Perfect imaging of three object points with only two analytic lens surfaces in two dimensions

In this work, a new two-dimensional analytic optics design method is presented that enables the coupling of three ray sets with two lens profiles. This method is particularly promising for optical systems designed for wide field of view and with clearly separated optical surfaces. However, this coupling can only be achieved if different ray sets will use different portions of the second lens profile. Based on a very basic example of a single thick lens, the Simultaneous Multiple Surfaces design method in two dimensions (SMS2D) will help to provide a better understanding of the practical implications on the design process by an increased lens thickness and a wider field of view. Fermat?s principle is used to deduce a set of functional differential equations fully describing the entire optical system. The transformation of these functional differential equations into an algebraic linear system of equations allows the successive calculation of the Taylor series coefficients up to an arbitrary order. The evaluation of the solution space reveals the wide range of possible lens configurations covered by this analytic design method. Ray tracing analysis for calculated 20th order Taylor polynomials demonstrate excellent performance and the versatility of this new analytical optics design concept.

Perfect imaging analysis of the spherical geodesic waveguide

Negative Refractive Lens (NRL) has shown that an optical system can produce images with details below the classic Abbe diffraction limit. This optical system transmits the electromagnetic fields, emitted by an object plane, towards an image plane producing the same field distribution in both planes. In particular, a Dirac delta electric field in the object plane is focused without diffraction limit to the Dirac delta electric field in the image plane. Two devices with positive refraction, the Maxwell Fish Eye lens (MFE) and the Spherical Geodesic Waveguide (SGW) have been claimed to break the diffraction limit using positive refraction with a different meaning. In these cases, it has been considered the power transmission from a point source to a point receptor, which falls drastically when the receptor is displaced from the focus by a distance much smaller than the wavelength. Although these systems can detect displacements up to ?/3000, they cannot be compared to the NRL, since the concept of image is different. The SGW deals only with point source and drain, while in the case of the NRL, there is an object and an image surface. Here, it is presented an analysis of the SGW with defined object and image surfaces (both are conical surfaces), similarly as in the case of the NRL. The results show that a Dirac delta electric field on the object surface produces an image below the diffraction limit on the image surface.

Super-resolution properties of the Spherical Geodesic Waveguides using the perfect drain

Perfect drain for the Maxwell Fish Eye (MFE) is a nonmagnetic dissipative region placed in the focal point to absorb all the incident radiation without reflection or scattering. The perfect drain was recently designed as a material with complex permittivity ? that depends on frequency. However, this material is only a theoretical material, so it can not be used in practical devices. Recently, the perfect drain has been claimed as necessary to achieve super-resolution [Leonhard 2009, New J. Phys. 11 093040], which has increased the interest for practical perfect drains suitable for manufacturing. Here, we analyze the superresolution properties of a device equivalent to the MFE, known as Spherical Geodesic Waveguide (SGW), loaded with the perfect drain. In the SGW the source and drain are implemented with coaxial probes. The perfect drain is realized using a circuit (made of a resistance and a capacitor) connected to the drain coaxial probes. Superresolution analysis for this device is done in Comsol Multiphysics. The results of simulations predict the superresolution up to ? /3000 and optimum power transmission from the source to the drain.

Perfect imaging of point sources with positive refraction

The capability of a device called the Spherical Geodesic Waveguide (SGW) to produce images with details below the classic Abbe diffraction limit (super-resolution) is analyzed here. The SGW is an optical system equivalent (by means of Transformation Optics) to the Maxwell Fish Eye (MFE) refractive index distribution. Recently, it has been claimed that the necessary condition to get super-resolution in the MFE and the SGW is the use of a Perfect Point Drain (PPD). The PPD is a punctual receptor placed in the focal point that absorbs the incident wave, without reflection or scattering. A microwave circuit comprising three elements, the SGW, the source and the drain (two coaxial lines loaded with specific impedances) is designed and simulated in COMSOL. The super-resolution properties have been analyzed for different position of the source and drain and for two different load impedances: the PPD and the characteristic line impedance. The results show that in both cases super-resolution occurs only for discrete number of frequencies. Out of these frequencies, the SGW does not show SR in the analysis carried out.

A characterization of conserved quantities in non-equilibrium thermodynamics

The well-known Noether theorem in Lagrangian and Hamiltonian mechanics associates symmetries in the evolution equations of a mechanical system with conserved quantities. In this work, we extend this classical idea to problems of non-equilibrium thermodynamics formulated within the GENERIC (General Equations for Non-Equilibrium Reversible-Irreversible Coupling) framework. The geometric meaning of symmetry is reviewed in this formal setting and then utilized to identify possible conserved quantities and the conditions that guarantee their strict conservation. Examples are provided that demonstrate the validity of the proposed definition in the context of finite and infinite dimensional thermoelastic problems.

Enhanced thermionic currents by non equilibrium electron population of metals

An analytical expression is derived for the electron thermionic current from heated metals by using a non equilibrium, modified Kappa energy distribution for electrons. This isotropic distribution characterizes the long high energy tails in the electron energy spectrum for low values of the index ? and also accounts for the Fermi energy for the metal electrons. The limit for large ? recovers the classical equilibrium Fermi-Dirac distribution. The predicted electron thermionic current for low ? increases between four and five orders of magnitude with respect to the predictions of the equilibrium Richardson-Dushmann current. The observed departures from this classical expression, also recovered for large ?, would correspond to moderate values of this index. The strong increments predicted by the thermionic emission currents suggest that, under appropriate conditions, materials with non equilibrium electron populations would become more efficient electron emitters at low temperatures.

Geometric Study of the Weak Equilibrium in a Weighted Case for a Two-Dimensional Competition Game

In this work, an improvement of the results presented by [1] Abellanas et al. (Weak Equilibrium in a Spatial Model. International Journal of Game Theory, 40(3), 449-459) is discussed. Concretely, this paper investigates an abstract game of competition between two players that want to earn the maximum number of points from a finite set of points in the plane. It is assumed that the distribution of these points is not uniform, so an appropriate weight to each position is assigned. A definition of equilibrium which is weaker than the classical one is included in order to avoid the uniqueness of the equilibrium position typical of the Nash equilibrium in these kinds of games. The existence of this approximated equilibrium in the game is analyzed by means of computational geometry techniques.

Conditions for perfect focusing multiple point sources with the SMS design method

In this work, we demonstrate how it is possible to sharply image multiple object points. The Simultaneous Multiple Surface (SMS) design method has usually been presented as a method to couple N wave-front pairs with N surfaces, but recent findings show that when using N surfaces, we can obtain M image points when N

Funicularity and equilibrium for high-performance conceptual structural design

Las estructuras que trabajan por forma se caracterizan por la íntima e indisociable relación entre geometría y comportamiento estructural. Por consiguiente, la elección de una apropiada geometría es el paso previo indispensable en el diseño conceptual de dichas estructuras. En esa tarea, la selección de las posibles geometrías antifuniculares para las distribuciones de cargas permanentes más habituales son más bien limitadas y, muchas veces, son criterios no estructurales (adaptabilidad funcional, estética, proceso constructivo, etc.) los que no permiten la utilización de dichas geometrías que garantizarían el máximo aprovechamiento del material. En este contexto, esta tesis estudia la posibilidad de obtener una estructura sin momentos flectores incluso si la geometría no es antifunicular para sus cargas permanentes. En efecto, esta tesis presenta un procedimiento, basado en la estática gráfica, que demuestra cómo un conjunto de cargas adicionales, introducidas a través de un sistema de pretensado exterior con elementos post-tesos, puede eliminar los momentos flectores debidos a cargas permanentes en cualquier geometría plana. Esto se traduce en una estructura antifunicular que proporciona respuestas innovadoras a demandas conjuntas de versatilidad arquitectónica y optimización del material. Dicha metodología gráfica ha sido implementada en un software distribuido libremente (EXOEQUILIBRIUM), donde el análisis estructural y la variación geométrica están incluidos en el mismo entorno interactivo y paramétrico. La utilización de estas herramientas permite más versatilidad en la búsqueda de nuevas formas eficientes, lo cual tiene gran importancia en el diseño conceptual de estructuras, liberando al ingeniero de la limitación del propio cálculo y de la incomprensión del comportamiento estructural, facilitando extraordinariamente el hecho creativo a la luz de una metodología de este estilo. Esta tesis incluye la aplicación de estos procedimientos a estructuras de cualquier geometría y distribución inicial de cargas, así como el estudio de diferentes posibles criterios de diseño para optimizar la posición del sistema de post-tesado. Además, la metodología ha sido empleada en el proyecto de maquetas a escala reducida y en la construcción de un pabellón hecho enteramente de cartón, lo que ha permitido obtener una validación física del procedimiento desarrollado. En definitiva, esta tesis expande de manera relevante el rango de posibles geometrías antifuniculares y abre enormes posibilidades para el diseño de estructuras que combinan eficiencia estructural y flexibilidad arquitectónica.Curved structures are characterized by the critical relationship between their geometry and structural behaviour, and selecting an appropriate shape in the conceptual design of such structures is important for achieving materialefficiency. However, the set of bending-free geometries are limited and, often, non-structural design criteria (e.g., usability, architectural needs, aesthetics) prohibit the selection of purely funicular or antifunicular shapes. In response to this issue, this thesis studies the possibility of achieving an axial-only behaviour even if the geometry departs from the ideally bending-free shape. This dissertation presents a new design approach, based on graphic statics that shows how bending moments in a two-dimensional geometry can be eliminated by adding forces through an external post-tensioning system. This results in bending-free structures that provide innovative answers to combined demands on versatility and material optimization. The graphical procedure has been implemented in a free-downloadable design-driven software (EXOEQUILIBRIUM) where structural performance evaluations and geometric variation are embedded within an interactive and parametric working environment. This provides greater versatility in finding new efficient structural configurations during the first design stages, bridging the gap between architectural shaping and structural analysis. The thesis includes the application of the developed graphical procedure to shapes with random curvature and distribution of loads. Furthermore, the effect of different design criteria on the internal force distribution has been analyzed. Finally, the construction of reduced- and large-scale models provides further physical validation of the method and insights about the structural behaviour of these structures. In summary, this work strongly expands the range of possible forms that exhibit a bending-free behaviour and, de facto, opens up new possibilities for designs that combine high-performing solutions with architectural freedom.

1950 En torno al Museo Louisiana 1970

La tesis “1950 En torno al Museo Louisiana 1970” analiza varias obras relacionadas con el espacio doméstico, que se realizaron entre 1950 y 1970 en Dinamarca, un periodo de esplendor de la Arquitectura Moderna. Tras el aislamiento y restricciones del conflicto bélico que asoló Europa, los jóvenes arquitectos daneses, estaban deseosos por experimentar nuevas ideas de procedencia internacional, favorecidos por diferentes circunstancias, encuentran el mejor campo de ensayo en el espacio doméstico. La mejor arquitectura doméstica en Dinamarca, de aquel periodo, debe entenderse como un sistema compuesto por diferentes autores, que tienen en común muchas más similitudes que diferencias, se complementan unos a otros. Para la comprensión y el entendimiento de ello se hace necesario el estudio de varias figuras y edificios, que completen este sistema cuya investigación está escasamente desarrollada. La tesis propone un viaje para conocer los nombres de algunos de sus protagonistas, que mostraron con su trabajo, que tradición y vanguardia no estarán reñidas. El objetivo es desvelar las claves de la Modernidad Danesa, reconocer, descubrir y recuperar el legado de algunos de sus protagonistas en el ámbito doméstico, cuya lección se considera de total actualidad. Una arquitectura que asume las aportaciones extranjeras con moderación y crítica, cuya íntima relación con la tradición arquitectónica y la artesanía propias, será una de sus notas especiales. Del estudio contrastado de varios proyectos y versiones, se obtienen valores comunes entre sus autores, al igual que se descubren sus afinidades o diferencias respecto a los mismos asuntos; que permitirán comprender sus actuaciones según las referencias e influencias, y definir las variables que configuran sus espacios arquitectónicos. La línea de conexión entre los edificios elegidos será su particular relación con la naturaleza y el lugar en que se integran. La fachada, lugar donde se negociará la relación entre el interior y el paisaje, será un elemento entendido de un modo diferente en cada uno de ellos, una relación que se extenderá en todas ellas, más allá de su perímetro. La investigación se ha estructurado en seis capítulos, que van precedidos de una Introducción. En el capítulo primero, se estudian y se señalan los antecedentes, las figuras y edificios más relevantes de la Tradición Danesa, para la comprensión y el esclarecimiento de algunas de las claves de su Modernidad en el campo de la Arquitectura, que se produce con una clara intención de encontrar su propia identidad y expresión. Esta Modernidad floreciente se caracteriza por la asimilación de otras culturas extranjeras desde la moderación, con un punto de vista crítico, y encuentra sus raíces ancladas a la tradición arquitectónica y la artesanía propia, que fragua en la aparición de un ideal común con enorme personalidad y que hoy se valora como una auténtica aportación de una cultura considerada entonces periférica. Se mostrará el debate y el camino seguido por las generaciones anteriores, a las obras análizadas. Las sensibilidades por lo vernáculo y lo clásico, que aparentemente son contradictorias, dominaran el debate con la misma veracidad y respetabilidad. La llamada tercera generación por Sigfried Giedion reanudará la práctica entre lo clásico y lo vernáculo, apoyados en el espíritu del trabajo artesanal y de la tradición, con el objetivo de conocer del acto arquitectónico su “la verdad” y “la esencia original”. El capítulo segundo, analiza la casa Varming, de 1953, situada en un área residencial de Gentofte, por Eva y Nils Koppel, que reinterpreta la visión de Asplund de un paisaje interior continuación del exterior, donde rompen la caja de ladrillo macizo convencional propia de los años 30. Es el ejemplo más poderoso de la unión de tradición e innovación en su obra residencial. Sus formas sobrias entre el Funcionalismo Danés y la Modernidad se singularizarán por su abstracción y volúmenes limpios que acentúan el efecto de su geometría, prismática y brutalista. El desplazamiento de los cuerpos que lo componen, unos sobre otros, generan un ritmo, que se producirá a otras escalas, ello unido a las variaciones de sus formas y a la elección de sus materiales, ladrillo y madera, le confieren a la casa un carácter orgánico. El edificio se ancla a la tierra resolviéndose en diferentes niveles tras el estudio del lugar y su topografía. El resultado es una versión construida del paisaje, en la cual el edificio da forma al lugar y ensalza la experiencia del escenario natural. La unidad de las estructuras primitivas, parece estar presente. Constituye un ejemplo de la “La idea de Promenade de Asplund”, el proyecto ofrece diferentes recorridos, permitiendo su propia vivencia de la casa, que ofrece la posibilidad vital de decidir. El capítulo tercero trata sobre el pabellón de invitados de Niels Bohr de 1957, situado un área boscosa, en Tisvilde Hegn, fue el primer edificio del arquitecto danés Vilhelm Wohlert. Arraigado a la Tradición Danesa, representa una renovación basada en la absorción de influencias extranjeras: la Arquitectura Americana y la Tradición Japonesa. La caja de madera, posada sobre un terreno horizontal, tiene el carácter sensible de un organismo vivo, siempre cambiante según las variaciones de luz del día o temperatura. Cuando se abre, crea una prolongación del espacio interior, que se extiende a la naturaleza circundante, y se expande hacia el espacio exterior, permitiendo su movilización. Se establece una arquitectura de flujos. Hay un interés por la materia, su textura y el efecto emocional que emana. Las proporciones y dimensiones del edificio están reguladas por un módulo, que se ajusta a la medida del hombre, destacando la gran unidad del edificio. La llave se su efecto estético está en su armonía y equilibrio, que transmiten serenidad y belleza. El encuentro con la naturaleza es la lección más básica del proyecto, donde un mundo de relaciones es amable al ser humano. El capítulo cuarto, analiza el proyecto del Museo Louisiana de 1958, en Humlebæk, primer proyecto de la pareja de arquitectos daneses Jørgen Bo y Vilhelm Wohlert. La experiencia en California de Wohlert donde será visitado por Bo, será trascendental para el desarrollo de Louisiana, donde la identidad Danesa se fusiona con la asimilación de otras culturas, la arquitectura de Frank Lloyd Wright, la del área de la Bahía y la Tradición Japonesa principalmente. La idea del proyecto es la de una obra de arte integral: arquitectura, arte y paisaje, coexistirían en un mismo lugar. Diferentes recursos realzarán su carácter residencial, como el uso de los materiales propios de un entorno doméstico, la realización a la escala del hombre, el modo de usar la iluminación. Cubiertas planas que muestran su artificialidad, parecen flotar sobre galerías acristaladas, acentuarán la fuerza del plano horizontal y establecerán un recorrido en zig-zag de marcado ritmo acompasado. Ritmo que tiene que ver con la encarnación del pulso de la naturaleza, que se acompaña de juegos de luz, y de otras vibraciones materiales a diferentes escalas, imagen, que encuentra una analogía semejante en la cultura japonesa. Todo se coordina con la trama estructural, que conlleva a una construcción y proporción disciplinada. Louisiana atiende al principio de crecimiento de la naturaleza, con la que su conexión es profunda. Hay un dinamismo expresado por el despliegue del edificio, que evoca a algunos proyectos de la Tradición Japonesa. Los blancos muros tienen su propia identidad como formas en sí mismas, avanzan prolongándose fuera de la línea del vidrio, se mueven libremente siguiendo el orden estructural, acompañando al espacio que fluye, en contacto directo con la naturaleza que está en un continuo estado de flujos. Se da todo un mundo de relaciones, donde existe un dialogo entre el paisaje, arte y arquitectura. El capítulo quinto, se dedica a analizar la segunda casa del arquitecto danés Halldor Gunnløgsson, de 1959. Evoca a la Arquitectura Japonesa y Americana, pero es principalmente resultado de una fuerte voluntad y disciplina artística personal. La cubierta, plana, suspendida sobre una gran plataforma pavimentada, que continúa la sección del terreno construyendo de lugar, tiene una gran presencia y arroja una profunda sombra bajo ella. En el interior un espacio único, que se puede dividir eventualmente, discurre en torno a un cuerpo central. El espacio libre fluye, extendiéndose a través de la transparencia de sus ventanales a dos espacios contrapuestos: un patio ajardinado íntimo, que inspira calma y sosiego; y la naturaleza salvaje del mar que proyecta el color del cielo, ambos en constante estado de cambio. El proyecto se elabora de un modo rigurosamente formal, existiendo al mismo tiempo un perfecto equilibrio entre la abstracción de su estructura y su programa. La estructura de madera cuyo orden se extiende más allá de los límites de su perímetro, está formada por pórticos completos como elementos libres, queda expuesta, guardando una estrecha relación con el concepto de modernidad de Mies, equivalente a la arquitectura clásica. La preocupación por el efecto estético es máxima, nada es improvisado. Pero además la combinación de materiales y el juego de las texturas hay una cualidad táctil, cierto erotismo, que flota alrededor de ella. La precisión constructiva y su refinamiento se acercan a Mies. La experiencia del espacio arquitectónico es una vivencia global. La influencia de la arquitectura japonesa, es más conceptual que formal, revelada en un respeto por la naturaleza, la búsqueda del refinamiento a través de la moderación, la eliminación de los objetos innecesarios que distraen de la experiencia del lugar y la preocupación por la luz y la sombra, donde se establece cierto paralelismo con el oscuro mundo del invierno nórdico. Hay un entendimiento de que el espacio, en lugar de ser un objeto inmaterial definido por superficies materiales se entiende como interacciones dinámicas. El capítulo sexto. Propone un viaje para conocer algunas de las viviendas unifamiliares más interesantes que se construyeron en el periodo, que forman parte del sistema investigado. Del estudio comparado y orientado en varios temas, se obtienen diversa conclusiones propias del sistema estudiado. La maestría de la sustancia y la forma será una característica distintiva en Dinamarca, se demuestra que hay un acercamiento a la cultura de Oriente, conceptual y formal, y unos intereses comunes con cierta arquitectura Americana. Su lección nos sensibiliza hacia un sentido fortalecido de proporción, escala, materialidad, textura y peso, densidad del espacio, se valora lo táctil y lo visual, hay una sensibilidad hacia la naturaleza, hacia lo humano, hacia el paisaje, la integridad de la obra. ABSTRACT The thesis “1950 around the Louisiana Museum 1970” analyses several works related to domestic space, which were carried out between 1950 and 1970 in Denmark, a golden age of modern architecture. After the isolation and limitations brought about by the war that blighted Europe, young Danish architects were keen to experiment with ideas of an international origin, encouraged by different circumstances. They find the best field of rehearsal to be the domestic space. The best architecture of that period in Denmark should be understood as a system composed of different authors, who have in common with each other many more similarities than differences, thus complimenting each other. In the interests of understanding, the study of a range of figures and buildings is necessary so that this system, the research of which is still in its infancy, can be completed. The thesis proposes a journey of discovery through the names of some of those protagonists who were showcased through their work so that tradition and avant- garde could go hand in hand. The objective is to unveil the keys to Danish Modernity; to recognise, discover and revive the legacy of some of its protagonists in the domestic field whose lessons are seen as entirely of the present. For an architect, the taking on of modern contributions with both moderation and caution, with its intimate relationship with architectural tradition and its own craft, will be one of his hallmarks. With the study set against several projects and versions, one can derive common values among their authors. In the same way their affinities and differences in respect of the same issue emerge. This will allow an understanding of their measures in line with references and influences and enable the defining of the variables of their architectural spaces. The common line between the buildings selected will be their particular relationship with nature and the space with which they integrate. The façade, the place where the relationship between the interior and the landscape would be negotiated, wouldl be the discriminating element in a distinct way for each one of them. It is through each of these facades that this relationship would extend, and far beyond their physical perimeter. The investigation has been structured into six chapters, preceded by an introduction. The first chapter outlines and analyses the backgrounds, figures and buildings most relevant to the Danish Tradition. This is to facilitate the understanding and elucidation of some of the keys to its modernity in the field of architecture, which came about with the clear intention to discover its own identity and expression. This thriving modernity is characterized by its moderate assimilation with foreign cultures with a critical eye, and finds its roots anchored in architectural tradition and its own handcraft. It is forged in the emergence of a common ideal of enormous personality which today has come to be valued as an authentic contribution to the sphere from a culture that was formerly seen as on the peripheries. What will be demonstrated is the path taken by previous generations to these works and the debate that surrounds them. The sensibilities for both the vernacular and the classic, which at first glance may seem contradictory, will dominate the debate with the same veracity and respectability. The so-called third generation of Sigfried Giedion will revive the process between the classic and the vernacular, supported in spirit by the handcraft work and by tradition, with the objective of discovering the “truth” and the “original essence” of the architectural act. The second chapter analyzes the Varming house, built by Eva and Nils Koppel 1953, which is situated in a residential area of Gentofte. This reinterprets Asplund’s vision of an interior landscape extending to the exterior, where we see a break with the conventional sturdy brick shell of the 1930s. It is the most powerful example of the union of tradition and innovation in his their residential work. Their sober forms caught between Danish Functionalism and modernity are characterized by their abstraction and clean shapes which accentuate their prismatic and brutal geometry, The displacement of the parts of which they are composed, one over the other, generate a rhythm. This is produced to varying scales and is closely linked to its forms and the selection of materials – brick and wood – that confer an organic character to the house. The building is anchored to the earth, finding solution at different levels through the study of place and topography. The result is an adaption constructed out of the landscape, in which the building gives form to the place and celebrates the experience of the natural setting. The unity of primitive structures appears to be present. It constitutes an example of “Asplund’s Promenade Idea”. Different routes of exploration within are available to the visitor, allowing for one’s own personal experience of the house, allowing in turn for the vital chance to decide. The third chapter deals with Niels Bohr’s guest pavilion. Built in 1957, it is situated in a wooded area of Tisvilde Hegn and was the architect Vilhelm Wohlert’s first building. Rooted in the Danish Tradition, it represents a renewal based on the absorption of foreign influences: American architecture and the Japanese tradition. The wooden box, perched atop a horizontal terrain, possesses the sensitive character of the living organism, ever-changing in accordance with the variations in daylight and temperature. When opened up, it creates an elongation of the interior space which extends into the surrounding nature and it expands towards the exterior space, allowing for its mobilisation. It establishes an architecture of flux. There is interest in the material, its texture and the emotional effect it inspires. The building’s proportions and dimensions are regulated by a module, which is adjusted by hand, bringing out the great unity of the building. The key to its aesthetic effect is its harmony and equilibrium, which convey serenity and beauty. The meeting with nature is the most fundamental lesson of the project, where a world of relationships softens the personality of the human being. The fourth chapter analyzes the Louisiana Museum project of 1958 in 1958. It was the first project of the Danish architects Jørgen Bo and Vilhelm Wohlert. Wohlert’s experience in California where he was visited by Bo would be essential to the development of Louisiana, where the Danish identity is fused in assimilation with other cultures, the architecture of Frank Lloyd Wright, that of the Bahía area and principally the Japanese tradition. The idea of the project was for an integrated work of art: architecture, art and landscape, which would coexist in the same space. A range of different resources would realize the residential character, such as the use of materials taken from a domestic environment, the attainment of human scale and the manner in which light was used. Flat roof plans that show their artificiality and appear to float over glassed galleries. They accentuate the strength of the horizontal plan and establish a zigzag route of marked and measured rhythm. It is a rhythm that has to do with the incarnation of nature’s pulse, which is accompanied with plays of light, as well as material vibrations of different scales, imagery which uncovers a parallel analogy with Japanese culture. Everything is coordinated along a structural frame, which involves a disciplined construction and proportion. Louisiana cherishes nature’s principle of growth, to which its connection is profound. Here is a dynamism expressed through the disposition of the building, which evokes in some projects the Japanese tradition. The white walls possess their own identity as forms in their own right. They advance, extending beyond the line of glass, moving freely along the structural line, accompanying a space that flows and in direct contact with nature that is itself in a constant state of flux. It creates a world of relationships, where dialogue exists between the landscape, art and architecture. The fifth chapter is dedicated to analyzing the Danish architect Halldor Gunnløgsson’s second house, built in 1959. It evokes both Japanese and American architecture but is principally the result of a strong will and personal artistic discipline. The flat roof suspended above a large paved platform – itself continuing the constructed terrain of the place – has great presence and casts a heavy shadow beneath. In the interior, a single space, which can at length be divided and which flows around a central space. The space flows freely, extending through the transparency of its windows which give out onto two contrasting locations: an intimate garden patio, inspiring calm and tranquillity, and the wild nature of the sea which projects the colour of sky, both in a constant state of change. The project is realized in a rigorously formal manner. A perfect balance exists between the abstraction of his structure and his project. The wooden structure, whose order extends beyond the limits of its perimeter, is formed of complete porticos of free elements. It remains exposed, maintaining a close relationship with Mies’ concept of modernity, analogous to classical architecture. The preoccupation with the aesthetic effect is paramount and nothing is improvised. But in addition to this - the combination of materials and the play of textures - there is a tactile quality, a certain eroticism, which lingers all about. The constructive precision and its refinement are close to Mies. The experience of the architectural space is universal. The influence of Japanese architecture, more conceptual than formal, is revealed in a respect for nature. It can be seen in the search for refinement through moderation, the elimination of the superfluous object that distract from the experience of place and the preoccupation with light and shade, where a certain parallel with the dark world of the Nordic winter is established. There is an understanding that space, rather than being an immaterial object defined by material surfaces, extends instead as dynamic interactions. The sixth chapter. This proposes a journey to discover some of the unfamiliar residences of most interest which were constructed in the period, and which form part of the system being investigated. Through the study of comparison and one which is geared towards various themes, diverse conclusions are drawn regarding the system being researched. The expertise in substance and form will be a distinctive characteristic in Denmark, demonstrating an approach to the culture of the Orient, both conceptual and formal, and some common interests in certain American architecture. Its teachings sensitize us to a strengthened sense of proportion, scale, materiality, texture and weight and density of space. It values both the tactile and the visual. There is a sensitivity to nature, to the human, to the landscape and to the integrity of the work.

Working to Form a More Perfect Union: Honoring Women in Public Service in the State of Missouri

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Working to Form a More Perfect Union: Honoring Women in Public Service in the State of Missouri

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Equilibrium distributions of topological states in circular DNA: Interplay of supercoiling and knotting

Two variables define the topological state of closed double-stranded DNA: the knot type, K, and ΔLk, the linking number difference from relaxed DNA. The equilibrium distribution of probabilities of these states, P(ΔLk, K), is related to two conditional distributions: P(ΔLk|K), the distribution of ΔLk for a particular K, and P(K|ΔLk) and also to two simple distributions: P(ΔLk), the distribution of ΔLk irrespective of K, and P(K). We explored the relationships between these distributions. P(ΔLk, K), P(ΔLk), and P(K|ΔLk) were calculated from the simulated distributions of P(ΔLk|K) and of P(K). The calculated distributions agreed with previous experimental and theoretical results and greatly advanced on them. Our major focus was on P(K|ΔLk), the distribution of knot types for a particular value of ΔLk, which had not been evaluated previously. We found that unknotted circular DNA is not the most probable state beyond small values of ΔLk. Highly chiral knotted DNA has a lower free energy because it has less torsional deformation. Surprisingly, even at |ΔLk| > 12, only one or two knot types dominate the P(K|ΔLk) distribution despite the huge number of knots of comparable complexity. A large fraction of the knots found belong to the small family of torus knots. The relationship between supercoiling and knotting in vivo is discussed.

Equilibrium constants and free energies in unfolding of proteins in urea solutions

A novel thermodynamic approach to the reversible unfolding of proteins in aqueous urea solutions has been developed based on the premise that urea ligands are bound cooperatively to the macromolecule. When successive stoichiometric binding constants have values larger than expected from statistical effects, an equation for moles of bound urea can be derived that contains imaginary terms. For a very steep unfolding curve, one can then show that the fraction of protein unfolded, B̄, depends on the square of the urea concentration, U, and is given by \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \setlength{\oddsidemargin}{-69pt} \begin{document} \begin{equation*}\bar {B}=\frac{{\mathit{A}}^{{\mathit{2}}}_{{\mathit{1}}}{\mathit{e}}^{{\mathrm{{\lambda}}}n\bar {B}}{\mathit{U}}^{{\mathit{2}}}}{{\mathrm{1\hspace{.167em}+\hspace{.167em}}}{\mathit{A}}^{{\mathrm{2}}}_{{\mathrm{1}}}{\mathit{e}}^{{\mathrm{{\lambda}}}\bar {B}}{\mathit{U}}^{{\mathrm{2}}}}{\mathrm{.}}\end{equation*}\end{document} A12 is the binding constant as B̄→ 0, and λ is a parameter that reflects the augmentation in affinities of protein for urea as the moles bound increases to the saturation number, n. This equation provides an analytic expression that reproduces the unfolding curve with good precision, suggests a simple linear graphical procedure for evaluating A12 and λ, and leads to the appropriate standard free energy changes. The calculated ΔG° values reflect the coupling of urea binding with unfolding of the protein. Some possible implications of this analysis to protein folding in vivo are described.

Kinetic equilibrium of forces and molecular events in muscle contraction

In biomolecular systems, the mechanical transfer of free energy occurs with both high efficiency and high speed. It is shown here that such a transfer can be achieved only if the participating free-energy-storing elements exhibit opposing relationships between their content of free energy and the force they exert in the transfer direction. A kinetic equilibrium of forces (KEF) results, in which the transfer of free energy is mediated essentially by thermal molecular motion. On the basis of present evidence, KEF is used as a guiding principle in developing a mechanical model of the crossbridge cycle in muscle contraction. The model allows the basic features of molecular events to be visualized in terms of plausible structures. Real understanding of the process will require identification of the elements that perform the functions described here. Besides chemomechanical energy transduction, KEF may have a role in other biomolecular processes in which free energy is transferred mechanically over large distances.