Ergodicity and Mixing Rate of One-Dimensional Cellular Automata

One-and two-dimensional cellular automata which are known to be fault-tolerant are very complex. On the other hand, only very simple cellular automata have actually been proven to lack fault-tolerance, i.e., to be mixing. The latter either have large noise probability ε or belong to the small family of two-state nearest-neighbor monotonic rules which includes local majority voting. For a certain simple automaton L called the soldiers rule, this problem has intrigued researchers for the last two decades since L is clearly more robust than local voting: in the absence of noise, L eliminates any finite island of perturbation from an initial configuration of all 0's or all 1's. The same holds for a 4-state monotonic variant of L, K, called two-line voting. We will prove that the probabilistic cellular automata Kε and Lε asymptotically lose all information about their initial state when subject to small, strongly biased noise. The mixing property trivially implies that the systems are ergodic. The finite-time information-retaining quality of a mixing system can be represented by its relaxation time Relax(⋅), which measures the time before the onset of significant information loss. This is known to grow as (1/ε)^c for noisy local voting. The impressive error-correction ability of L has prompted some researchers to conjecture that Relax(Lε) = 2^(c/ε). We prove the tight bound 2^(c1log^21/ε) ＜ Relax(Lε) ＜ 2^(c2log^21/ε) for a biased error model. The same holds for Kε. Moreover, the lower bound is independent of the bias assumption. The strong bias assumption makes it possible to apply sparsity/renormalization techniques, the main tools of our investigation, used earlier in the opposite context of proving fault-tolerance.

Quasi-aplanatic free-form V-groove collimators for LED colour mixing

Two quasi-aplanatic free-form solid V-groove collimators are presented in this work. Both optical designs are originally designed using the Simultaneous Multiple Surface method in three dimensions (SMS 3D). The second optically active surface in both free-form V-groove devices is designed a posteriori as a grooved surface. First two mirror (XX) design is designed in order to clearly show the design procedure and working principle of these devices. Second, RXI free-form design is comparable with existing RXI collimators; it is a compact and highly efficient design made of polycarbonate (PC) performing very good colour mixing of the RGGB LED sources placed off-axis. There have been presented rotationally symmetric non-aplanatic high efficiency collimators with colour mixing property to be improved and rotationally symmetric aplanatic devices with good colour mixing property and efficiency to be improved. The aim of this work was to design a free-form device in order to improve colour mixing property of the rotationally symmetric nonaplanatic RXI devices and the efficiency of the aplanatic ones.

Modelling and Analysis of Some Time Series

The thesis deals with some of the non-linear Gaussian and non-Gaussian time models and mainly concentrated in studying the properties and application of a first order autoregressive process with Cauchy marginal distribution. In this thesis some of the non-linear Gaussian and non-Gaussian time series models and mainly concentrated in studying the properties and application of a order autoregressive process with Cauchy marginal distribution. Time series relating to prices, consumptions, money in circulation, bank deposits and bank clearing, sales and profit in a departmental store, national income and foreign exchange reserves, prices and dividend of shares in a stock exchange etc. are examples of economic and business time series. The thesis discuses the application of a threshold autoregressive(TAR) model, try to fit this model to a time series data. Another important non-linear model is the ARCH model, and the third model is the TARCH model. The main objective here is to identify an appropriate model to a given set of data. The data considered are the daily coconut oil prices for a period of three years. Since it is a price data the consecutive prices may not be independent and hence a time series based model is more appropriate. In this study the properties like ergodicity, mixing property and time reversibility and also various estimation procedures used to estimate the unknown parameters of the process.

A family of autoregressive conditional duration models

This paper develops a family of autoregressive conditional duration (ACD) models that encompasses most specifications in the literature. The nesting relies on a Box-Cox transformation with shape parameter λ to the conditional duration process and a possibly asymmetric shocks impact curve. We establish conditions for the existence of higher-order moments, strict stationarity, geometric ergodicity and β-mixing property with exponential decay. We next derive moment recursion relations and the autocovariance function of the power λ of the duration process. Finally, we assess the practical usefulness of our family of ACD models using NYSE transactions data, with special attention to IBM price durations. The results warrant the extra flexibility provided either by the Box-Cox transformation or by the asymmetric response to shocks.

A family of autoregressive conditional duration models

This paper develops a family of autoregressive conditional duration (ACD) models that encompasses most specifications in the literature. The nesting relies on a Box-Cox transformation with shape parameter λ to the conditional duration process and a possibly asymmetric shocks impact curve. We establish conditions for the existence of higher-order moments, strict stationarity, geometric ergodicity and β-mixing property with exponential decay. We next derive moment recursion relations and the autocovariance function of the power λ of the duration process. Finally, we assess the practical usefulness of our family of ACD models using NYSE price duration data on the IBM stock. The results warrant the extra flexibility provided either by the Box-Cox transformation or by the asymmetric response to shocks.

Free-form optical systems for nonimaging applications : Sistemas ópticos anamórficos para aplicaciones anidólicas

La óptica anidólica es una rama de la óptica cuyo desarrollo comenzó a mediados de la década de 1960. Este relativamente nuevo campo de la óptica se centra en la transferencia eficiente de la luz, algo necesario en muchas aplicaciones, entre las que destacamos los concentradores solares y los sistemas de iluminación. Las soluciones de la óptica clásica a los problemas de la transferencia de energía de la luz sólo son adecuadas cuando los rayos de luz son paraxiales. La condición paraxial no se cumple en la mayoría de las aplicaciones para concentración e iluminación. Esta tesis contiene varios diseños free-form (aquellos que no presentan ninguna simetría, ni de rotación ni lineal) cuyas aplicaciones van destinadas a estos dos campos. El término nonimaging viene del hecho de que estos sistemas ópticos no necesitan formar una imagen del objeto, aunque no formar la imagen no es una condición necesaria. Otra palabra que se utiliza a veces en lugar de nonimaging es la palabra anidólico, viene del griego "an+eidolon" y tiene el mismo significado. La mayoría de los sistemas ópticos diseñados para aplicaciones anidólicas no presentan ninguna simetría, es decir, son free-form (anamórficos). Los sistemas ópticos free-form están siendo especialmente relevantes durante los últimos años gracias al desarrollo de las herramientas para su fabricación como máquinas de moldeo por inyección y el mecanizado multieje. Sin embargo, solo recientemente se han desarrollado técnicas de diseño anidólicas capaces de cumplir con estos grados de libertad. En aplicaciones de iluminación el método SMS3D permite diseñar dos superficies free-form para controlar las fuentes de luz extensas. En los casos en que se requiere una elevada asimetría de la fuente, el objeto o las restricciones volumétricos, las superficies free-form permiten obtener soluciones de mayor eficiencia, o disponer de menos elementos en comparación con las soluciones de simetría de rotación, dado que las superficies free-form tienen más grados de libertad y pueden realizar múltiples funciones debido a su naturaleza anamórfica. Los concentradores anidólicos son muy adecuados para la captación de energía solar, ya que el objetivo no es la reproducción de una imagen exacta del sol, sino sencillamente la captura de su energía. En este momento, el campo de la concentración fotovoltaica (CPV) tiende hacia sistemas de alta concentración con el fin de compensar el gasto de las células solares multi-unión (MJ) utilizadas como receptores, reduciendo su área. El interés en el uso de células MJ radica en su alta eficiencia de conversión. Para obtener sistemas competitivos en aplicaciones terrestres se recurre a sistemas fotovoltaicos de alta concentración (HCPV), con factores de concentración geométrica por encima de 500x. Estos sistemas se componen de dos (o más) elementos ópticos (espejos y/o lentes). En los sistemas presentados a lo largo de este trabajo se presentan ejemplos de concentradores HCPV con elementos reflexivos como etapa primaria, así como concentradores con elementos refractivos (lente de Fresnel). Con la necesidad de aumentar la eficiencia de los sistemas HCPV reales y con el fin de proporcionar la división más eficiente del espectro solar, células conteniendo cuatro o más uniones (con un potencial de alcanzar eficiencias de más del 45% a una concentración de cientos de soles) se exploran hoy en día. En esta tesis se presenta una de las posibles arquitecturas de división del espectro (spectrum-splitting en la literatura anglosajona) que utilizan células de concentración comercial. Otro campo de aplicación de la óptica nonimaging es la iluminación, donde es necesario proporcionar un patrón de distribución de la iluminación específico. La iluminación de estado sólido (SSL), basada en la electroluminiscencia de materiales semiconductores, está proporcionando fuentes de luz para aplicaciones de iluminación general. En la última década, los diodos emisores de luz (LED) de alto brillo han comenzado a reemplazar a las fuentes de luz convencionales debido a la superioridad en la calidad de la luz emitida, elevado tiempo de vida, compacidad y ahorro de energía. Los colimadores utilizados con LEDs deben cumplir con requisitos tales como tener una alta eficiencia, un alto control del haz de luz, una mezcla de color espacial y una gran compacidad. Presentamos un colimador de luz free-form con microestructuras capaz de conseguir buena colimación y buena mezcla de colores con una fuente de LED RGGB. Una buena mezcla de luz es importante no sólo para simplificar el diseño óptico de la luminaria sino también para evitar hacer binning de los chips. La mezcla de luz óptica puede reducir los costes al evitar la modulación por ancho de pulso y otras soluciones electrónicas patentadas para regulación y ajuste de color. Esta tesis consta de cuatro capítulos. Los capítulos que contienen la obra original de esta tesis son precedidos por un capítulo introductorio donde se presentan los conceptos y definiciones básicas de la óptica geométrica y en el cual se engloba la óptica nonimaging. Contiene principios de la óptica no formadora de imagen junto con la descripción de sus problemas y métodos de diseño. Asimismo se describe el método de Superficies Múltiples Simultáneas (SMS), que destaca por su versatilidad y capacidad de controlar varios haces de rayos. Adicionalmente también se describe la integración Köhler y sus aplicaciones en el campo de la energía fotovoltaica. La concentración fotovoltaica y la iluminación de estado sólido son introducidas junto con la revisión de su estado actual. El Segundo y Tercer Capítulo contienen diseños ópticos avanzados con aplicación en la concentración solar principalmente, mientras que el Cuarto Capítulo describe el colimador free-form con surcos que presenta buena mezcla de colores para aplicaciones de iluminación. El Segundo Capítulo describe dos concentradores ópticos HCPV diseñados con el método SMS en tres dimensiones (SMS3D) que llevan a cabo integración Köhler en dos direcciones con el fin de proporcionar una distribución de irradiancia uniforme libre de aberraciones cromáticas sobre la célula solar. Uno de los diseños es el concentrador XXR free-form diseñado con el método SMS3D, donde el espejo primario (X) y la lente secundaria (R) se dividen en cuatro sectores simétricos y llevan a cabo la integración Köhler (proporcionando cuatro unidades del array Köhler), mientras que el espejo intermedio (X) presenta simetría rotacional. Otro concentrador HCPV presentado es el Fresnel-RXI (FRXI) con una lente de Fresnel funcionando como elemento primario (POE) y una lente RXI como elemento óptico secundario (SOE), que presenta configuración 4-fold con el fin de realizar la integración Köhler. Las lentes RXI son dispositivos nonimaging conocidos, pero su aplicación como elemento secundario es novedosa. Los concentradores XXR y FRXI Köhler son ejemplos académicos de muy alta concentración (más de 2,000x, mientras que los sistemas convencionales hoy en día no suelen llegar a 1,000x) preparados para las células solares N-unión (con N>3), que probablemente requerirán una mayor concentración y alta uniformidad espectral de irradiancia con el fin de obtener sistemas CPV terrestres eficientes y rentables. Ambos concentradores están diseñados maximizando funciones de mérito como la eficiencia óptica, el producto concentración-aceptancia (CAP) y la uniformidad de irradiancia sobre la célula libre de la aberración cromática (integración Köhler). El Tercer Capítulo presenta una arquitectura para la división del espectro solar basada en un módulo HCPV con alta concentración (500x) y ángulo de aceptancia alto (>1º) que tiene por objeto reducir ambas fuentes de pérdidas de las células triple unión (3J) comerciales: el uso eficiente del espectro solar y la luz reflejada de los contactos metálicos y de la superficie de semiconductor. El módulo para la división del espectro utiliza el espectro solar más eficiente debido a la combinación de una alta eficiencia de una célula de concentración 3J (GaInP/GaInAs/Ge) y una de contacto posterior (BPC) de concentración de silicio (Si), así como la técnica de confinamiento externo para la recuperación de la luz reflejada por la célula 3J con el fin de ser reabsorbida por la célula. En la arquitectura propuesta, la célula 3J opera con su ganancia de corriente optimizada (concentración geométrica de 500x), mientras que la célula de silicio trabaja cerca de su óptimo también (135x). El módulo de spectrum-splitting consta de una lente de Fresnel plana como POE y un concentrador RXI free-form como SOE con un filtro paso-banda integrado en él. Tanto POE como SOE realizan la integración Köhler para producir homogeneización de luz sobre la célula. El filtro paso banda envía los fotones IR en la banda 900-1,150nm a la célula de silicio. Hay varios aspectos prácticos de la arquitectura del módulo presentado que ayudan a reducir la complejidad de los sistemas spectrum-splitting (el filtro y el secundario forman una sola pieza sólida, ambas células son coplanarias simplificándose el cableado y la disipación de calor, etc.). Prototipos prueba-de-concepto han sido ensamblados y probados a fin de demostrar la fabricabilidad del filtro y su rendimiento cuando se combina con la técnica de reciclaje de luz externa. Los resultados obtenidos se ajustan bastante bien a los modelos y a las simulaciones e invitan al desarrollo de una versión más compleja de este prototipo en el futuro. Dos colimadores sólidos con surcos free-form se presentan en el Cuarto Capítulo. Ambos diseños ópticos están diseñados originalmente usando el método SMS3D. La segunda superficie ópticamente activa está diseñada a posteriori como una superficie con surcos. El diseño inicial de dos espejos (XX) está diseñado como prueba de concepto. En segundo lugar, el diseño RXI free-form es comparable con los colimadores RXI existentes. Se trata de un diseño muy compacto y eficiente que proporciona una muy buena mezcla de colores cuando funciona con LEDs RGB fuera del eje óptico como en los RGB LEDs convencionales. Estos dos diseños son dispositivos free-form diseñados con la intención de mejorar las propiedades de mezcla de colores de los dispositivos no aplanáticos RXI con simetría de revolución y la eficiencia de los aplanáticos, logrando una buena colimación y una buena mezcla de colores. La capacidad de mezcla de colores del dispositivo no-aplanático mejora añadiendo características de un aplanático a su homólogo simétrico sin pérdida de eficiencia. En el caso del diseño basado en RXI, su gran ventaja consiste en su menor coste de fabricación ya que el proceso de metalización puede evitarse. Aunque algunos de los componentes presentan formas muy complejas, los costes de fabricación son relativamente insensibles a la complejidad del molde, especialmente en el caso de la producción en masa (tales como inyección de plástico), ya que el coste del molde se reparte entre todas las piezas fabricadas. Por último, las últimas dos secciones son las conclusiones y futuras líneas de investigación. ABSTRACT Nonimaging optics is a branch of optics whose development began in the mid-1960s. This rather new field of optics focuses on the efficient light transfer necessary in many applications, among which we highlight solar concentrators and illumination systems. The classical optics solutions to the problems of light energy transfer are only appropriate when the light rays are paraxial. The paraxial condition is not met in most applications for the concentration and illumination. This thesis explores several free-form designs (with neither rotational nor linear symmetry) whose applications are intended to cover the above mentioned areas and more. The term nonimaging comes from the fact that these optical systems do not need to form an image of the object, although it is not a necessary condition not to form an image. Another word sometimes used instead of nonimaging is anidolic, and it comes from the Greek “an+eidolon” and has the same meaning. Most of the optical systems designed for nonimaging applications are without any symmetry, i.e. free-form. Free-form optical systems become especially relevant lately with the evolution of free-form tooling (injection molding machines, multi-axis machining techniques, etc.). Nevertheless, only recently there are nonimaging design techniques that are able to meet these degrees of freedom. In illumination applications, the SMS3D method allows designing two free-form surfaces to control very well extended sources. In cases when source, target or volumetric constrains have very asymmetric requirements free-form surfaces are offering solutions with higher efficiency or with fewer elements in comparison with rotationally symmetric solutions, as free-forms have more degrees of freedom and they can perform multiple functions due to their free-form nature. Anidolic concentrators are well suited for the collection of solar energy, because the goal is not the reproduction of an exact image of the sun, but instead the collection of its energy. At this time, Concentration Photovoltaics (CPV) field is turning to high concentration systems in order to compensate the expense of multi-junction (MJ) solar cells used as receivers by reducing its area. Interest in the use of MJ cells lies in their very high conversion efficiency. High Concentration Photovoltaic systems (HCPV) with geometric concentration of more than 500x are required in order to have competitive systems in terrestrial applications. These systems comprise two (or more) optical elements, mirrors and/or lenses. Systems presented in this thesis encompass both main types of HCPV architectures: concentrators with primary reflective element and concentrators with primary refractive element (Fresnel lens). Demand for the efficiency increase of the actual HCPV systems as well as feasible more efficient partitioning of the solar spectrum, leads to exploration of four or more junction solar cells or submodules. They have a potential of reaching over 45% efficiency at concentration of hundreds of suns. One possible architectures of spectrum splitting module using commercial concentration cells is presented in this thesis. Another field of application of nonimaging optics is illumination, where a specific illuminance distribution pattern is required. The Solid State Lighting (SSL) based on semiconductor electroluminescence provides light sources for general illumination applications. In the last decade high-brightness Light Emitting Diodes (LEDs) started replacing conventional light sources due to their superior output light quality, unsurpassed lifetime, compactness and energy savings. Collimators used with LEDs have to meet requirements like high efficiency, high beam control, color and position mixing, as well as a high compactness. We present a free-form collimator with microstructures that performs good collimation and good color mixing with RGGB LED source. Good light mixing is important not only for simplifying luminaire optical design but also for avoiding die binning. Optical light mixing may reduce costs by avoiding pulse-width modulation and other patented electronic solutions for dimming and color tuning. This thesis comprises four chapters. Chapters containing the original work of this thesis are preceded by the introductory chapter that addresses basic concepts and definitions of geometrical optics on which nonimaging is developed. It contains fundamentals of nonimaging optics together with the description of its design problems, principles and methods, and with the Simultaneous Multiple Surface (SMS) method standing out for its versatility and ability to control several bundles of rays. Köhler integration and its applications in the field of photovoltaics are described as well. CPV and SSL fields are introduced together with the review on their background and their current status. Chapter 2 and Chapter 3 contain advanced optical designs with primarily application in solar concentration; meanwhile Chapter 4 portrays the free-form V-groove collimator with good color mixing property for illumination application. Chapter 2 describes two HCPV optical concentrators designed with the SMS method in three dimensions (SMS3D). Both concentrators represent Köhler integrator arrays that provide uniform irradiance distribution free from chromatic aberrations on the solar cell. One of the systems is the XXR free-form concentrator designed with the SMS3D method. The primary mirror (X) of this concentrator and secondary lens (R) are divided in four symmetric sectors (folds) that perform Köhler integration; meanwhile the intermediate mirror (X) is rotationally symmetric. Second HCPV concentrator is the Fresnel-RXI (FRXI) with flat Fresnel lens as the Primary Optical Element (POE) and an RXI lens as the Secondary Optical Element (SOE). This architecture manifests 4-fold configuration for performing Köhler integration (4 array units), as well. The RXI lenses are well-known nonimaging devices, but their application as SOE is novel. Both XXR and FRXI Köhler HCPV concentrators are academic examples of very high concentration (more than 2,000x meanwhile conventional systems nowadays have up to 1,000x) prepared for the near future N-junction (N>3) solar cells. In order to have efficient and cost-effective terrestrial CPV systems, those cells will probably require higher concentrations and high spectral irradiance uniformity. Both concentrators are designed by maximizing merit functions: the optical efficiency, concentration-acceptance angle (CAP) and cell-irradiance uniformity free from chromatic aberrations (Köhler integration). Chapter 3 presents the spectrum splitting architecture based on a HCPV module with high concentration (500x) and high acceptance angle (>1º). This module aims to reduce both sources of losses of the actual commercial triple-junction (3J) solar cells with more efficient use of the solar spectrum and with recovering the light reflected from the 3J cells’ grid lines and semiconductor surface. The solar spectrum is used more efficiently due to the combination of a high efficiency 3J concentration cell (GaInP/GaInAs/Ge) and external Back-Point-Contact (BPC) concentration silicon (Si) cell. By employing external confinement techniques, the 3J cell’s reflections are recovered in order to be re-absorbed by the cell. In the proposed concentrator architecture, the 3J cell operates at its optimized current gain (at geometrical concentration of 500x), while the Si cell works near its optimum, as well (135x). The spectrum splitting module consists of a flat Fresnel lens (as the POE), and a free-form RXI-type concentrator with a band-pass filter embedded in it (as the SOE), both POE and SOE performing Köhler integration to produce light homogenization. The band-pass filter sends the IR photons in the 900-1,150nm band to the Si cell. There are several practical aspects of presented module architecture that help reducing the added complexity of the beam splitting systems: the filter and secondary are forming a single solid piece, both cells are coplanar so the heat management and wiring is simplified, etc. Two proof-of-concept prototypes are assembled and tested in order to prove filter manufacturability and performance, as well as the potential of external light recycling technique. Obtained measurement results agree quite well with models and simulations, and show an opened path to manufacturing of the Fresnel RXI-type secondary concentrator with spectrum splitting strategy. Two free-form solid V-groove collimators are presented in Chapter 4. Both free-form collimators are originally designed with the SMS3D method. The second mirrored optically active surface is converted in a grooved surface a posteriori. Initial two mirror (XX) design is presented as a proof-of-concept. Second, RXI free-form design is comparable with existing RXI collimators as it is a highly compact and a highly efficient design. It performs very good color mixing of the RGGB LED sources placed off-axis like in conventional RGB LEDs. Collimators described here improve color mixing property of the prior art rotationally symmetric no-aplanatic RXI devices, and the efficiency of the aplanatic ones, accomplishing both good collimation and good color mixing. Free-form V-groove collimators enhance the no-aplanatic device's blending capabilities by adding aplanatic features to its symmetric counterpart with no loss in efficiency. Big advantage of the RXI design is its potentially lower manufacturing cost, since the process of metallization may be avoided. Although some components are very complicated for shaping, the manufacturing costs are relatively insensitive to the complexity of the mold especially in the case of mass production (such as plastic injection), as the cost of the mold is spread in many parts. Finally, last two sections are conclusions and future lines of investigation.

Diesel spray mixing limited vaporization with non-ideal and multi-component fuel thermophysical property effects

Internal combustion engines are, and will continue to be, a primary mode of power generation for ground transportation. Challenges exist in meeting fuel consumption regulations and emission standards while upholding performance, as fuel prices rise, and resource depletion and environmental impacts are of increasing concern. Diesel engines are advantageous due to their inherent efficiency advantage over spark ignition engines; however, their NOx and soot emissions can be difficult to control and reduce due to an inherent tradeoff. Diesel combustion is spray and mixing controlled providing an intrinsic link between spray and emissions, motivating detailed, fundamental studies on spray, vaporization, mixing, and combustion characteristics under engine relevant conditions. An optical combustion vessel facility has been developed at Michigan Technological University for these studies, with detailed tests and analysis being conducted. In this combustion vessel facility a preburn procedure for thermodynamic state generation is used, and validated using chemical kinetics modeling both for the MTU vessel, and institutions comprising the Engine Combustion Network international collaborative research initiative. It is shown that minor species produced are representative of modern diesel engines running exhaust gas recirculation and do not impact the autoignition of n-heptane. Diesel spray testing of a high-pressure (2000 bar) multi-hole injector is undertaken including non-vaporizing, vaporizing, and combusting tests, with sprays characterized using Mie back scatter imaging diagnostics. Liquid phase spray parameter trends agree with literature. Fluctuations in liquid length about a quasi-steady value are quantified, along with plume to plume variations. Hypotheses are developed for their causes including fuel pressure fluctuations, nozzle cavitation, internal injector flow and geometry, chamber temperature gradients, and turbulence. These are explored using a mixing limited vaporization model with an equation of state approach for thermopyhysical properties. This model is also applied to single and multi-component surrogates. Results include the development of the combustion research facility and validated thermodynamic state generation procedure. The developed equation of state approach provides application for improving surrogate fuels, both single and multi-component, in terms of diesel spray liquid length, with knowledge of only critical fuel properties. Experimental studies are coupled with modeling incorporating improved thermodynamic non-ideal gas and fuel

Study of the CP property of the Higgs boson at a photon collider using gamma gamma -> t(t)over-bar -> lX

We study the possible effects of CP violation in the Higgs sector on t (t) over bar production at a gammagamma collider. These studies are performed in a model-independent way in terms of six form factors {R(S-gamma), J(S-gamma), R(P-gamma), J(P-gamma), S-t, P-t} which parametrize the CP mixing in the Higgs sector, and a strategy for their determination is developed. We observe that the angular distribution of the decay lepton from t/(t) over bar produced in this process is independent of any CP violation in the tbW vertex and hence best suited for studying CP mixing in the Higgs sector. Analytical expressions are obtained for the angular distribution of leptons in the c.m. frame of the two colliding photons for a general polarization state of the incoming photons. We construct combined asymmetries in the initial state lepton (photon) polarization and the final state lepton charge. They involve CP even (x's) and odd (y's) combinations of the mixing parameters. We study limits up to which the values of x and y, with only two of them allowed to vary at a time, can be probed by measurements of these asymmetries, using circularly polarized photons. We use the numerical values of the asymmetries predicted by various models to discriminate among them. We show that this method can be sensitive to the loop-induced CP violation in the Higgs sector in the minimal supersymmetric standard model.

Wavelength conversion based on degenerate-four-wave-mixing with continuous-wave pumping in silicon nanowire waveguide

We present a comprehensive numerical study on the all-optical wavelength conversion based on the degenerate four-wave-mixing with continuous-wave pumping in the silicon nanowire waveguide. It is well known that the conversion efficiency and the 3-dB bandwidth can be greatly affected by the phase-matching condition. Through proper design of the waveguide cross-section, its dispersion property can be adjusted to satisfy the phase-matching condition and therefore effective wavelength conversion can be achieved in a large wavelength range. Generally, the group velocity dispersion plays a dominant role in the wavelength conversion. However, the fourth-order dispersion takes an important effect on the wavelength conversion when the group velocity dispersion is near the zero-point. Furthermore, the conversion efficiency and the 3-dB bandwidth can also be affected by the interactive length and the initial pump power. Through the numerical simulation, the optimal values for the interactive length and the initial pump power, which are functions of the propagation loss, are obtained to realize the maximum conversion efficiency. (C) 2008 Elsevier B.V. All rights reserved.

STUDY ON STRUCTURE-PROPERTY RELATIONSHIP OF POLYIMIDE BLENDS .1. A DYNAMIC MECHANICAL STUDY OF THE MISCIBILITY OF POLYIMIDE POLYIMIDE BLENDS

Three pairs of polyimide/polyimide blends (50/50 wt%) with different molecular structures were prepared by two ways, i.e. mixing of the polyamic acid precursors with subsequent imidization, and direct solution mixing of the polyimides. The blends were studied with DMA technique. The results obtained show that all the blends prepared with these two different ways are miscible, as there existed only one glass transition temperature(Tg) for all the blends. It is suggested that the miscibility of these polyimide/polyimide blends is a result of the strong inter-molecular charge-transfer interaction between the chains of their components.

Critical evaluation of pulse-echo ultrasonic test method for the determination of setting and mechanical properties of acrylic bone cement: Influence of mixing technique

Currently there is no reliable objective method to quantify the setting properties of acrylic bone cements within an operating theatre environment. Ultrasonic technology can be used to determine the acoustic properties of the polymerising bone cement, which are linked to material properties and provide indications of the physical and chemical changes occurring within the cement. The focus of this study was the critical evaluation of pulse-echo ultrasonic test method in determining the setting and mechanical properties of three different acrylic bone cement when prepared under atmospheric and vacuum mixing conditions. Results indicated that the ultrasonic pulse-echo technique provided a highly reproducible and accurate method of monitoring the polymerisation reaction and indicating the principal setting parameters when compared to ISO 5833 standard, irrespective of the acrylic bone cement or mixing method used. However, applying the same test method to predict the final mechanical properties of acrylic bone cement did not prove a wholly accurate approach. Inhomogeneities within the cement microstructure and specimen geometry were found to have a significant influence on mechanical property predictions. Consideration of all the results suggests that the non-invasive and non-destructive pulse-echo ultrasonic test method is an effective and reliable method for following the full polymerisation reaction of acrylic bone cement in real-time and then determining the setting properties within a surgical theatre environment. However the application of similar technology for predicting the final mechanical properties of acrylic bone cement on a consistent basis may prove difficult.

Third order nonlinear optical studies in europium naphthalocyanine using degenerate four wave mixing and Z-scan

Third order nonlinear susceptibility χ(3) and second hyperpolarizability (γ) of a bis-naphthalocyanine viz. europium naphthalocyanines, Eu(Nc)2, were measured in dimethyl formamide solution using degenerate four wave mixing at 532 nm under nanosecond pulse excitation. Effective nonlinear absorption coefficient, βeff and imaginary part of nonlinear susceptibility, Im(χ(3)) were obtained using open aperture /Z-scan technique at the same wavelength. Optical limiting property of the sample was also investigated. The role of excited state absorption in deciding the nonlinear properties of this material is discussed.

Thermoselective phase property of silica tethered with fluorinated chains for controlled 'release' and 'capture' of catalytic fluorous tin species

The temperature dependent mixing of organic and fluorous phases is one of the key principals of fluorous biphasic systems (FBS). Given the high cost of the perfluorous solvents and their impacts to the environment, it is apparent that elimination of these solvents in bulk quantity in the FBS is advantageous. We report for the first time, the surface coverage of silica with a fluorous solvent like material that traps (at ambient temperatures) and releases (at elevated temperatures) a fluorous tin bromide in organic solvent. Here, we demonstrate the catalytic utilisation of this species for the hydrocyclisation of 6-bromo-1-hexene with NaBH4. (C) 2002 Elsevier Science B.V. All rights reserved.

Molecular recognition between functionalized gold nanoparticles and healable, supramolecular polymer blends – a route to property enhancement

A new, healable, supramolecular nanocomposite material has been developed and evaluated. The material comprises a blend of three components: a pyrene-functionalized polyamide, a polydiimide and pyrenefunctionalized gold nanoparticles (P-AuNPs). The polymeric components interact by forming well-defined p–p stacked complexes between p-electron rich pyrenyl residues and p-electron deficient polydiimide residues. Solution studies in the mixed solvent chloroform–hexafluoroisopropanol (6 : 1, v/v) show that mixing the three components (each of which is soluble in isolation), results in the precipitation of a supramolecular, polymer nanocomposite network. The precipitate thus formed can be re-dissolved on heating, with the thermoreversible dissolution/precipitation procedure repeatable over at least 5 cycles. Robust, self-supporting composite films containing up to 15 wt% P-AuNPs could be cast from 2,2,2- trichloroethanol. Addition of as little as 1.25 wt% P-AuNPs resulted in significantly enhanced mechanical properties compared to the supramolecular blend without nanoparticles. The nanocomposites showed a linear increase in both tensile moduli and ultimate tensile strength with increasing P-AuNP content. All compositions up to 10 wt% P-AuNPs exhibited essentially quantitative healing efficiencies. Control experiments on an analogous nanocomposite material containing dodecylamine-functionalized AuNPs (5 wt%) exhibited a tensile modulus approximately half that of the corresponding nanocomposite that incorporated 5 wt% pyrene functionalized-AuNPs, clearly demonstrating the importance of the designed interactions between the gold filler and the supramolecular polymer matrix.

Weak mixing and eigenvalues for arnoux-rauzy sequences

We define by simple conditions two wide subclasses of the socalled Arnoux-Rauzy systems; the elements of the first one share the property of (measure-theoretic) weak mixing, thus we generalize and improve a counterexample to the conjecture that these systems are codings of rotations; those of the second one have eigenvalues, which was known hitherto only for a very small set of examples.