New Directions for Contact Integrators

Contact integrators are a family of geometric numerical schemes which guarantee the conservation of the contact structure. In this work we review the construction of both the variational and Hamiltonian versions of these methods. We illustrate some of the advantages of geometric integration in the dissipative setting by focusing on models inspired by recent studies in celestial mechanics and cosmology.Comment: To appear as Chapter 24 in GSI 2021, Springer LNCS 1282

Nonlinear Data: Theory and Algorithms

Techniques and concepts from differential geometry are used in many parts of applied mathematics today. However, there is no joint community for users of such techniques. The workshop on Nonlinear Data assembled researchers from fields like numerical linear algebra, partial differential equations, and data analysis to explore differential geometry techniques, share knowledge, and learn about new ideas and applications

Recolección de luz mediante cristales fotónicos para aplicaciones fotovoltaicas

Tesis inédita de la Universidad Complutense de Madrid, Facultad de Ciencias Físicas, Departamento de Óptica, leída el 14/12/2016Photovoltaic solar cells base their operation on the efficient light absorption and the subsequent conversion into electricity by separation of electric charges. Generally, solar cells use interferencial layers and/or thick absorbers to minimize the optical losses. In recent years, the photovoltaic community has a growing interest in using various types of nanostructures to increase the efficiency, minimizing either the reflectivity and/or increasing the absorption. These techniques are known as light trapping. The use of nanostructures with periodic permittivity, i.e. photonic crystals, can be very beneficial compared to the conventional interferential layers and this enhancement justifies the possible disadvantage of requiring a more complex fabrication. Indeed, photonic crystals have great flexibility in designing the optical response of a system, namely the reflection, transmission and absorption. This flexibility allows to improve efficiency, either by reducing the reflection of the cell and/or increasing the absorption by increasing the effective optical path. This thesis focuses on the design of photonic crystals for 111-V solar cells. These cells achieve the greatest efficiency in converting light to electricity. There is a high interest in improving the already high efficiency to reduce the cost of the produced electricity in terms of kWh/$. These materials are generally used with optical concentration systems, with the consequence that the surface of the semiconductor layer can be reduced three orders of magnitude in comparison to conventional solar cells. This factor obviously lowers the cost of using nanostructures in concentration technology...Las células fotovoltaicas basan su funcionamiento en el atrapamiento eficiente de luz para su posterior conversión en energía eléctrica mediante la separación de cargas. Habitualmente, los sistemas usados paraminimizar las perdidas por fotones no absorbidos se basan en láminas delgadas interferenciales y/o en aumentar el espesor del medio activo. En los últimos años dentro de la comunidad fotovoltaica existe un interés creciente en usar diversos tipos de nanoestructuras para aumentar la eficiencia, ya sea minimizando la reflexión o aumentando la absorción. Estas técnicas son conocidas como light-trapping o de atrapamiento de luz. El uso de nanostructuras ópticas periódicas, es decir cristales fotónicos, puede ser muy beneficioso frente a las laminas interferenciales convencionales y así justificar las posibles desventajas derivadas de necesitar una fabricación más compleja. De hecho, los cristales fotónicos presentan una mayor flexibilidad a la hora de diseñar la respuesta óptica del sistema: reflexión, transmisión y absorción. Esto permite mejorar la eficiencia, ya sea reduciendo la reflexión del sistema y/o incrementando la absorción mediante el aumento del camino óptico efectivo. Esta tesis se centra en el diseño de cristales fotónicos para células basadas en materiales III-V. Estos materiales son los que alcanzan una mayor eficiencia en la conversión de luz a electricidad. Existe un alto interés en mejorar la ya de por si elevada eficiencia de esta tecnología, con el objetivo de reducir el coste de la electricidad producida en terminos de kWh/$. Una característica importante a tener en cuenta es que estos materiales son usados de forma habitual en sistemas ópticos de concentración, con la consecuencia de que la superficie de la capa semiconductora puede reducirse tres ordenes de magnitud con respecto a la de módulos convencionales. Esto obviamente abarata el coste de introducir nanoestructuras en el proceso de fabricación...Depto. de ÓpticaFac. de Ciencias FísicasTRUEunpu

Information Geometry

This Special Issue of the journal Entropy, titled “Information Geometry I”, contains a collection of 17 papers concerning the foundations and applications of information geometry. Based on a geometrical interpretation of probability, information geometry has become a rich mathematical field employing the methods of differential geometry. It has numerous applications to data science, physics, and neuroscience. Presenting original research, yet written in an accessible, tutorial style, this collection of papers will be useful for scientists who are new to the field, while providing an excellent reference for the more experienced researcher. Several papers are written by authorities in the field, and topics cover the foundations of information geometry, as well as applications to statistics, Bayesian inference, machine learning, complex systems, physics, and neuroscience

Shape Dynamical Models for Activity Recognition and Coded Aperture Imaging for Light-Field Capture

Classical applications of Pattern recognition in image processing and computer vision have typically dealt with modeling, learning and recognizing static patterns in images and videos. There are, of course, in nature, a whole class of patterns that dynamically evolve over time. Human activities, behaviors of insects and animals, facial expression changes, lip reading, genetic expression profiles are some examples of patterns that are dynamic. Models and algorithms to study these patterns must take into account the dynamics of these patterns while exploiting the classical pattern recognition techniques. The first part of this dissertation is an attempt to model and recognize such dynamically evolving patterns. We will look at specific instances of such dynamic patterns like human activities, and behaviors of insects and develop algorithms to learn models of such patterns and classify such patterns. The models and algorithms proposed are validated by extensive experiments on gait-based person identification, activity recognition and simultaneous tracking and behavior analysis of insects. The problem of comparing dynamically deforming shape sequences arises repeatedly in problems like activity recognition and lip reading. We describe and evaluate parametric and non-parametric models for shape sequences. In particular, we emphasize the need to model activity execution rate variations and propose a non-parametric model that is insensitive to such variations. These models and the resulting algorithms are shown to be extremely effective for a wide range of applications from gait-based person identification to human action recognition. We further show that the shape dynamical models are not only effective for the problem of recognition, but also can be used as effective priors for the problem of simultaneous tracking and behavior analysis. We validate the proposed algorithm for performing simultaneous behavior analysis and tracking on videos of bees dancing in a hive. In the last part of this dissertaion, we investigate computational imaging, an emerging field where the process of image formation involves the use of a computer. The current trend in computational imaging is to capture as much information about the scene as possible during capture time so that appropriate images with varying focus, aperture, blur and colorimetric settings may be rendered as required. In this regard, capturing the 4D light-field as opposed to a 2D image allows us to freely vary viewpoint and focus at the time of rendering an image. In this dissertation, we describe a theoretical framework for reversibly modulating {4D} light fields using an attenuating mask in the optical path of a lens based camera. Based on this framework, we present a novel design to reconstruct the {4D} light field from a {2D} camera image without any additional refractive elements as required by previous light field cameras. The patterned mask attenuates light rays inside the camera instead of bending them, and the attenuation recoverably encodes the rays on the {2D} sensor. Our mask-equipped camera focuses just as a traditional camera to capture conventional {2D} photos at full sensor resolution, but the raw pixel values also hold a modulated {4D} light field. The light field can be recovered by rearranging the tiles of the {2D} Fourier transform of sensor values into {4D} planes, and computing the inverse Fourier transform. In addition, one can also recover the full resolution image information for the in-focus parts of the scene

Light harvesting using photonic crystals for photovoltaic applications

Photovoltaic solar cells base their operation on the efficient light absorption and the subsequent conversion into electricity by separation of electric charges. Generally, solar cells use interferencial layers and/or thick absorbers to minimize the optical losses. In recent years, the photovoltaic community has a growing interest in using various types of nanostructures to increase the efficiency, minimizing either the reflectivity and/or increasing the absorption. These techniques are known as light trapping. The use of nanostructures with periodic permittivity, i.e. photonic crystals, can be very beneficial compared to the conventional interferential layers and this enhancement justifies the possible disadvantage of requiring a more complex fabrication. Indeed, photonic crystals have great flexibility in designing the optical response of a system, namely the reflection, transmission and absorption. This flexibility allows to improve efficiency, either by reducing the reflection of the cell and/or increasing the absorption by increasing the effective optical path. This thesis focuses on the design of photonic crystals for 111-V solar cells. These cells achieve the greatest efficiency in converting light to electricity. There is a high interest in improving the already high efficiency to reduce the cost of the produced electricity in terms of kWh/$. These materials are generally used with optical concentration systems, with the consequence that the surface of the semiconductor layer can be reduced three orders of magnitude in comparison to conventional solar cells. This factor obviously lowers the cost of using nanostructures in concentration technology..

Information geometry

This Special Issue of the journal Entropy, titled “Information Geometry I”, contains a collection of 17 papers concerning the foundations and applications of information geometry. Based on a geometrical interpretation of probability, information geometry has become a rich mathematical field employing the methods of differential geometry. It has numerous applications to data science, physics, and neuroscience. Presenting original research, yet written in an accessible, tutorial style, this collection of papers will be useful for scientists who are new to the field, while providing an excellent reference for the more experienced researcher. Several papers are written by authorities in the field, and topics cover the foundations of information geometry, as well as applications to statistics, Bayesian inference, machine learning, complex systems, physics, and neuroscience

System- and Data-Driven Methods and Algorithms

An increasing complexity of models used to predict real-world systems leads to the need for algorithms to replace complex models with far simpler ones, while preserving the accuracy of the predictions. This two-volume handbook covers methods as well as applications. This first volume focuses on real-time control theory, data assimilation, real-time visualization, high-dimensional state spaces and interaction of different reduction techniques

Aeronautical engineering: A continuing bibliography with indexes (supplement 319)

This report lists 349 reports, articles and other documents recently announced in the NASA STI Database. The coverage includes documents on the engineering and theoretical aspects of design, construction, evaluation, testing, operation, and performance of aircraft (including aircraft engines) and associated components, equipment, and systems. It also includes research and development in aerodynamics, aeronautics, and ground support equipment for aeronautical vehicles