An evolutionary algorithm for the surface structure problem

Many macroscopic properties: hardness, corrosion, catalytic activity, etc. are directly related to the surface structure, that is, to the position and chemical identity of the outermost atoms of the material. Current experimental techniques for its determination produce a “signature” from which the structure must be inferred by solving an inverse problem: a solution is proposed, its corresponding signature computed and then compared to the experiment. This is a challenging optimization problem where the search space and the number of local minima grows exponentially with the number of atoms, hence its solution cannot be achieved for arbitrarily large structures. Nowadays, it is solved by using a mixture of human knowledge and local search techniques: an expert proposes a solution that is refined using a local minimizer. If the outcome does not fit the experiment, a new solution must be proposed again. Solving a small surface can take from days to weeks of this trial and error method. Here we describe our ongoing work in its solution. We use an hybrid algorithm that mixes evolutionary techniques with trusted region methods and reuses knowledge gained during the execution to avoid repeated search of structures. Its parallelization produces good results even when not requiring the gathering of the full population, hence it can be used in loosely coupled environments such as grids. With this algorithm, the solution of test cases that previously took weeks of expert time can be automatically solved in a day or two of uniprocessor time.

Study about the Problem of Dropping of Subjects by Students During an Academinc Year at the University.

In university studies, it is not unusual for students to drop some of the subjects they have enrolled in for the academic year. They start by not attending lectures, sometimes due to neglect or carelessness, or because they find the subject too difficult, this means that they lose the continuity in the topics that the professor follows. If they try to attend again they discover that they hardly understand anything and become discouraged and so decide to give up attending lectures and study on their own. However some fail to turn up to do their final exams and the failure rate of those who actually do the exams is high. The problem is that this is not only the case with one specific subject, but it is often the same with many subjects. The result is that students arent’s productive enough, wasting time and also prolonging their years of study which entails a great cost for families. Degree courses structured to be conducted and completed in three academic courses, it may in fact take up to an average of six or more academic courses. In this paper, we have studied this problem, which apart from the waste of money and time, produces frustration in the student, who finds that he has not been able to achieve what he had proposed at the beginning of the course. It is quite common, to find students who do not even pass nor 50% of the subjects they had enrolled in for the academic year. If this happens repeatedly to a student, it can be the point when he considers dropping out altogether. This is also a concern for the universities, especially in the early courses. In our experience as professors, we have found that students, who attend lectures regularly and follow the explanations, approach the final exams with confidence and rarely fail the subject. In this proposal we present some techniques and methods carried out to solve in possible, the problem of lack of attendance to lectures. This involves "rewarding students for their assistance and participation in lectures". Rewarding assistance with a "prize" that counts for the final mark on the subject and involving more participation in the development of lectures. We believe that we have to teach students to use the lectures as part of their learning in a non-passive way. We consider the professor's work as fundamental in terms of how to convey the usefulness of these topics explained and the applications that they will have for their professional life in the future. In this way the student see for himself the use and importance of what he is learning. When his participation is required, he will feel more involved and confident participating in the educational system. Finally we present statistical results of studies carried out on different degrees and on different subjects over two consecutive years. In the first year we assessed only the final exams without considering the students attendance, or participation. In the second year, we have applied the techniques and methods proposed here. In addition we have compared the two ways of assessing subjects.

A guided heuristic approach to the MEG inverse problem.

There is general agreement within the scientific community in considering Biology as the science with more potential to develop in the XXI century. This is due to several reasons, but probably the most important one is the state of development of the rest of experimental and technological sciences. In this context, there are a very rich variety of mathematical tools, physical techniques and computer resources that permit to do biological experiments that were unbelievable only a few years ago. Biology is nowadays taking advantage of all these newly developed technologies, which are been applied to life sciences opening new research fields and helping to give new insights in many biological problems. Consequently, biologists have improved a lot their knowledge in many key areas as human function and human diseases. However there is one human organ that is still barely understood compared with the rest: The human brain. The understanding of the human brain is one of the main challenges of the XXI century. In this regard, it is considered a strategic research field for the European Union and the USA. Thus, there is a big interest in applying new experimental techniques for the study of brain function. Magnetoencephalography (MEG) is one of these novel techniques that are currently applied for mapping the brain activity1. This technique has important advantages compared to the metabolic-based brain imagining techniques like Functional Magneto Resonance Imaging2 (fMRI). The main advantage is that MEG has a higher time resolution than fMRI. Another benefit of MEG is that it is a patient friendly clinical technique. The measure is performed with a wireless set up and the patient is not exposed to any radiation. Although MEG is widely applied in clinical studies, there are still open issues regarding data analysis. The present work deals with the solution of the inverse problem in MEG, which is the most controversial and uncertain part of the analysis process3. This question is addressed using several variations of a new solving algorithm based in a heuristic method. The performance of those methods is analyzed by applying them to several test cases with known solutions and comparing those solutions with the ones provided by our methods.

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.

Aerodynamic study of a blended wing body, comparison with a conventional transport airplane.

Blended-wing-body (BWB) aircraft are being studied with interest and effort to improve economic efficiency and to overcome operational and infrastructure related problems associated to the increasing size of conventional transport airplanes. The objective of the research reported here is to assess the aerodynamic feasibility and operational efficiency of a great size, blended wing body layout, a configuration which has many advantages. To this end, the conceptual aerodynamic design process of an 800 seat BWB has been done completed with a comparison of performance and operational issues with last generation of conventional very large aircraft. The results are greatly encouraging and predict about 20 percent increase in transport productivity efficiency, without the burden of new or aggravated safety or operational problems.

Caracterización de un robot para aplicaciones de mecanizado con requerimientos de tolerancias

El presente Trabajo fin Fin de Máster, versa sobre una caracterización preliminar del comportamiento de un robot de tipo industrial, configurado por 4 eslabones y 4 grados de libertad, y sometido a fuerzas de mecanizado en su extremo. El entorno de trabajo planteado es el de plantas de fabricación de piezas de aleaciones de aluminio para automoción. Este tipo de componentes parte de un primer proceso de fundición que saca la pieza en bruto. Para series medias y altas, en función de las propiedades mecánicas y plásticas requeridas y los costes de producción, la inyección a alta presión (HPDC) y la fundición a baja presión (LPC) son las dos tecnologías más usadas en esta primera fase. Para inyección a alta presión, las aleaciones de aluminio más empleadas son, en designación simbólica según norma EN 1706 (entre paréntesis su designación numérica); EN AC AlSi9Cu3(Fe) (EN AC 46000) , EN AC AlSi9Cu3(Fe)(Zn) (EN AC 46500), y EN AC AlSi12Cu1(Fe) (EN AC 47100). Para baja presión, EN AC AlSi7Mg0,3 (EN AC 42100). En los 3 primeros casos, los límites de Silicio permitidos pueden superan el 10%. En el cuarto caso, es inferior al 10% por lo que, a los efectos de ser sometidas a mecanizados, las piezas fabricadas en aleaciones con Si superior al 10%, se puede considerar que son equivalentes, diferenciándolas de la cuarta. Las tolerancias geométricas y dimensionales conseguibles directamente de fundición, recogidas en normas como ISO 8062 o DIN 1688-1, establecen límites para este proceso. Fuera de esos límites, las garantías en conseguir producciones con los objetivos de ppms aceptados en la actualidad por el mercado, obligan a ir a fases posteriores de mecanizado. Aquellas geometrías que, funcionalmente, necesitan disponer de unas tolerancias geométricas y/o dimensionales definidas acorde a ISO 1101, y no capaces por este proceso inicial de moldeado a presión, deben ser procesadas en una fase posterior en células de mecanizado. En este caso, las tolerancias alcanzables para procesos de arranque de viruta se recogen en normas como ISO 2768. Las células de mecanizado se componen, por lo general, de varios centros de control numérico interrelacionados y comunicados entre sí por robots que manipulan las piezas en proceso de uno a otro. Dichos robots, disponen en su extremo de una pinza utillada para poder coger y soltar las piezas en los útiles de mecanizado, las mesas de intercambio para cambiar la pieza de posición o en utillajes de equipos de medición y prueba, o en cintas de entrada o salida. La repetibilidad es alta, de centésimas incluso, definida según norma ISO 9283. El problema es que, estos rangos de repetibilidad sólo se garantizan si no se hacen esfuerzos o éstos son despreciables (caso de mover piezas). Aunque las inercias de mover piezas a altas velocidades hacen que la trayectoria intermedia tenga poca precisión, al inicio y al final (al coger y dejar pieza, p.e.) se hacen a velocidades relativamente bajas que hacen que el efecto de las fuerzas de inercia sean menores y que permiten garantizar la repetibilidad anteriormente indicada. No ocurre así si se quitara la garra y se intercambia con un cabezal motorizado con una herramienta como broca, mandrino, plato de cuchillas, fresas frontales o tangenciales… Las fuerzas ejercidas de mecanizado generarían unos pares en las uniones tan grandes y tan variables que el control del robot no sería capaz de responder (o no está preparado, en un principio) y generaría una desviación en la trayectoria, realizada a baja velocidad, que desencadenaría en un error de posición (ver norma ISO 5458) no asumible para la funcionalidad deseada. Se podría llegar al caso de que la tolerancia alcanzada por un pretendido proceso más exacto diera una dimensión peor que la que daría el proceso de fundición, en principio con mayor variabilidad dimensional en proceso (y por ende con mayor intervalo de tolerancia garantizable). De hecho, en los CNCs, la precisión es muy elevada, (pudiéndose despreciar en la mayoría de los casos) y no es la responsable de, por ejemplo la tolerancia de posición al taladrar un agujero. Factores como, temperatura de la sala y de la pieza, calidad constructiva de los utillajes y rigidez en el amarre, error en el giro de mesas y de colocación de pieza, si lleva agujeros previos o no, si la herramienta está bien equilibrada y el cono es el adecuado para el tipo de mecanizado… influyen más. Es interesante que, un elemento no específico tan común en una planta industrial, en el entorno anteriormente descrito, como es un robot, el cual no sería necesario añadir por disponer de él ya (y por lo tanto la inversión sería muy pequeña), puede mejorar la cadena de valor disminuyendo el costo de fabricación. Y si se pudiera conjugar que ese robot destinado a tareas de manipulación, en los muchos tiempos de espera que va a disfrutar mientras el CNC arranca viruta, pudiese coger un cabezal y apoyar ese mecanizado; sería doblemente interesante. Por lo tanto, se antoja sugestivo poder conocer su comportamiento e intentar explicar qué sería necesario para llevar esto a cabo, motivo de este trabajo. La arquitectura de robot seleccionada es de tipo SCARA. La búsqueda de un robot cómodo de modelar y de analizar cinemática y dinámicamente, sin limitaciones relevantes en la multifuncionalidad de trabajos solicitados, ha llevado a esta elección, frente a otras arquitecturas como por ejemplo los robots antropomórficos de 6 grados de libertad, muy populares a nivel industrial. Este robot dispone de 3 uniones, de las cuales 2 son de tipo par de revolución (1 grado de libertad cada una) y la tercera es de tipo corredera o par cilíndrico (2 grados de libertad). La primera unión, de tipo par de revolución, sirve para unir el suelo (considerado como eslabón número 1) con el eslabón número 2. La segunda unión, también de ese tipo, une el eslabón número 2 con el eslabón número 3. Estos 2 brazos, pueden describir un movimiento horizontal, en el plano X-Y. El tercer eslabón, está unido al eslabón número 4 por la unión de tipo corredera. El movimiento que puede describir es paralelo al eje Z. El robot es de 4 grados de libertad (4 motores). En relación a los posibles trabajos que puede realizar este tipo de robot, su versatilidad abarca tanto operaciones típicas de manipulación como operaciones de arranque de viruta. Uno de los mecanizados más usuales es el taladrado, por lo cual se elige éste para su modelización y análisis. Dentro del taladrado se elegirá para acotar las fuerzas, taladrado en macizo con broca de diámetro 9 mm. El robot se ha considerado por el momento que tenga comportamiento de sólido rígido, por ser el mayor efecto esperado el de los pares en las uniones. Para modelar el robot se utiliza el método de los sistemas multicuerpos. Dentro de este método existen diversos tipos de formulaciones (p.e. Denavit-Hartenberg). D-H genera una cantidad muy grande de ecuaciones e incógnitas. Esas incógnitas son de difícil comprensión y, para cada posición, hay que detenerse a pensar qué significado tienen. Se ha optado por la formulación de coordenadas naturales. Este sistema utiliza puntos y vectores unitarios para definir la posición de los distintos cuerpos, y permite compartir, cuando es posible y se quiere, para definir los pares cinemáticos y reducir al mismo tiempo el número de variables. Las incógnitas son intuitivas, las ecuaciones de restricción muy sencillas y se reduce considerablemente el número de ecuaciones e incógnitas. Sin embargo, las coordenadas naturales “puras” tienen 2 problemas. El primero, que 2 elementos con un ángulo de 0 o 180 grados, dan lugar a puntos singulares que pueden crear problemas en las ecuaciones de restricción y por lo tanto han de evitarse. El segundo, que tampoco inciden directamente sobre la definición o el origen de los movimientos. Por lo tanto, es muy conveniente complementar esta formulación con ángulos y distancias (coordenadas relativas). Esto da lugar a las coordenadas naturales mixtas, que es la formulación final elegida para este TFM. Las coordenadas naturales mixtas no tienen el problema de los puntos singulares. Y la ventaja más importante reside en su utilidad a la hora de aplicar fuerzas motrices, momentos o evaluar errores. Al incidir sobre la incógnita origen (ángulos o distancias) controla los motores de manera directa. El algoritmo, la simulación y la obtención de resultados se ha programado mediante Matlab. Para realizar el modelo en coordenadas naturales mixtas, es preciso modelar en 2 pasos el robot a estudio. El primer modelo se basa en coordenadas naturales. Para su validación, se plantea una trayectoria definida y se analiza cinemáticamente si el robot satisface el movimiento solicitado, manteniendo su integridad como sistema multicuerpo. Se cuantifican los puntos (en este caso inicial y final) que configuran el robot. Al tratarse de sólidos rígidos, cada eslabón queda definido por sus respectivos puntos inicial y final (que son los más interesantes para la cinemática y la dinámica) y por un vector unitario no colineal a esos 2 puntos. Los vectores unitarios se colocan en los lugares en los que se tenga un eje de rotación o cuando se desee obtener información de un ángulo. No son necesarios vectores unitarios para medir distancias. Tampoco tienen por qué coincidir los grados de libertad con el número de vectores unitarios. Las longitudes de cada eslabón quedan definidas como constantes geométricas. Se establecen las restricciones que definen la naturaleza del robot y las relaciones entre los diferentes elementos y su entorno. La trayectoria se genera por una nube de puntos continua, definidos en coordenadas independientes. Cada conjunto de coordenadas independientes define, en un instante concreto, una posición y postura de robot determinada. Para conocerla, es necesario saber qué coordenadas dependientes hay en ese instante, y se obtienen resolviendo por el método de Newton-Rhapson las ecuaciones de restricción en función de las coordenadas independientes. El motivo de hacerlo así es porque las coordenadas dependientes deben satisfacer las restricciones, cosa que no ocurre con las coordenadas independientes. Cuando la validez del modelo se ha probado (primera validación), se pasa al modelo 2. El modelo número 2, incorpora a las coordenadas naturales del modelo número 1, las coordenadas relativas en forma de ángulos en los pares de revolución (3 ángulos; ϕ1, ϕ 2 y ϕ3) y distancias en los pares prismáticos (1 distancia; s). Estas coordenadas relativas pasan a ser las nuevas coordenadas independientes (sustituyendo a las coordenadas independientes cartesianas del modelo primero, que eran coordenadas naturales). Es necesario revisar si el sistema de vectores unitarios del modelo 1 es suficiente o no. Para este caso concreto, se han necesitado añadir 1 vector unitario adicional con objeto de que los ángulos queden perfectamente determinados con las correspondientes ecuaciones de producto escalar y/o vectorial. Las restricciones habrán de ser incrementadas en, al menos, 4 ecuaciones; una por cada nueva incógnita. La validación del modelo número 2, tiene 2 fases. La primera, al igual que se hizo en el modelo número 1, a través del análisis cinemático del comportamiento con una trayectoria definida. Podrían obtenerse del modelo 2 en este análisis, velocidades y aceleraciones, pero no son necesarios. Tan sólo interesan los movimientos o desplazamientos finitos. Comprobada la coherencia de movimientos (segunda validación), se pasa a analizar cinemáticamente el comportamiento con trayectorias interpoladas. El análisis cinemático con trayectorias interpoladas, trabaja con un número mínimo de 3 puntos máster. En este caso se han elegido 3; punto inicial, punto intermedio y punto final. El número de interpolaciones con el que se actúa es de 50 interpolaciones en cada tramo (cada 2 puntos máster hay un tramo), resultando un total de 100 interpolaciones. El método de interpolación utilizado es el de splines cúbicas con condición de aceleración inicial y final constantes, que genera las coordenadas independientes de los puntos interpolados de cada tramo. Las coordenadas dependientes se obtienen resolviendo las ecuaciones de restricción no lineales con el método de Newton-Rhapson. El método de las splines cúbicas es muy continuo, por lo que si se desea modelar una trayectoria en el que haya al menos 2 movimientos claramente diferenciados, es preciso hacerlo en 2 tramos y unirlos posteriormente. Sería el caso en el que alguno de los motores se desee expresamente que esté parado durante el primer movimiento y otro distinto lo esté durante el segundo movimiento (y así sucesivamente). Obtenido el movimiento, se calculan, también mediante fórmulas de diferenciación numérica, las velocidades y aceleraciones independientes. El proceso es análogo al anteriormente explicado, recordando la condición impuesta de que la aceleración en el instante t= 0 y en instante t= final, se ha tomado como 0. Las velocidades y aceleraciones dependientes se calculan resolviendo las correspondientes derivadas de las ecuaciones de restricción. Se comprueba, de nuevo, en una tercera validación del modelo, la coherencia del movimiento interpolado. La dinámica inversa calcula, para un movimiento definido -conocidas la posición, velocidad y la aceleración en cada instante de tiempo-, y conocidas las fuerzas externas que actúan (por ejemplo el peso); qué fuerzas hay que aplicar en los motores (donde hay control) para que se obtenga el citado movimiento. En la dinámica inversa, cada instante del tiempo es independiente de los demás y tiene una posición, una velocidad y una aceleración y unas fuerzas conocidas. En este caso concreto, se desean aplicar, de momento, sólo las fuerzas debidas al peso, aunque se podrían haber incorporado fuerzas de otra naturaleza si se hubiese deseado. Las posiciones, velocidades y aceleraciones, proceden del cálculo cinemático. El efecto inercial de las fuerzas tenidas en cuenta (el peso) es calculado. Como resultado final del análisis dinámico inverso, se obtienen los pares que han de ejercer los cuatro motores para replicar el movimiento prescrito con las fuerzas que estaban actuando. La cuarta validación del modelo consiste en confirmar que el movimiento obtenido por aplicar los pares obtenidos en la dinámica inversa, coinciden con el obtenido en el análisis cinemático (movimiento teórico). Para ello, es necesario acudir a la dinámica directa. La dinámica directa se encarga de calcular el movimiento del robot, resultante de aplicar unos pares en motores y unas fuerzas en el robot. Por lo tanto, el movimiento real resultante, al no haber cambiado ninguna condición de las obtenidas en la dinámica inversa (pares de motor y fuerzas inerciales debidas al peso de los eslabones) ha de ser el mismo al movimiento teórico. Siendo así, se considera que el robot está listo para trabajar. Si se introduce una fuerza exterior de mecanizado no contemplada en la dinámica inversa y se asigna en los motores los mismos pares resultantes de la resolución del problema dinámico inverso, el movimiento real obtenido no es igual al movimiento teórico. El control de lazo cerrado se basa en ir comparando el movimiento real con el deseado e introducir las correcciones necesarias para minimizar o anular las diferencias. Se aplican ganancias en forma de correcciones en posición y/o velocidad para eliminar esas diferencias. Se evalúa el error de posición como la diferencia, en cada punto, entre el movimiento teórico deseado en el análisis cinemático y el movimiento real obtenido para cada fuerza de mecanizado y una ganancia concreta. Finalmente, se mapea el error de posición obtenido para cada fuerza de mecanizado y las diferentes ganancias previstas, graficando la mejor precisión que puede dar el robot para cada operación que se le requiere, y en qué condiciones. -------------- This Master´s Thesis deals with a preliminary characterization of the behaviour for an industrial robot, configured with 4 elements and 4 degrees of freedoms, and subjected to machining forces at its end. Proposed working conditions are those typical from manufacturing plants with aluminium alloys for automotive industry. This type of components comes from a first casting process that produces rough parts. For medium and high volumes, high pressure die casting (HPDC) and low pressure die casting (LPC) are the most used technologies in this first phase. For high pressure die casting processes, most used aluminium alloys are, in simbolic designation according EN 1706 standard (between brackets, its numerical designation); EN AC AlSi9Cu3(Fe) (EN AC 46000) , EN AC AlSi9Cu3(Fe)(Zn) (EN AC 46500), y EN AC AlSi12Cu1(Fe) (EN AC 47100). For low pressure, EN AC AlSi7Mg0,3 (EN AC 42100). For the 3 first alloys, Si allowed limits can exceed 10% content. Fourth alloy has admisible limits under 10% Si. That means, from the point of view of machining, that components made of alloys with Si content above 10% can be considered as equivalent, and the fourth one must be studied separately. Geometrical and dimensional tolerances directly achievables from casting, gathered in standards such as ISO 8062 or DIN 1688-1, establish a limit for this process. Out from those limits, guarantees to achieve batches with objetive ppms currently accepted by market, force to go to subsequent machining process. Those geometries that functionally require a geometrical and/or dimensional tolerance defined according ISO 1101, not capable with initial moulding process, must be obtained afterwards in a machining phase with machining cells. In this case, tolerances achievables with cutting processes are gathered in standards such as ISO 2768. In general terms, machining cells contain several CNCs that they are interrelated and connected by robots that handle parts in process among them. Those robots have at their end a gripper in order to take/remove parts in machining fixtures, in interchange tables to modify position of part, in measurement and control tooling devices, or in entrance/exit conveyors. Repeatibility for robot is tight, even few hundredths of mm, defined according ISO 9283. Problem is like this; those repeatibilty ranks are only guaranteed when there are no stresses or they are not significant (f.e. due to only movement of parts). Although inertias due to moving parts at a high speed make that intermediate paths have little accuracy, at the beginning and at the end of trajectories (f.e, when picking part or leaving it) movement is made with very slow speeds that make lower the effect of inertias forces and allow to achieve repeatibility before mentioned. It does not happens the same if gripper is removed and it is exchanged by an spindle with a machining tool such as a drilling tool, a pcd boring tool, a face or a tangential milling cutter… Forces due to machining would create such big and variable torques in joints that control from the robot would not be able to react (or it is not prepared in principle) and would produce a deviation in working trajectory, made at a low speed, that would trigger a position error (see ISO 5458 standard) not assumable for requested function. Then it could be possible that tolerance achieved by a more exact expected process would turn out into a worst dimension than the one that could be achieved with casting process, in principle with a larger dimensional variability in process (and hence with a larger tolerance range reachable). As a matter of fact, accuracy is very tight in CNC, (its influence can be ignored in most cases) and it is not the responsible of, for example position tolerance when drilling a hole. Factors as, room and part temperature, manufacturing quality of machining fixtures, stiffness at clamping system, rotating error in 4th axis and part positioning error, if there are previous holes, if machining tool is properly balanced, if shank is suitable for that machining type… have more influence. It is interesting to know that, a non specific element as common, at a manufacturing plant in the enviroment above described, as a robot (not needed to be added, therefore with an additional minimum investment), can improve value chain decreasing manufacturing costs. And when it would be possible to combine that the robot dedicated to handling works could support CNCs´ works in its many waiting time while CNCs cut, and could take an spindle and help to cut; it would be double interesting. So according to all this, it would be interesting to be able to know its behaviour and try to explain what would be necessary to make this possible, reason of this work. Selected robot architecture is SCARA type. The search for a robot easy to be modeled and kinematically and dinamically analyzed, without significant limits in the multifunctionality of requested operations, has lead to this choice. Due to that, other very popular architectures in the industry, f.e. 6 DOFs anthropomorphic robots, have been discarded. This robot has 3 joints, 2 of them are revolute joints (1 DOF each one) and the third one is a cylindrical joint (2 DOFs). The first joint, a revolute one, is used to join floor (body 1) with body 2. The second one, a revolute joint too, joins body 2 with body 3. These 2 bodies can move horizontally in X-Y plane. Body 3 is linked to body 4 with a cylindrical joint. Movement that can be made is paralell to Z axis. The robt has 4 degrees of freedom (4 motors). Regarding potential works that this type of robot can make, its versatility covers either typical handling operations or cutting operations. One of the most common machinings is to drill. That is the reason why it has been chosen for the model and analysis. Within drilling, in order to enclose spectrum force, a typical solid drilling with 9 mm diameter. The robot is considered, at the moment, to have a behaviour as rigid body, as biggest expected influence is the one due to torques at joints. In order to modelize robot, it is used multibodies system method. There are under this heading different sorts of formulations (f.e. Denavit-Hartenberg). D-H creates a great amount of equations and unknown quantities. Those unknown quatities are of a difficult understanding and, for each position, one must stop to think about which meaning they have. The choice made is therefore one of formulation in natural coordinates. This system uses points and unit vectors to define position of each different elements, and allow to share, when it is possible and wished, to define kinematic torques and reduce number of variables at the same time. Unknown quantities are intuitive, constrain equations are easy and number of equations and variables are strongly reduced. However, “pure” natural coordinates suffer 2 problems. The first one is that 2 elements with an angle of 0° or 180°, give rise to singular positions that can create problems in constrain equations and therefore they must be avoided. The second problem is that they do not work directly over the definition or the origin of movements. Given that, it is highly recommended to complement this formulation with angles and distances (relative coordinates). This leads to mixed natural coordinates, and they are the final formulation chosen for this MTh. Mixed natural coordinates have not the problem of singular positions. And the most important advantage lies in their usefulness when applying driving forces, torques or evaluating errors. As they influence directly over origin variable (angles or distances), they control motors directly. The algorithm, simulation and obtaining of results has been programmed with Matlab. To design the model in mixed natural coordinates, it is necessary to model the robot to be studied in 2 steps. The first model is based in natural coordinates. To validate it, it is raised a defined trajectory and it is kinematically analyzed if robot fulfils requested movement, keeping its integrity as multibody system. The points (in this case starting and ending points) that configure the robot are quantified. As the elements are considered as rigid bodies, each of them is defined by its respectively starting and ending point (those points are the most interesting ones from the point of view of kinematics and dynamics) and by a non-colinear unit vector to those points. Unit vectors are placed where there is a rotating axis or when it is needed information of an angle. Unit vectors are not needed to measure distances. Neither DOFs must coincide with the number of unit vectors. Lengths of each arm are defined as geometrical constants. The constrains that define the nature of the robot and relationships among different elements and its enviroment are set. Path is generated by a cloud of continuous points, defined in independent coordinates. Each group of independent coordinates define, in an specific instant, a defined position and posture for the robot. In order to know it, it is needed to know which dependent coordinates there are in that instant, and they are obtained solving the constraint equations with Newton-Rhapson method according to independent coordinates. The reason to make it like this is because dependent coordinates must meet constraints, and this is not the case with independent coordinates. When suitability of model is checked (first approval), it is given next step to model 2. Model 2 adds to natural coordinates from model 1, the relative coordinates in the shape of angles in revoluting torques (3 angles; ϕ1, ϕ 2 and ϕ3) and distances in prismatic torques (1 distance; s). These relative coordinates become the new independent coordinates (replacing to cartesian independent coordinates from model 1, that they were natural coordinates). It is needed to review if unit vector system from model 1 is enough or not . For this specific case, it was necessary to add 1 additional unit vector to define perfectly angles with their related equations of dot and/or cross product. Constrains must be increased in, at least, 4 equations; one per each new variable. The approval of model 2 has two phases. The first one, same as made with model 1, through kinematic analysis of behaviour with a defined path. During this analysis, it could be obtained from model 2, velocities and accelerations, but they are not needed. They are only interesting movements and finite displacements. Once that the consistence of movements has been checked (second approval), it comes when the behaviour with interpolated trajectories must be kinematically analyzed. Kinematic analysis with interpolated trajectories work with a minimum number of 3 master points. In this case, 3 points have been chosen; starting point, middle point and ending point. The number of interpolations has been of 50 ones in each strecht (each 2 master points there is an strecht), turning into a total of 100 interpolations. The interpolation method used is the cubic splines one with condition of constant acceleration both at the starting and at the ending point. This method creates the independent coordinates of interpolated points of each strecht. The dependent coordinates are achieved solving the non-linear constrain equations with Newton-Rhapson method. The method of cubic splines is very continuous, therefore when it is needed to design a trajectory in which there are at least 2 movements clearly differents, it is required to make it in 2 steps and join them later. That would be the case when any of the motors would keep stopped during the first movement, and another different motor would remain stopped during the second movement (and so on). Once that movement is obtained, they are calculated, also with numerical differenciation formulas, the independent velocities and accelerations. This process is analogous to the one before explained, reminding condition that acceleration when t=0 and t=end are 0. Dependent velocities and accelerations are calculated solving related derivatives of constrain equations. In a third approval of the model it is checked, again, consistence of interpolated movement. Inverse dynamics calculates, for a defined movement –knowing position, velocity and acceleration in each instant of time-, and knowing external forces that act (f.e. weights); which forces must be applied in motors (where there is control) in order to obtain requested movement. In inverse dynamics, each instant of time is independent of the others and it has a position, a velocity, an acceleration and known forces. In this specific case, it is intended to apply, at the moment, only forces due to the weight, though forces of another nature could have been added if it would have been preferred. The positions, velocities and accelerations, come from kinematic calculation. The inertial effect of forces taken into account (weight) is calculated. As final result of the inverse dynamic analysis, the are obtained torques that the 4 motors must apply to repeat requested movement with the forces that were acting. The fourth approval of the model consists on confirming that the achieved movement due to the use of the torques obtained in the inverse dynamics, are in accordance with movements from kinematic analysis (theoretical movement). For this, it is necessary to work with direct dynamics. Direct dynamic is in charge of calculating the movements of robot that results from applying torques at motors and forces at the robot. Therefore, the resultant real movement, as there was no change in any condition of the ones obtained at the inverse dynamics (motor torques and inertial forces due to weight of elements) must be the same than theoretical movement. When these results are achieved, it is considered that robot is ready to work. When a machining external force is introduced and it was not taken into account before during the inverse dynamics, and torques at motors considered are the ones of the inverse dynamics, the real movement obtained is not the same than the theoretical movement. Closed loop control is based on comparing real movement with expected movement and introducing required corrrections to minimize or cancel differences. They are applied gains in the way of corrections for position and/or tolerance to remove those differences. Position error is evaluated as the difference, in each point, between theoretical movemment (calculated in the kinematic analysis) and the real movement achieved for each machining force and for an specific gain. Finally, the position error obtained for each machining force and gains are mapped, giving a chart with the best accuracy that the robot can give for each operation that has been requested and which conditions must be provided.

MILP for the inventory and routing problem for replenishment the car assembly line.

The inbound logistic for feeding the workstation inside the factory represents a critical issue in the car manufacturing industry. Nowadays, this issue is even more critical than in the past since more types of car are being produced in the assembly lines. Consequently, as workstations have to install many types of components, they also need to have an inventory of different types of the component in a compact space. The replenishment is a critical issue since a lack of inventory could cause line stoppage or reworking. On the other hand, an excess of inventory could increase the holding cost or even block the replenishment paths. The decision of the replenishment routes cannot be made without taking into consideration the inventory needed by each station during the production time which will depend on the production sequence. This problem deals with medium-sized instances and it is solved using online solvers. The contribution of this paper is a MILP for the replenishment and inventory of the components in a car assembly line.

Aerodynamic external pressure loads on a semi-circular bluff body under wind gusts

This brief communication concerns the unsteady aerodynamic external pressure loads acting on a semi-circular bluff body lying on a floor under wind gusts and describes the theoretical model, experimental setup, and experimental results obtained. The experimental setup is based on an open circuit, closed test section, low speed wind tunnel, which includes a sinusoidal gust generating mechanism, designed and built at the Instituto de Microgravedad “Ignacio Da Riva” of the Universidad Politécnica de Madrid (IDR/UPM). Based on the potential flow theory, a theoretical model has been proposed to analyse the problem, and experimental tests have been performed to study the unsteady aerodynamic loads on a semi-circular bluff body. By fitting the theoretical model predictions with the experimental results, influencing parameters of the unsteady aerodynamic loads are ascertained. The values of these parameters can help in clarifying the phenomenon of the external pressure loads on semi-circular bluff body under various gust frequencies. The theoretical model proposed allows the pressure variation to be split into two contributions, a quasi-steady term and an unsteady term with a simple physical meaning

El Problema de Lambert en el Contexto de Optimización de Trayectorias Espaciales

Esta tesis se basa en el estudio de la trayectoria que pasa por dos puntos en el problema de los dos cuerpos, inicialmente desarrollado por Lambert, del que toma su nombre. En el pasado, el Problema de Lambert se ha utilizado para la determinación de órbitas a partir de observaciones astronómicas de los cuerpos celestes. Actualmente, se utiliza continuamente en determinación de órbitas, misiones planetaria e interplanetarias, encuentro espacial e interceptación, o incluso en corrección de orbitas. Dada su gran importancia, se decide investigar especialmente sobre su solución y las aplicaciones en las misiones espaciales actuales. El campo de investigación abierto, es muy amplio, así que, es necesario determinar unos objetivos específicos realistas, en el contexto de ejecución de una Tesis, pero que sirvan para mostrar con suficiente claridad el potencial de los resultados aportados en este trabajo, e incluso poder extenderlos a otros campos de aplicación. Como resultado de este análisis, el objetivo principal de la Tesis se enfoca en el desarrollo de algoritmos para resolver el Problema de Lambert, que puedan ser aplicados de forma muy eficiente en las misiones reales donde aparece. En todos los desarrollos, se ha considerado especialmente la eficiencia del cálculo computacional necesario en comparación con los métodos existentes en la actualidad, destacando la forma de evitar la pérdida de precisión inherente a este tipo de algoritmos y la posibilidad de aplicar cualquier método iterativo que implique el uso de derivadas de cualquier orden. En busca de estos objetivos, se desarrollan varias soluciones para resolver el Problema de Lambert, todas ellas basadas en la resolución de ecuaciones transcendentes, con las cuales, se alcanzan las siguientes aportaciones principales de este trabajo: • Una forma genérica completamente diferente de obtener las diversas ecuaciones para resolver el Problema de Lambert, mediante desarrollo analítico, desde cero, a partir de las ecuaciones elementales conocidas de las cónicas (geométricas y temporal), proporcionando en todas ellas fórmulas para el cálculo de derivadas de cualquier orden. • Proporcionar una visión unificada de las ecuaciones más relevantes existentes, mostrando la equivalencia con variantes de las ecuaciones aquí desarrolladas. • Deducción de una nueva variante de ecuación, el mayor logro de esta Tesis, que destaca en eficiencia sobre todas las demás (tanto en coste como en precisión). • Estudio de la sensibilidad de la solución ante variación de los datos iniciales, y como aplicar los resultados a casos reales de optimización de trayectorias. • También, a partir de los resultados, es posible deducir muchas propiedades utilizadas en la literatura para simplificar el problema, en particular la propiedad de invariancia, que conduce al Problema Transformado Simplificado. ABSTRACT This thesis is based on the study of the two-body, two-point boundary-value problem, initially developed by Lambert, from who it takes its name. Since the past, Lambert's Problem has been used for orbit determination from astronomical observations of celestial bodies. Currently, it is continuously used in orbit determinations, for planetary and interplanetary missions, space rendezvous, and interception, or even in orbit corrections. Given its great importance, it is decided to investigate their solution and applications in the current space missions. The open research field is very wide, it is necessary to determine specific and realistic objectives in the execution context of a Thesis, but that these serve to show clearly enough the potential of the results provided in this work, and even to extended them to other areas of application. As a result of this analysis, the main aim of the thesis focuses on the development of algorithms to solve the Lambert’s Problem which can be applied very efficiently in real missions where it appears. In all these developments, it has been specially considered the efficiency of the required computational calculation compared to currently existing methods, highlighting how to avoid the loss of precision inherent in such algorithms and the possibility to apply any iterative method involving the use of derivatives of any order. Looking to meet these objectives, a number of solutions to solve the Lambert’s Problem are developed, all based on the resolution of transcendental equations, with which the following main contributions of this work are reached: • A completely different generic way to get the various equations to solve the Lambert’s Problem by analytical development, from scratch, from the known elementary conic equations (geometrics and temporal), by providing, in all cases, the calculation of derivatives of any order. • Provide a unified view of most existing relevant equations, showing the equivalence with variants of the equations developed here. • Deduction of a new variant of equation, the goal of this Thesis, which emphasizes efficiency (both computational cost and accuracy) over all other. • Estudio de la sensibilidad de la solución ante la variación de las condiciones iniciales, mostrando cómo aprovechar los resultados a casos reales de optimización de trayectorias. • Study of the sensitivity of the solution to the variation of the initial data, and how to use the results to real cases of trajectories’ optimization. • Additionally, from results, it is possible to deduce many properties used in literature to simplify the problem, in particular the invariance property, which leads to a simplified transformed problem.

Analysing the complexity of the model-based decision making processes within the industrial management context

PURPOSE The decision-making process plays a key role in organizations. Every decision-making process produces a final choice that may or may not prompt action. Recurrently, decision makers find themselves in the dichotomous question of following a traditional sequence decision-making process where the output of a decision is used as the input of the next stage of the decision, or following a joint decision-making approach where several decisions are taken simultaneously. The implication of the decision-making process will impact different players of the organization. The choice of the decision- making approach becomes difficult to find, even with the current literature and practitioners’ knowledge. The pursuit of better ways for making decisions has been a common goal for academics and practitioners. Management scientists use different techniques and approaches to improve different types of decisions. The purpose of this decision is to use the available resources as well as possible (data and techniques) to achieve the objectives of the organization. The developing and applying of models and concepts may be helpful to solve managerial problems faced every day in different companies. As a result of this research different decision models are presented to contribute to the body of knowledge of management science. The first models are focused on the manufacturing industry and the second part of the models on the health care industry. Despite these models being case specific, they serve the purpose of exemplifying that different approaches to the problems and could provide interesting results. Unfortunately, there is no universal recipe that could be applied to all the problems. Furthermore, the same model could deliver good results with certain data and bad results for other data. A framework to analyse the data before selecting the model to be used is presented and tested in the models developed to exemplify the ideas. METHODOLOGY As the first step of the research a systematic literature review on the joint decision is presented, as are the different opinions and suggestions of different scholars. For the next stage of the thesis, the decision-making process of more than 50 companies was analysed in companies from different sectors in the production planning area at the Job Shop level. The data was obtained using surveys and face-to-face interviews. The following part of the research into the decision-making process was held in two application fields that are highly relevant for our society; manufacturing and health care. The first step was to study the interactions and develop a mathematical model for the replenishment of the car assembly where the problem of “Vehicle routing problem and Inventory” were combined. The next step was to add the scheduling or car production (car sequencing) decision and use some metaheuristics such as ant colony and genetic algorithms to measure if the behaviour is kept up with different case size problems. A similar approach is presented in a production of semiconductors and aviation parts, where a hoist has to change from one station to another to deal with the work, and a jobs schedule has to be done. However, for this problem simulation was used for experimentation. In parallel, the scheduling of operating rooms was studied. Surgeries were allocated to surgeons and the scheduling of operating rooms was analysed. The first part of the research was done in a Teaching hospital, and for the second part the interaction of uncertainty was added. Once the previous problem had been analysed a general framework to characterize the instance was built. In the final chapter a general conclusion is presented. FINDINGS AND PRACTICAL IMPLICATIONS The first part of the contributions is an update of the decision-making literature review. Also an analysis of the possible savings resulting from a change in the decision process is made. Then, the results of the survey, which present a lack of consistency between what the managers believe and the reality of the integration of their decisions. In the next stage of the thesis, a contribution to the body of knowledge of the operation research, with the joint solution of the replenishment, sequencing and inventory problem in the assembly line is made, together with a parallel work with the operating rooms scheduling where different solutions approaches are presented. In addition to the contribution of the solving methods, with the use of different techniques, the main contribution is the framework that is proposed to pre-evaluate the problem before thinking of the techniques to solve it. However, there is no straightforward answer as to whether it is better to have joint or sequential solutions. Following the proposed framework with the evaluation of factors such as the flexibility of the answer, the number of actors, and the tightness of the data, give us important hints as to the most suitable direction to take to tackle the problem. RESEARCH LIMITATIONS AND AVENUES FOR FUTURE RESEARCH In the first part of the work it was really complicated to calculate the possible savings of different projects, since in many papers these quantities are not reported or the impact is based on non-quantifiable benefits. The other issue is the confidentiality of many projects where the data cannot be presented. For the car assembly line problem more computational power would allow us to solve bigger instances. For the operation research problem there was a lack of historical data to perform a parallel analysis in the teaching hospital. In order to keep testing the decision framework it is necessary to keep applying more case studies in order to generalize the results and make them more evident and less ambiguous. The health care field offers great opportunities since despite the recent awareness of the need to improve the decision-making process there are many opportunities to improve. Another big difference with the automotive industry is that the last improvements are not spread among all the actors. Therefore, in the future this research will focus more on the collaboration between academia and the health care sector.

El centro comercial : una teoría tipológica : claves para el reconocimiento de una arquitectura ignorada

Existe en el panorama edificado un patrimonio construido que se reconoce como Centro Comercial. Un conjunto entendido, en sentido genérico, como familia arquitectónica que tiene características propias y específicas que la identifican. El objeto de la presente tesis doctoral consiste en argumentar que este conjunto constituye un nuevo tipo en el panorama de las tipologías arquitectónicas. Un tipo con entidad propia, que se conecta a una forma diferente de entender la idea de modelo. Un concepto que va más allá de la consideración tradicional del término. Modelo virtual. Este tipo, que surge de una estructura teórica que hemos denominado teoría tipológica, se constituye en una herramienta más para el estudio y el desarrollo proyectual de los espacios arquitectónicos, tanto del propio Centro Comercial como del conjunto de la disciplina arquitectónica, como referencia legítima. El presente trabajo de tesis se inicia con un bloque introductorio denominado Método. Definimos en él una metodología que hemos llamado emocional. Trata de la oportunidad de la tesis. Del porqué de un título que recoge la palabra ignorada. Del interés que suscita el asunto en el contexto del momento presente. Oportunidad e interés en base a una vida profesional dedicada al mundo del Centro Comercial y a la importancia del patrimonio elegido como objeto de estudio. También ha sido un aliciente detectar como las planificaciones del territorio y de los ámbitos de las relaciones colectivas no han sido capaces de integrar un resultado satisfactorio. Quizás por no considerar la complejidad de sus muchas facetas. En consecuencia, el texto busca la esencia del Centro Comercial como soporte para la crítica de su impacto en los nuevos escenarios de relación que la sociedad y el entorno físico imponen. Ámbitos donde los mecanismos históricos del asociacionismo tradicional han dado paso a otros, como el Centro Comercial, de exaltación del individualismo, pero demandados por una sociedad que se identifica con ellos. Espacios que, con Galbraith, existen por de la perversidad intrínseca del binomio consumo-producción que inducen la perplejidad. Ésta pasa a formar parte de la esencia del nuevo espacio comercial, como quedó de manifiesto en el Congreso de Minnesota de 1997, sobre el Centro Comercial. Una sociedad que ha girado hacia el logro material en términos de culto, ocasionando creciente valor significante del consumo. Razón última de la humanidad al decir de Rem Koolhaas. Culto que desemboca en la urgencia de alcanzar niveles de estatus y de identificación con el grupo. Dos parámetros que marcan la relación con el otro. Relación de comparación que excita la necesidad de posesión de objetos que llevaban a recrear en el consumidor la ilusión de ser especiales, de no pasar desapercibidos. El producto de consumo, el objeto, se eleva a la consideración de valor social. En el Centro Comercial se venden valores. Marketing de valores. El deseo del individuo, no la necesidad, queda involucrado en el proceso. La oportunidad y el interés de este estudio surgen además para aclarar el significado de un espacio que sirve al consumidor y a su entorno. Un significado que alcanza sentido, entre otros, por la aparición de un nuevo contexto tras la Segunda Guerra Mundial. Suburbanización, automóvil, nivel de vida, un nuevo papel de la mujer. La Era del Consumo. Una era que genera la paradoja de un individuo con autodeterminación y autosuficiencia crecientes, en un mundo cada vez más condicionado y controlado por dinámicas de ofertas mediatizadas e ilimitadas. La arquitectura en este contexto ha de juzgarse por su relación con un hombre contemporáneo que camina hacia una progresiva excepcionalidad. Cerramos la presentación justificando el término ignorada que aparece en el Título de la Tesis. Subrayamos la escasa existencia de estudios estructurados que relacionen Centro Comercial y arquitectura. Realidad que se constata partiendo del libro de Pevsner, Historia de las Tipologías Arquitectónicas, de 1976. Analizamos también la aceptación que el Centro Comercial, valorado en algunos ámbitos como arquitectura populista. Primer Capítulo, los antecedentes. Se propone un recorrido histórico por la arquitectura comercial de todos los tiempos. El Documento busca concretar las características de la arquitectura comercial a lo largo de la historia para determinar relaciones entre ella y el Centro Comercial. Estas correspondencias van a permitir contestar la pregunta retórica que nos hacemos al inicio del Capítulo: ¿Es la arquitectura del Centro Comercial una arquitectura subsidiaria, o tiene personalidad propia independiente de la del mundo comercial? Con Zevi40, queremos dejar constancia que la relación arquitectura-historia es imprescindible en la tarea proyectual. Un análisis novedoso solo es posible desde la búsqueda de unas raíces auténticas. Así mismo, con Guy de Maupassant, estamos convencidos que “La arquitectura, a través de los siglos, ha tenido el privilegio de dar un símbolo a cada una de las épocas, de resumir con un pequeñísimo número de monumentos típicos, el modo de pensar, de soñar de una raza y de una civilización”. Este recorrido se inicia interpretando la arquitectura comercial minoica. Llegaremos, paso a paso, hasta el siglo XX, los grandes itinerarios comerciales y el Centro Comercial. Se descubren una serie de invariantes que permiten comparar y extraer conclusiones. Resulta novedoso constatar que el Centro Comercial nace para dar respuesta al hombre contemporáneo en su afán consumista. También lo es la rápida implantación y evolución del Centro Comercial en un corto periodo de sesenta años frente al ritmo sosegado de otras soluciones comerciales. Novedad es ver como el comercio y sus arquitecturas nacen abiertos, bajo tenderetes y el Centro Comercial se presenta cerrado. Así mismo, las referencias sacras constituyen un elemento de novedad para la reflexión, en un contexto materialista. Y tantas otras. En Minos, la óptica comercial ofrece otra visión de su legendaria cultura. ¿Palacio o plataforma logística?, gestión centralizada del intercambio, ¿vida pública y vida privada? Así, hasta llegar al siglo XIX. Sus las galerías y sus pasajes acristalados concebidos en primera instancia como medida de recomposición urbana. Espacio entendido desde lo público-privado, desde lo interior-exterior, desde el dentro-afuera, desde lo cerrado-abierto. Con los nuevos mercados de abastos, representan una revolución en el ámbito de la funcionalidad, de la máquina, de la gestión moderna y de las relaciones del ciudadano con la ciudad apoyado en base al intercambio de bienes de consumo. El Centro Comercial es heredero de esta transformación. El Gran Almacén, por otra parte, es el reflejo de otra gran revolución. La que va ligada a la producción y comercialización en masa, las comunicaciones, el precio fijo y el aumento del nivel de vida. El Centro Comercial reinterpreta estas situaciones insertándolas en un nuevo modelo de gestión. En el siglo XX, maestro en técnicas de venta, aparece el hipermercado. El Híper, con su carga de pedagogía, se incorpora al esquema orgánico del Centro Comercial. La tienda en si misma constituye la pieza base de dicho puzle orgánico. Es en esta época cuando la tienda empieza su despegue autónomo como arquitectura, aportando su experiencia. Tras ello, llegamos a las grandes rutas comerciales, que proponemos como metáfora del shopping. Cerramos el capítulo concluyendo con Eugenio Ferrer que “si establecemos una relación entre el espacio y el capitalismo, entonces podemos inferir que los espacios del consumo de masas (ECM) son configuraciones nuevas respecto al pasado (...), pero el sistema que lo introduce no lo es del todo”. Segundo Capítulo. Búsqueda de claves que permitan el reconocimiento del Centro Comercial. Llegados a este punto y con la perspectiva del tiempo cabe preguntarnos, ¿qué entendemos pues por Centro Comercial? ¿Cómo lo percibimos? Abordamos ahora el problema de la percepción del Centro Comercial y su significado. Además de constituirse en símbolo, referencia siempre presente, la eficacia del Shopping es una de las principales causas de su poder de atracción. El Centro Comercial resulta de la síntesis de la revolución del consumo y de la revolución de la gestión. Espacio eficaz del entretenimiento como destino. El usuario resuelve su vida cotidiana dentro de un hábitat que considera propio y que se entiende como el lugar hiperbólico de la transacción comercial. Espacio de la abundancia para el disfrute. Una arquitectura involucrada en esta eficacia. Su sentido del lugar no es otro que el Shopping, que se desenvuelve de forma análoga en todas partes. El hogar del consumidor. Las nuevas catedrales. Las catedrales del consumo. Destino místico. Lugar de peregrinación para el consumidor fervoroso. Espacio sagrado que integra al usuario en la cultura dominante. Cultura del consumo. Templos, donde el tiempo ha perdido su sentido. Paraíso. Un espacio donde la altura, la luz natural, la dimensión general refuerzan el carácter sacro de un espacio para una nueva religión laica. Un espacio seguro, protegido que nos acerca a ideas como la de útero materno, con su carga de calidez y de significación erótica aplicado al encuentro compra-comprador y, ligado a ello, la literatura especializada habla del Centro Comercial como nave espacial hiperesterilizada o de agujero negro que absorbe la energía cultural. Más allá, la simulación, donde se percibe un simulacro de ciudad. Simulacro coherente con todo lo que el Shopping desencadena a su alrededor. El lugar de los sueños, de la fantasía. Aquí los productos se han metamorfoseado en fetiches, en significados. Televisión tridimensional, donde el usuario actúa guiado por una pulsión similar al zapping. Espacio lúdico de la fascinación por comprar o de imaginar que se compra. Espacio de simulaciones que llevan a la ensoñación. Un nuevo lugar que sustituye al espacio cotidiano, con el señuelo de la protección, en un contexto imaginariamente público. Espacio de la hiperrealidad donde no se distingue la realidad de la fantasía, donde tras episodios de confusión y desconcierto, se borran las fronteras con lo imaginario. Espacio mágico, escenario del gran espectáculo del consumo, controlado milimétricamente, al modo de la visita a un gran monumento, que ha de sobrevivir a los tiempos para dar testimonio de nuestro momento. Un icono, un símbolo que transmite un mensaje, que solo el consumidor es capaz de interpretar. Una agitada mezcla, sin precedentes, de percepciones que hablan de perplejidad y asombro ante el fenómeno del Centro Comercial, su espacio y las reacciones del hombre contemporáneo. ¿Cuáles serían las claves que nos permitirían reconocer la calidad esencial de un Centro Comercial, en esta concurrencia de perplejidades? Primero, la función de servicio. Un espacio donde ocurren muchas más cosas que lo obvio, que la compra. Un edificio que se involucra con el entorno de la mano de lo inesperado, la sorpresa y las expectativas. Esta vocación de servicio conecta Centro Comercial y naturaleza arquitectónica. Función que sugiere percepciones ligadas a la experiencia de compra. Organismo que vive y late al unísono con su visitante, colocándose al servicio de sus necesidades, de su afán de consumo, del que vive. Segundo, la comunidad servida. El Centro comercial sirve a una sociedad concreta. La sociedad consumista. Una nueva sociedad que se identifica con el edificio desarrollando un sentido de comunidad al nivel de sus deseos. Esta comunidad que se configura a su alrededor, constituye el activo más poderoso para el éxito de su realidad cotidiana y de su futuro. Tercero, un compromiso de carácter holístico. La economía de la experiencia aplicada al afán consumista de una sociedad identificada con su Centro, da lugar a una experiencia holística planificada. Diseño emocional. Colaboración para el éxito de un conjunto de establecimientos comerciales que participan en la aventura espacio-comercial del Centro Comercial. Ellos son los inductores primarios del consumo. Pero esta colaboración tiene su culminación en la amplificación del mensaje, como un inmenso altavoz, que proviene de la unidad configurada por todos ellos. El reflejo de esta amplificación de mensajes, desde la poderosa unidad constituida, es el aumento de la rentabilidad, fin último de la operación. Cuarto, la forma a través de una identificación de carácter gestáltico. Desde la lectura gestáltica que hacemos de la unidad holística, se advierte una poderosa capacidad de comunicación del sistema con su contexto. Centro y entorno se tornan entonces cómplices que complementan sus realidades. El Centro Comercial, arquitectura estructurada como sistema se percibe –ha de percibirse- como forma unitaria que procede de una mirada de raíz gestáltica que continuamente la recompone desde una óptica espacial y física, ligada a la experiencia individual. Esta unidad formal, más allá de la forma real, se constituye en esencia de de su arquitectura. Quinto, el Centro Comercial como sistema. Un sistema soportado por la Teoría General de Sistemas. La consideración del Centro Comercial como sistema es consecuencia de su estructura holística. El todo no se comporta como la suma de las partes y estas no lo hacen como lo harían en solitario. De aquí surge la necesidad de diálogo permanente entre la comercialización –proceso de incorporación de partes- y su traducción al mundo del diseño –proceso de articular arquitectónicamente las partes. Como sistema así configurado, el Centro Comercial se inserta en el paradigma contemporáneo, lo que genera realidades duales que no son excluyentes y reacciones de perplejidad e incertidumbre que el sistema corrige con su capacidad de autorregulación. Aparece también el espectador cuántico, el visitante, el consumidor, que interactúa con el sistema. Desde las herramientas que nos aporta la idea de sistema complejo, afrontamos el Mix Comercial -en definitiva la eficaz localización de las piezas en orden a sus relaciones y al organismo resultante- y su incidencia en la arquitectura que estamos concibiendo. Una arquitectura impredecible por lo mutable, que se erige en reto de la operación y del diseñador. Diseño que, de la mano del concepto de sistema se convierte en herramienta a mayor gloria de la operación global. El debate del estilismo no será más que el resultado del análisis en busca del éxito de esta operación. Sexto, una arquitectura de la negociación. Negociación como mecanismo proyectual y como resultado. La solución de proyecto nunca resulta evidente en el Centro Comercial como consecuencia de lo imprevisible del propio proceso de configuración. Su concreción solo puede ser fruto del compromiso de todos los agentes por conseguir el objetivo de la operación. Esto se consigue desde el equilibrio de intereses. Comerciales y de diseño. Un compromiso con la negociación y una negociación íntimamente ligada a la coordinación. Séptimo, el espacio y el tiempo. El debate espacio-tiempo condiciona y estructura la percepción del Centro Comercial. Introducimos conceptos como cronotopo –el instante y el lugar donde ocurre algo- y paradoja –incoherencia de la relación causa efecto- que sitúan el vínculo entre el tiempo y el espacio del Centro Comercial en un contexto de Shopping. En el discurrir paralelo del tiempo histórico –el tiempo de fuera- y del tiempo interior, el de dentro del Centro Comercial –tiempo presente o intemporalidad-, se produce el triunfo social del Centro Comercial que se traduce en haber sabido resolver en el espacio y en el tiempo las paradojas postmodernas del hombre contemporáneo. Octavo, de lo global. Globalidad que no es ajena a lo local. Una arquitectura que insertada en la dinámica de una economía de ámbito mundial, refleja las contradicciones que ella impone, fundamentalmente en los procesos de inclusión y exclusión, afectando de manera decisiva al debate de lo local, que el Centro Comercial debe incorporar como herramienta ineludible de reconocimiento. Terminamos el capítulo segundo manifestando como estas ocho claves, asumidas en su conjunto, confirman que el Centro Comercial puede aparecer como un todo conceptual cohesionado, pasando a formar parte de una familia arquitectónica coherente, cuya estructura funcional somos capaces de establecer. El Capítulo Tercero presenta con detalle la figura del arquitecto Víctor Gruen, creador reconocido del moderno Centro Comercial. Presentamos su trayectoria profesional observando como las diferentes claves analizadas en capítulos anteriores van apareciendo de manera natural a lo largo de ella "Victor Gruen may well have been the most influential architect of the twentieth century." Malcolm Gladwell. The Terrazo Jungle. Fifty Years Ago, The Mall Was Born. America Never Would Be The Same. 2004. In The New Yorker. Hombre complejo, conflictivo. Las paradojas a lo largo de su carrera fueron notables. Sin embargo siempre apareció como un hombre recto. Garret Eckbo, reconocido paisajista y colaborador de Gruen en el Centro Comercial peatonal del Centro urbano de Fresno, California, se asombraba de que alguien como Gruen hubiese sido capaz de combinar cortesía y humanidad en la carrera de ratas (sic) en la que se convirtió el universo de la comercialización americana y mantener la integridad542. Philip Johnson, en 1962, ponderando las muchas habilidades de Gruen manifestó que no estaba seguro si alguno de ellos, arquitectos artistas, hubiera sido capaz de hacer lo que Gruen hizo. A más, sobre Gruen, manifestó lo siguiente: "... El va más allá de la creación de un bello edificio. En jugar con la gente y sugerir lo que tienen que hacer, es un maestro. Y obtiene buenos resultados como hace la escultura. El suyo es un arte cívico, un sentido cívico.... Él es capaz de sentarse y poner cosas juntas. No es pomposo ni vano. Yo no me reuniría con él para hablar del diseño (de edificios). Víctor siente que cuando se habla de diseño se está ignorando todo el contexto... Su arquitectura es poderosamente limpia, no vuela la fantasía. Pero cuando te haces con su complejidad, ves que has descubierto algo más allá del diseño.... No puedes decir que haya alguien como él. La arquitectura tiene la suerte de tenerle como arquitecto..." Philip Johnson. Article in Fortune Review. 1962. El Documento de tesis cierra la visión de Gruen realizando un recorrido por los diferentes capítulos de su libro esencial, Shopping Towns Usa: The Planning of Shopping Centers. Solo su índice resulta un monumento al proceso de gestación del Centro Comercial. El libro, aquí simplemente mostrado en su estructura básica como un silencioso testigo, es la referencia canónica los Centros Comerciales contemporáneos, desde su aparición. . El Cuarto Capítulo del Documento de tesis es una recapitulación del trabajo anterior, en el que se sintetizan los conceptos de función y estilo relacionados con el Centro Comercial, se define en qué consiste cada uno de ellos y como, a partir de ahí, podemos afirmar que nos encontramos ante un tipo arquitectónico nuevo en el panorama de la disciplina arquitectónica. Terminamos el Capítulo integrando el Centro Comercial con un cuerpo teórico de referencias que se remiten a un tipo arquitectónico concreto y particular, acogiendo su singularidad como fenómeno arquitectónico autónomo. Como Conclusión de la tesis, resultado de todo lo anterior es decir, como consecuencia de la integración de un torrente de percepciones e intuiciones en un cuerpo teórico de referencias, deducidas de la existencia de unas claves que estructuran y penetran la esencia del singular modelo estudiado, haciéndolo detectable y seductor, resultan las características de un tipo arquitectónico con entidad propia que ordena, orienta y supedita la realidad y la existencia de esta nueva arquitectura. Una arquitectura nunca antes definida como tal, en el panorama tipológico de la disciplina. Teoría tipológica para una nueva arquitectura, que hemos ido proponiendo a lo largo del trabajo y que es coherente con los diferentes parámetros que se han analizado. Un conjunto edificado que, desde el estudio de sus claves esenciales y de sus invariantes perceptibles, aparece ahora más cercano, más familiar. Tanto que es posible destilar desde este conocimiento cercano e íntimo, una síntesis útil como referencia proyectual y como referencia para las grandes cuestiones que preocupan al discurrir del debate arquitectónico y sus ideas. El debate de la disciplina. El objeto de esta tesis, que consistía en establecer que el conjunto edificado que conocemos como Centro Comercial se constituye en un nuevo tipo en el panorama de las tipologías arquitectónicas, entendido el Centro Comercial en sentido genérico como familia arquitectónica con características propias y específicas que la hacen autónoma y reconocible, queda a nuestro juicio argumentado y justificado. ABSTRACT Within the frame of the built heritage there is a construction that is recognized as Shopping Center. An ensemble understood as an architectural family with its own specific recognizable characteristics. This thesis aims to explain that this building complex constitutes a new type in the panorama of architectural typology. This typology, with its singular identity, is connected to a way of understanding the idea of the model beyond an orthodox conception of the term understood as virtual model. This typology comes from a theoretical structure that we called typological theory, and it serves as yet another tool to reference the study and development design of the architectural spaces. In this first section, the Method, we emotionally explore the opportunities of this thesis. Why this typology has been ignored and the interest this work has in the present moment. An opportunity and an interest explained from an experience of a life dedicated to the world of Shopping Centers. The text then introduces the need for a rigorous knowledge of the Shopping Center’s essence in order to understand its impact in the frame of a new society and a new physical environment. A frame time where the historical mechanisms of association of civic community have given way to other gathering spaces like the Shopping Center, which encourages individualism, but is demanded by a society that relates to them. Spaces that, according to Galbraith, are a result of the intrinsic perversity of the unstoppable movement of the wheel of consumption-production. A society that has turned to worship of material achievement. Worship that provokes the appearance of an increasing value of consumption, according to Koolhaas, the only goal of humanity. Worship that ends in the need to reach certain status levels in the plane of a permanent comparison where the need of possession excites the consumer and gives them the illusion of being special. The product of consumption rises up to consideration of social values, entering a dynamic of marketing values, not only objects, but the desire of the individual remains. The study appears also to clarify the meaning of a space that serves the consumer and its context. A meaning that makes sense with the appearance of the suburbanization, the massive utilization of the car, the increase of living standards and the new role of women in the society after the Second World War, giving rise to the Age of Consumption. A world now determined and controlled by media and unlimited offers, where it’s necessary to place them in the context of the ordinary. An architecture that has to be judged precisely for its relation with this specific contemporary man. This section ends justifying the term ignored that appears in the Title of the Thesis, considering it in relation with the lack of studies structured about the Shopping Center and its architecture, drawing from Pevsner's work, A history of building types, 1976. Finally, the Shopping Center is analyzed with the most critical of thoughts, which considers it as populist architecture. The First Chapter, Precedents, proposes an historical tour of the commercial architecture throughout history. The Document looks to place on record the characteristics of the commercial architecture to set the connection between them and the Mall itself. These correspondences are going to allow us to answer the rhetorical question: is it the architecture of the Shopping Center a subsidiary architecture, or does it have its own personality independent from that of the commercial world? The reason of this historical search, citing Bruno Zevi, is that it is indispensable to establish the relationship between architecture and history, understating that an analysis is only possible when researching for their roots. Moreover, according to Guy de Maupassant, we are sure that architecture has had the privilege, across the centuries, of symbolizing as it were each age(…), through the harmony of lines and the charm of ornamentation all the grace and grandeur of an epoch. This historical reading, inseparable from a consistent design action, begins interpreting the commercial architecture of the Minoan to the 20th Century. Though this analysis of the big commercial itineraries and the study of the Shopping Center itself. A reading where we have found a series of constants that make it possible to draw conclusions from this comparison. The Mall appears to give response to the needs of a consumerist society. Comparing to the calm pace of the evolution of other commercial solutions, it is relevant its fast implantation and evolution in a short period of sixty years. Though via different solutions, the commercial spaces are considered taking into account the public-private relation, the interior-exterior, the inside-out, the closed-opened. Through that, the 19th century galleries and the food markets represent a revolution in functionality, in the machine, the modern management and the relations of the citizen within the city. All of this, the Mall inheritor feels. Likewise, the Department Store is the reflection of another great revolution. Production and commercialization en-mass, communications, the fixed price and increase of the living standard. The Mall reinterprets these situations inserting them in a new model of management. Already in the 20th century Mall and mass technologies of sale, the hypermarket is enthusiastically incorporated into the configuration of this organic scheme, constituting the base of one of the models, the French, that will be highly developed in the European continent. The shop itself constitutes, on the other hand, the key piece that completes the puzzle of the Mall and is in this epoch when it starts taking off as architecture, has an autonomous character. After all this, finally, we come to the big commercial routes, which we propose as metaphor of the shopping. Citing Eugenio Ferrer we can conclude that “If we establish a relation between the space and the capitalism, then we can infer that the spaces of the consumption of masses (ECM) are new configurations with regard to the past (...), but the system that introduces it it is not completely” Now we arrive at this point and with the perspective of time it is necessary to ask us, what do we understand about the Shopping Center? How do we perceive it? The second Chapter approaches the problem of the perception of the Mall and from this it is possible to detect and to identify key drivers that orientate the architectural comprehension of the space. The efficiency of the Shopping Center is its main power of attraction. A world that has ensued from the synthesis of the revolution of consumption and management. An effective cavern-like place of entertainment where the user, the consumer, the postmodern man solves his daily life inside a considered habitat. The hyperbolic place of commercial transaction. An abundance of space, that makes us perceive it as destination of entertainment. An architecture has evolved this efficiency, where the sense of place is at one with the sense of the Shopping. The home of the consumer. The new cathedrals. The cathedral of consumption. The place of peregrination for the fervent consumer. A sacred space that integrates the user in the dominant culture. A temple, where time itself has stopped existing. In this paroxysm, an expression of the Garden of Eden or Paradise itself. A space where the height, the natural daylight and the spatial dimension reinforce the sacred character of a new lay religion. Another common perception is that of a protected area, which leads to metaphors and considerations that suggest the idea of maternal womb, with its weight of erotic meaning, referring to the encounter of the shopper making a purchase. The literature also tells us about its perception as a sterile space capsule, a black hole that absorbs all cultural energy. Likewise, a world simulation where a mock city is perceived at first instance. Consistent with all that shopping triggers inside. A city, a space conceived as a place of dreams, fantasy, where the products have been metamorphosed into fetishes. Entertaining a television, three-dimensional television, where the user acts guided by a drive similar to zapping. A play area where the latest fascination is in the act of buying. Space simulations that unite and transcend creating atmospheres that lead to reverie. A new space replacing the daily space with the lure of safe space in a public context. A hyper-reality space with reality and fantasy, where borders are erased with imaginary episodes of confusion and bewilderment, without distinction. The charm and fascination of a space that reads like magic. The magic of a space which is defined as stage extravaganza, the large theatre, the consumer surveys in the fine control mode in which you visit a national monument. The shopping center has to survive the times to be a testimony of our time. An icon, a symbol that conveys a message, the message reads ‘consumer’. In short, a Shopping Center is a mix of unprecedented insights that speak of a widespread phenomenon of bewilderment. Its space and the reactions of contemporary man unfold in it like a fish in water. What are the key aspects which allow us to recognize the essential quality of a shopping center in this concurrence of perplexities? First, we want to record a service function of space much deeper than the immediately obvious, i.e. a purchase occurs. A building that appears to be involved with the environment and its people from the hand of the unexpected circumstances; surprise and attention. And that, in turn, also involves the visitor beyond the purchase. This dedication to service closely links the mall with its architectural nature. It is not the function of a lifeless machine. It is a feature that suggests unsuspected perceptions linked to the purchase, which speaks of an organism that lives and breathes in unison with the visitor. Second, in addition to the vocation of service-oriented desire for consumption, the Mall environment serves a particular society - The consumer society. A new society which relates to building a sense of community developed to the level of their desires. This community also constitutes the most powerful asset to the success of the daily life of the Shopping Center. Third, we emphasize that the so called economy of the experience is combined with the consumer zeal of a company that is identified by the Shopping Center. It connects to form a holistic and planned experience. This experience takes shape in the entity that ensues from the premeditated association and synergy, in the sense of a collaboration for success. A set of concrete commercial and independent establishments, take part in the spatial and commercial adventure that is the Mall and they are the instigators of the consumption. This holistic behavior finds culmination in the amplification of a claim that becomes unitary, like an immense force that leads to an increased profitability to all the levels. Consummation is a reference of one human being overturned in an architecture assimilated into a legitimate, emotional design with stability. A holistic quality is born of the essence of the building - and by virtue of the Conditions of Alexander, Christopher Alexander, determines the system condition of the Shopping Center. Fourth, we propose to establish what character the Mall will form when joined with the concept of its typology. This is going to allow the architectural work to be formed. As a result of the holistic structure that we see, the Mall is perceived as a system whose parts have their own function, justifying their existence in the ecosystem. Across a gestalt there is a powerful capacity of communication between the system and its context. We visualize on the one that stands out our building, turning both, Center and environment, in accomplices of a few special relations who complement each other in his realities. This relationship within a complex and diverse environment gives the Mall a range of unique spatial perceptions, the result of disparate experiences, which because of its root origin of gestalt, are integrated into a unified and coordinated manner fully intelligible and organized. This is the final formal essence of the Shopping Center. We can conclude here that the Mall as architecture is a structured system and should be perceived as a unit both from a physical and spatial perspective as this is the essence of its architecture. Fifth, the Mall as a system. A system which is being supported by a broad theoretical corpus, the General Systems Theory, which offers sufficient methodology to descend into consideration and give an enlightened conclusion on the overall understanding of the Mall. Consideration of the Mall as a system is a result of its holistic structure. The whole does not behave like any of the parties and they do not behave the way they used to before belonging to the whole, because they inhibit many of their qualities to their advantage. It arises the need for an ongoing dialogue between marketing processes and its translation into the physical world, the design. The system generates multiple perceptions to be integrated into a body which is to be understood as unitary. As a system, the Mall is inserted into the contemporary paradigm, creating dual realities that are not exclusive and are reactions of uncertainty that the system be properly designed at all levels, faced with their ability to self-regulate. Likewise, considering the visitor, the customer, like the quantum spectator who interacts with the system permanently. Moreover, a complex system confronts us with the Commercial mix, the effective location of parts in order to relate to the body and its importance in the architecture we are conceiving. Unpredictable architecture, which stands as the challenge of the operation and the designer. Design that becomes the tool of the system to create success for the overall operation. The discussion of the styling is merely the result of analysis that also seeks the success of the system, i.e. the styling should send the right message for the environment to ensure its survival. Sixth, the idea of negotiation as an architecture project, a mechanism inherent to the status of the proposed system. The project solution is never evident at the Shopping Center because of the unpredictability of the process itself. It can only be the fruit of the commitment of all stakeholders to achieve the objective of the operation. This is achieved from the balance of interests, of commercial and design. A commitment to negotiation and a negotiation linked to coordination. The pursuit of stability is key, as instability is always present and constantly requires strategies to build the object you are configuring. Seventh, proposes space-time itself as a circumstance that determines and structures the perception of the Mall in a singular way. We introduce concepts as chronotope and paradox to help us place the relationship between time and space within the Mall in the context of shopping. A consequence of the parallel flow of historical time - the time outside - and the time inside the Mall, the big shopping center formula is precisely that of having the feeling of timelessness in the space. The social triumph of the mall is the ability to resolve in space and in time all postmodern paradoxes and, beyond that, of contemporary man, condensing into a small space and time an enormous amount of cultural symbols, often contradictory, but they attract the practice of consumerism. Eighth, global level. Globalization which doesn’t ignore the local level. Architecture that is inserted into the dynamics of a global economy, reflects the contradictions that it imposes, mainly in the processes of inclusion and exclusion. Inclusion and exclusion affect the debate of the local level, which the Mall must incorporate as an unavoidable tool of recognition. The eight fundamental principles, when applied as a whole, confirm that the built heritage, which corresponds to the general Mall idea, can be presented as a cohesive conceptual whole. This becomes part of a coherent architectural family, whose functional structures are able to be established. The Third chapter presents in a detailed way the figure of the architect Victor Gruen, recognized as the creator of the modern Mall. Studying his professional experience, it is shown how the different keys analyzed in previous chapters are appearing in a natural way. "Victor Gruen may well have been the most influential architect of the twentieth century." Malcolm Gladwell. The Terrazo Jungle. Fifty Years Ago, The Mall Was Born. America Never Would Be The Same. 2004. In The New Yorker. He was a complex, troubled man and the paradoxes along his career were notable. Nevertheless, always he appeared as a straight man. Garret Eckbo, the recognized landscape painter and collaborator of Gruen was astonished how Gruen had been capable of combining comity and humanity in this career of rates, into that the American commercialization turned, Johnson, in 1962, weighting many Gruen's skills demonstrated that he was not sure if anyone of them, architects artists, had been capable of doing what Gruen did. He goes beyond just the creation of a beautiful building. In playing on people and suggesting what they ought to do, he is a master. (…) his architecture is clean - hardly architecture, no flights of fancy. But when you get hold of its complexity, you've got something beyond the design... You can't say there's someone like him. Architecture is lucky to have him as an architect." Philip Johnson. Article in Fortune Review. 1962. The Document of the thesis closes with Gruen's vision of realizing a tour through the different chapters of his essential book, Shopping towns USA: The Planning of Shopping Centers. It’s mere index turns out to be a monument to the process of the gestation of the Mall. The book, simply acted in its basic structure as a silent witness, as the canonical reference for the contemporary Malls. The Fourth Chapter of the Document of the thesis is a recapitulation of the previous work, which synthesizes the concepts of function and style related to the Shopping Center, and clearly defines how they are defined so we can conclude that we have found an architectural new type in the panorama of the architectural discipline. Therefore, the Conclusion of the thesis integrates this development in a theoretical body of references that relate to an architectural specific and particular type, which receives the singularity of the Shopping Center as an architectural independent phenomenon as it has tried to demonstrate from the beginning of the work. To conclude, as a result of the integrative process and the development of the theoretical body of references, the essential characteristics of the order and concept of the architectural typology form the existence of a new architecture; architecture never before defined as such, in the theoretical typology of the discipline. A theoretical typology for a new architecture is proposed throughout the discussed research and forms a conclusion of the different parameters that have been analysed. As a building complex, from the study of the essential characteristics and of the perceptible constants, the typology is more clearly defined and thus, becomes a useful tool and precedent for the consideration of the discipline. The thesis then justifies how the building complex known as Shopping Center constitutes a new type of architectural typology.

Gordon Matta-Clark a través de Rem Koolhaas : adición a través de eliminación

Gordon Matta-Clark es el origen de la presente investigación. Su obra, de total actualidad, ha ido ganando interés entre la comunidad de arquitectos, si bien su dimensión teórica se ha visto a menudo eclipsada por el poderoso atractivo de sus aberturas, cortes y extracciones. Son muchos los investigadores que detectan una carencia en el estudio de su corpus de pensamiento desde el campo de la crítica arquitectónica a la que está inevitablemente vinculado, a pesar de haber puesto en marcha una potente maquinaria de criticismo. Se constata a su vez la problem��tica existente al construir dialécticas entre la obra de Gordon Matta-Clark y el ámbito de la práctica arquitectónica. Surgen áreas forzadas de reflexión al elevar ambas esferas al mismo plano, achacado a un desconocimiento de las motivaciones críticas e históricas del proyecto del arquitecto. Aparece de modo recurrente un intento por establecer una dialéctica que, sin embargo, es relegada constantemente a una colección de notas al pie de página: Rem Koolhaas es sesgadamente mencionado por la crítica como el digno continuador accidental de las teorías de Gordon Matta-Clark. Se inicia así la construcción de una dialéctica que permanece aún sin resolver. Rem Koolhaas, en una entrevista en la que vierte su opinión sobre Gordon Matta-Clark, lo considera el precursor accidental de su ‘estrategia de vacío’, reconociendo en su trabajo procesos de adición a través de eliminación como método de creación de espacio arquitectónico. Una visión incisiva que desdeña su faceta de artista destructor destacando su habilidad para inocular el vacío mediante el empleo de herramientas de adición a través de eliminación. Estas premisas dan lugar de forma automática a la hipótesis de partida: la formalización de una investigación que llene ese vacío estableciendo un fuego cruzado entre ambos arquitectos, los cuales comparten de manera fortuita época y escenarios. El discurso de Rem Koolhaas iluminará el pensamiento de Gordon Matta-Clark vinculando sus respectivas plataformas de producción teórica, construyendo un espacio metafórico común en torno a la palabra y la imagen, herramientas que ambos manejan con habilidad y fluidez. Las propuestas del grupo Anarchitecture y las Art Cards o recortes anárquicos de soliloquios mattaclarkianos encuentran su réplica en el diccionario de términos e imágenes “Small, Medium, Large, Extra-Large”, descrito por Rem Koolhaas como una acumulación de palabras e imágenes que ilumina la condición de la arquitectura actual. La investigación establece una profusa asociación de ideas, imágenes y parlamentos que navegan en el universo referencial de Rem Koolhaas aportando una nueva visión sobre la dimensión crítica de Gordon Matta-Clark. Una visión poliédrica alrededor de cinco conceptos clave y un glosario de estrategias de proyecto que abren nuevos umbrales en los que la adición a través de la eliminación se repite hasta la saciedad transformado en mantra arquitectónico. ABSTRACT The present research finds its origins in Gordon Matta-Clark. His work, still relevant today, has been gaining interest within the community of architects, although its theoretical dimension has often been overshadowed by the powerful attraction of his openings, cuts and extractions. Many researchers detect a lack in the study of his body of thought from the field of architectural criticism to which he is inevitably associated, despite having launched a powerful machinery of criticism. It is noted at the same time the problem appeared when different dialectics between the work of Gordon Matta-Clark and the field of architectural practice are established. Forced areas of thought emerge when both fields are observed from the same point of view, derived from a lack of knowledge of the critical and historical motivations of the architect project. An attempt to establish a dialectical relationship with another architect appears recurrently in different books and writings. However it is steadily consigned to a collection of insignificant footnotes: the critics mention Rem Koolhaas as the worthy accidental successor of the theories of Gordon Matta-Clark. The construction of a dialectic that remains unresolved begins at this point. Gordon Matta-Clark is considered by Rem Koolhaas the accidental predecessor of his ‘strategy of emptiness’ -in an interview in which he pours his opinion on him- recognizing processes of addition through elimination in the work of Matta-Clark as a method of building architectural space. Rem Koolhaas rejects his role as destructor artist highlighting his ability to inoculate the emptiness by using addition tools through elimination. These premises lead us automatically to the hypothesis of the research: the formalization of research that will fill the emptiness by setting a crossfire between both architects, who share by chance the same scenarios and time. The discourse given by Rem Koolhaas illuminates Gordon Matta-Clark´s thought by linking their respective theoretical work platforms, building a common metaphorical space around word and image as tools managed by both of them with expertise and fluency. The Anarchitecture proposals and the Art Cards -anarchic cuts of Matta-Clark´s thought- find its counterpart in the dictionary of terms and images included in “Small, Medium, Large, Extra- Large”, described by Rem Koolhaas as an accumulation of words and images that illuminates the condition of architecture today. The research provides a wide range of associations of ideas, images and discussions around the universe of references of Rem Koolhaas, offering a new insight into the critical dimension of the work of Gordon Matta-Clark. A multifaceted vision around five key concepts and a glossary of project strategies that opens up new thresholds in which addition through elimination is repeated endlessly becoming an architectural mantra.

The anatomy of urban social networks and its implications in the searchability problem

The appearance of large geolocated communication datasets has recently increased our understanding of how social networks relate to their physical space. However, many recurrently reported properties, such as the spatial clustering of network communities, have not yet been systematically tested at different scales. In this work we analyze the social network structure of over 25 million phone users from three countries at three different scales: country, provinces and cities. We consistently find that this last urban scenario presents significant differences to common knowledge about social networks. First, the emergence of a giant component in the network seems to be controlled by whether or not the network spans over the entire urban border, almost independently of the population or geographic extension of the city. Second, urban communities are much less geographically clustered than expected. These two findings shed new light on the widely-studied searchability in self-organized networks. By exhaustive simulation of decentralized search strategies we conclude that urban networks are searchable not through geographical proximity as their country-wide counterparts, but through an homophily-driven community structure.

Solution of the pulse width modulation problem using orthogonal polynomials and Korteweg-de Vries equations

The mathematical underpinning of the pulse width modulation (PWM) technique lies in the attempt to represent “accurately” harmonic waveforms using only square forms of a fixed height. The accuracy can be measured using many norms, but the quality of the approximation of the analog signal (a harmonic form) by a digital one (simple pulses of a fixed high voltage level) requires the elimination of high order harmonics in the error term. The most important practical problem is in “accurate” reproduction of sine-wave using the same number of pulses as the number of high harmonics eliminated. We describe in this paper a complete solution of the PWM problem using Padé approximations, orthogonal polynomials, and solitons. The main result of the paper is the characterization of discrete pulses answering the general PWM problem in terms of the manifold of all rational solutions to Korteweg-de Vries equations.

Kinematic geometry of mass-triangles and reduction of Schrödinger’s equation of three-body systems to partial differential equations solely defined on triangular parameters

Schrödinger’s equation of a three-body system is a linear partial differential equation (PDE) defined on the 9-dimensional configuration space, ℝ9, naturally equipped with Jacobi’s kinematic metric and with translational and rotational symmetries. The natural invariance of Schrödinger’s equation with respect to the translational symmetry enables us to reduce the configuration space to that of a 6-dimensional one, while that of the rotational symmetry provides the quantum mechanical version of angular momentum conservation. However, the problem of maximizing the use of rotational invariance so as to enable us to reduce Schrödinger’s equation to corresponding PDEs solely defined on triangular parameters—i.e., at the level of ℝ6/SO(3)—has never been adequately treated. This article describes the results on the orbital geometry and the harmonic analysis of (SO(3),ℝ6) which enable us to obtain such a reduction of Schrödinger’s equation of three-body systems to PDEs solely defined on triangular parameters.