Analytic free-form lens design for imaging applications with high aspect ratio

A new three-dimensional analytic optics design method is presented that enables the coupling of three ray sets with only two free-form lens surfaces. Closely related to the Simultaneous Multiple Surface method in three dimensions (SMS3D), it is derived directly from Fermat?s principle, leading to multiple sets of functional differential equations. The general solution of these equations makes it possible to calculate more than 80 coefficients for each implicit surface function. Ray tracing simulations of these free-form lenses demonstrate superior imaging performance for applications with high aspect ratio, compared to conventional rotational symmetric systems.

Analytic free-form lens design for tracking integration in concentrating photovoltaics

In this work the concept of tracking integration in concentrating photovoltaics (CPV) is revisited and developed further. With respect to conventional CPV, tracking integration eliminates the clear separation between stationary units of optics and solar cells, and external solar trackers. This approach is capable of further increasing the concentration ratio and makes high concentrating photovoltaics (> 500x) available for single-axis tracker installations. The reduced external solar tracking effort enables possibly cheaper and more compact installations. Our proposed optical system uses two laterally moving plano-convex lenses to achieve high concentration over a wide angular range of ±24°. The lateral movement allows to combine both steering and concentration of the incident direct sun light. Given the specific symmetry conditions of the underlying optical design problem, rotational symmetric lenses are not ideal for this application. For this type of design problems, a new free-form optics design method presented in previous papers perfectly matches the symmetry. It is derived directly from Fermat's principle, leading to sets of functional differential equations allowing the successive calculation of the Taylor series coeficients of each implicit surface function up to very high orders. For optical systems designed for wide field of view and with clearly separated optical surfaces, this new analytic design method has potential application in both fields of nonimaging and imaging optics.

Decomposition driven interface evolution for layers of binary mixtures: I. Model dirivation and base states

Algebraic topology (homology) is used to analyze the state of spiral defect chaos in both laboratory experiments and numerical simulations of Rayleigh-Bénard convection. The analysis reveals topological asymmetries that arise when non-Boussinesq effects are present. The asymmetries are found in different flow fields in the simulations and are robust to substantial alterations to flow visualization conditions in the experiment. However, the asymmetries are not observable using conventional statistical measures. These results suggest homology may provide a new and general approach for connecting spatiotemporal observations of chaotic or turbulent patterns to theoretical models.

On real analytic functions of unbounded type

In this paper we prove several results on the existence of analytic functions on an infinite dimensional real Banach space which are bounded on some given collection of open sets and unbounded on others. In addition, we also obtain results on the density of some subsets of the space of all analytic functions for natural locally convex topologies on this space. RESUMEN. Los autores demuestran varios resultados de existencia de funciones analíticas en espacios de Banach reales de dimensión infinita que están acotadas en un colección de subconjuntos abiertos y no acotadas en los conjuntos de otra colección. Además, se demuestra la densidad de ciertos subconjuntos de funciones analíticas para varias topologías localmente convexas.

The analytic hierarchy process to support decision-making processes in infrastructure projects with social impact

There is an increasing awareness among all kinds of organisations (in business,government and civil society) about the benefits of jointly working with stakeholders to satisfy both their goals and the social demands placed upon them. This is particularly the case within corporate social responsibility (CSR) frameworks. In this regard, multi-criteria tools for decision-making like the analytic hierarchy process (AHP) described in the paper can be useful for the building relationships with stakeholders. Since these tools can reveal decision-maker’s preferences, the integration of opinions from various stakeholders in the decision-making process may result in better and more innovative solutions with significant shared value. This paper is based on ongoing research to assess the feasibility of an AHP-based model to support CSR decisions in large infrastructure projects carried out by Red Electrica de España, the sole transmission agent and operator of the Spanishelectricity system.

Meromorphic continuation of functions and arbitrary distribution of interpolation points

We characterize the region of meromorphic continuation of an analytic function ff in terms of the geometric rate of convergence on a compact set of sequences of multi-point rational interpolants of ff. The rational approximants have a bounded number of poles and the distribution of interpolation points is arbitrary.

Analyzing climate change adaptation in the agriculture and water sectors: screening risks and opportunities.

As part of the Mediterranean area, the Guadiana basin in Spain is particularly exposed to increasing water stress due to climate change. Future warmer and drier climate will have negative implications for the sustainability of water resources and irrigation agriculture, the main socio- economic sector in the region. This paper illustrates a systematic analysis of climate change impacts and adaptation in the Guadiana basin based on a two-stage modeling approach. First, an integrated hydro-economic modeling framework was used to simulate the potential effects of regional climate change scenarios for the period 2000-2069. Second, a participatory multi-criteria technique, namely the Analytic Hierarchy Process (AHP), was applied to rank potential adaptation measures based on agreed criteria. Results show that, in the middle-long run and under severe climate change, reduced water availability, lower crop yields and increased irrigation demands might lead to water shortages, crop failure, and up to ten percent of income losses to irrigators. AHP results show how private farming adaptation measures, including improving irrigation efficiency and adjusting crop varieties, are preferred to public adaptation measures, such as building new dams. The integrated quantitative and qualitative methodology used in this research can be considered a socially-based valuable tool to support adaptation decision-making.

A multi-criteria optimization and decision-making approach for improvement of food engineering processes.

The objective of this study was to propose a multi-criteria optimization and decision-making technique to solve food engineering problems. This technique was demostrated using experimental data obtained on osmotic dehydratation of carrot cubes in a sodium chloride solution. The Aggregating Functions Approach, the Adaptive Random Search Algorithm, and the Penalty Functions Approach were used in this study to compute the initial set of non-dominated or Pareto-optimal solutions. Multiple non-linear regression analysis was performed on a set of experimental data in order to obtain particular multi-objective functions (responses), namely water loss, solute gain, rehydration ratio, three different colour criteria of rehydrated product, and sensory evaluation (organoleptic quality). Two multi-criteria decision-making approaches, the Analytic Hierarchy Process (AHP) and the Tabular Method (TM), were used simultaneously to choose the best alternative among the set of non-dominated solutions. The multi-criteria optimization and decision-making technique proposed in this study can facilitate the assessment of criteria weights, giving rise to a fairer, more consistent, and adequate final compromised solution or food process. This technique can be useful to food scientists in research and education, as well as to engineers involved in the improvement of a variety of food engineering processes.

Probabilistic analysis of water availability for agriculture and associated crop net margins.

Rising water demands are difficult to meet in many regions of the world. In consequence, under meteorological adverse conditions, big economic losses in agriculture can take place. This paper aims to analyze the variability of water shortage in an irrigation district and the effect on farmer?s income. A probabilistic analysis of water availability for agriculture in the irrigation district is performed, through a supply-system simulation approach, considering stochastically generated series of stream-flows. Net margins associated to crop production are as well estimated depending on final water allocations. Net margins are calculated considering either single-crop farming, either a polyculture system. In a polyculture system, crop distribution and water redistribution are calculated through an optimization approach using the General Algebraic Modeling System (GAMS) for several scenarios of irrigation water availability. Expected net margins are obtained by crop and for the optimal crop and water distribution. The maximum expected margins are obtained for the optimal crop combination, followed by the alfalfa monoculture, maize, rice, wheat and finally barley. Water is distributed as follows, from biggest to smallest allocation: rice, alfalfa, maize, wheat and barley.

First order mem-circuits: modeling, nonlinear oscillations and bifurcations

This paper presents a theoretical framework intended to accommodate circuit devices described by characteristics involving more than two fundamental variables. This framework is motivated by the recent appearance of a variety of so-called mem-devices in circuit theory, and makes it possible to model the coexistence of memory effects of different nature in a single device. With a compact formalism, this setting accounts for classical devices and also for circuit elements which do not admit a two-variable description. Fully nonlinear characteristics are allowed for all devices, driving the analysis beyond the framework of Chua and Di Ventra We classify these fully nonlinear circuit elements in terms of the variables involved in their constitutive relations and the notions of the differential- and the state-order of a device. We extend the notion of a topologically degenerate configuration to this broader context, and characterize the differential-algebraic index of nodal models of such circuits. Additionally, we explore certain dynamical features of mem-circuits involving manifolds of non-isolated equilibria. Related bifurcation phenomena are explored for a family of nonlinear oscillators based on mem-devices.

Hybrid analysis of nonlinear circuits: DAE models with indices zero and one

We extend in this paper some previous results concerning the differential-algebraic index of hybrid models of electrical and electronic circuits. Specifically, we present a comprehensive index characterization which holds without passivity requirements, in contrast to previous approaches, and which applies to nonlinear circuits composed of uncoupled, one-port devices. The index conditions, which are stated in terms of the forest structure of certain digraph minors, do not depend on the specific tree chosen in the formulation of the hybrid equations. Additionally, we show how to include memristors in hybrid circuit models; in this direction, we extend the index analysis to circuits including active memristors, which have been recently used in the design of nonlinear oscillators and chaotic circuits. We also discuss the extension of these results to circuits with controlled sources, making our framework of interest in the analysis of circuits with transistors, amplifiers, and other multiterminal devices.

On the approximate parametrization problem of algebraic curves.

The problem of parameterizing approximately algebraic curves and surfaces is an active research field, with many implications in practical applications. The problem can be treated locally or globally. We formally state the problem, in its global version for the case of algebraic curves (planar or spatial), and we report on some algorithms approaching it, as well as on the associated error distance analysis.

Sparse differential resultant formulas: between the linear and the nonlinear case

A matrix representation of the sparse differential resultant is the basis for efficient computation algorithms, whose study promises a great contribution to the development and applicability of differential elimination techniques. It is shown how sparse linear differential resultant formulas provide bounds for the order of derivation, even in the nonlinear case, and they also provide (in many cases) the bridge with results in the nonlinear algebraic case.

Rational conchoid and offset constructions: algorithms and implementation

This paper is framed within the problem of analyzing the rationality of the components of two classical geometric constructions, namely the offset and the conchoid to an algebraic plane curve and, in the affirmative case, the actual computation of parametrizations. We recall some of the basic definitions and main properties on offsets (see [13]), and conchoids (see [15]) as well as the algorithms for parametrizing their rational components (see [1] and [16], respectively). Moreover, we implement the basic ideas creating two packages in the computer algebra system Maple to analyze the rationality of conchoids and offset curves, as well as the corresponding help pages. In addition, we present a brief atlas where the offset and conchoids of several algebraic plane curves are obtained, their rationality analyzed, and parametrizations are provided using the created packages.

Low Work-Function Thermionic Emission and Orbital-Motion-Limited Ion Collection at Bare-Tether Cathodic Contact

Una amarra electrodinámica (electrodynamic tether) opera sobre principios electromagnéticos intercambiando momento con la magnetosfera planetaria e interactuando con su ionosfera. Es un subsistema pasivo fiable para desorbitar etapas de cohetes agotadas y satélites al final de su misión, mitigando el crecimiento de la basura espacial. Una amarra sin aislamiento captura electrones del plasma ambiente a lo largo de su segmento polarizado positivamente, el cual puede alcanzar varios kilómetros de longitud, mientras que emite electrones de vuelta al plasma mediante un contactor de plasma activo de baja impedancia en su extremo catódico, tal como un cátodo hueco (hollow cathode). En ausencia de un contactor catódico activo, la corriente que circula por una amarra desnuda en órbita es nula en ambos extremos de la amarra y se dice que ésta está flotando eléctricamente. Para emisión termoiónica despreciable y captura de corriente en condiciones limitadas por movimiento orbital (orbital-motion-limited, OML), el cociente entre las longitudes de los segmentos anódico y catódico es muy pequeño debido a la disparidad de masas entre iones y electrones. Tal modo de operación resulta en una corriente media y fuerza de Lorentz bajas en la amarra, la cual es poco eficiente como dispositivo para desorbitar. El electride C12A7 : e−, que podría presentar una función de trabajo (work function) tan baja como W = 0.6 eV y un comportamiento estable a temperaturas relativamente altas, ha sido propuesto como recubrimiento para amarras desnudas. La emisión termoiónica a lo largo de un segmento así recubierto y bajo el calentamiento de la operación espacial, puede ser más eficiente que la captura iónica. En el modo más simple de fuerza de frenado, podría eliminar la necesidad de un contactor catódico activo y su correspondientes requisitos de alimentación de gas y subsistema de potencia, lo que resultaría en un sistema real de amarra “sin combustible”. Con este recubrimiento de bajo W, cada segmento elemental del segmento catódico de una amarra desnuda de kilómetros de longitud emitiría corriente como si fuese parte de una sonda cilíndrica, caliente y uniformemente polarizada al potencial local de la amarra. La operación es similar a la de una sonda de Langmuir 2D tanto en los segmentos catódico como anódico. Sin embargo, en presencia de emisión, los electrones emitidos resultan en carga espacial (space charge) negativa, la cual reduce el campo eléctrico que los acelera hacia fuera, o incluso puede desacelerarlos y hacerlos volver a la sonda. Se forma una doble vainas (double sheath) estable con electrones emitidos desde la sonda e iones provenientes del plasma ambiente. La densidad de corriente termoiónica, variando a lo largo del segmento catódico, podría seguir dos leyes distintas bajo diferentes condiciones: (i) la ley de corriente limitada por la carga espacial (space-charge-limited, SCL) o (ii) la ley de Richardson-Dushman (RDS). Se presenta un estudio preliminar sobre la corriente SCL frente a una sonda emisora usando la teoría de vainas (sheath) formada por la captura iónica en condiciones OML, y la corriente electrónica SCL entre los electrodos cilíndricos según Langmuir. El modelo, que incluye efectos óhmicos y el efecto de transición de emisión SCL a emisión RDS, proporciona los perfiles de corriente y potencial a lo largo de la longitud completa de la amarra. El análisis muestra que en el modo más simple de fuerza de frenado, bajo condiciones orbitales y de amarras típicas, la emisión termoiónica proporciona un contacto catódico eficiente y resulta en una sección catódica pequeña. En el análisis anterior, tanto la transición de emisión SCL a RD como la propia ley de emisión SCL consiste en un modelo muy simplificado. Por ello, a continuación se ha estudiado con detalle la solución de vaina estacionaria de una sonda con emisión termoiónica polarizada negativamente respecto a un plasma isotrópico, no colisional y sin campo magnético. La existencia de posibles partículas atrapadas ha sido ignorada y el estudio incluye tanto un estudio semi-analítico mediante técnica asintóticas como soluciones numéricas completas del problema. Bajo las tres condiciones (i) alto potencial, (ii) R = Rmax para la validez de la captura iónica OML, y (iii) potencial monotónico, se desarrolla un análisis asintótico auto-consistente para la estructura de plasma compleja que contiene las tres especies de cargas (electrones e iones del plasma, electrones emitidos), y cuatro regiones espaciales distintas, utilizando teorías de movimiento orbital y modelos cinéticos de las especies. Aunque los electrones emitidos presentan carga espacial despreciable muy lejos de la sonda, su efecto no se puede despreciar en el análisis global de la estructura de la vaina y de dos capas finas entre la vaina y la región cuasi-neutra. El análisis proporciona las condiciones paramétricas para que la corriente sea SCL. También muestra que la emisión termoiónica aumenta el radio máximo de la sonda para operar dentro del régimen OML y que la emisión de electrones es mucho más eficiente que la captura iónica para el segmento catódico de la amarra. En el código numérico, los movimientos orbitales de las tres especies son modelados para potenciales tanto monotónico como no-monotónico, y sonda de radio R arbitrario (dentro o más allá del régimen de OML para la captura iónica). Aprovechando la existencia de dos invariante, el sistema de ecuaciones Poisson-Vlasov se escribe como una ecuación integro-diferencial, la cual se discretiza mediante un método de diferencias finitas. El sistema de ecuaciones algebraicas no lineal resultante se ha resuelto de con un método Newton-Raphson paralelizado. Los resultados, comparados satisfactoriamente con el análisis analítico, proporcionan la emisión de corriente y la estructura del plasma y del potencial electrostático. ABSTRACT An electrodynamic tether operates on electromagnetic principles and exchanges momentum through the planetary magnetosphere, by continuously interacting with the ionosphere. It is a reliable passive subsystem to deorbit spent rocket stages and satellites at its end of mission, mitigating the growth of orbital debris. A tether left bare of insulation collects electrons by its own uninsulated and positively biased segment with kilometer range, while electrons are emitted by a low-impedance active device at the cathodic end, such as a hollow cathode, to emit the full electron current. In the absence of an active cathodic device, the current flowing along an orbiting bare tether vanishes at both ends and the tether is said to be electrically floating. For negligible thermionic emission and orbital-motion-limited (OML) collection throughout the entire tether (electron/ion collection at anodic/cathodic segment, respectively), the anodic-to-cathodic length ratio is very small due to ions being much heavier, which results in low average current and Lorentz drag. The electride C12A7 : e−, which might present a possible work function as low as W = 0.6 eV and moderately high temperature stability, has been proposed as coating for floating bare tethers. Thermionic emission along a thus coated cathodic segment, under heating in space operation, can be more efficient than ion collection and, in the simplest drag mode, may eliminate the need for an active cathodic device and its corresponding gas-feed requirements and power subsystem, which would result in a truly “propellant-less” tether system. With this low-W coating, each elemental segment on the cathodic segment of a kilometers-long floating bare-tether would emit current as if it were part of a hot cylindrical probe uniformly polarized at the local tether bias, under 2D probe conditions that are also applied to the anodic-segment analysis. In the presence of emission, emitted electrons result in negative space charge, which decreases the electric field that accelerates them outwards, or even reverses it, decelerating electrons near the emitting probe. A double sheath would be established with electrons being emitted from the probe and ions coming from the ambient plasma. The thermionic current density, varying along the cathodic segment, might follow two distinct laws under different con ditions: i) space-charge-limited (SCL) emission or ii) full Richardson-Dushman (RDS) emission. A preliminary study on the SCL current in front of an emissive probe is presented using the orbital-motion-limited (OML) ion-collection sheath and Langmuir’s SCL electron current between cylindrical electrodes. A detailed calculation of current and bias profiles along the entire tether length is carried out with ohmic effects considered and the transition from SCL to full RDS emission is included. Analysis shows that in the simplest drag mode, under typical orbital and tether conditions, thermionic emission provides efficient cathodic contact and leads to a short cathodic section. In the previous analysis, both the transition between SCL and RDS emission and the current law for SCL condition have used a very simple model. To continue, considering an isotropic, unmagnetized, colissionless plasma and a stationary sheath, the probe-plasma contact is studied in detail for a negatively biased probe with thermionic emission. The possible trapped particles are ignored and this study includes both semianalytical solutions using asymptotic analysis and complete numerical solutions. Under conditions of i) high bias, ii) R = Rmax for ion OML collection validity, and iii) monotonic potential, a self-consistent asymptotic analysis is carried out for the complex plasma structure involving all three charge species (plasma electrons and ions, and emitted electrons) and four distinct spatial regions using orbital motion theories and kinetic modeling of the species. Although emitted electrons present negligible space charge far away from the probe, their effect cannot be neglected in the global analysis for the sheath structure and two thin layers in between the sheath and the quasineutral region. The parametric conditions for the current to be space-chargelimited are obtained. It is found that thermionic emission increases the range of probe radius for OML validity and is greatly more effective than ion collection for cathodic contact of tethers. In the numerical code, the orbital motions of all three species are modeled for both monotonic and non-monotonic potential, and for any probe radius R (within or beyond OML regime for ion collection). Taking advantage of two constants of motion (energy and angular momentum), the Poisson-Vlasov equation is described by an integro differential equation, which is discretized using finite difference method. The non-linear algebraic equations are solved using a parallel implementation of the Newton-Raphson method. The results, which show good agreement with the analytical results, provide the results for thermionic current, the sheath structure, and the electrostatic potential.