The sigma-isotypic decomposition and the sigma-index of reversible-equivariant systems

This work is concerned with dynamical systems in presence of symmetries and reversing symmetries. We describe a construction process of subspaces that are invariant by linear Gamma-reversible-equivariant mappings, where Gamma is the compact Lie group of all the symmetries and reversing symmetries of such systems. These subspaces are the sigma-isotypic components, first introduced by Lamb and Roberts in (1999) [10] and that correspond to the isotypic components for purely equivariant systems. In addition, by representation theory methods derived from the topological structure of the group Gamma, two algebraic formulae are established for the computation of the sigma-index of a closed subgroup of Gamma. The results obtained here are to be applied to general reversible-equivariant systems, but are of particular interest for the more subtle of the two possible cases, namely the non-self-dual case. Some examples are presented. (C) 2011 Elsevier BM. All rights reserved.

Integral form of Yang-Mills equations and its gauge invariant conserved charges

Despite the fact that the integral form of the equations of classical electrodynamics is well known, the same is not true for non-Abelian gauge theories. The aim of the present paper is threefold. First, we present the integral form of the classical Yang-Mills equations in the presence of sources and then use it to solve the long-standing problem of constructing conserved charges, for any field configuration, which are invariant under general gauge transformations and not only under transformations that go to a constant at spatial infinity. The construction is based on concepts in loop spaces and on a generalization of the non-Abelian Stokes theorem for two-form connections. The third goal of the paper is to present the integral form of the self-dual Yang-Mills equations and calculate the conserved charges associated with them. The charges are explicitly evaluated for the cases of monopoles, dyons, instantons and merons, and we show that in many cases those charges must be quantized. Our results are important in the understanding of global properties of non-Abelian gauge theories.

Tank experiments with borehole self-potential data

Despite their importance in the evaluation of petroleum and gas reservoirs, measurements of self-potential data under borehole conditions (well-logging) have found only minor applications in aquifer and waste-site characterization. This can be attributed to lower signals from the diffusion fronts in near-surface environments because measurements are made long after the drilling of the well, when concentration fronts are already disappearing. Proportionally higher signals arise from streaming potentials that prevent using simple interpretation models that assume signals from diffusion only. Our laboratory experiments found that dual-source self-potential signals can be described by a simple linear model, and that contributions (from diffusion and streaming potentials) can be isolated by slightly perturbing the borehole conditions. Perturbations are applied either by changing the concentration of the borehole-filling solution or its column height. Parameters useful for formation evaluation can be estimated from data measured during perturbations, namely, pore water resistivity, pressure drop across the borehole wall, and electrokinetic coupling parameter. These are important parameters to assess, respectively, water quality, aquifer lateral continuity, and interfacial properties of permeable formations.

Effect of Temperature on the Degree of Conversion and Working Time of Dual-Cured Resin Cements Exposed to Different Curing Conditions

Objectives: This study evaluated the degree of conversion (DC) and working time (WT) of two commercial, dual-cured resin cements polymerized at varying temperatures and under different curing-light accessible conditions, using Fourier transformed infrared analysis (FTIR). Materials and Methods: Calibra (Cal; Dentsply Caulk) and Variolink II (Ivoclar Vivadent) were tested at 25 degrees C or preheated to 37 degrees C or 50 degrees C and applied to a similar-temperature surface of a horizontal attenuated-total-reflectance unit (ATR) attached to an infrared spectrometer. The products were polymerized using one of four conditions: direct light exposure only (600 mW/cm(2)) through a glass slide or through a 1.5- or 3.0-mm-thick ceramic disc (A2 shade, IPS e.max, Ivoclar Vivadent) or allowed to self-cure in the absence of light curing. FTIR spectra were recorded for 20 min (1 spectrum/s, 16 scans/spectrum, resolution 4 cm(-1)) immediately after application to the ATR. DC was calculated using standard techniques of observing changes in aliphatic-to-aromatic peak ratios precuring and 20-min postcuring as well as during each 1-second interval. Time-based monomer conversion analysis was used to determine WT at each temperature. DC and WT data (n=6) were analyzed by two-way analysis of variance and Tukey post hoc test (p=0.05). Results: Higher temperatures increased DC regardless of curing mode and product. For Calibra, only the 3-mm-thick ceramic group showed lower DC than the other groups at 25 degrees C (p=0.01830), while no significant difference was observed among groups at 37 degrees C and 50 degrees C. For Variolink, the 3-mm-thick ceramic group showed lower DC than the 1-mm-thick group only at 25 degrees C, while the self-cure group showed lower DC than the others at all temperatures (p=0.00001). WT decreased with increasing temperature: at 37 degrees C near 70% reduction and at 50 degrees C near 90% for both products, with WT reduction reaching clinically inappropriate times in some cases (p=0.00001). Conclusion: Elevated temperature during polymerization of dual-cured cements increased DC. WT was reduced with elevated temperature, but the extent of reduction might not be clinically acceptable.