Comment on "Correlated electron-nuclear dynamics: Exact factorization of the molecular wavefunction" [J. Chem. Phys. 137, 22A530 (2012)]

In spite of the relevance of the proposal introduced in the recent work A. Abedi, N. T. Maitra and E. K. U. Gross, J. Chem. Phys. 137, 22A530, 2012, there is an important ingredient which is missing. Namely, the proof that the norms of the electronic and nuclear wavefunctions which are the solutions to the nonlinear equations of motion are preserved by the evolution. To prove the conservation of these norms is precisely the objective of this Comment.Comment: 2 pages, published versio

Blade loss transient dynamics analysis, volume 1. Task 1: Survey and perspective

An analytical technique was developed to predict the behavior of a rotor system subjected to sudden unbalance. The technique is implemented in the Turbine Engine Transient Rotor Analysis (TETRA) computer program using the component element method. The analysis was particularly aimed toward blade-loss phenomena in gas turbine engines. A dual-rotor, casing, and pylon structure can be modeled by the computer program. Blade tip rubs, Coriolis forces, and mechanical clearances are included. The analytical system was verified by modeling and simulating actual test conditions for a rig test as well as a full-engine, blade-release demonstration

Nonextensive thermodynamic functions in the Schr\"odinger-Gibbs ensemble

Schr\"odinger suggested that thermodynamical functions cannot be based on the gratuitous allegation that quantum-mechanical levels (typically the orthogonal eigenstates of the Hamiltonian operator) are the only allowed states for a quantum system [E. Schr\"odinger, Statistical Thermodynamics (Courier Dover, Mineola, 1967)]. Different authors have interpreted this statement by introducing density distributions on the space of quantum pure states with weights obtained as functions of the expectation value of the Hamiltonian of the system. In this work we focus on one of the best known of these distributions, and we prove that, when considered in composite quantum systems, it defines partition functions that do not factorize as products of partition functions of the noninteracting subsystems, even in the thermodynamical regime. This implies that it is not possible to define extensive thermodynamical magnitudes such as the free energy, the internal energy or the thermodynamic entropy by using these models. Therefore, we conclude that this distribution inspired by Schr\"odinger's idea can not be used to construct an appropriate quantum equilibrium thermodynamics.Comment: 32 pages, revtex 4.1 preprint style, 5 figures. Published version with several changes with respect to v2 in text and reference

Blade loss transient dynamics analysis, volume 2. Task 2: Theoretical and analytical development. Task 3: Experimental verification

The component element method was used to develop a transient dynamic analysis computer program which is essentially based on modal synthesis combined with a central, finite difference, numerical integration scheme. The methodology leads to a modular or building-block technique that is amenable to computer programming. To verify the analytical method, turbine engine transient response analysis (TETRA), was applied to two blade-out test vehicles that had been previously instrumented and tested. Comparison of the time dependent test data with those predicted by TETRA led to recommendations for refinement or extension of the analytical method to improve its accuracy and overcome its shortcomings. The development of working equations, their discretization, numerical solution scheme, the modular concept of engine modelling, the program logical structure and some illustrated results are discussed. The blade-loss test vehicles (rig full engine), the type of measured data, and the engine structural model are described

Statistics and Nos\'e formalism for Ehrenfest dynamics

Quantum dynamics (i.e., the Schr\"odinger equation) and classical dynamics (i.e., Hamilton equations) can both be formulated in equal geometric terms: a Poisson bracket defined on a manifold. In this paper we first show that the hybrid quantum-classical dynamics prescribed by the Ehrenfest equations can also be formulated within this general framework, what has been used in the literature to construct propagation schemes for Ehrenfest dynamics. Then, the existence of a well defined Poisson bracket allows to arrive to a Liouville equation for a statistical ensemble of Ehrenfest systems. The study of a generic toy model shows that the evolution produced by Ehrenfest dynamics is ergodic and therefore the only constants of motion are functions of the Hamiltonian. The emergence of the canonical ensemble characterized by the Boltzmann distribution follows after an appropriate application of the principle of equal a priori probabilities to this case. Once we know the canonical distribution of a Ehrenfest system, it is straightforward to extend the formalism of Nos\'e (invented to do constant temperature Molecular Dynamics by a non-stochastic method) to our Ehrenfest formalism. This work also provides the basis for extending stochastic methods to Ehrenfest dynamics.Comment: 28 pages, 1 figure. Published version. arXiv admin note: substantial text overlap with arXiv:1010.149

Ehrenfest dynamics is purity non-preserving: a necessary ingredient for decoherence

We discuss the evolution of purity in mixed quantum/classical approaches to electronic nonadiabatic dynamics in the context of the Ehrenfest model. As it is impossible to exactly determine initial conditions for a realistic system, we choose to work in the statistical Ehrenfest formalism that we introduced in Ref. 1. From it, we develop a new framework to determine exactly the change in the purity of the quantum subsystem along the evolution of a statistical Ehrenfest system. In a simple case, we verify how and to which extent Ehrenfest statistical dynamics makes a system with more than one classical trajectory and an initial quantum pure state become a quantum mixed one. We prove this numerically showing how the evolution of purity depends on time, on the dimension of the quantum state space $D$, and on the number of classical trajectories $N$ of the initial distribution. The results in this work open new perspectives for studying decoherence with Ehrenfest dynamics.Comment: Revtex 4-1, 14 pages, 2 figures. Final published versio

Teacher participation & qualifications regarding extra-curricula sport activities

En la presente investigación se aborda el estudio y análisis de la intervención docente del profesorado de las actividades físico-deportivas extraescolares en los centros educativos de Educación Secundaria de la Comunidad de Madrid en función de su formación inicial. La investigación sigue una metodología cuantitativa de corte descriptivo, a través de la encuesta. El tamaño de la muestra es de 350 personas y para su cálculo se consideraron varios aspectos: la población era finita; se recurre en la varianza poblacional al supuesto más desfavorable donde “P” y “Q” son iguales con el 50% cada uno; el intervalo de confianza es del 95,5%, con un margen de error del ± 4,75%. Los resultados revelan que existe un alto porcentaje de profesores que no realizan una programación de sus actividades ni tampoco evalúan a sus alumnos. Asimismo, los resultados sugieren que la intervención docente de las personas no tituladas es menos adecuada.In this research is done the study and analysis of teacher intervention in the extra-curricular sport activities of educational centres for secondary education in Comunidad de Madrid. The research follows a quantitative methodology with a descriptive profile which, across survey, in which a cross-sectional survey have been carried out.The size of the sample is 350 people and for its calculation, several aspects have been considered: The population was finite; the least favourable hypothesis is considered in the population variation, where “P” and “Q” are equal, with 50% each; the confidence interval is 95%, with an error margin of ± 4.75%. The results reveal that exits a high percentage of teachers who don’t programme their activities and don’t evaluate their students. Furthermore, the results suggest that the teacher intervention is less adequate to the teachers who don’t have any qualification

Orientaciones metodológicas : la titulación de farmacia y las tecnologías de la infomación y las comunicaciones en el espacio europeo de enseñanza superior

Entre las orientaciones metodológicas de las administraciones educativas para el desarrollo de las programaciones docentes de la titulación de Licenciado en Farmacia, centramos nuestra atención en el uso de las tecnologías de la información y las comunicaciones (TIC), intentado determinar su estatus actual dentro del área de conocimiento farmacéutico, en cuanto a su nivel de desarrollo y utilización por parte de los docentes y el alumnado. Para ello, realizamos un análisis del uso de estas tecnologías entre estos dos grupos dentro de la Facultad de Farmacia de la Universidad de Granada. Además, realizamos una discusión sobre lo que debe ser su futura evolución y expansión como herramienta del proceso de enseñanza/aprendizaje dentro del Espacio Europeo de Enseñanza Superior (EEES)