCl₂ complex shows a unidimensional network due to strong π–π interactions, its Hg(SCN)₂ counterpart displays a supramolecular arrangement resulting from non classical hydrogen bond formation.     

Renormalization Group Flow¶of the Two-Dimensional Hierarchical Coulomb Gas

We consider a quasilinear parabolic differential equation associated with the renormalization group transformation of the two-dimensional hierarchical Coulomb system in the limit as the size of the block L&\darr; 1. We show that the initial value problem is well defined in a suitable function space and the solution converges, as t→∞, to one of the countably infinite equilibrium solutions. The j ^th nontrivial equilibrium solution bifurcates from the trivial one at . These solutions are fully described and we provide a complete analysis of their local and global stability for all values of inverse temperature β >0. Gallavotti and Nicoló's conjecture on infinite sequence of “phases transitions” is also addressed. Our results rule out an intermediate phase between the plasma and the Kosterlitz–Thouless phases, at least in the hierarchical model we consider. Received: 29 November 1999 / Accepted: 13 January 2001     

Topological duality for Tarski algebras

In this paper we will generalize the representation theory developed for finite Tarski algebras given in [7]. We will introduce the notion of Tarski space as a generalization of the notion of dense Tarski set, and we will prove that the category of Tarski algebras with semi-homomorphisms is dually equivalent to the category of Tarski spaces with certain closed relations, called T-relations. By these results we will obtain that the algebraic category of Tarski algebras is dually equivalent to the category of Tarski spaces with certain partial functions. We will apply these results to give a topological characterization of the subalgebras. Received August 21, 2005; accepted in final form December 5, 2006.