Generalized isotropic Lipkin-Meshkov-Glick models: ground state entanglement and quantum entropies

We introduce a new class of generalized isotropic Lipkin–Meshkov–Glick models with su(m+1) spin and long-range non-constant interactions, whose non-degenerate ground state is a Dicke state of su(m+1) type. We evaluate in closed form the reduced density matrix of a block of Lspins when the whole system is in its ground state, and study the corresponding von Neumann and Rényi entanglement entropies in the thermodynamic limit. We show that both of these entropies scale as a log L when L tends to infinity, where the coefficient a is equal to (m  −  k)/2 in the ground state phase with k vanishing magnon densities. In particular, our results show that none of these generalized Lipkin–Meshkov–Glick models are critical, since when L-->∞ their Rényi entropy R_q becomes independent of the parameter q. We have also computed the Tsallis entanglement entropy of the ground state of these generalized su(m+1) Lipkin–Meshkov–Glick models, finding that it can be made extensive by an appropriate choice of its parameter only when m-k≥3. Finally, in the su(3) case we construct in detail the phase diagram of the ground state in parameter space, showing that it is determined in a simple way by the weights of the fundamental representation of su(3). This is also true in the su(m+1) case; for instance, we prove that the region for which all the magnon densities are non-vanishing is an (m  +  1)-simplex in R^m whose vertices are the weights of the fundamental representation of su(m+1).

Surface irregularity factor as a parameter to evaluate the fatigue damage state of CFRP

This work presents an optical non-contact technique to evaluate the fatigue damage state of CFRP structures measuring the irregularity factor of the surface. This factor includes information about surface topology and can be measured easily on field, by techniques such as optical perfilometers. The surface irregularity factor has been correlated with stiffness degradation, which is a well-accepted parameter for the evaluation of the fatigue damage state of composite materials. Constant amplitude fatigue loads (CAL) and realistic variable amplitude loads (VAL), representative of real in- flight conditions, have been applied to “dog bone” shaped tensile specimens. It has been shown that the measurement of the surface irregularity parameters can be applied to evaluate the damage state of a structure, and that it is independent of the type of fatigue load that has caused the damage. As a result, this measurement technique is applicable for a wide range of inspections of composite material structures, from pressurized tanks with constant amplitude loads, to variable amplitude loaded aeronautical structures such as wings and empennages, up to automotive and other industrial applications.

The 12-Item General Health Questionnaire (GHQ-12): Reliability,external validity and factor structure in the Spanish population

The purpose of this study was to analyze the internal consistency and the external and structure validity of the 12-Item General Health Questionnaire (GHQ-12) in the Spanish general population. A stratified sample of 1001 subjects, ages between 25 and 65 years, taken from the general Spanish population was employed. The GHQ-12 and the Inventory of Situations and Responses of Anxiety-ISRA were administered. A Cronbach’s alpha of .76 (Standardized Alpha: .78) and a 3-factor structure (with oblique rotation and maximum likelihood procedure) were obtained. External validity of Factor I (Successful Coping) with the ISRA is very robust (.82; Factor II, .70; Factor III, .75). The GHQ-12 shows adequate reliability and validity in the Spanish population. Therefore, the GHQ-12 can be used with efficacy to assess people’s overall psychological well-being and to detect non-psychotic psychiatric problems. Additionally, our results confirm that the GHQ-12 can best be thought of as a multidimensional scale that assesses several distinct aspects of distress, rather than just a unitary screening measure.