Spatiotemporal and statistical symmetries

The notion of symmetries, either statistical or deterministic, can be useful for the characterization of complex systems and their bifurcations. In this paper, we investigate the connection between the (microscopic) spatiotemporal symmetries of a space-time functionu(x, t), on the one hand, and the (macroscopic) symmetries of statistical quantities such as the spatial (resp. temporal) two-point correlations and the spatial (resp. temporal) average, on the other hand. We show, how, under certain conditions, these symmetries are related to the symmetries of the orbits described byu(x, t) in the characteristic (phase) spaces. We also determine the largest group of spatiotemporal symmetries (in the sense introduced in our earlier work) satisfied by a given space-time functionu(x, t) and indicate how to extract the subgroups of point symmetries, namely those directly implemented on the space and time variables. Conversely, we determine all the functions invariant by a given space-time symmetry group. Finally, we illustrate all the previous points with specific examples.     

Structural and electronic effects in metallocene catalysts studied by x‐ray techniques

A series of metallocenes, namely, [Cp₂ZrCl₂], [(MeCp)₂ZrCl₂], [(nBuCp)₂ZrCl₂], [(iBuCp)₂ZrCl₂], [(tBuCp)₂ZrCl₂], [Et(Ind)₂ZrCl₂], [Et(IndH₄)₂ZrCl₂], and [MeSi₂(Ind)₂ZrCl₂)] were analyzed by extended x‐ray absorption fine structure (EXAFS) and x‐ray photoelectron spectroscopy (XPS). Complementary techniques, UV–vis spectroscopy and cyclic and differential pulse voltammetry, were employed to characterize the organometallic complexes. The catalysts were evaluated in ethylene polymerization, having methylaluminoxane (MAO) as the cocatalyst, and the resulting polymers were characterized by gel permeation chromatography. The structural and electronic effects caused by the coordination sphere around the metal center and their effects on the catalytic activity and polymer characteristics are discussed. Copyright © 2008 John Wiley & Sons, Ltd.     

Nonextensive thermostatistics and the H theorem

The kinetic foundations of Tsallis' nonextensive thermostatistics are investigated through Boltzmann's transport equation approach. Our analysis follows from a nonextensive generalization of the "molecular chaos hypothesis." For q>0, the q-transport equation satisfies an H theorem based on Tsallis entropy. It is also proved that the collisional equilibrium is given by Tsallis' q-nonextensive velocity distribution.     

Gated-controlled electron pumping in connected quantum rings

We study the electronic transport across connected quantum rings attached to leads and subjected to time-harmonic side-gate voltages. Using the Floquet formalism, we calculate the net pumped current generated and controlled by the side-gate voltage. The control of the current is achieved by varying the phase shift between the two side-gate voltages as well as the Fermi energy. In particular, the maximum current is reached when the side-gate voltages are in quadrature. This new design based on connected quantum rings controlled without magnetic fields can be easily integrated in standard electronic devices.     

EDXRF and multivariate statistical analysis of fragments from Marajoara ceramics

In this work, 102 fragments of Marajoara ceramics, belonging to the National Museum collection (Rio de Janeiro, Brazil), were analyzed using energy dispersive X‐ray fluorescence (EDXRF) and principal component analysis (PCA) in order to identify possible groups of samples that present similar behaviors or different characteristics. This information will give an important aid to a more accurate classification of these artifacts. The EDXRF measurements were carried out with a portable system developed in the Nuclear Instrumentation Laboratory consisting of an Oxford TF3005 X‐ray tube, with W anode, and an Si‐PIN XR‐100CR detector from Amptek, working at 25 kV and 100 µA, acquisition time of 600 s and a beam collimation of 2 mm. PCA applied to the X‐ray fluorescence results revealed a clear cluster separation to the samples. Copyright © 2009 John Wiley & Sons, Ltd.     

Entropic information for travelling solitons in Lorentz and CPT breaking systems

In this work we group four research topics apparently disconnected, namely solitons, Lorentz symmetry breaking, supersymmetry, and entropy. Following a recent work (Gleiser and Stamatopoulos, 2012), we show that it is possible to construct in the context of travelling wave solutions a configurational entropy measure in functional space, from the field configurations. Thus, we investigate the existence and properties of travelling solitons in Lorentz and CPT breaking scenarios for a class of models with two interacting scalar fields. Here, we obtain a complete set of exact solutions for the model studied which display both double and single-kink configurations. In fact, such models are very important in applications that include Bloch branes, Skyrmions, Yang–Mills, Q-balls, oscillons and various superstring-motivated theories. We find that the so-called Configurational Entropy (CE) for travelling solitons shows that the best value of parameter responsible to break the Lorentz symmetry is one where the energy density is distributed equally around the origin. In this way, the information-theoretical measure of travelling solitons in Lorentz symmetry violation scenarios opens a new window to probe situations where the parameters responsible for breaking the symmetries are arbitrary. In this case, the CE selects the best value of the parameter in the model.