Aportaciones de la prospección geofísica al estudio del subsuelo del Berguedà y Solsonés, (pre-pirineo Catalán, N.E. de la Península Ibérica)

En este trabajo se presenta la interpretaciónpor métodos geofísicos combinados de un sector del contacto entre el Pre-Pirineo y la La zona objeto del presente estudio se halla a Depresión Central Catalana...

Thermal and back-action noises in dual-sphere gravitational-wave detectors

We study the sensitivity limits of a broadband gravitational-wave detector based on dual resonators such as nested spheres. We determine both the thermal and back-action noises when the resonators displacements are read out with an optomechanical sensor. We analyze the contributions of all mechanical modes, using a new method to deal with the force-displacement transfer functions in the intermediate frequency domain between the two gravitational-wave sensitive modes associated with each resonator. This method gives an accurate estimate of the mechanical response, together with an evaluation of the estimate error. We show that very high sensitivities can be reached on a wide frequency band for realistic parameters in the case of a dual-sphere detector.

Optimized back-focal-plane interferometry directly measures forces of optically trapped particles

Back-focal-plane interferometry is used to measure displacements of optically trapped samples with very high spatial and temporal resolution. However, the technique is closely related to a method that measures the rate of change in light momentum. It has long been known that displacements of the interference pattern at the back focal plane may be used to track the optical force directly, provided that a considerable fraction of the light is effectively monitored. Nonetheless, the practical application of this idea has been limited to counter-propagating, low-aperture beams where the accurate momentum measurements are possible. Here, we experimentally show that the connection can be extended to single-beam optical traps. In particular, we show that, in a gradient trap, the calibration product κ·β (where κ is the trap stiffness and 1/β is the position sensitivity) corresponds to the factor that converts detector signals into momentum changes; this factor is uniquely determined by three construction features of the detection instrument and does not depend, therefore, on the specific conditions of the experiment. Then, we find that force measurements obtained from back-focal-plane displacements are in practice not restricted to a linear relationship with position and hence they can be extended outside that regime. Finally, and more importantly, we show that these properties are still recognizable even when the system is not fully optimized for light collection. These results should enable a more general use of back-focal-plane interferometry whenever the ultimate goal is the measurement of the forces exerted by an optical trap.

Optimized back-focal-plane interferometry directly measures forces of optically trapped particles

Back-focal-plane interferometry is used to measure displacements of optically trapped samples with very high spatial and temporal resolution. However, the technique is closely related to a method that measures the rate of change in light momentum. It has long been known that displacements of the interference pattern at the back focal plane may be used to track the optical force directly, provided that a considerable fraction of the light is effectively monitored. Nonetheless, the practical application of this idea has been limited to counter-propagating, low-aperture beams where the accurate momentum measurements are possible. Here, we experimentally show that the connection can be extended to single-beam optical traps. In particular, we show that, in a gradient trap, the calibration product κ·β (where κ is the trap stiffness and 1/β is the position sensitivity) corresponds to the factor that converts detector signals into momentum changes; this factor is uniquely determined by three construction features of the detection instrument and does not depend, therefore, on the specific conditions of the experiment. Then, we find that force measurements obtained from back-focal-plane displacements are in practice not restricted to a linear relationship with position and hence they can be extended outside that regime. Finally, and more importantly, we show that these properties are still recognizable even when the system is not fully optimized for light collection. These results should enable a more general use of back-focal-plane interferometry whenever the ultimate goal is the measurement of the forces exerted by an optical trap.

On the upper bound of the number of limit cycles obtained by the second order averaging method I

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On the upper bound of the number of limit cycles obtained by the second order averaging method II

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Una Aproximació a la construcció significativa del coneixement matemàtic a l'ESO

This study displays and analyzes the contents of the Mathematics subject in ESO’s second cycle from a constructivist perspective. This analysis has been carried out by contrasting two groups of participants (control group and experimental group). These groups were formed by a sample of 240 students between the ages of 14 and 16 from four different educational centres of the Osona area. Research – Action methodology has been employed, combining quantitative techniques (statistical study with the SPSS package) with qualitative analysis (transcriptions of interviews and discussion group). This study has been carried out after years of classroom observation, reflection and action. The theoretical framework employed is a cognitive one, based on Ausubel’s Significative Learning Theory. Quantitative analysis shows how the researcher’s design improves, on the one hand, the students’ academic motivation and, on the other hand, their comprehensive memory, enabling them to achieve a more significant learning of the subjects’ contents. Furthermore, our analysis shows that the proposed method is more comprehensive than those employed by teachers collaborating with control groups. The main aim of the qualitative analysis is that of identifying the elements which configure the programme and contribute to an improvement of the aspects mentioned above. The key elements here are: co-operation as the basis of group dynamics; the employment, in some cases, of easily handled materials; the type of interaction between teacher and students, where, through open discussion, students are lead by teaching staff towards the course objectives; induction, that is, deducing formulae by initially using examples which are close to the students’ knowledge and experience or taken from everyday life (what we could call “down-top” mathematics). We should add here that the qualitative analysis does not only corroborate the results obtained by quantitative techniques, but also displays an increase of motivation in teaching staff. Teachers did show a positive attitude and welcomed the use and development of these materials in the next academic year. Finally, we discuss possible directions for further research.

A rotation method which gives linear Lp-Estimates for powers of the Ahlfors-Beurling operator

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Stability of periodic solutions obtained via the averaging method for nonsmooth Lipschitz system

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What works best for getting the unemployed back to work: employment services or small-business assistance programs? evidence from Romania

Recent empirical evidence has found that employment services and small-business assistance programmes are often successful at getting the unemployed back to work. Â One important concern of policy makers is to decide which of these two programmes is more effective and for whom. Â Using unusually rich (for transition economies) survey data and matching methods, I evaluate the relative effectiveness of these two programmes in Romania. Â While I find that employment services (ES) are, on average, more successful than a small-business assistance programme (SBA), estimation of heterogeneity effects reveals that, compared to non-participation, ES are effective for workers with little access to informal search channels, and SBA works for less-qualified workers and those living in rural areas. Â When comparing ES to SBA, I find that ES tend to be more efficient than SBA for workers without a high-school degree, and that the opposite holds for the more educated workers.

Hopf bifurcation in higher dimensional differential systems via the averaging method

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Simulación de fluidos inmiscibles con el Particle Finite Element Method (PFEM)

Proyecto de investigación realizado a partir de una estancia en el Centro Internacional de Métodos Computacionales en Ingeniería (CIMEC), Argentina, entre febrero y abril del 2007. La simulación numérica de problemas de mezclas mediante el Particle Finite Element Method (PFEM) es el marco de estudio de una futura tesis doctoral. Éste es un método desarrollado conjuntamente por el CIMEC y el Centre Internacional de Mètodos Numèrics en l'Enginyeria (CIMNE-UPC), basado en la resolución de las ecuaciones de Navier-Stokes en formulación Lagrangiana. El mallador ha sido implementado y desarrollado por Dr. Nestor Calvo, investigador del CIMEC. El desarrollo del módulo de cálculo corresponde al trabajo de tesis de la beneficiaria. La correcta interacción entre ambas partes es fundamental para obtener resultados válidos. En esta memoria se explican los principales aspectos del mallador que fueron modificados (criterios de refinamiento geométrico) y los cambios introducidos en el módulo de cálculo (librería PETSc, algoritmo predictor-corrector) durante la estancia en el CIMEC. Por último, se muestran los resultados obtenidos en un problema de dos fluidos inmiscibles con transferencia de calor.

La història es repeteix?: estudi comparatiu de la crisi del 29 amb l'actual

Treball de recerca realitzat per un alumne d'ensenyament secundari i guardonat amb un Premi CIRIT per fomentar l'esperit científic del Jovent l'any 2009. L’objectiu d’aquest treball ha estat donar pautes de reflexió sobre la crisi i el moment econòmic actual. Es volia valorar si era certa la idea que la situació econòmica dels nostres dies té certs paral•lelismes amb la crisi que va patir el món occidental el 1929. Per tal d’establir la veracitat de la hipòtesi plantejada es va dissenyar un model d’investigació basat en les entrevistes i en el recull i buidatge d’articles de premsa relacionats amb el tema, durant un període de temps no gaire extens, període que correspon als tres mesos a partir dels quals s’evidencia la situació de crisi. Al mateix temps era interessant copsar l’opinió de dos grans mestres en l’estudi de l’economia del nostre país, el Dr. Fabià Estapé i el Dr. Anton Costas, mestre i deixeble respectivament.. Sense esperar massa sorpreses, la crisi actual presenta molts punts de similitud amb el procés inciat l’any 1929. Ambdós esdeveniments econòmics tenen molts punts de connexió i les mesures proposades per solucionar o per pal•liar les conseqüències són també similars. En tots dos casos la figura de l’economista britànic John Maynard Keynes és cabdal per part dels diversos governs a l’hora de reconduir i adreçar la situació econòmica.

A mixed finite element method for nonlinear diffusion equations

We propose a mixed finite element method for a class of nonlinear diffusion equations, which is based on their interpretation as gradient flows in optimal transportation metrics. We introduce an appropriate linearization of the optimal transport problem, which leads to a mixed symmetric formulation. This formulation preserves the maximum principle in case of the semi-discrete scheme as well as the fully discrete scheme for a certain class of problems. In addition solutions of the mixed formulation maintain exponential convergence in the relative entropy towards the steady state in case of a nonlinear Fokker-Planck equation with uniformly convex potential. We demonstrate the behavior of the proposed scheme with 2D simulations of the porous medium equations and blow-up questions in the Patlak-Keller-Segel model.