Aging and fluctuation-dissipation ratio in a nonequilibrium qq-state lattice model

A generalized version of the nonequilibrium linear Glauber model with $q$ states in $d$ dimensions is introduced and analyzed. The model is fully symmetric, its dynamics being invariant under all permutations of the $q$ states. Exact expressions for the two-time autocorrelation and response functions on a $d$-dimensional lattice are obtained. In the stationary regime, the fluctuation-dissipation theorem holds, while in the transient the aging is observed with the fluctuation-dissipation ratio leading to the value predicted for the linear Glauber model

G\"{o}del-type universes in Palatini f(R) gravity

We examine the question as to whether the Palatini f(R) gravity theories permit space-times in which the causality is violated. We show that every perfect-fluid G\"{o}del-type solution of Palatini f(R) gravity with density $\rho$ and pressure $p$ that satisfy the weak energy condition $\rho+p \geq 0$ is necessarily isometric to the G\"odel geometry, demonstrating therefore that these theories present causal anomalies in the form of closed time-like curves. This result extends a theorem on G\"{o}del-type models to the framework of Palatini f(R) gravity theory. We concretely examine the G\"odel-type perfect-fluid solutions in specific $f(R) = R - \alpha/R^{n}$ Palatini gravity theory, where the free parameters $\alpha$ and $n$ have been recently constrained by a diverse set of observational data. We show that for positive matter density and for $\alpha$ and $n$ within the interval permitted by the observational data, this theory does not admit the G\"odel geometry as a perfect-fluid solution of its field equations. In this sense, this theory remedies the causal pathology in the form of closed time-like curves which is allowed in general relativity. We derive an expression for a critical radius $r_c$ (beyond which the causality is violated) for an arbitrary Palatini f(R) theory, thus making apparent that the violation of causality depends on the form of f(R) and on the matter content components. We also examine the violation of causality of G\"odel-type by considering a single scalar field as the matter content. For this source we show that Palatini f(R) gravity gives rise to a unique G\"odel-type solution with no violation of causality.Comment: 7 pages, no figures. V2: Version published in Phys. Rev. D (2010). References added. Typos correcte

The role of four-hour blocks in promoting active learning strategies: the impressions of students and teachers

The technological degrees offered at the Polytechnic School of Águeda – University of Aveiro have been organized, since 2001, around a project-based learning environment [1]. One of the features of the curriculum implementation is that courses’ contact hours are not divided in several types of classes, as in traditional learning environments. Following an idea adapted from the Aalborg model [2], all courses are taught in four-hour blocks that can be organized differently according to the course, or the learning needs at any stage of the process, thus enhancing flexibility and allowing for reorganization of the provision for teaching according to students’ needs. This format was also meant to encourage the adoption of active learning strategies within the classroom, since traditional lectures in such a format would be little less than excruciating. This article describes an investigation into the “on the field” experience of both students and teachers with these four-hour blocks. The research questions were: How are four-hour classes being implemented “on the field”? What are the advantages and disadvantages of this format? Does the format actually foster the implementation of active learning strategies? Discussion sessions were organized for three groups of students, one for each of the academic years of the Electrical Engineering program, with the goal of identifying the various categories of four-hour classes to which they have been exposed so far. Each group of students elected a “secretary” and were left alone to discuss for about twenty minutes, after which the Author re-entered the room and discussed with the students any issues in need of clarification. Afterwards, each of the participating students was asked to list, in writing, the three most positive and the three least positive aspects of each of the blocks’ categories identified earlier [3]. All teachers involved in the program were also asked to list, in writing, the three most positive and the three least positive aspects of teaching in four-hour blocks. The results of the discussion sessions and the lists, from both students and teachers, were qualitatively analysed to answer the research questions. The results of the investigation show that students identify four categories of classes, ranging from more traditional approaches, to very engaging active-learning organized sessions, namely: “Full lecture”, “Traditional layout”, “Tutorial-like organisation” and “Active learning sessions”. From the analysis of the results presented in the article, it is possible to hint that the four-hour format pressures teachers to engage in less traditionally organized classes. Students also value more engaging learning environments, which are fostered by this format of classes. This trend becomes more apparent for students in more advanced stages of the programme, which may reflect their greater exposure to the PBL environment and also their increased maturity. However, students also value the formal structure provided by more traditional environments, possibly a consequence of their previous learning experiences and study habits. Naturally, further research into these findings is needed in order to get a better grasp of the dynamics of four-hour blocks and their role in ESTGA’s PBL environment. The results of this study will guide that research, establishing the general lines on which to pursue further enquiries. REFERENCES [1] Oliveira, J.M, Estima de Oliveira, J.P. (2009), Project-Based Learning in Engineering: an Actual Case, Proc. of the 37th SEFI Annual Conference (CD, ISBN: 978-2-87352-001-4), Rotterdam, The Netherlands. [2] Kjersdam, F, Enemark, S. (1994), The Aalborg Experiment, project innovation in university education, The University of Aalborg Press, Aalborg. [3] Savin-Baden, M. (2000), Problem-Based Learning in Higher Education: Untold Stories, SRHE & Open University Press, Buckingham