High-precision confocal reflection measurement for two dimensional refractive index mapping of optical fibers

We introduce a new fiber-optical approach for reflection based refractive index mapping. Our approach leads to improved stability and reliability over existing free-space confocal instruments and significantly cuts alignment efforts and reduces the number of components needed. Other than properly cleaved fiber end-faces, this setup requires no additional sample preparation. The instrument is calibrated by means of a set of samples with known refractive indices. The index steps of commercially available fibers are measured accurately down to < 10⁻³. The precision limit of the instrument is currently of the order of 10⁻⁴.

Space requirement of a prefabricated bar on two interforaminal implants: a prospective clinical study

OBJECTIVES This clinical study measured the dimensional changes of existing lower complete dentures due to the integration of a prefabricated implant bar. Additionally, the impact of this dimensional change on patient satisfaction and oral function was analyzed. METHODS Twenty edentulous patients (10 men/10 women; aged 65.9 ± 11.8 years) received two interforaminal implants. Subsequent to surgery, a chair side adapted, prefabricated bar (SFI Bar(®), C+M, Biel, Switzerland) was inserted, and the matrix was polymerized into the existing lower denture. The change of the denture's lingual dimension was recorded by means of a bicolored, silicone denture duplicate that was sectioned in the oro-vestibular direction in the regions of the symphysis (S) and the implants (I-left, I-right). On the sections, the dimensional increase was measured using a light microscope. Six months after bar insertion, patients answered a standardized questionnaire. RESULTS All dentures exhibited increased lingual volume, more extensively at S than at I (P = 0.001). At S, the median diagonal size of the denture was doubled (+4.33 mm), and at I, the median increase was 50% (I-left/-right = +2.66/+2.62 mm). The original denture size influenced the volume increase (P = 0.024): smaller dentures led to a larger increase. The amount of denture increase did not have negative impact on either self-perceived oral function or patient satisfaction. Approximately, 95% of the patients were satisfied with the treatment results. CONCLUSIONS The lingual size of a lower denture was enlarged by the integration of a prefabricated bar without any negative side effects. Thus, this attachment system is suitable to convert an existing full denture into an implant-supported overdenture.

On the Closure of the Tame Automorphism Group of Affine Three-Space

We provide explicit families of tame automorphisms of the complex affine three-space which degenerate to wild automorphisms. This shows that the tame subgroup of the group of polynomial automorphisms of C3 is not closed, when the latter is seen as an infinite-dimensional algebraic group.

Multifractal analysis of the pore- and solid-phases in binary two-dimensional images of natural porous structures

We use multifractal analysis (MFA) to investigate how the Rényi dimensions of the solid mass and the pore space in porous structures are related to each other. To our knowledge, there is no investigation about the relationship of Rényi or generalized dimensions of two phases of the same structure.

Self-similar motion of laser half-space plasmas. I. Deflagration regime

The one-dimensional self-similar motion of an initially cold, half-space plasma of electron density 0,produced by the (anomalous) absorption of a laser pulse of irradiation = (j>0f/T(0< (< T) at the critical density nc(«c/«0=eoKe)213, where k, m, are Boltzmann's constant and the ion mass, and Ke X (electron temperature)5'2 = heat conductivity. If a >e- 4 ' 3 , a deflagration wave separates an isentropic compression with a shock bounding the undisturbed plasma, and an isentropic expansion flow to the vacuum. The structures of these three regions are completely determined; in particular, the Chapman-Jouguet condition is proved and the density behind the deflagration is found. The deflagration-compression thickness ratio is large (small) for a^e- 5 ' 3(a>e- 5 ' 3 ) . The compression to expansion ratio for both energy and thickness is 0(e"2). For Z,- large, a deflagration exists even if a~e~413. Condition a>e~4'3 may be applied to pulses that are not linear.

Self-similar motion of laser half-space plasmas. II. Thermal waves and intermediate regimes

The one-dimensional self-similar motion of an initially cold, half-space plasma of electron density n,produced by the (anomalous) absorption of a laser pulse of irradiation

€~4'3, a qualitative discussion of how plasma behavior changes with a, is given.

Analysis of Magnetic Nozzles For Space Plasma Thrusters = Análisis de Toberas Magnéticas para Motores Espaciales de Plasma

Esta tesis presenta un análisis teórico del funcionamiento de toberas magnéticas para la propulsión espacial por plasmas. El estudio está basado en un modelo tridimensional y bi-fluido de la expansión supersónica de un plasma caliente en un campo magnético divergente. El modelo básico es ampliado progresivamente con la inclusión de términos convectivos dominantes de electrones, el campo magnético inducido por el plasma, poblaciones electrónicas múltiples a distintas temperaturas, y la capacidad de integrar el flujo en la región de expansión lejana. La respuesta hiperbólica del plasma es integrada con alta precisión y eficiencia haciendo uso del método de las líneas características. Se realiza una caracterización paramétrica de la expansión 2D del plasma en términos del grado de magnetización de iones, la geometría del campo magnético, y el perfil inicial del plasma. Se investigan los mecanismos de aceleración, mostrando que el campo ambipolar convierte la energía interna de electrones en energía dirigida de iones. Las corrientes diamagnéticas de Hall, que pueden hallarse distribuidas en el volumen del plasma o localizadas en una delgada capa de corriente en el borde del chorro, son esenciales para la operación de la tobera, ya que la fuerza magnética repulsiva sobre ellas es la encargada de confinar radialmente y acelerar axialmente el plasma. El empuje magnético es la reacción a esta fuerza sobre el motor. La respuesta del plasma muestra la separación gradual hacia adentro de los tubos de iones respecto de los magnéticos, lo cual produce la formación de corrientes eléctricas longitudinales y pone el plasma en rotación. La ganancia de empuje obtenida y las pérdidas radiales de la pluma de plasma se evalúan en función de los parámetros de diseño. Se analiza en detalle la separación magnética del plasma aguas abajo respecto a las líneas magnéticas (cerradas sobre sí mismas), necesaria para la aplicación de la tobera magnética a fines propulsivos. Se demuestra que tres teorías existentes sobre separación, que se fundamentan en la resistividad del plasma, la inercia de electrones, y el campo magnético que induce el plasma, son inadecuadas para la tobera magnética propulsiva, ya que producen separación hacia afuera en lugar de hacia adentro, aumentando la divergencia de la pluma. En su lugar, se muestra que la separación del plasma tiene lugar gracias a la inercia de iones y la desmagnetización gradual del plasma que tiene lugar aguas abajo, que permiten la separación ilimitada del flujo de iones respecto a las líneas de campo en condiciones muy generales. Se evalúa la cantidad de plasma que permanece unida al campo magnético y retorna hacia el motor a lo largo de las líneas cerradas de campo, mostrando que es marginal. Se muestra cómo el campo magnético inducido por el plasma incrementa la divergencia de la tobera magnética y por ende de la pluma de plasma en el caso propulsivo, contrariamente a las predicciones existentes. Se muestra también cómo el inducido favorece la desmagnetización del núcleo del chorro, acelerando la separación magnética. La hipótesis de ambipolaridad de corriente local, común a varios modelos de tobera magnética existentes, es discutida críticamente, mostrando que es inadecuada para el estudio de la separación de plasma. Una inconsistencia grave en la derivación matemática de uno de los modelos más aceptados es señalada y comentada. Incluyendo una especie adicional de electrones supratérmicos en el modelo, se estudia la formación y geometría de dobles capas eléctricas en el interior del plasma. Cuando dicha capa se forma, su curvatura aumenta cuanto más periféricamente se inyecten los electrones supratérmicos, cuanto menor sea el campo magnético, y cuanto más divergente sea la tobera magnética. El plasma con dos temperaturas electrónicas posee un mayor ratio de empuje magnético frente a total. A pesar de ello, no se encuentra ninguna ventaja propulsiva de las dobles capas, reforzando las críticas existentes frente a las propuestas de estas formaciones como un mecanismo de empuje. Por último, se presenta una formulación general de modelos autosemejantes de la expansión 2D de una pluma no magnetizada en el vacío. El error asociado a la hipótesis de autosemejanza es calculado, mostrando que es pequeño para plumas hipersónicas. Tres modelos de la literatura son particularizados a partir de la formulación general y comparados. Abstract This Thesis presents a theoretical analysis of the operation of magnetic nozzles for plasma space propulsion. The study is based on a two-dimensional, two-fluid model of the supersonic expansion of a hot plasma in a divergent magnetic field. The basic model is extended progressively to include the dominant electron convective terms, the plasma-induced magnetic field, multi-temperature electron populations, and the capability to integrate the plasma flow in the far expansion region. The hyperbolic plasma response is integrated accurately and efficiently with the method of the characteristic lines. The 2D plasma expansion is characterized parametrically in terms of the ion magnetization strength, the magnetic field geometry, and the initial plasma profile. Acceleration mechanisms are investigated, showing that the ambipolar electric field converts the internal electron energy into directed ion energy. The diamagnetic electron Hall current, which can be distributed in the plasma volume or localized in a thin current sheet at the jet edge, is shown to be central for the operation of the magnetic nozzle. The repelling magnetic force on this current is responsible for the radial confinement and axial acceleration of the plasma, and magnetic thrust is the reaction to this force on the magnetic coils of the thruster. The plasma response exhibits a gradual inward separation of the ion streamtubes from the magnetic streamtubes, which focuses the jet about the nozzle axis, gives rise to the formation of longitudinal currents and sets the plasma into rotation. The obtained thrust gain in the magnetic nozzle and radial plasma losses are evaluated as a function of the design parameters. The downstream plasma detachment from the closed magnetic field lines, required for the propulsive application of the magnetic nozzle, is investigated in detail. Three prevailing detachment theories for magnetic nozzles, relying on plasma resistivity, electron inertia, and the plasma-induced magnetic field, are shown to be inadequate for the propulsive magnetic nozzle, as these mechanisms detach the plume outward, increasing its divergence, rather than focusing it as desired. Instead, plasma detachment is shown to occur essentially due to ion inertia and the gradual demagnetization that takes place downstream, which enable the unbounded inward ion separation from the magnetic lines beyond the turning point of the outermost plasma streamline under rather general conditions. The plasma fraction that remains attached to the field and turns around along the magnetic field back to the thruster is evaluated and shown to be marginal. The plasmainduced magnetic field is shown to increase the divergence of the nozzle and the resulting plasma plume in the propulsive case, and to enhance the demagnetization of the central part of the plasma jet, contrary to existing predictions. The increased demagnetization favors the earlier ion inward separation from the magnetic field. The local current ambipolarity assumption, common to many existing magnetic nozzle models, is critically discussed, showing that it is unsuitable for the study of plasma detachment. A grave mathematical inconsistency in a well-accepted model, related to the acceptance of this assumption, is found out and commented on. The formation and 2D shape of electric double layers in the plasma expansion is studied with the inclusion of an additional suprathermal electron population in the model. When a double layer forms, its curvature is shown to increase the more peripherally suprathermal electrons are injected, the lower the magnetic field strength, and the more divergent the magnetic nozzle is. The twoelectron- temperature plasma is seen to have a greater magnetic-to-total thrust ratio. Notwithstanding, no propulsive advantage of the double layer is found, supporting and reinforcing previous critiques to their proposal as a thrust mechanism. Finally, a general framework of self-similar models of a 2D unmagnetized plasma plume expansion into vacuum is presented and discussed. The error associated with the self-similarity assumption is calculated and shown to be small for hypersonic plasma plumes. Three models of the literature are recovered as particularizations from the general framework and compared.

Entire functions uniformly bounded on balls of a Banach space

Let X be an in�finite-dimensional complex Banach space. Very recently, several results on the existence of entire functions on X bounded on a given ball B1 � X and unbounded on another given ball B2 � X have been obtained. In this paper we consider the problem of �finding entire functions which are uniformly bounded on a collection of balls and unbounded on the balls of some other collection. RESUMEN. Sea X un espacio de Banach complejo de dimensión infinita. En este trabajo, los autores estudian el problema de encontrar una función entera en X que esté uniformemente acotada en una colección de de bolas en X y que no esté acotada en las bolas de otra colección.

A method for revealing phase space structures of general time dependent dynamical systems

In this paper we develop new techniques for revealing geometrical structures in phase space that are valid for aperiodically time dependent dynamical systems, which we refer to as Lagrangian descriptors. These quantities are based on the integration, for a finite time, along trajectories of an intrinsic bounded, positive geometrical and/or physical property of the trajectory itself. We discuss a general methodology for constructing Lagrangian descriptors, and we discuss a “heuristic argument” that explains why this method is successful for revealing geometrical structures in the phase space of a dynamical system. We support this argument by explicit calculations on a benchmark problem having a hyperbolic fixed point with stable and unstable manifolds that are known analytically. Several other benchmark examples are considered that allow us the assess the performance of Lagrangian descriptors in revealing invariant tori and regions of shear. Throughout the paper “side-by-side” comparisons of the performance of Lagrangian descriptors with both finite time Lyapunov exponents (FTLEs) and finite time averages of certain components of the vector field (“time averages”) are carried out and discussed. In all cases Lagrangian descriptors are shown to be both more accurate and computationally efficient than these methods. We also perform computations for an explicitly three dimensional, aperiodically time-dependent vector field and an aperiodically time dependent vector field defined as a data set. Comparisons with FTLEs and time averages for these examples are also carried out, with similar conclusions as for the benchmark examples.

Morphological Functions to Quantify Three-Dimensional Tomograms of Macropore Structure in a Vineyard Soil with Two Different Management Regimes

Soil tomography and morphological functions built over Minkowski functionals were used to describe the impact on pore structure of two soil management practices in a Mediterranean vineyard. Soil structure controls important physical and biological processes in soil–plant–microbial systems. Those processes are dominated by the geometry of soil pore structure, and a correct model of this geometry is critical for understanding them. Soil tomography has been shown to provide rich three-dimensional digital information on soil pore geometry. Recently, mathematical morphological techniques have been proposed as powerful tools to analyze and quantify the geometrical features of porous media. Minkowski functionals and morphological functions built over Minkowski functionals provide computationally efficient means to measure four fundamental geometrical features of three-dimensional geometrical objects, that is, volume, boundary surface, mean boundary surface curvature, and connectivity. We used the threshold and the dilation and erosion of three-dimensional images to generate morphological functions and explore the evolution of Minkowski functionals as the threshold and as the degree of dilation and erosion changes. We analyzed the three-dimensional geometry of soil pore space with X-ray computed tomography (CT) of intact soil columns from a Spanish Mediterranean vineyard by using two different management practices (conventional tillage versus permanent cover crop of resident vegetation). Our results suggested that morphological functions built over Minkowski functionals provide promising tools to characterize soil macropore structure and that the evolution of morphological features with dilation and erosion is more informative as an indicator of structure than moving threshold for both soil managements studied.

Three-dimensional distribution of cortical synapses: a replicated point pattern-based analysis

The biggest problem when analyzing the brain is that its synaptic connections are extremely complex. Generally, the billions of neurons making up the brain exchange information through two types of highly specialized structures: chemical synapses (the vast majority) and so-called gap junctions (a substrate of one class of electrical synapse). Here we are interested in exploring the three-dimensional spatial distribution of chemical synapses in the cerebral cortex. Recent research has showed that the three-dimensional spatial distribution of synapses in layer III of the neocortex can be modeled by a random sequential adsorption (RSA) point process, i.e., synapses are distributed in space almost randomly, with the only constraint that they cannot overlap. In this study we hypothesize that RSA processes can also explain the distribution of synapses in all cortical layers. We also investigate whether there are differences in both the synaptic density and spatial distribution of synapses between layers. Using combined focused ion beam milling and scanning electron microscopy (FIB/SEM), we obtained three-dimensional samples from the six layers of the rat somatosensory cortex and identified and reconstructed the synaptic junctions. A total volume of tissue of approximately 4500μm3 and around 4000 synapses from three different animals were analyzed. Different samples, layers and/or animals were aggregated and compared using RSA replicated spatial point processes. The results showed no significant differences in the synaptic distribution across the different rats used in the study. We found that RSA processes described the spatial distribution of synapses in all samples of each layer. We also found that the synaptic distribution in layers II to VI conforms to a common underlying RSA process with different densities per layer. Interestingly, the results showed that synapses in layer I had a slightly different spatial distribution from the other layers.

Three-dimensional spatial distribution of synapses in the neocortex: A dual-beam electron microscopy study

In the cerebral cortex, most synapses are found in the neuropil, but relatively little is known about their 3-dimensional organization. Using an automated dual-beam electron microscope that combines focused ion beam milling and scanning electron microscopy, we have been able to obtain 10 three-dimensional samples with an average volume of 180 µm(3) from the neuropil of layer III of the young rat somatosensory cortex (hindlimb representation). We have used specific software tools to fully reconstruct 1695 synaptic junctions present in these samples and to accurately quantify the number of synapses per unit volume. These tools also allowed us to determine synapse position and to analyze their spatial distribution using spatial statistical methods. Our results indicate that the distribution of synaptic junctions in the neuropil is nearly random, only constrained by the fact that synapses cannot overlap in space. A theoretical model based on random sequential absorption, which closely reproduces the actual distribution of synapses, is also presented.

Análisis Constructivo y Dimensional de las Fachadas de la Gran Vía madrileña en el primer tramo de la calle

Esta investigación analiza la solución constructiva y dimensional de las fachadas del primer tramo de la Gran Vía madrileña y señala, entre otros aspectos, la aportación que supuso en el Sector de la Construcción español, la incorporación de perfilería metálica a la fábrica en los edificios del primer tramo de la calle, constituyendo el punto de partida del construir moderno del Madrid de principios del Siglo XX. Se han analizado sistemas y modulaciones que sintetizan, en un catálogo de fichas el modo constructivo de los primeros lustros del SXX. La metodología se ha centrado en el diseño de las fichas que describo a continuación: • Ficha de Histórica de datos generales (hitos históricos), esta ficha resume la historia de la construcción del edificio, indicando usos tanto originales como actuales, propiedad, fecha de construcción, e intervenciones constatadas. Especial significado para el desarrollo del trabajo tiene la definición de usos tanto originales como actuales. El uso del edificio se ha interpretado como la función. • Ficha dimensional, muestra medidas tanto en el eje X como en el Y, o en Z, en concreto intereje de huecos, medidas de entrepaños, ancho de huecos; medidas de suelo a suelo, medida del hueco más dintel; medidas de vuelos de balcones y/o miradores, y otros parámetros como porcentaje de huecos en fachada, frecuencia de aparición de los distintos huecos, su proporción alto ancho; parámetros que definen dimensionalmente los elementos que constituyen la fachada del edificio. Esta Ficha se acompaña del alzado de cada edificio acotado y de una fotografía actual. • Ficha de elementos y sistemas constructivos, en función del soporte (composición) y/o del material de acabado recogen datos obtenidos de la documentación gráfica y memorias existente en el archivo histórico y/o de documentación gráfica realizada por arquitectos que han intervenido en estos edificios. Tanto el contacto establecido con los arquitectos intervinientes, propietarios y empresas constructoras, como la localización de manuales de construcción fechados entre 1870 y 1925, han ayudado a definir a través de este catálogo de Fichas, los tipos (sistemas) constructivos y las modulaciones empleadas, una métrica que define con matemáticas la geometría del diseño, expresando además toda la carga de magia, encantamiento y siempre de modelo y orden que permanece en las fachadas de estos edificios. El desarrollo de estas técnicas denominadas en 1915 modernas han supuesto un cambio importante en el diseño, pues éste es un hecho diferencial en esta arquitectura con estructura metálica con respecto a los sistemas constructivos anteriores, permitiendo reducir el espesor del muro, y conseguir luces superiores tanto en huecos como en los vuelos de elementos salientes (balcones y miradores ) y consiguiendo un diseño acorde con la importancia del edificio. Una vez analizado el uso del edificio, sus dimensiones y los sistemas empleados, (siempre referidos al estudio de fachadas), se ha podido comprobar la relación entre Dimensión, Sistema y Función y los casos concretos en que esto sucede. La inspección visual y seguimiento de la calle han constatado la frecuencia de las labores de mantenimiento, reparación, o restauración en las fachadas de estos edificios. Estos conocimientos serán importantes de cara a intervenciones posteriores en el tiempo, quizá en los próximos 100 años. ABSTRACT Innovative techniques used in Spanish construction (for houses and buildings) emerged at the beginning of the 20th century. Reinforced steel profiles instead of traditional masonry was one of the most important innovations that was introduced. In order to make the most of the space available, masonry had to be as light as possible. This paper will examine the façades of these first buildings in “Gran Vía” Street and aims to show how they were constructed. Field work was carried out in order to analyze both the history of how the buildings were constructed and the construction and dimensional systems of the façade elements. Comprehending these building techniques and characteristics is the purpose of this Investigation. Some data sheets (cards) have been designed for finding out about historical information, uses, modulations and construction systems, in order to determine the relation between the Function, Dimension and System in these buildings. • The historical card shows date of construction, uses, propertys not only the original ones but nowadays, interventions special interest keeps the use or finality of the building. • The dimensional card shows measurements not only of axis X but also Y and Z, specifically the centre distance of openings, measurements of stretches of walls, the width of openings; floor to floor measurements, measurement of windows plus lintels; balcony overhangs and / or bay windows, and other parameters such as the percentage of façade openings, the frequency of the appearance of different openings, their proportion regarding height and width; parameters that dimensionally define the elements that make the façade of the building. This Card accompanies of the elevation of every measured building plus a current photograph. • Card of elements and building systems, depending on the support (composition) and / or the finish material that compiles information obtained from the existing graphic documentation and reports from historic files and / or graphic documentation drawn up by architects who have intervened in these buildings. The visual inspection and follow-up of the street confirm the frequency of maintenance work, repairs, or restoration of the façades of these buildings. Comprehension of these techniques and characteristics will enable future intervention, maybe in the next century.

Tight frames of k-plane ridgelets and the problem of representing objects that are smooth away from d-dimensional singularities in Rn

For each pair (n, k) with 1 ≤ k < n, we construct a tight frame (ρλ : λ ∈ Λ) for L2 (Rn), which we call a frame of k-plane ridgelets. The intent is to efficiently represent functions that are smooth away from singularities along k-planes in Rn. We also develop tools to help decide whether k-plane ridgelets provide the desired efficient representation. We first construct a wavelet-like tight frame on the X-ray bundle χn,k—the fiber bundle having the Grassman manifold Gn,k of k-planes in Rn for base space, and for fibers the orthocomplements of those planes. This wavelet-like tight frame is the pushout to χn,k, via the smooth local coordinates of Gn,k, of an orthonormal basis of tensor Meyer wavelets on Euclidean space Rk(n−k) × Rn−k. We then use the X-ray isometry [Solmon, D. C. (1976) J. Math. Anal. Appl. 56, 61–83] to map this tight frame isometrically to a tight frame for L2(Rn)—the k-plane ridgelets. This construction makes analysis of a function f ∈ L2(Rn) by k-plane ridgelets identical to the analysis of the k-plane X-ray transform of f by an appropriate wavelet-like system for χn,k. As wavelets are typically effective at representing point singularities, it may be expected that these new systems will be effective at representing objects whose k-plane X-ray transform has a point singularity. Objects with discontinuities across hyperplanes are of this form, for k = n − 1.

Tissue engineering of cartilage in space

Tissue engineering of cartilage, i.e., the in vitro cultivation of cartilage cells on synthetic polymer scaffolds, was studied on the Mir Space Station and on Earth. Specifically, three-dimensional cell-polymer constructs consisting of bovine articular chondrocytes and polyglycolic acid scaffolds were grown in rotating bioreactors, first for 3 months on Earth and then for an additional 4 months on either Mir (10−4–10−6 g) or Earth (1 g). This mission provided a unique opportunity to study the feasibility of long-term cell culture flight experiments and to assess the effects of spaceflight on the growth and function of a model musculoskeletal tissue. Both environments yielded cartilaginous constructs, each weighing between 0.3 and 0.4 g and consisting of viable, differentiated cells that synthesized proteoglycan and type II collagen. Compared with the Earth group, Mir-grown constructs were more spherical, smaller, and mechanically inferior. The same bioreactor system can be used for a variety of controlled microgravity studies of cartilage and other tissues. These results may have implications for human spaceflight, e.g., a Mars mission, and clinical medicine, e.g., improved understanding of the effects of pseudo-weightlessness in prolonged immobilization, hydrotherapy, and intrauterine development.