The variability and interdependence of spider viscid line tensile properties

True stress-true strain curves of naturally spun viscid line fibers retrieved directly from the spiral of orb-webs built by Argiope trifasciata spiders were measured using a novel methodology. This new procedure combines a method for removing the aqueous coating of the fibers and a technique that allows the accurate measurement of their cross sectional area. Comparison of the tensile behaviour of different samples indicates that naturally spun viscid lines show a large variability, comparable to that of other silks, such as major ampullate gland silk and silkworm silk. Nevertheless, application of a statistical analysis allowed identifying two independent parameters that underlie the variability and characterize the observed range of true stress-true strain curves. Combination of this result with previous mechanical and microstructural data suggested the assignment of these two independent effects to the degree of alignment of the protein chains and to the local relative humidity which, in turn, depends on the composition of the viscous coating and on the external environmental conditions.

Arquifanía: la arquitectura como manifestación

Arquifanía: arquitectura y epifanía. La revelación que se da en el proyectar, en el construir y en el habitar. Desentrañar los protagonistas y el escenario de ese encuentro es el objetivo de esta tesis. Nace de una doble inquietud: la relación entre literatura y arquitectura y la constatación de algo inconmensurable en la arquitectura. A lo largo de los siglos la teoría de la arquitectura ha hecho un gran esfuerzo por racionalizar todos los aspectos de la disciplina. La sistematización del orden y jerarquía de los espacios, el uso de parámetros más rigurosos en los cálculos estructurales, el desarrollo de la técnica y el estudio de los esquemas funcionales han supuesto una fuente inagotable de manifestaciones arquitectónicas. Los paradigmas científicos, incluso, han resultado fundamentales en la creación de nuevos lenguajes. Sin embargo, en este camino de racionalización se han orillado aspectos de difícil cuantificación. Pese a que en la experiencia diaria del arquitecto se constata la presencia de parámetros inconmensurables, la teoría de la arquitectura no ha integrado de forma sistemática este conocimiento. De aquí nace la presente tesis doctoral. En ella se estudia, por analogía con el resto de artes, el concepto de manifestación. Se analiza de qué manera la obra arquitectónica se manifiesta, haciendo uso de su autonomía, y se convierte en la que dirige al arquitecto en todos los tiempos de la existencia de la obra: desde su génesis en el tiempo del proyecto hasta la experiencia de la obra terminada en el tiempo de la historia. Se considera que reflexionar en el concepto de manifestación puede aportar luces sobre la disciplina arquitectónica en un doble momento. Se estudia por una parte la actitud y el proceder del arquitecto ante la génesis del proyecto y por otra su posicionamiento ante la obra ya existente, sometida a su análisis (para la posterior síntesis) generando una espiral de conocimiento siempre abierta y en continuo enriquecimiento. Se analiza la obra de María Zambrano, filósofa, y José Ángel Valente, poeta, en busca de la definición del concepto de manifestación. El momento creativo, la naturaleza de la palabra poética, la actitud del poeta ante su obra, el conocimiento y la revelación de la belleza son temas recurrentes en sus obras y crean un corpus teórico que permite elaborar una teoría poética sólida y abierta, llena de sugerencias que se dirige con precisión al momento de la generación de la forma: su epifanía. A continuación se repasa el concepto de manifestación en la actividad de algunos artistas de la modernidad que, de manera implícita o explícita, han hablado del concepto de epifanía. A menudo de forma intuitiva, los artistas han detectado en su actividad la condición de ser depositarios de un don que se renueva en cada obra ejecutada. Entrelazado con su trabajo y con la disciplina diaria los artistas experimentan un diálogo con la obra, que se revela libre y con voluntad de manifestarse. Enunciado el problema y hecho el repaso por el mundo de la creación artística, nos enfrentamos con el núcleo de la tesis: ¿hasta qué punto y de qué manera el concepto de manifestación es válido en arquitectura? El discurso busca en la actividad de múltiples arquitectos la validez del concepto de manifestación. Se rastrean testimonios, textos, obras y análisis de obras. De esta investigación surge una topografía, un atlas de revelaciones de manifestaciones arquitectónicas: constataciones explícitas, testimonios implícitos o intuiciones. A través de este periplo entre el concepto de manifestación que la razón poética ofrece y la experiencia de muchos arquitectos se intenta responder, aunque sea parcialmente, a las preguntas que surgen al llevar a las últimas consecuencias la arquifanía: ¿En qué momento existe una voluntad de forma? ¿De qué manera encuentra el arquitecto la forma? ¿Cómo se le presenta? ¿Es el arquitecto el verdadero artífice de la obra? ¿O es en cambio un ser a la espera de la aparición? ABSTRACT Archiphany: architecture and epiphany. The revelation taking place in designing, building and living. The objective of the present dissertation is to unravel the protagonists and the scenario of this encounter. It stems from a double interest: the relationship between literature and architecture and the discovery of something incommensurable in architecture. Over the centuries, architectural theory has made a great effort in order to rationalise all aspects of this discipline. Thus, the systematization of the order and hierarchy of space, the use of more rigorous parameters on the structural analysis, the development of technical capacities and the study of functional schemes have been an inexhaustible source of architectural manifestations. Even scientific paradigms have been essential in the creation of new languages. However, aspects of difficult quantification have been relegated in this path of rationalisation. Whereas the presence of immeasurable parameters are encountered in the daily experience of the architect, architectural theory has failed to systematically integrate this knowledge. This is the driving force of this thesis. It explores, by analogy with the other arts, the concept of manifestation. It discusses how the architectural work manifests itself, making use of its autonomy, becoming the one leading the architect during the whole existence of the work: from its genesis in the designing time until the experience of the completed work in the historical time. In the present dissertation, it is assumed that reflecting on the concept of manifestation might shed light on two different moments on the way to project architecture. The architect approach to the project genesis is studied on the one hand, while in the other hand it is considered his positioning in front of the existing work, as well as his analysis (for a following synthesis) that generates an ever-open and ever-enriching spiral of knowledge. In the search for a definition of the concept of manifestation, the work of the philosopher María Zambrano and the poet José Ángel Valente are analysed. The creative moment, the nature of the poetic word, the attitude of the poet in front of his work, the knowledge and the revelation of beauty are persistent issues in their works. They create a theoretical corpus allowing to develop a sound and open poetical theory full of suggestions, accurately directed to the time of the form generation: its epiphany. The concept of manifestation is then reviewed in the activity of some modern artists that talked about the concept of epiphany –either implicitly or explicitly. Often in an intuitive way, artists have come to realize in their activity to be the depositories of a gift that is renewed in each work. Intertwined with their work and with their daily discipline, artists experience a dialogue with the work, which proves to be free and willing to manifest itself. Having stated the problem and having reviewed the world of artistic creation, we are confronted with the core of the thesis: Up to which extent and in which way is the concept of manifestation valid for architecture? Validity and evidence of this concept is sought in the activity of multiple architects. Texts, works, analysis, reviews and testimonies are investigated. From this research, a topography, an atlas of revelations of architectural manifestations arises: explicit findings, implicit witnesses or intuitions. By means of this journey going from the concept of manifestation hinted by the poetic reason to the experience of many architects, the ultimate questions risen by archiphany are meant to be answered (though partially): When does a will of form emerge? How does the architect find the form? How does it appear? Is the architect the true creator of the work? Or is he instead a being waiting for the vision?

Geometric diagnostics of complex patterns: Spiral defect chaos

Motivated by the observation of spiral patterns in a wide range of physical, chemical, and biological systems, we present an automated approach that aims at characterizing quantitatively spiral-like elements in complex stripelike patterns. The approach provides the location of the spiral tip and the size of the spiral arms in terms of their arc length and their winding number. In addition, it yields the number of pattern components (Betti number of order 1), as well as their size and certain aspects of their shape. We apply the method to spiral defect chaos in thermally driven Rayleigh- Bénard convection and find that the arc length of spirals decreases monotonically with decreasing Prandtl number of the fluid and increasing heating. By contrast, the winding number of the spirals is nonmonotonic in the heating. The distribution function for the number of spirals is significantly narrower than a Poisson distribution. The distribution function for the winding number shows approximately an exponential decay. It depends only weakly on the heating, but strongly on the Prandtl number. Large spirals arise only for larger Prandtl numbers. In this regime the joint distribution for the spiral length and the winding number exhibits a three-peak structure, indicating the dominance of Archimedean spirals of opposite sign and relatively straight sections. For small Prandtl numbers the distribution function reveals a large number of small compact pattern components.

The logarithmic spiral, autoisoptic curve

In the Line of Investigation that in the department of “Technical Drawing” in the School of Agriculture Engineering of Madrid, we carry out on the study of The Technical Curves and his singularities, we demonstrate an interesting property of the Logarithmic Spiral. The demonstrated property consists of which the logarithmic spiral is a autoisoptic curve, that is to say that if from a point P anyone of the spiral tangent straight lines draw up to the previous arc, these form a constant angle α. This demonstration is novel and in addition we get to contribute a method to calculate the angle α given the equation of the spiral.

Spiral optical designs for nonimaging applications

Manufacturing technologies as injection molding or embossing specify their production limits for minimum radii of the vertices or draft angle for demolding, for instance. In some demanding nonimaging applications, these restrictions may limit the system optical efficiency or affect the generation of undesired artifacts on the illumination pattern. A novel manufacturing concept is presented here, in which the optical surfaces are not obtained from the usual revolution symmetry with respect to a central axis (z axis), but they are calculated as free-form surfaces describing a spiral trajectory around z axis. The main advantage of this new concept lies in the manufacturing process: a molded piece can be easily separated from its mold just by applying a combination of rotational movement around axis z and linear movement along axis z, even for negative draft angles. Some of these spiral symmetry examples will be shown here, as well as their simulated results.

Novel free-form optical surface design with spiral symmetry

Manufacturing technologies as injection molding or embossing specify their production limits for minimum radii of the vertices or draft angle for demolding, for instance. These restrictions may limit the system optical efficiency or affect the generation of undesired artifacts on the illumination pattern when dealing with optical design. A novel manufacturing concept is presented here, in which the optical surfaces are not obtained from the usual revolution symmetry with respect to a central axis (z axis), but they are calculated as free-form surfaces describing a spiral trajectory around z axis. The main advantage of this new concept lies in the manufacturing process: a molded piece can be easily separated from its mold just by applying a combination of rotational movement around axis z and linear movement along axis z, even for negative draft angles. The general designing procedure will be described in detail

Spiral nonimaging optical designs

Manufacturing technologies as injection molding or embossing specify their production limits for minimum radii of the vertices or draft angle for demolding, for instance. In some demanding nonimaging applications, these restrictions may limit the system optical efficiency or affect the generation of undesired artifacts on the illumination pattern. A novel manufacturing concept is presented here, in which the optical surfaces are not obtained from the usual revolution symmetry with respect to a central axis (z axis), but they are calculated as free-form surfaces describing a spiral trajectory around z axis. The main advantage of this new concept lies in the manufacturing process: a molded piece can be easily separated from its mold just by applying a combination of rotational movement around axis z and linear movement along axis z, even for negative draft angles. Some of these spiral symmetry examples will be shown here, as well as their simulated results.

Contribution to the design of waveguide-fed compound-slot arrays by means of equivalent circuit modelling

Los arrays de ranuras son sistemas de antennas conocidos desde los años 40, principalmente destinados a formar parte de sistemas rádar de navíos de combate y grandes estaciones terrenas donde el tamaño y el peso no eran altamente restrictivos. Con el paso de los años y debido sobre todo a importantes avances en materiales y métodos de fabricación, el rango de aplicaciones de este tipo de sistemas radiantes creció en gran medida. Desde nuevas tecnologías biomédicas, sistemas anticolisión en automóviles y navegación en aviones, enlaces de comunicaciones de alta tasa binaria y corta distancia e incluso sistemas embarcados en satélites para la transmisión de señal de televisión. Dentro de esta familia de antennas, existen dos grupos que destacan por ser los más utilizados: las antennas de placas paralelas con las ranuras distribuidas de forma circular o espiral y las agrupaciones de arrays lineales construidos sobre guia de onda. Continuando con las tareas de investigación desarrolladas durante los últimos años en el Instituto de Tecnología de Tokyo y en el Grupo de Radiación de la Universidad Politécnica de Madrid, la totalidad de esta tesis se centra en este último grupo, aunque como se verá se separa en gran medida de las técnicas de diseño y metodologías convencionales. Los arrays de ranuras rectas y paralelas al eje de la guía rectangular que las alimenta son, sin ninguna duda, los modelos más empleados debido a la fiabilidad que presentan a altas frecuencias, su capacidad para gestionar grandes cantidades de potencia y la sencillez de su diseño y fabricación. Sin embargo, también presentan desventajas como estrecho ancho de banda en pérdidas de retorno y rápida degradación del diagrama de radiación con la frecuencia. Éstas son debidas a la naturaleza resonante de sus elementos radiantes: al perder la resonancia, el sistema global se desajusta y sus prestaciones degeneran. En arrays bidimensionales de slots rectos, el campo eléctrico queda polarizado sobre el plano transversal a las ranuras, correspondiéndose con el plano de altos lóbulos secundarios. Esta tesis tiene como objetivo el desarrollo de un método sistemático de diseño de arrays de ranuras inclinadas y desplazadas del centro (en lo sucesivo “ranuras compuestas”), definido en 1971 como uno de los desafíos a superar dentro del mundo del diseño de antennas. La técnica empleada se basa en el Método de los Momentos, la Teoría de Circuitos y la Teoría de Conexión Aleatoria de Matrices de Dispersión. Al tratarse de un método circuital, la primera parte de la tesis se corresponde con el estudio de la aplicabilidad de las redes equivalentes fundamentales, su capacidad para recrear fenómenos físicos de la ranura, las limitaciones y ventajas que presentan para caracterizar las diferentes configuraciones de slot compuesto. Se profundiza en las diferencias entre las redes en T y en ! y se condiciona la selección de una u otra dependiendo del tipo de elemento radiante. Una vez seleccionado el tipo de red a emplear en el diseño del sistema, se ha desarrollado un algoritmo de cascadeo progresivo desde el puerto alimentador hacia el cortocircuito que termina el modelo. Este algoritmo es independiente del número de elementos, la frecuencia central de funcionamiento, del ángulo de inclinación de las ranuras y de la red equivalente seleccionada (en T o en !). Se basa en definir el diseño del array como un Problema de Satisfacción de Condiciones (en inglés, Constraint Satisfaction Problem) que se resuelve por un método de Búsqueda en Retroceso (Backtracking algorithm). Como resultado devuelve un circuito equivalente del array completo adaptado a su entrada y cuyos elementos consumen una potencia acorde a una distribución de amplitud dada para el array. En toda agrupación de antennas, el acoplo mutuo entre elementos a través del campo radiado representa uno de los principales problemas para el ingeniero y sus efectos perjudican a las prestaciones globales del sistema, tanto en adaptación como en capacidad de radiación. El empleo de circuito equivalente se descartó por la dificultad que suponía la caracterización de estos efectos y su inclusión en la etapa de diseño. En esta tesis doctoral el acoplo también se ha modelado como una red equivalente cuyos elementos son transformadores ideales y admitancias, conectada al conjunto de redes equivalentes que representa el array. Al comparar los resultados estimados en términos de pérdidas de retorno y radiación con aquellos obtenidos a partir de programas comerciales populares como CST Microwave Studio se confirma la validez del método aquí propuesto, el primer método de diseño sistemático de arrays de ranuras compuestos alimentados por guía de onda rectangular. Al tratarse de ranuras no resonantes, el ancho de banda en pérdidas de retorno es mucho mas amplio que el que presentan arrays de slots rectos. Para arrays bidimensionales, el ángulo de inclinación puede ajustarse de manera que el campo quede polarizado en los planos de bajos lóbulos secundarios. Además de simulaciones se han diseñado, construido y medido dos prototipos centrados en la frecuencia de 12GHz, de seis y diez elementos. Las medidas de pérdidas de retorno y diagrama de radiación revelan excelentes resultados, certificando la bondad del método genuino Method of Moments - Forward Matching Procedure desarrollado a lo largo de esta tésis. Abstract The slot antenna arrays are well known systems from the decade of 40s, mainly intended to be part of radar systems of large warships and terrestrial stations where size and weight were not highly restrictive. Over the years, mainly due to significant advances in materials and manufacturing methods, the range of applications of this type of radiating systems grew significantly. From new biomedical technologies, collision avoidance systems in cars and aircraft navigation, short communication links with high bit transfer rate and even embedded systems in satellites for television broadcast. Within this family of antennas, two groups stand out as being the most frequent in the literature: parallel plate antennas with slots placed in a circular or spiral distribution and clusters of waveguide linear arrays. To continue the vast research work carried out during the last decades in the Tokyo Institute of Technology and in the Radiation Group at the Universidad Politécnica de Madrid, this thesis focuses on the latter group, although it represents a technique that drastically breaks with traditional design methodologies. The arrays of slots straight and parallel to the axis of the feeding rectangular waveguide are without a doubt the most used models because of the reliability that they present at high frequencies, its ability to handle large amounts of power and their simplicity of design and manufacturing. However, there also exist disadvantages as narrow bandwidth in return loss and rapid degradation of the radiation pattern with frequency. These are due to the resonant nature of radiating elements: away from the resonance status, the overall system performance and radiation pattern diminish. For two-dimensional arrays of straight slots, the electric field is polarized transverse to the radiators, corresponding to the plane of high side-lobe level. This thesis aims to develop a systematic method of designing arrays of angled and displaced slots (hereinafter "compound slots"), defined in 1971 as one of the challenges to overcome in the world of antenna design. The used technique is based on the Method of Moments, Circuit Theory and the Theory of Scattering Matrices Connection. Being a circuitry-based method, the first part of this dissertation corresponds to the study of the applicability of the basic equivalent networks, their ability to recreate the slot physical phenomena, their limitations and advantages presented to characterize different compound slot configurations. It delves into the differences of T and ! and determines the selection of the most suitable one depending on the type of radiating element. Once the type of network to be used in the system design is selected, a progressive algorithm called Forward Matching Procedure has been developed to connect the proper equivalent networks from the feeder port to shorted ending. This algorithm is independent of the number of elements, the central operating frequency, the angle of inclination of the slots and selected equivalent network (T or ! networks). It is based on the definition of the array design as a Constraint Satisfaction Problem, solved by means of a Backtracking Algorithm. As a result, the method returns an equivalent circuit of the whole array which is matched at its input port and whose elements consume a power according to a given amplitude distribution for the array. In any group of antennas, the mutual coupling between elements through the radiated field represents one of the biggest problems that the engineer faces and its effects are detrimental to the overall performance of the system, both in radiation capabilities and return loss. The employment of an equivalent circuit for the array design was discarded by some authors because of the difficulty involved in the characterization of the coupling effects and their inclusion in the design stage. In this thesis the coupling has also been modeled as an equivalent network whose elements are ideal transformers and admittances connected to the set of equivalent networks that represent the antennas of the array. By comparing the estimated results in terms of return loss and radiation with those obtained from popular commercial software as CST Microwave Studio, the validity of the proposed method is fully confirmed, representing the first method of systematic design of compound-slot arrays fed by rectangular waveguide. Since these slots do not work under the resonant status, the bandwidth in return loss is much wider than the longitudinal-slot arrays. For the case of two-dimensional arrays, the angle of inclination can be adjusted so that the field is polarized at the low side-lobe level plane. Besides the performed full-wave simulations two prototypes of six and ten elements for the X-band have been designed, built and measured, revealing excellent results and agreement with the expected results. These facts certify that the genuine technique Method of Moments - Matching Forward Procedure developed along this thesis is valid and trustable.

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

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

Hexagons and spiral defect chaos in non-Boussinesq convection at low Prandtl numbers

We study the stability and dynamics of non-Boussinesq convection in pure gases ?CO2 and SF6? with Prandtl numbers near Pr? 1 and in a H2-Xe mixture with Pr= 0.17. Focusing on the strongly nonlinear regime we employ Galerkin stability analyses and direct numerical simulations of the Navier-Stokes equations. For Pr ? 1 and intermediate non-Boussinesq effects we find reentrance of stable hexagons as the Rayleigh number is increased. For stronger non-Boussinesq effects the usual, transverse side-band instability is superseded by a longitudinal side-band instability. Moreover, the hexagons do not exhibit any amplitude instability to rolls. Seemingly, this result contradicts the experimentally observed transition from hexagons to rolls. We resolve this discrepancy by including the effect of the lateral walls. Non-Boussinesq effects modify the spiral defect chaos observed for larger Rayleigh numbers. For convection in SF6 we find that non-Boussinesq effects strongly increase the number of small, compact convection cells and with it enhance the cellular character of the patterns. In H2-Xe, closer to threshold, we find instead an enhanced tendency toward roll-like structures. In both cases the number of spirals and of targetlike components is reduced. We quantify these effects using recently developed diagnostics of the geometric properties of the patterns.