Higher order Lagrangian systems: Geometric structures, Dynamics, and Constraints

In order to study the connections between Lagrangian and Hamiltonian formalisms constructed from aperhaps singularhigher-order Lagrangian, some geometric structures are constructed. Intermediate spaces between those of Lagrangian and Hamiltonian formalisms, partial Ostrogradskiis transformations and unambiguous evolution operators connecting these spaces are intrinsically defined, and some of their properties studied. Equations of motion, constraints, and arbitrary functions of Lagrangian and Hamiltonian formalisms are thoroughly studied. In particular, all the Lagrangian constraints are obtained from the Hamiltonian ones. Once the gauge transformations are taken into account, the true number of degrees of freedom is obtained, both in the Lagrangian and Hamiltonian formalisms, and also in all the intermediate formalisms herein defined.

Stochastic semiclassical gravity

In the first part of this paper, we show that the semiclassical Einstein-Langevin equation, introduced in the framework of a stochastic generalization of semiclassical gravity to describe the back reaction of matter stress-energy fluctuations, can be formally derived from a functional method based on the influence functional of Feynman and Vernon. In the second part, we derive a number of results for background solutions of semiclassical gravity consisting of stationary and conformally stationary spacetimes and scalar fields in thermal equilibrium states. For these cases, fluctuation-dissipation relations are derived. We also show that particle creation is related to the vacuum stress-energy fluctuations and that it is enhanced by the presence of stochastic metric fluctuations.

Mode decomposition and renormalization in semiclassical gravity

We compute the influence action for a system perturbatively coupled to a linear scalar field acting as the environment. Subtleties related to divergences that appear when summing over all the modes are made explicit and clarified. Being closely connected with models used in the literature, we show how to completely reconcile the results obtained in the context of stochastic semiclassical gravity when using mode decomposition with those obtained by other standard functional techniques.

Proposed gravitational wave observatory based on solid elastic spheres

Spherical gravitational wave (GW) detectors offer a wealth of so far unexplored possibilities to detect gravitational radiation. We find that a sphere can be used as a powerful testbed for any metric theory of gravity, not only general relativity as considered so far, by making use of a deconvolution procedure for all the electric components of the Riemann tensor. We also find that the spheres cross section is large at two frequencies, and advantageous at higher frequencies in the sense that a single antenna constitutes a real xylophone in its own. Proposed GW networks will greatly benefit from this. The main features of a two large sphere observatory are reported.

Induced quantum metric fluctuations and the validity of semiclassical gravity

We propose a criterion for the validity of semiclassical gravity (SCG) which is based on the stability of the solutions of SCG with respect to quantum metric fluctuations. We pay special attention to the two-point quantum correlation functions for the metric perturbations, which contain both intrinsic and induced fluctuations. These fluctuations can be described by the Einstein-Langevin equation obtained in the framework of stochastic gravity. Specifically, the Einstein-Langevin equation yields stochastic correlation functions for the metric perturbations which agree, to leading order in the large N limit, with the quantum correlation functions of the theory of gravity interacting with N matter fields. The homogeneous solutions of the Einstein-Langevin equation are equivalent to the solutions of the perturbed semiclassical equation, which describe the evolution of the expectation value of the quantum metric perturbations. The information on the intrinsic fluctuations, which are connected to the initial fluctuations of the metric perturbations, can also be retrieved entirely from the homogeneous solutions. However, the induced metric fluctuations proportional to the noise kernel can only be obtained from the Einstein-Langevin equation (the inhomogeneous term). These equations exhibit runaway solutions with exponential instabilities. A detailed discussion about different methods to deal with these instabilities is given. We illustrate our criterion by showing explicitly that flat space is stable and a description based on SCG is a valid approximation in that case.

Cosmological perturbations from stochastic gravity

In inflationary cosmological models driven by an inflaton field the origin of the primordial inhomogeneities which are responsible for large-scale structure formation are the quantum fluctuations of the inflaton field. These are usually calculated using the standard theory of cosmological perturbations, where both the gravitational and the inflaton fields are linearly perturbed and quantized. The correlation functions for the primordial metric fluctuations and their power spectrum are then computed. Here we introduce an alternative procedure for calculating the metric correlations based on the Einstein-Langevin equation which emerges in the framework of stochastic semiclassical gravity. We show that the correlation functions for the metric perturbations that follow from the Einstein-Langevin formalism coincide with those obtained with the usual quantization procedures when the scalar field perturbations are linearized. This method is explicitly applied to a simple model of chaotic inflation consisting of a Robertson-Walker background, which undergoes a quasi-de Sitter expansion, minimally coupled to a free massive quantum scalar field. The technique based on the Einstein-Langevin equation can, however, deal naturally with the perturbations of the scalar field even beyond the linear approximation, as is actually required in inflationary models which are not driven by an inflaton field, such as Starobinsky¿s trace-anomaly driven inflation or when calculating corrections due to nonlinear quantum effects in the usual inflaton driven models.

Stability of de Sitter spacetime under isotropic perturbations in semiclassical gravity

A spatially flat Robertson-Walker spacetime driven by a cosmological constant is nonconformally coupled to a massless scalar field. The equations of semiclassical gravity are explicitly solved for this case, and a self-consistent de Sitter solution associated with the Bunch-Davies vacuum state is found (the effect of the quantum field is to shift slightly the effective cosmological constant). Furthermore, it is shown that the corrected de Sitter spacetime is stable under spatially isotropic perturbations of the metric and the quantum state. These results are independent of the free renormalization parameters.

Gravity in the Randall-Sundrum brane world

We discuss the weak gravitational field created by isolated matter sources in the Randall-Sundrum brane world. For the case of a single wall of positive tension, the field stays localized near the wall if the source is stationary. We calculate the leading Kaluza-Klein corrections to the linearized gravitational field of a nonrelativistic spherical object, which is different from the Schwarzschild solution at large distances. In the case of two branes of opposite tension, linearized Brans-Dicke (BD) gravity is recovered on either wall, with different BD parameters. On the wall with positive tension the BD parameter is larger than 3000 provided that the separation between walls is larger than 4 times the AdS radius. The gravitational field due to shadow matter is also considered.

Quantization of AdS3 black holes in external fields: semiclassical results from pure gravity

(2+1)-dimensional anti-de Sitter (AdS) gravity is quantized in the presence of an external scalar field. We find that the coupling between the scalar field and gravity is equivalently described by a perturbed conformal field theory at the boundary of AdS3. This allows us to perform a microscopic computation of the transition rates between black hole states due to absorption and induced emission of the scalar field. Detailed thermodynamic balance then yields Hawking radiation as spontaneous emission, and we find agreement with the semiclassical result, including greybody factors. This result also has application to four and five-dimensional black holes in supergravity.

Further insights on dynamic morphological transitions in quasi-two-dimensional electrodeposition

Dynamic morphological transitions in thin-layer electrodeposits obtained from copper sulphate solutions have been studied. The chemical composition of the electrodeposits indicates that they appear as a consequence of the competition between copper and cuprous oxide formation. In addition, the Ohmic control of the process is verified at initial stages of the deposit growth. At higher deposit developments, gravity-induced convection currents play a role in the control of the whole process and affect the position of these transitions.

Open licensing's impact on higher education resources colombian and catalan approaches

A new initiative has sprung on the path created by the Open Access (OA) movement: Open Education (OE). The initiative's aim is to open up all educational resources at all learning levels. In order to achieve this goal, several international institutions, like UNESCO and the OECD, have published reports, surveys and documents to help educational institutions in this endeavor. This global initiative needs a legal framework; as a result, efforts thus far have usually resorted to Open Licensing (OL), especially Creative Commons (CC) licensing. In fact, as a response to this new movement, Creative Commons launched a new program, ccLearn , which recognizes open licensing's impact on education and directly supports the idea of open educational resources (OER). However, there still remain a good amount of open questions: What is happening locally with OL in higher education? How are educational institutions receiving the initiative? How is it that the OL initiative relates to educational resources? Are there local examples of open educational resources (OER)? How do these local instances incorporate CC into their educational frameworks?. To this effect, this analysis aims to focus on the legal approach and specifically on the way the educational sector is using open licenses outside the English speaking world. It will do so by looking at the current situation in two specific scenarios, the Colombian and the Catalan experiences with open educational projects at the higher education level.

The european higher education area at work: Lights and shadows defining continuous assessment

The aim of this paper is to analyse how learning assessment, particularly the Continuous Assessment system, has been defined in the Public Administration and Management Diploma Course of the University of Barcelona (Spain). This course was a pioneering experiment at this university in implementing the guidelines of the European Higher Education Area (EHEA), and thus represents a good case study for verifying whether one of the cornerstones of the EHEA has been accomplished with success. Using data obtained from the Teaching Plans elaborated by the lecturers of each subject, we are able to establish that the CA system has been progressively accepted to such an extent that it is now the assessment formula used by practically all of the lecturers, conforming in this way to the protocols laid down by the Faculty of Law in which this diploma course is taught. Nevertheless, we find that high dispersion exists in how Continuous Assessment is actually defined. Indeed, it seems that there is no unified view of how Continuous Assessment should be performed. This dispersion, however, seems to diminish over time and raises some questions about the advisability of agreement on criteria, considering the potential which CA has as a pedagogical tool. Moreover, we find that the Unique Assessment system, which students may also apply for, is an option chosen only by a minority, with lecturers usually defining it as merely a theoretical and/or practical test, of little innovation in relation to traditional tests.

The european higher education area at work: Lights and shadows defining continuous assessment

The aim of this paper is to analyse how learning assessment, particularly the Continuous Assessment system, has been defined in the Public Administration and Management Diploma Course of the University of Barcelona (Spain). This course was a pioneering experiment at this university in implementing the guidelines of the European Higher Education Area (EHEA), and thus represents a good case study for verifying whether one of the cornerstones of the EHEA has been accomplished with success. Using data obtained from the Teaching Plans elaborated by the lecturers of each subject, we are able to establish that the CA system has been progressively accepted to such an extent that it is now the assessment formula used by practically all of the lecturers, conforming in this way to the protocols laid down by the Faculty of Law in which this diploma course is taught. Nevertheless, we find that high dispersion exists in how Continuous Assessment is actually defined. Indeed, it seems that there is no unified view of how Continuous Assessment should be performed. This dispersion, however, seems to diminish over time and raises some questions about the advisability of agreement on criteria, considering the potential which CA has as a pedagogical tool. Moreover, we find that the Unique Assessment system, which students may also apply for, is an option chosen only by a minority, with lecturers usually defining it as merely a theoretical and/or practical test, of little innovation in relation to traditional tests.

The european higher education area at work: Lights and shadows defining continuous assessment

The aim of this paper is to analyse how learning assessment, particularly the Continuous Assessment system, has been defined in the Public Administration and Management Diploma Course of the University of Barcelona (Spain). This course was a pioneering experiment at this university in implementing the guidelines of the European Higher Education Area (EHEA), and thus represents a good case study for verifying whether one of the cornerstones of the EHEA has been accomplished with success. Using data obtained from the Teaching Plans elaborated by the lecturers of each subject, we are able to establish that the CA system has been progressively accepted to such an extent that it is now the assessment formula used by practically all of the lecturers, conforming in this way to the protocols laid down by the Faculty of Law in which this diploma course is taught. Nevertheless, we find that high dispersion exists in how Continuous Assessment is actually defined. Indeed, it seems that there is no unified view of how Continuous Assessment should be performed. This dispersion, however, seems to diminish over time and raises some questions about the advisability of agreement on criteria, considering the potential which CA has as a pedagogical tool. Moreover, we find that the Unique Assessment system, which students may also apply for, is an option chosen only by a minority, with lecturers usually defining it as merely a theoretical and/or practical test, of little innovation in relation to traditional tests.

Effects of math anxiety on student success in higher education

This study examines whether math anxiety and negative attitudes toward mathematics have an effect on university students" academic achievement in a methodological course forming part of their degree. A total of 193 students were presented with a math anxiety test and some questions about their enjoyment, self-confidence and motivation regarding mathematics, and their responses were assessed in relation to the grades they had obtained during continuous assessment on a course entitled"Research Design". Results showed that low performance on the course was related to math anxiety and negative attitudes toward mathematics. We suggest that these factors may affect students" performance and should therefore be taken into account in attempts to improve students" learning processes in methodological courses of this kind.