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.

Design and development of compact optical systems = Diseño y desarrollo de sistemas ópticos compactos

Esta tesis considera dos tipos de aplicaciones del diseño óptico: óptica formadora de imagen por un lado, y óptica anidólica (nonimaging) o no formadora de imagen, por otro. Las ópticas formadoras de imagen tienen como objetivo la obtención de imágenes de puntos del objeto en el plano de la imagen. Por su parte, la óptica anidólica, surgida del desarrollo de aplicaciones de concentración e iluminación, se centra en la transferencia de energía en forma de luz de forma eficiente. En general, son preferibles los diseños ópticos que den como resultado sistemas compactos, para ambos tipos de ópticas (formadora de imagen y anidólica). En el caso de los sistemas anidólicos, una óptica compacta permite tener costes de producción reducidos. Hay dos razones: (1) una óptica compacta presenta volúmenes reducidos, lo que significa que se necesita menos material para la producción en masa; (2) una óptica compacta es pequeña y ligera, lo que ahorra costes en el transporte. Para los sistemas ópticos de formación de imagen, además de las ventajas anteriores, una óptica compacta aumenta la portabilidad de los dispositivos, que es una gran ventaja en tecnologías de visualización portátiles, tales como cascos de realidad virtual (HMD del inglés Head Mounted Display). Esta tesis se centra por tanto en nuevos enfoques de diseño de sistemas ópticos compactos para aplicaciones tanto de formación de imagen, como anidólicas. Los colimadores son uno de los diseños clásicos dentro la óptica anidólica, y se pueden utilizar en aplicaciones fotovoltaicas y de iluminación. Hay varios enfoques a la hora de diseñar estos colimadores. Los diseños convencionales tienen una relación de aspecto mayor que 0.5. Con el fin de reducir la altura del colimador manteniendo el área de iluminación, esta tesis presenta un diseño de un colimador multicanal. En óptica formadora de imagen, las superficies asféricas y las superficies sin simetría de revolución (o freeform) son de gran utilidad de cara al control de las aberraciones de la imagen y para reducir el número y tamaño de los elementos ópticos. Debido al rápido desarrollo de sistemas de computación digital, los trazados de rayos se pueden realizar de forma rápida y sencilla para evaluar el rendimiento del sistema óptico analizado. Esto ha llevado a los diseños ópticos modernos a ser generados mediante el uso de diferentes técnicas de optimización multi-paramétricas. Estas técnicas requieren un buen diseño inicial como punto de partida para el diseño final, que será obtenido tras un proceso de optimización. Este proceso precisa un método de diseño directo para superficies asféricas y freeform que den como resultado un diseño cercano al óptimo. Un método de diseño basado en ecuaciones diferenciales se presenta en esta tesis para obtener un diseño óptico formado por una superficie freeform y dos superficies asféricas. Esta tesis consta de cinco capítulos. En Capítulo 1, se presentan los conceptos básicos de la óptica formadora de imagen y de la óptica anidólica, y se introducen las técnicas clásicas del diseño de las mismas. El Capítulo 2 describe el diseño de un colimador ultra-compacto. La relación de aspecto ultra-baja de este colimador se logra mediante el uso de una estructura multicanal. Se presentará su procedimiento de diseño, así como un prototipo fabricado y la caracterización del mismo. El Capítulo 3 describe los conceptos principales de la optimización de los sistemas ópticos: función de mérito y método de mínimos cuadrados amortiguados. La importancia de un buen punto de partida se demuestra mediante la presentación de un mismo ejemplo visto a través de diferentes enfoques de diseño. El método de las ecuaciones diferenciales se presenta como una herramienta ideal para obtener un buen punto de partida para la solución final. Además, diferentes técnicas de interpolación y representación de superficies asféricas y freeform se presentan para el procedimiento de optimización. El Capítulo 4 describe la aplicación del método de las ecuaciones diferenciales para un diseño de un sistema óptico de una sola superficie freeform. Algunos conceptos básicos de geometría diferencial son presentados para una mejor comprensión de la derivación de las ecuaciones diferenciales parciales. También se presenta un procedimiento de solución numérica. La condición inicial está elegida como un grado de libertad adicional para controlar la superficie donde se forma la imagen. Basado en este enfoque, un diseño anastigmático se puede obtener fácilmente y se utiliza como punto de partida para un ejemplo de diseño de un HMD con una única superficie reflectante. Después de la optimización, dicho diseño muestra mejor rendimiento. El Capítulo 5 describe el método de las ecuaciones diferenciales ampliado para diseños de dos superficies asféricas. Para diseños ópticos de una superficie, ni la superficie de imagen ni la correspondencia entre puntos del objeto y la imagen pueden ser prescritas. Con esta superficie adicional, la superficie de la imagen se puede prescribir. Esto conduce a un conjunto de tres ecuaciones diferenciales ordinarias implícitas. La solución numérica se puede obtener a través de cualquier software de cálculo numérico. Dicho procedimiento también se explica en este capítulo. Este método de diseño da como resultado una lente anastigmática, que se comparará con una lente aplanática. El diseño anastigmático converge mucho más rápido en la optimización y la solución final muestra un mejor rendimiento. ABSTRACT We will consider optical design from two points of view: imaging optics and nonimaging optics. Imaging optics focuses on the imaging of the points of the object. Nonimaging optics arose from the development of concentrators and illuminators, focuses on the transfer of light energy, and has wide applications in illumination and concentration photovoltaics. In general, compact optical systems are necessary for both imaging and nonimaging designs. For nonimaging optical systems, compact optics use to be important for reducing cost. The reasons are twofold: (1) compact optics is small in volume, which means less material is needed for mass-production; (2) compact optics is small in size and light in weight, which saves cost in transportation. For imaging optical systems, in addition to the above advantages, compact optics increases portability of devices as well, which contributes a lot to wearable display technologies such as Head Mounted Displays (HMD). This thesis presents novel design approaches of compact optical systems for both imaging and nonimaging applications. Collimator is a typical application of nonimaging optics in illumination, and can be used in concentration photovoltaics as well due to the reciprocity of light. There are several approaches for collimator designs. In general, all of these approaches have an aperture diameter to collimator height not greater than 2. In order to reduce the height of the collimator while maintaining the illumination area, a multichannel design is presented in this thesis. In imaging optics, aspheric and freeform surfaces are useful in controlling image aberrations and reducing the number and size of optical elements. Due to the rapid development of digital computing systems, ray tracing can be easily performed to evaluate the performance of optical system. This has led to the modern optical designs created by using different multi-parametric optimization techniques. These techniques require a good initial design to be a starting point so that the final design after optimization procedure can reach the optimum solution. This requires a direct design method for aspheric and freeform surface close to the optimum. A differential equation based design method is presented in this thesis to obtain single freeform and double aspheric surfaces. The thesis comprises of five chapters. In Chapter 1, basic concepts of imaging and nonimaging optics are presented and typical design techniques are introduced. Readers can obtain an understanding for the following chapters. Chapter 2 describes the design of ultra-compact collimator. The ultra-low aspect ratio of this collimator is achieved by using a multichannel structure. Its design procedure is presented together with a prototype and its evaluation. The ultra-compactness of the device has been approved. Chapter 3 describes the main concepts of optimizing optical systems: merit function and Damped Least-Squares method. The importance of a good starting point is demonstrated by presenting an example through different design approaches. The differential equation method is introduced as an ideal tool to obtain a good starting point for the final solution. Additionally, different interpolation and representation techniques for aspheric and freeform surface are presented for optimization procedure. Chapter 4 describes the application of differential equation method in the design of single freeform surface optical system. Basic concepts of differential geometry are presented for understanding the derivation of partial differential equations. A numerical solution procedure is also presented. The initial condition is chosen as an additional freedom to control the image surface. Based on this approach, anastigmatic designs can be readily obtained and is used as starting point for a single reflective surface HMD design example. After optimization, the evaluation shows better MTF. Chapter 5 describes the differential equation method extended to double aspheric surface designs. For single optical surface designs, neither image surface nor the mapping from object to image can be prescribed. With one more surface added, the image surface can be prescribed. This leads to a set of three implicit ordinary differential equations. Numerical solution can be obtained by MATLAB and its procedure is also explained. An anastigmatic lens is derived from this design method and compared with an aplanatic lens. The anastigmatic design converges much faster in optimization and the final solution shows better performance.

Finite Element Model of the Innovation Diffusion: An Application to Photovoltaic Systems

This paper presents a Finite Element Model, which has been used for forecasting the diffusion of innovations in time and space. Unlike conventional models used in diffusion literature, the model considers the spatial heterogeneity. The implementation steps of the model are explained by applying it to the case of diffusion of photovoltaic systems in a local region in southern Germany. The applied model is based on a parabolic partial differential equation that describes the diffusion ratio of photovoltaic systems in a given region over time. The results of the application show that the Finite Element Model constitutes a powerful tool to better understand the diffusion of an innovation as a simultaneous space-time process. For future research, model limitations and possible extensions are also discussed.

Co-simulation Methodologies for Hybrid and Electric Vehicle Dynamics

In recent decades, full electric and hybrid electric vehicles have emerged as an alternative to conventional cars due to a range of factors, including environmental and economic aspects. These vehicles are the result of considerable efforts to seek ways of reducing the use of fossil fuel for vehicle propulsion. Sophisticated technologies such as hybrid and electric powertrains require careful study and optimization. Mathematical models play a key role at this point. Currently, many advanced mathematical analysis tools, as well as computer applications have been built for vehicle simulation purposes. Given the great interest of hybrid and electric powertrains, along with the increasing importance of reliable computer-based models, the author decided to integrate both aspects in the research purpose of this work. Furthermore, this is one of the first final degree projects held at the ETSII (Higher Technical School of Industrial Engineers) that covers the study of hybrid and electric propulsion systems. The present project is based on MBS3D 2.0, a specialized software for the dynamic simulation of multibody systems developed at the UPM Institute of Automobile Research (INSIA). Automobiles are a clear example of complex multibody systems, which are present in nearly every field of engineering. The work presented here benefits from the availability of MBS3D software. This program has proven to be a very efficient tool, with a highly developed underlying mathematical formulation. On this basis, the focus of this project is the extension of MBS3D features in order to be able to perform dynamic simulations of hybrid and electric vehicle models. This requires the joint simulation of the mechanical model of the vehicle, together with the model of the hybrid or electric powertrain. These sub-models belong to completely different physical domains. In fact the powertrain consists of energy storage systems, electrical machines and power electronics, connected to purely mechanical components (wheels, suspension, transmission, clutch…). The challenge today is to create a global vehicle model that is valid for computer simulation. Therefore, the main goal of this project is to apply co-simulation methodologies to a comprehensive model of an electric vehicle, where sub-models from different areas of engineering are coupled. The created electric vehicle (EV) model consists of a separately excited DC electric motor, a Li-ion battery pack, a DC/DC chopper converter and a multibody vehicle model. Co-simulation techniques allow car designers to simulate complex vehicle architectures and behaviors, which are usually difficult to implement in a real environment due to safety and/or economic reasons. In addition, multi-domain computational models help to detect the effects of different driving patterns and parameters and improve the models in a fast and effective way. Automotive designers can greatly benefit from a multidisciplinary approach of new hybrid and electric vehicles. In this case, the global electric vehicle model includes an electrical subsystem and a mechanical subsystem. The electrical subsystem consists of three basic components: electric motor, battery pack and power converter. A modular representation is used for building the dynamic model of the vehicle drivetrain. This means that every component of the drivetrain (submodule) is modeled separately and has its own general dynamic model, with clearly defined inputs and outputs. Then, all the particular submodules are assembled according to the drivetrain configuration and, in this way, the power flow across the components is completely determined. Dynamic models of electrical components are often based on equivalent circuits, where Kirchhoff’s voltage and current laws are applied to draw the algebraic and differential equations. Here, Randles circuit is used for dynamic modeling of the battery and the electric motor is modeled through the analysis of the equivalent circuit of a separately excited DC motor, where the power converter is included. The mechanical subsystem is defined by MBS3D equations. These equations consider the position, velocity and acceleration of all the bodies comprising the vehicle multibody system. MBS3D 2.0 is entirely written in MATLAB and the structure of the program has been thoroughly studied and understood by the author. MBS3D software is adapted according to the requirements of the applied co-simulation method. Some of the core functions are modified, such as integrator and graphics, and several auxiliary functions are added in order to compute the mathematical model of the electrical components. By coupling and co-simulating both subsystems, it is possible to evaluate the dynamic interaction among all the components of the drivetrain. ‘Tight-coupling’ method is used to cosimulate the sub-models. This approach integrates all subsystems simultaneously and the results of the integration are exchanged by function-call. This means that the integration is done jointly for the mechanical and the electrical subsystem, under a single integrator and then, the speed of integration is determined by the slower subsystem. Simulations are then used to show the performance of the developed EV model. However, this project focuses more on the validation of the computational and mathematical tool for electric and hybrid vehicle simulation. For this purpose, a detailed study and comparison of different integrators within the MATLAB environment is done. Consequently, the main efforts are directed towards the implementation of co-simulation techniques in MBS3D software. In this regard, it is not intended to create an extremely precise EV model in terms of real vehicle performance, although an acceptable level of accuracy is achieved. The gap between the EV model and the real system is filled, in a way, by introducing the gas and brake pedals input, which reflects the actual driver behavior. This input is included directly in the differential equations of the model, and determines the amount of current provided to the electric motor. For a separately excited DC motor, the rotor current is proportional to the traction torque delivered to the car wheels. Therefore, as it occurs in the case of real vehicle models, the propulsion torque in the mathematical model is controlled through acceleration and brake pedal commands. The designed transmission system also includes a reduction gear that adapts the torque coming for the motor drive and transfers it. The main contribution of this project is, therefore, the implementation of a new calculation path for the wheel torques, based on performance characteristics and outputs of the electric powertrain model. Originally, the wheel traction and braking torques were input to MBS3D through a vector directly computed by the user in a MATLAB script. Now, they are calculated as a function of the motor current which, in turn, depends on the current provided by the battery pack across the DC/DC chopper converter. The motor and battery currents and voltages are the solutions of the electrical ODE (Ordinary Differential Equation) system coupled to the multibody system. Simultaneously, the outputs of MBS3D model are the position, velocity and acceleration of the vehicle at all times. The motor shaft speed is computed from the output vehicle speed considering the wheel radius, the gear reduction ratio and the transmission efficiency. This motor shaft speed, somehow available from MBS3D model, is then introduced in the differential equations corresponding to the electrical subsystem. In this way, MBS3D and the electrical powertrain model are interconnected and both subsystems exchange values resulting as expected with tight-coupling approach.When programming mathematical models of complex systems, code optimization is a key step in the process. A way to improve the overall performance of the integration, making use of C/C++ as an alternative programming language, is described and implemented. Although this entails a higher computational burden, it leads to important advantages regarding cosimulation speed and stability. In order to do this, it is necessary to integrate MATLAB with another integrated development environment (IDE), where C/C++ code can be generated and executed. In this project, C/C++ files are programmed in Microsoft Visual Studio and the interface between both IDEs is created by building C/C++ MEX file functions. These programs contain functions or subroutines that can be dynamically linked and executed from MATLAB. This process achieves reductions in simulation time up to two orders of magnitude. The tests performed with different integrators, also reveal the stiff character of the differential equations corresponding to the electrical subsystem, and allow the improvement of the cosimulation process. When varying the parameters of the integration and/or the initial conditions of the problem, the solutions of the system of equations show better dynamic response and stability, depending on the integrator used. Several integrators, with variable and non-variable step-size, and for stiff and non-stiff problems are applied to the coupled ODE system. Then, the results are analyzed, compared and discussed. From all the above, the project can be divided into four main parts: 1. Creation of the equation-based electric vehicle model; 2. Programming, simulation and adjustment of the electric vehicle model; 3. Application of co-simulation methodologies to MBS3D and the electric powertrain subsystem; and 4. Code optimization and study of different integrators. Additionally, in order to deeply understand the context of the project, the first chapters include an introduction to basic vehicle dynamics, current classification of hybrid and electric vehicles and an explanation of the involved technologies such as brake energy regeneration, electric and non-electric propulsion systems for EVs and HEVs (hybrid electric vehicles) and their control strategies. Later, the problem of dynamic modeling of hybrid and electric vehicles is discussed. The integrated development environment and the simulation tool are also briefly described. The core chapters include an explanation of the major co-simulation methodologies and how they have been programmed and applied to the electric powertrain model together with the multibody system dynamic model. Finally, the last chapters summarize the main results and conclusions of the project and propose further research topics. In conclusion, co-simulation methodologies are applicable within the integrated development environments MATLAB and Visual Studio, and the simulation tool MBS3D 2.0, where equation-based models of multidisciplinary subsystems, consisting of mechanical and electrical components, are coupled and integrated in a very efficient way.

Nonlinear analysis of a simple model of temperature evolution in a satellite

We analyze a simple model of the heat transfer to and from a small satellite orbiting round a solar system planet. Our approach considers the satellite isothermal, with external heat input from the environment and from internal energy dissipation, and output to the environment as black-body radiation. The resulting nonlinear ordinary differential equation for the satellite’s temperature is analyzed by qualitative, perturbation and numerical methods, which prove that the temperature approaches a periodic pattern (attracting limit cycle). This approach can occur in two ways, according to the values of the parameters: (i) a slow decay towards the limit cycle over a time longer than the period, or (ii) a fast decay towards the limit cycle over a time shorter than the period. In the first case, an exactly soluble average equation is valid. We discuss the consequences of our model for the thermal stability of satellites.

Mathematical modelling of neural processes within the oculomotor system

It is presented a mathematical model of the oculomotor plant, based on experimental data in cats. The system that generates, from the neuronal processes at the motoneuron, the control signals to the eye muscles that moves the eye. In contrast with previous models, that base the eye movement related motoneuron behavior on a first order linear differential equation, non-linear effects are described: A dependency on the eye angular position of the model parameters.

Impedance of foundations using the Boundary Integral Equation Method

Dynamic soil-structure interaction has been for a long time one of the most fascinating areas for the engineering profession. The building of large alternating machines and their effects on surrounding structures as well as on their own functional behavior, provided the initial impetus; a large amount of experimental research was done,and the results of the Russian and German groups were especially worthwhile. Analytical results by Reissner and Sehkter were reexamined by Quinlan, Sung, et. al., and finally Veletsos presented the first set of reliable results. Since then, the modeling of the homogeneous, elastic halfspace as a equivalent set of springs and dashpots has become an everyday tool in soil engineering practice, especially after the appearance of the fast Fourier transportation algorithm, which makes possible the treatment of the frequency-dependent characteristics of the equivalent elements in a unified fashion with the general method of analysis of the structure. Extensions to the viscoelastic case, as well as to embedded foundations and complicated geometries, have been presented by various authors. In general, they used the finite element method with the well known problems of geometric truncations and the subsequent use of absorbing boundaries. The properties of boundary integral equation methods are, in our opinion, specially well suited to this problem, and several of the previous results have confirmed our opinion. In what follows we present the general features related to steady-state elastodynamics and a series of results showing the splendid results that the BIEM provided. Especially interesting are the outputs obtained through the use of the so-called singular elements, whose description is incorporated at the end of the paper. The reduction in time spent by the computer and the small number of elements needed to simulate realistically the global properties of the halfspace make this procedure one of the most interesting applications of the BIEM.

Resonancias de los paradigmas científicos en las arquitecturas de la Escuela de Madrid

Los años cincuenta y sesenta son los años de la incorporación definitiva de la arquitectura española al panorama internacional. Entre los arquitectos que protagonizan ese salto sin retorno, se encuentra el grupo de aquellos que unos años más tarde serán denominados por Juan Daniel Fullaondo como Escuela de Madrid. Carlos Flores, en su libro Arquitectura Española Contemporánea 1880-1950, se refiere a esos arquitectos como aquellos que se aplicaban a la difícil tarea de restablecer en España un tipo de arquitectura que conectaba con las teorías, soluciones y lenguajes establecidos por Europa durante las primeras décadas del siglo XX. Sigfried Giedion plantea en Espacio, Tiempo y Arquitectura el origen de una nueva tradición, surgida a partir de la revolución óptica de principios de siglo. Con tradición se refiere a una nueva cultura, que abarca la interrelación de las diferentes actividades del hombre: la similitud de los métodos que se usan en la arquitectura, la construcción, la pintura, el urbanismo o la ciencia. Esa novedad, fundamentada en su independencia y desvinculación con el periodo anterior, se inscribe dentro del esquema evolutivo que Thomas Kuhn plantea en su texto La Estructura de la Revoluciones Científicas, conforme a periodos no acumulativos. Kuhn habla del surgimiento de anomalías en cada periodo, origen de las crisis de pensamiento cuya explicación precisará un necesario cambio paradigmático. En la ciencia, en el campo de la óptica Thomas Young demuestra a principios del siglo XIX la naturaleza ondulatoria de la luz con su experimento de doble rendija; en el electromagnetismo se produce el salto conceptual que supone la postulación de la existencia del campo eléctrico por parte de Michael Faraday, y en termodinámica la consideración apuntada por Planck de que la radiación de la energía de produce de forma discreta, a través de cuantos. En las artes plásticas, paralelamente, Gleizes y Metzinger, en su recopilación de logros cubistas recogida en Sobre el Cubismo, hablan de la evolución sufrida durante el siglo XIX por la pintura: desde el idealismo de principios de siglo, para pasando por el realismo y la representación impresionista de la realidad, concluir prescindiendo de la perspectiva clásica. También la matemática, una vez desarrolladas por Gauss o Lobachevsky y Bolyai geometrías coherentes que incumplen el quinto postulado de Euclides, terminará dando validez a través de Riemann a los espacios ambiente en los que habitan dichas geometrías, desvinculando la relación directa entre espacio geométrico –el espacio ambiente al que da lugar un tipo de geometría- y el espacio físico. Capi Corrales refleja en su libro Contando el Espacio, cómo hasta la teoría de la relatividad y el cubismo, las geometrías no euclídeas no se hicieron notorias también fuera del campo de las matemáticas. El origen de la nueva tradición con la que Giedion se refiere a la nueva cultura de la modernidad coincide con los saltos paradigmáticos que suponen la teoría de la relatividad en las ciencias y el cubismo en las artes plásticas. Ambas se prolongan durante las primeras décadas hasta la teoría cuántica y la abstracción absoluta, barreras que los dos principales precursores de la relatividad y el cubismo, Einstein y Picasso, nunca llegan a franquear. En ese sentido Giedion habla también, además del origen, de su desarrollo, e incorpora las aportaciones periféricas en la arquitectura de Brasil, Japón o Finlandia, incluyendo por tanto la revisión orgánica propugnada por Zevi como parte de esa nueva tradición, quedando abierta a la incorporación tardía de nuevas aportaciones al desarrollo de esa cultura de la modernidad. Eliminado el concepto de la estética trascendental de Kant del tiempo como una referencia absoluta, y asumido el valor constante de la velocidad de la luz, para la teoría de la relatividad no existe una simultaneidad auténtica. Queda así fijada la velocidad de la luz como uno de los límites del universo, y la equivalencia entre masa y energía. En el cubismo la simultaneidad espacial viene motivada por la eliminación del punto de vista preferente, cuyo resultado es la multiplicidad descriptiva de la realidad, que se visualiza en la descomposición en planos, tanto del objeto como del espacio, y la consecuente continuidad entre fondo y figura que en arquitectura se refleja en la continuidad entre edificio y territorio. Sin la consideración de un punto de vista absoluto, no existe una forma auténtica. El cubismo, y su posterior desarrollo por las vanguardias plásticas, hacen uso de la geometría como mecanismo de recomposición de la figura y el espacio, adoptando mecanismos de penetración, superposición y transparencia. Gyorgy Kepes indica en El Lenguaje de la Visión que la descomposición cubista del objeto implica la sucesiva autonomía de los planos, hasta convertirse en elementos constituyentes. Algo que refleja las axonometrías arquitectónicas de Van Doesburg y que culmina con los espacios propuestos por Mies van der Rohe en sus primeros proyectos europeos. Estos mecanismos, encuentran eco en los primeros planteamientos de Javier Carvajal: en la ampliación del Panteón de españoles del cementerio de Campo Verano, un recinto virtual reconstruido mentalmente a partir del uso de tres únicos planos; o en el Pabellón de Nueva York, que organiza su planta baja desde el recorrido, introduciendo el parámetro temporal como una dimensión más. Al uso diferenciado del plano como elemento constituyente, Carvajal incorpora su plegado y su disposición conformando envolventes como mecanismo de cualificación espacial y formal, potenciando la prolongación entre arquitectura y territorio. Una continuidad que quedará culminada en las dos viviendas unifamiliares construidas en Somosaguas. La descomposición volumétrica conduce a unos niveles de abstracción que hace precisa la incorporación de elementos de la memoria -fuentes, patios, celosías…- a modo de red de señales, como las que Picasso y Braque introducen en sus cuadros para permitir su interpretación. Braque insiste en el interés por el espacio que rodea a los objetos. Una búsqueda de la tactilidad del espacio contraria a la perspectiva que aleja el objeto del observador, y que en los jardines de las viviendas de Somosaguas parece emanar de su propia materialidad. Un espacio táctil alejado del espacio geométrico y que Braque identifica con el espacio representativo en el que Poincaré, en La Ciencia y la Hipótesis, ubica nuestras sensaciones. Desdibujar los límites del objeto prolonga el espacio indefinidamente. Con el paso en el arte griego del mito al logos, se abre paso a la matemática como herramienta de comprensión de la naturaleza hasta el siglo XIX. Leon Lederman, en Simetría y la Belleza del Universo, apunta a que una de las mayores contribuciones de la teoría de Einstein es hacer cambiar el modo de pensar la naturaleza, orientándolo hacia la búsqueda de los principios de simetría que subyacen bajo las leyes físicas. Considerando que la simetría es la invariancia de un objeto o un sistema frente a una transformación y que las leyes físicas son las mismas en cualquier punto del espacio, el espacio de nuestro universo posee una simetría traslacional continua. En la ocupación del espacio de las primeras propuestas de Corrales y Molezún aparecen estructuras subyacentes que responden a enlosetados: paralelogramos sometidos a transformaciones continuas, que la naturaleza identifica tridimensionalmente con los grupos cristalográficos. Las plantas del museo de Arte Contemporáneo de la Castellana, la residencia de Miraflores, el pabellón de Bruselas o la torre Peugeot pertenecen a este grupo. La arquitectura como proceso de ocupación continua del territorio y de su trasposición al plano de cubierta, se materializa en líneas estructurales coincidentes con la estructura matemática de sus simetrías de traslación cuya posibilidad de prolongación infinita queda potenciada por el uso de la envolvente transparente. Junto a esta transparencia literal, inherente al material, Colin Rowe y Robert Slutzky nos alertan sobre otra transparencia inherente a la estructura: la transparencia fenomenal, ilustrada por los cuadros de Juan Gris, y cuya intuición aparece reflejada en la casa Huarte en Puerta de Hierro de Madrid. Corrales y Molezún insisten en una lectura de su volumetría alejada de la frontalidad, en la que los contornos de sus cubiertas inclinadas y las visuales tangenciales sugeridas por la organización de sus recorridos introducen una estructura diagonal que se superpone al entendimiento ortogonal de su planta, dibujando una intrincada red de líneas quebradas que permiten al espacio fluctuar entre las secuencia volumétrica propuesta. Los datos relativos al contenido energético de la luz y el concepto de átomo parten de la consideración de la emisión de energía en cuantos realizada por Planck, y concluyen con una circunstancia paradójica: la doble naturaleza de la luz -demostrada por la explicación de Einstein del efecto fotoeléctrico- y la doble naturaleza de la materia -asumida por Bohr y demostrada por el efecto Compton-. Schrödinger y Heisenberg formularán finalmente la ecuación universal del movimiento que rige en las ondas de materia, y cuya representación matemática es lo que se conoce como función de onda. El objeto es así identificado con su función de onda. Su ondulatoriedad expresará la probabilidad de encontrarse en un lugar determinado. Gyorgy Kepes subraya la necesidad de simplificar el lenguaje para pasar de la objetividad que aún permanece en la pintura cubista a la abstracción total del espacio. Y es así como los artistas plásticos reducen los objetos a simples formas geométricas, haciendo aflorar a la vez, las fuerzas plásticas que los tensionan o equilibran, en un proceso que acaba por eliminar cualquier atisbo de materia. Robert Rosenblum en La Pintura Moderna y la Tradición del Romanticismo Nórdico habla de cómo ese rechazo de la materia en favor de un vacío casi impalpable, campos luminosos de color denso que difunden un sereno resplandor y parecen engendrar las energías elementales de la luz natural, está directamente vinculado a la relación con la naturaleza que establece el romanticismo nórdico. La expresión de la energía de la naturaleza concentrada en un vacío que ya había sido motivo de reflexión para Michael Faraday en su postulación del concepto de campo eléctrico. Sáenz de Oíza incide en la expresión de la condición material de la energía en su propuesta junto a José Luis Romany para la capilla en el Camino de Santiago. La evocación de diferentes fuerzas electromagnéticas, las únicas junto a las gravitatorias susceptibles de ser experimentadas por el hombre, aparecerán visualizadas también en el carácter emergente de algunas de sus obras: el Santuario de Aránzazu o Torres Blancas; pero también en la naturaleza fluyente de sus contornos, la dispersión perimetral de los espacios -el umbral como centro del universoo la configuración del límite como respuesta a las tensiones germinales de la naturaleza. Miguel Fisac, a la vuelta de su viaje a los países nórdicos, aborda una simplificación lingüística orientada hacia la adecuación funcional de los espacios. En el Instituto de Daimiel, el Instituto de formación del profesorado o los complejos para los Padres Dominicos en Valladolid o Alcobendas, organiza progresivamente la arquitectura en diferentes volúmenes funcionales, incidiendo de un modo paralelo en la manifestación de los vínculos que se establecen entre dichos volúmenes como una visualización de las fuerzas que los tensionan y equilibran. En ellos la prolongación de la realidad física más allá de los límites de la envolvente ya es algo más que una simple intuición. Un proceso en el que el tratamiento de la luz como un material de construcción más, tendrá un especial protagonismo. En la iglesia de la Coronación, la iluminación del muro curvo escenifica la condición ondulatoria de la luz, manifestándose como si de un patrón de interferencia se tratara. Frente a la disolución de lo material, el espacio se manifiesta aquí como un medio denso, alejado de la tradicional noción de vacío. Una doble naturaleza, onda y partícula, que será intuido también por Fisac en la materia a través de su uso comprometido del hormigón como único material de construcción. Richard Feynmann nos alerta de la ocupación del espacio por multitud de fuerzas electromagnéticas que, al igual que la luz, precisan de receptores específicos para captar su presencia. Sus célebres diagramas suponen además la visualización definitiva de los procesos subatómicos. Al igual que la abstracción absoluta en las artes plásticas, esas representaciones diagramáticas no son asimilables a imágenes obtenidas de nuestra experiencia. Una intuición plasmada en el uso del diagrama, que irán adquiriendo progresivamente los dibujos de Alejandro de la Sota. La sección del gimnasio Maravillas recoge los trazos de sus principales elementos constructivos: estructura, cerramientos, compartimentaciones…, pero también, y con la misma intensidad, los de las fuerzas que generan su espacio, considerando así su condición de elementos constituyentes. El vacío, nos deja claro Sota, es el lugar donde habitan dichas tensiones. La posterior simplificación de las formas acompañadas de la obsesión por su aligeramiento, la casi desaparición de la envolvente, incide en aquella idea con la que Paul Klee define la actividad del artista en su Teoría del Arte Moderno, y en la que se transmite el distanciamiento hacia lo aparente: No se trata de reproducir lo visible, se trata de volver visible. Así, en Bankunión y Aviaco, como en tantos otros proyectos, frente al objetivo de la forma, Sota plantea el límite como la acotación de un ámbito de actuación. Su propia representación aséptica y diagramática transmite la renuncia a una especificidad espacial. Gilles Deleuze expresa ese posicionamiento en Pintura, el Concepto de Diagrama: el diagrama como la posibilidad de cuadros infinitos, o la posibilidad infinita de cuadros. Aparece así una concepción probabilística del espacio en la que frente a la renuncia por la forma, la tendencia al aligeramiento, y lo difuso de su definición – ideas claras, definición borrosa, en palabras de Llinás referidas al modo de operar de Sota-, la insistente atención a algunos elementos como escaleras, protecciones o miradores parece trasmitir la idea de que la arquitectura queda condensada en aquellos acontecimientos que delatan su condición dinámica, transitoria. Primando la relación frente al objeto, el vínculo frente a lo tangible. English summary. The fifties and sixties were the years of the final incorporation of Spanish architecture to the international scene. Among the architects who star that no return leap, is the group of those who a few years later will be named by Juan Daniel Fullaondo as Escuela de Madrid. Carlos Flores, in his book Arquitectura Española Contemporánea 1880-1950, refers to those architects as those that applied to the difficult task of restoring in Spain an architecture that connected with theories, solutions and established languages in Europe during the first decades of the twentieth century. Sigfried Giedion proposes in Space, Time and Architecture, the origin of a new tradition, arising from the optical revolution at the beginning of the century. With tradition he refers to a new culture, covering the interplay of different human activities: the similarity of the methods used in architecture, building, painting, urban planning or science. This new feature, based on its independence and detachment from the previous period, is part of the evolutionary scheme that Thomas Kuhn proposes in his text The Structure of Scientific Revolutions, according to non-accumulative periods. Kuhn talks about the emergence of anomalies in each period, origin of thought crisis whose explanation will require a paradigm shift needed. In science, in the field of optical Thomas Young demonstrates at the early nineteenth century the wave nature of light with its double-slit experiment , in electromagnetism the postulation of the existence of the electric field by Michael Faraday involves a conceptual leap, and in thermodynamic, the consideration pointed by Planck about quantum energy radiation. In the arts, in a parallel process, Gleizes and Metzinger , in his collection of cubism achievements on their book Du Cubisme, speak of evolution occurring during the nineteenth century by the painting: from the idealism of beginning of the century, going for realism and impressionist representation of reality, and finishing regardless of the classical perspective . Mathematics also, once developed by Gauss and Lobachevsky and Bolyai consistent geometries that violate Euclid's fifth postulate , will end validating Riemann’s ambient spaces in which these geometries inhabit, decoupling the direct relationship between geometric space -the space environment that results in a type of geometry- , and physical space. Capi Corrales reflectes in his book Contando el Espacio, that non-Euclidean geometries were not noticeable outside the field of mathematics until the theory of relativity and cubism. The origin of the new tradition that Giedion relates to the new culture of modernity coincides with paradigmatic leaps pointed by the theory of relativity in science and Cubism in the visual arts. Both are extended during the first decades until quantum theory and absolute abstraction, barriers that the two main precursors of relativity and cubism, Einstein and Picasso never overcome. In that sense Giedion speaks about the origin, but also the development, and incorporates peripheral inputs from Brazil, Japan and Finland architecture, thus including organic revision advocated by Zevi as part of this new tradition, being open to the late addition of new contributions to the development of that culture of modernity. Removed the concept of Kant's transcendental aesthetics, of time as an absolute reference, and assumed the constant value of the speed of light, theory of relativity says there is no authentic concurrency. It is thus fixed the speed of light as one of the limits of the universe, and the equivalence of mass and energy. In cubism, spatial simultaneity results from the elimination of preferential points of view, resulting in the multiplicity descriptive of reality, which is displayed in decomposition levels, both the object and the space, and the resulting continuity between figure and background that architecture is reflected in the continuity between building and land. Without the consideration of an absolute point of view, there isn’t an authentic shape. Cubism, and its subsequent development by the vanguard arts, make use of geometry as a means of rebuilding the figure and space, taking penetration mechanisms, overlapping and transparency. Gyorgy Kepes suggest in Languaje of Vision, that cubist decomposition of the object involves successive planes autonomy, to become constituent elements. Something that reflects the Van Doesburg’s architectural axonometrics and culminates with the spaces proposed by Mies van der Rohe in his first European projects. These mechanisms are reflected in the first approaches by Javier Carvajal: the extension of Spanish Pantheon in Campo Verano Cemetery, virtual enclosure mentally reconstructed from 24 the use of only three planes, or in the Spanish Pavilion of New York, which organizes its ground floor from the tour, introducing the time parameter as an additional dimension. Carvajal adds to the differential use of the plane as a constituent, Carvajal incorporates its folding and forming enclosures available as a mechanism for spatial and formal qualification, promoting the extension between architecture and territory. A continuity that will be completed in the two houses built in Somosaguas. Volumetric decomposition, as the fragmentation achieved in the last cubist experiences, needs the incorporation of elements of memory - fountains, patios, shutters...- as a network of signals, such as those introduced by Picasso and Braque in their paintings to allow their interpretation. Braque insists in his interest in the space surrounding the objects. A search of the tactility of space contrary to the perspective, which moves the observer away from the object, and that in the gardens of Somosaguas seems to emanate from its own materiality. A tactile space away from the geometric space and Braque identified with the representative space in which Poincaré in La Science et l´hypothèse, located our feelings. To blur those boundaries of the object extends the space indefinitely. With the passage in Greek art from myth to logos, it opens up to mathematics as a tool for understanding the nature until the nineteenth century. Leon Lederman, in Symmetry and beautiful Universe, suggests that one of the greatest contributions of Einstein's theory is to change the mindset of nature, namely the search for symmetry principles that underlie physical laws. Considering that symmetry is the invariance of an object or system from a transformation and that physical laws are the same at any point in space, the space of our universe has a continuous translational symmetry. In the space occupation of the first proposals by Corrales and Molezún underlying structures appear that match enlosetados: parallelograms under continuous transformations, which nature identifies tridimensionally with the crystallographic groups. Plants in the Contemporary Art Museum in La Castellana, the residence in Miraflores, the Brussels pavilion or the Peugeot tower belong to this group. The architecture as a process of continuous occupation of the territory and of its transposition to the deck, embodied in structural lines coincide with the mathematical structure of the translational symmetry and infinite extension whose possibility is enhanced by the use of the transparent cover. Alongside this literal transparency inherent to the material, Colin Rowe and Robert Slutzky alert us another transparency inherent in the structure: phenomenal transparency, illustrated by the Juan Gris’ works, and whose intuition is reflected in the Huarte’s house in Puerta de Hierro in Madrid. Corrales and Molezún insist on a reading of its volume away from the frontal, in which the outline of their inclined roofs and tangential visual suggested by the organization of his circulations introduce a diagonal structure which overlaps the orthogonal understanding of its plant, drawing an intricate web of broken lines that allow the space fluctuate between the volumetric sequence proposal. Information concerning to the energy mean of light and the concept of atom start from the consideration by Plank about the energy emission, and conclude with a paradoxical situation: the dual nature of light - demonstrated by the explanation of Einstein's photoelectric effect-, and the dual nature of matter -assumed by Bohr and demonstrated by the Compton effect-. Finally, Schrödinger and Heisenberg will formulate the universal movement equation governing in undulatory matter, whose mathematical representation is what is known as a wave function. The object is thus identified with its wave function. Its undulatory expression speaks about the probability of being found in a certain place. Gyorgy Kepes emphasizess the need to simplify the language to move from the objectivity that still remains in the cubist painting to the total abstraction of the space. And this is how artists reduced the objects to simple geometric shapes, making emerge at a time, the plastic forces that tense or balance them, in a process that eventually eliminate any trace of matter. Robert Rosenblum in Modern Painting and the Northern Romantic Tradition. Friedrich to Rothko talks about how this rejection of matter in an almost impalpable vacuum: dense color light fields that broadcast a serene glow and seem to generate the elemental energies of natural light is directly linked to the relationship with nature that sets the northern romanticism. An expression of the power of nature concentrated in a vacuum which had been reason for thought by Michael Faraday in his application of the concept of electric field. Saenz de Oíza touches upon the material expression of the energy in its proposal with Jose Luis Romany to the chapel on the Camino de Santiago. The presence of electromagnetic forces, the only ones with the gravitational one capable of being experienced by the man will also visualize in the emerging nature of some of his works: the sanctuary of Aránzazu or Torres Blancas, but also in the flowing nature of its contours, and the inclusion of interest in the realization of space fluctuating boundary: the threshold as the center of the universe. Miguel Fisac, back from his trip to the Northern Countries, starts on a linguistic simplification oriented to the functional adequacy of spaces. In the Daimiel Institute, in the Institute to Teacher Formation or in the complex to the Dominican Fathers in Valladolid or Alcobendas, progressively organized into different functional volumes architecture, focusing in a parallel way in the manifestation of the links established between these volumes as a visualization of the forces that tense and balance them. The prolongation of the physical reality beyond the limits of the envelope is already something more than a simple intuition. A process in which the treatment of light as a construction material, have a special role. In the Coronation church, curved wall lighting dramatizes the undulatory condition of the light, manifesting as if an interference pattern is involved. Versus the dissolution of the material, the space is expressed here as a dense atmosphere, away from the traditional notion of the vacuum. A dual nature, wave and particle, which is also sensed by Fisac in his committed use of concrete as a unique construction material. Richard Feynman alerts us to the occupation of space by many electromagnetic forces, which like the light, require specific receptors to capture their presence. His famous diagrams also involve the final visualization of atomic processes. As absolute abstraction in the visual arts, these representations are not assimilated to images obtained from our experience. A diagrammatic nature, abstracted from figuration, which will obtein the pictures of Alejandro de la Sota. The section of Maravillas gym collects traces of its main building blocks: structure, enclosures... but also, and with the same intensity, of the forces that generate their space as constituent elements. Sota makes it clear: the vacuum is where inhabit these tensions. The subsequent simplification of forms, accompanied by the obsession with his lightening, the near disappearance of the envelope, touches upon that idea which Paul Klee defines the activity of the artist in his Modern Art Theory, the spacing out to the apparent: it is not to reproduce the visible, it is to turn visible. Thus, in Bankunión and Aviaco, as in many other projects, against the shape, raises the limit as the dimension of a scope. His own aseptic and diagrammatic representation transmits waiver to a spatial specificity that Gilles Deleuze clearly expressed in Painting. The Concept Diagram: The diagram as the possibility of infinite pictures, or infinite possibility of the picture. Thus appears the probabilistic concept of space in which, opposite to the diffuse of its definition -clear ideas, diffuse definition, as Llinas said- the insistent attention to some elements like stairs, guards or lookouts seems to concentrate the architecture in its dynamic condition, transitional. The relationship opposite the object, the link opposite the tangible.

Large-scale identification of gibberellin-related transcription factor defines group VII ERFs as functional of DELLA partners

DELLA proteins are the master negative regulators in gibberellin (GA) signaling acting in the nucleus as transcriptional regulators. The current view of DELLA action indicates that their activity relies on the physical interaction with transcription factors (TFs). Therefore, the identification of TFs through which DELLAs regulate GA responses is key to understanding these responses from a mechanistic point of view. Here, we have determined the TF interactome of the Arabidopsis (Arabidopsis thaliana) DELLA protein GIBBERELLIN INSENSITIVE and screened a collection of conditional TF overexpressors in search of those that alter GA sensitivity. As a result, we have found RELATED TO APETALA2.3, an ethylene-induced TF belonging to the group VII ETHYLENE RESPONSE FACTOR of the APETALA2/ethylene responsive element binding protein superfamily, as a DELLA interactor with physiological relevance in the context of apical hook development. The combination of transactivation assays and chromatin immunoprecipitation indicates that the interaction with GIBBERELLIN INSENSITIVE impairs the activity of RELATED TO APETALA2.3 on the target promoters. This mechanism represents a unique node in the cross regulation between the GA and ethylene signaling pathways controlling differential growth during apical hook development.

Characterizing chaos in a type of fractional duffing's equation

We characterize the chaos in a fractional Duffing’s equation computing the Lyapunov exponents and the dimension of the strange attractor in the effective phase space of the system. We develop a specific analytical method to estimate all Lyapunov exponents and check the results with the fiduciary orbit technique and a time series estimation method.

Functional response of Ulmus minor Mill. to drought, flooding and dutch elm disease

Ulmus minor es una especie arbórea originaria de Europa cuyas poblaciones han sido diezmadas por el hongo patógeno causante de la enfermedad de la grafiosis. La conservación de los olmos exige plantearse su propagación a través de plantaciones y conocer mejor su ecología y biología. Ulmus minor es un árbol de ribera, pero frecuentemente se encuentra alejado del cauce de arroyos y ríos, donde la capa freática sufre fuertes oscilaciones. Por ello, nuestra hipótesis general es que esta especie es moderadamente resistente tanto a la inundación como a la sequía. El principal objetivo de esta tesis doctoral es entender desde un punto de vista funcional la respuesta de U. minor a la inundación, la sequía y la infección por O. novo-ulmi; los factores que posiblemente más influyen en la distribución actual de U. minor. Con este objetivo se persigue dar continuidad a los esfuerzos de conservación de esta especie que desde hace años se dedican en varios centros de investigación a nivel mundial, ya que, entender mejor los mecanismos que contribuyen a la resistencia de U. minor ante la inoculación con O. novo-ulmi y factores de estrés abiótico ayudará en la selección y propagación de genotipos resistentes a la grafiosis. Se han planteado tres experimentos en este sentido. Primero, se ha comparado la tolerancia de brinzales de U. minor y U. laevis – otro olmo ibérico – a una inmersión controlada con el fin de evaluar su tolerancia a la inundación y comprender los mecanismos de aclimatación. Segundo, se ha comparado la tolerancia de brinzales de U. minor y Quercus ilex – una especie típica de ambientes Mediterránea secos – a la falta de agua en el suelo con el fin de evaluar el grado de tolerancia y los mecanismos de aclimatación a la sequía. El hecho de comparar dos especies contrastadas responde al interés en entender mejor cuales son los procesos que conducen a la muerte de una planta en condiciones de sequía – asunto sobre el que hay una interesante discusión desde hace algunos años. En tercer lugar, con el fin de entender mejor la resistencia de algunos genotipos de U. minor a la grafiosis, se han estudiado las diferencias fisiológicas y químicas constitutivas e inducidas por O. novo-ulmi entre clones de U. minor seleccionados a priori por su variable grado de resistencia a esta enfermedad. En el primer experimento se observó que los brinzales de U. minor sobrevivieron 60 días inmersos en una piscina con agua no estancada hasta una altura de 2-3 cm por encima del cuello de la raíz. A los 60 días, los brinzales de U. laevis se sacaron de la piscina y, a lo largo de las siguientes semanas, fueron capaces de recuperar las funciones fisiológicas que habían sido alteradas anteriormente. La conductividad hidráulica de las raíces y la tasa de asimilación de CO2 neta disminuyeron en ambas especies. Por el contrario, la tasa de respiración de hojas, tallos y raíces aumentó en las primeras semanas de la inundación, posiblemente en relación al aumento de energía necesario para desarrollar mecanismos de aclimatación a la inundación, como la hipertrofia de las lenticelas que se observó en ambas especies. Por ello, el desequilibrio del balance de carbono de la planta podría ser un factor relevante en la mortalidad de las plantas ante inundaciones prolongadas. Las plantas de U. minor (cultivadas en envases de 16 litros a media sombra) sobrevivieron por un prolongado periodo de tiempo en verano sin riego; la mitad de las plantas murieron tras 90 días sin riego. El cierre de los estomas y la pérdida de hojas contribuyeron a ralentizar las pérdidas de agua y tolerar la sequía en U. minor. Las obvias diferencias en tolerancia a la sequía con respecto a Q. ilex se reflejaron en la distinta capacidad para ralentizar la aparición del estrés hídrico tras dejar de regar y para transportar agua en condiciones de elevada tensión en el xilema. Más relevante es que las plantas con evidentes síntomas de decaimiento previo a su muerte exhibieron pérdidas de conductividad hidráulica en las raíces del 80% en ambas especies, mientras que las reservas de carbohidratos apenas variaron y lo hicieron de forma desigual en ambas especies. Árboles de U. minor de 5 y 6 años de edad (plantados en eras con riego mantenido) exhibieron una respuesta a la inoculación con O. novo-ulmi consistente con ensayos previos de resistencia. La conductividad hidráulica del tallo, el potencial hídrico foliar y la tasa de asimilación de CO2 neta disminuyeron significativamente en relación a árboles inoculados con agua, pero solo en los clones susceptibles. Este hecho enlaza con el perfil químico “más defensivo” de los clones resistentes, es decir, con los mayores niveles de suberina, ácidos grasos y compuestos fenólicos en estos clones que en los susceptibles. Ello podría restringir la propagación del hongo en el árbol y preservar el comportamiento fisiológico de los clones resistentes al inocularlos con el patógeno. Los datos indican una respuesta fisiológica común de U. minor a la inundación, la sequía y la infección por O. novo-ulmi: pérdida de conductividad hidráulica, estrés hídrico y pérdida de ganancia neta de carbono. Pese a ello, U. minor desarrolla varios mecanismos que le confieren una capacidad moderada para vivir en suelos temporalmente anegados o secos. Por otro lado, el perfil químico es un factor relevante en la resistencia de ciertos genotipos a la grafiosis. Futuros estudios deberían examinar como este perfil químico y la resistencia a la grafiosis se ven alteradas por el estrés abiótico. ABSTRACT Ulmus minor is a native European elm species whose populations have been decimated by the Dutch elm disease (DED). An active conservation of this species requires large-scale plantations and a better understanding of its biology and ecology. U. minor generally grows close to water channels. However, of the Iberian riparian tree species, U. minor is the one that spread farther away from rivers and streams. For these reasons, we hypothesize that this species is moderately tolerant to both flooding and drought stresses. The main aim of the present PhD thesis is to better understand the functional response of U. minor to the abiotic stresses – flooding and drought – and the biotic stress – DED – that can be most influential on its distribution. The overarching goal is to aid in the conservation of this emblematic species through a better understanding of the mechanisms that contribute to resistance to abiotic and biotic stresses; an information that can help in the selection of resistant genotypes and their expansion in large-scale plantations. To this end, three experiments were set up. First, we compared the tolerance to experimental immersion between seedlings of U. minor and U. laevis – another European riparian elm species – in order to assess their degree of tolerance and understand the mechanisms of acclimation to this stress. Second, we investigated the tolerance to drought of U. minor seedlings in comparison with Quercus ilex (an oak species typical of dry Mediterranean habitats). Besides assessing and understanding U. minor tolerance to drought at the seedling stage, the aim was to shed light into the functional alterations that trigger drought-induced plant mortality – a matter of controversy in the last years. Third, we studied constitutive and induced physiological and biochemical differences among clones of variable DED resistance, before and following inoculation with Ophiostoma novo-ulmi. The goal is to shed light into the factors of DED resistance that is evident in some genotypes of U. minor, but not others. Potted seedlings of U. minor survived for 60 days immersed in a pool with running water to approximately 2-3 cm above the stem collar. By this time, U. minor seedlings died, whereas U. laevis seedlings moved out of the pool were able to recover most physiological functions that had been altered by flooding. For example, root hydraulic conductivity and leaf photosynthetic CO2 uptake decreased in both species; while respiration initially increased with flooding in leaves, stems and roots possibly to respond to energy demands associated to mechanisms of acclimation to soil oxygen deficiency; as example, a remarkable hypertrophy of lenticels was soon observed in flooded seedlings of both species. Therefore, the inability to maintain a positive carbon balance somehow compromises seedling survival under flooding, earlier in U. minor than U. laevis, partly explaining their differential habitats. Potted seedlings of U. minor survived for a remarkable long time without irrigation – half of plants dying only after 90 days of no irrigation in conditions of high vapour pressure deficit typical of summer. Some mechanisms that contributed to tolerate drought were leaf shedding and stomata closure, which reduced water loss and the risk of xylem cavitation. Obviously, U. minor was less tolerant to drought than Q. ilex, differences in drought tolerance resulting mostly from the distinct capacity to postpone water stress and conduct water under high xylem tension among species. More relevant was that plants of both species exhibited similar symptoms of root hydraulic failure (i.e. approximately 80% loss of hydraulic conductivity), but a slight and variable depletion of non-structural carbohydrate reserves preceding dieback. Five- and six-year-old trees of U. minor (planted in the field with supplementary watering) belonging to clones of contrasted susceptibility to DED exhibited a different physiological response to inoculation with O. novo-ulmi. Stem hydraulic conductivity, leaf water potential and photosynthetic CO2 uptake decreased significantly relative to control trees inoculated with water only in DED susceptible clones. This is consistent with the “more defensive” chemical profile observed in resistant clones, i.e. with higher levels of saturated hydrocarbons (suberin and fatty acids) and phenolic compounds than in susceptible clones. These compounds could restrict the spread of O. novo-ulmi and contribute to preserving the near-normal physiological function of resistant trees when exposed to the pathogen. These results evidence common physiological responses of U. minor to flooding, drought and pathogen infection leading to xylem water disruption, leaf water stress and reduced net carbon gain. Still, seedlings of U. minor develop various mechanisms of acclimation to abiotic stresses that can play a role in surviving moderate periods of flood and drought. The chemical profile appears to be an important factor for the resistance of some genotypes of U. minor to DED. How abiotic stresses such as flooding and drought affect the capacity of resistant U. minor clones to face O. novo-ulmi is a key question that must be contemplated in future research.

Classical solutions for a logarithmic fractional diffusion equation

We prove global existence and uniqueness of strong solutions to the logarithmic porous medium type equation with fractional diffusion ?tu + (?)1/2 log(1 + u) = 0, posed for x ? R, with nonnegative initial data in some function space of LlogL type. The solutions are shown to become bounded and C? smooth in (x, t) for all positive times. We also reformulate this equation as a transport equation with nonlocal velocity and critical viscosity, a topic of current relevance. Interesting functional inequalities are involved.