Negative second virial coefficients as predictors of protein crystal growth: Evidence from sedimentation equilibrium studies that refutes the designation of those light scattering parameters as osmotic virial coefficients

The effects of ammonium sulphate concentration on the osmotic second virial coefficient (B-AA/M-A) for equine serum albumin (pH 5.6, 20 degrees C) have been examined by sedimentation equilibrium. After an initial steep decrease with increasing ammonium sulphate concentration, B-AA/M-A assumes an essentially concentration-independent magnitude of 8-9 ml/g. Such behaviour conforms with the statistical-mechanical prediction that a sufficient increase in ionic strength should effectively eliminate the contributions of charge interactions to B-AA/M-A but have no effect on the covolume contribution (8.4 ml/g for serum albumin). A similar situation is shown to apply to published sedimentation equilibrium data for lysozyme (pH 4.5). Although termed osmotic second virial coefficients and designated as such (B-22), the negative values obtained in published light scattering studies of both systems have been described incorrectly because of the concomitant inclusion of the protein-salt contribution to thermodynamic nonideality of the protein. Those negative values are still valid predictors of conditions conducive to crystal growth inasmuch as they do reflect situations in which there is net attraction between protein molecules. However, the source of attraction responsible for the negative virial coefficient stems from the protein-salt rather than the protein-protein contribution, which is necessarily positive. (c) 2005 Elsevier B.V. All rights reserved.

Canonical quantum potential scattering theory

A new formulation of potential scattering in quantum mechanics is developed using a close structural analogy between partial waves and the classical dynamics of many non-interacting fields. Using a canonical formalism we find nonlinear first-order differential equations for the low-energy scattering parameters such as scattering length and effective range. They significantly simplify typical calculations, as we illustrate for atom-atom and neutron-nucleus scattering systems. A generalization to charged particle scattering is also possible.

The effect of core electrons in e(+)-Na scattering

The scattering of positrons off sodium targets has been investigated using the coupled static model. The sodium atom is represented by the one-active-electron model in which all the electrons of the target have been considered explicitly and the loosely bound valence electron is only involved in transitions. The scattering parameters are presented at low and medium energies. Appreciable differences are noticed between the present results and those obtained by the one-electron model with and without the core potential.

First principles calculation of electron-phonon and alloy scattering in strained SiGe

First-principles electronic structure methods are used to predict the mobility of n-type carrier scattering in strained SiGe. We consider the effects of strain on the electron-phonon deformation potentials and the alloy scattering parameters. We calculate the electron-phonon matrix elements and fit them up to second order in strain. We find, as expected, that the main effect of strain on mobility comes from the breaking of the degeneracy of the six Δ and L valleys, and the choice of transport direction. The non-linear effects on the electron-phonon coupling of the Δ valley due to shear strain are found to reduce the mobility of Si-like SiGe by 50% per % strain. We find increases in mobility between 2 and 11 times that of unstrained SiGe for certain fixed Ge compositions, which should enhance the thermoelectric figure of merit in the same order, and could be important for piezoresistive applications.

First-principles calculation of carrier-phonon scattering in n-type Si1−xGex alloys

First-principles electronic structure methods are used to find the rates of inelastic intravalley and intervalley n-type carrier scattering in Si1-xGex alloys. Scattering parameters for all relevant Delta and L intra- and intervalley scattering are calculated. The short-wavelength acoustic and the optical phonon modes in the alloy are computed using the random mass approximation, with interatomic forces calculated in the virtual crystal approximation using density functional perturbation theory. Optical phonon and intervalley scattering matrix elements are calculated from these modes of the disordered alloy. It is found that alloy disorder has only a small effect on the overall inelastic intervalley scattering rate at room temperature. Intravalley acoustic scattering rates are calculated within the deformation potential approximation. The acoustic deformation potentials are found directly and the range of validity of the deformation potential approximation verified in long-wavelength frozen phonon calculations. Details of the calculation of elastic alloy scattering rates presented in an earlier paper are also given. Elastic alloy disorder scattering is found to dominate over inelastic scattering, except for almost pure silicon (x approximate to 0) or almost pure germanium (x approximate to 1), where acoustic phonon scattering is predominant. The n-type carrier mobility, calculated from the total (elastic plus inelastic) scattering rate, using the Boltzmann transport equation in the relaxation time approximation, is in excellent agreement with experiments on bulk, unstrained alloys..

First-principles calculation of alloy scattering in GexSi1-x

First-principles electronic structure methods are used to find the rates of intravalley and intervalley n-type carrier scattering due to alloy disorder in Si1-xGex alloys. The required alloy scattering matrix elements are calculated from the energy splitting of nearly degenerate Bloch states which arises when one average host atom is replaced by a Ge or Si atom in supercells containing up to 128 atoms. Scattering parameters for all relevant Delta and L intravalley and intervalley alloy scattering are calculated. Atomic relaxation is found to have a substantial effect on the scattering parameters. f-type intervalley scattering between Delta valleys is found to be comparable to other scattering channels. The n-type carrier mobility, calculated from the scattering rate using the Boltzmann transport equation in the relaxation time approximation, is in excellent agreement with experiments on bulk, unstrained alloys.

Microstrip circular phased array design and development using microwave antenna CAD tools

The complex design and development of a planar multilayer phased array antenna in microstrip technology can be simplified using two commercially available design tools 1) Ansoft Ensemble and 2) HP-EEsof Touchstone. In the approach presented here, Touchstone is used to design RF switches and phase shifters whose scattering parameters are incorporated in Ensemble simulations using its black box tool. Using this approach, Ensemble is able to fully analyze the performance of radiating and beamforming layers of a phased array prior to its manufacturing. This strategy is demonstrated in a design example of a 12-element linearly-polarized circular phased array operating at L band. A comparison between theoretical and experimental results of the array is demonstrated.

Extracción de parámetros de un resonador FBAR por optimización

L’objectiu d’aquest projecte que consisteix a elaborar un algoritme d’optimització que permeti, mitjançant un ajust de dades per mínims quadrats, la extracció dels paràmetres del circuit equivalent que composen el model teòric d’un ressonador FBAR, a partir de les mesures dels paràmetres S. Per a dur a terme aquest treball, es desenvolupa en primer lloc tota la teoria necessària de ressonadors FBAR. Començant pel funcionament i l’estructura, i mostrant especial interès en el modelat d’aquests ressonadors mitjançant els models de Mason, Butterworth Van-Dyke i BVD Modificat. En segon terme, s’estudia la teoria sobre optimització i programació No-Lineal. Un cop s’ha exposat la teoria, es procedeix a la descripció de l’algoritme implementat. Aquest algoritme utilitza una estratègia de múltiples passos que agilitzen l'extracció dels paràmetres del ressonador.

Photopolymerizable hydrogels for implants: Monte-Carlo modeling and experimental in vitro validation.

Photopolymerization is commonly used in a broad range of bioapplications, such as drug delivery, tissue engineering, and surgical implants, where liquid materials are injected and then hardened by means of illumination to create a solid polymer network. However, photopolymerization using a probe, e.g., needle guiding both the liquid and the curing illumination, has not been thoroughly investigated. We present a Monte Carlo model that takes into account the dynamic absorption and scattering parameters as well as solid-liquid boundaries of the photopolymer to yield the shape and volume of minimally invasively injected, photopolymerized hydrogels. In the first part of the article, our model is validated using a set of well-known poly(ethylene glycol) dimethacrylate hydrogels showing an excellent agreement between simulated and experimental volume-growth-rates. In the second part, in situ experimental results and simulations for photopolymerization in tissue cavities are presented. It was found that a cavity with a volume of 152  mm3 can be photopolymerized from the output of a 0.28-mm2 fiber by adding scattering lipid particles while only a volume of 38  mm3 (25%) was achieved without particles. The proposed model provides a simple and robust method to solve complex photopolymerization problems, where the dimension of the light source is much smaller than the volume of the photopolymerizable hydrogel.

Estudo comparativo de técnicas de cascateamento de superfícies seletivas em frequência

This work presents a theoretical and numerical analysis for the cascading of frequency selective surfaces, which uses rectangular patches and triangular Koch fractals as elements. Two cascading techniques are used to determine the transmission and reflection characteristics. Frequency selective surfaces includes a large area of Telecommunications and have been widely used due to its low cost, low weight and ability to integrate with others microwaves circuits. They re especially important in several applications, such as airplane, antennas systems, radomes, rockets, missiles, etc.. FSS applications in high frequency ranges have been investigated, as well as applications of cascading structures or multi-layer, and active FSS. Furthermore, the analyses uses the microwave circuit theory, with the Floquet harmonics, it allows to obtain the expressions of the scattering parameters of each structure and also of the composed structure of two or more FSS. In this work, numeric results are presented for the transmission characteristics. Comparisons are made with experimental results and simulated results using the commercial software Ansoft Designer® v3. Finally, some suggestions are presented for future works on this subject

Análise teórica e experimental de superfícies seletivas de freqüência e suas aplicações em antenas planares

This work presents a theoretical and numerical analysis of structures using frequency selective surfaces applied on patch antennas. The FDTD method is used to determine the time domain reflected fields. Applications of frequency selective surfaces and patch antennas cover a wide area of telecommunications, especially mobile communications, filters and WB antennas. scattering parameters are obteained from Fourier Transformer of transmited and reflected fields in time domain. The PML are used as absorbing boundary condition, allowing the determination of the fields with a small interference of reflections from discretized limit space. Rectangular patches are considered on dielectric layer and fed by microstrip line. Frequency selective surfaces with periodic and quasi-periodic structures are analyzed on both sides of antenna. A literature review of the use of frequency selective surfaces in patch antennas are also performed. Numerical results are also compared with measured results for return loss of analyzed structures. It is also presented suggestions of continuity to this work

Calculation Methodology and Fabrication Procedures for Particle Accelerator Strip-Line Kickers: Application to the CTF3 Combiner Ring Extraction Kicker and TL2 Tail Clippers

A particle accelerator is any device that, using electromagnetic fields, is able to communicate energy to charged particles (typically electrons or ionized atoms), accelerating and/or energizing them up to the required level for its purpose. The applications of particle accelerators are countless, beginning in a common TV CRT, passing through medical X-ray devices, and ending in large ion colliders utilized to find the smallest details of the matter. Among the other engineering applications, the ion implantation devices to obtain better semiconductors and materials of amazing properties are included. Materials supporting irradiation for future nuclear fusion plants are also benefited from particle accelerators. There are many devices in a particle accelerator required for its correct operation. The most important are the particle sources, the guiding, focalizing and correcting magnets, the radiofrequency accelerating cavities, the fast deflection devices, the beam diagnostic mechanisms and the particle detectors. Most of the fast particle deflection devices have been built historically by using copper coils and ferrite cores which could effectuate a relatively fast magnetic deflection, but needed large voltages and currents to counteract the high coil inductance in a response in the microseconds range. Various beam stability considerations and the new range of energies and sizes of present time accelerators and their rings require new devices featuring an improved wakefield behaviour and faster response (in the nanoseconds range). This can only be achieved by an electromagnetic deflection device based on a transmission line. The electromagnetic deflection device (strip-line kicker) produces a transverse displacement on the particle beam travelling close to the speed of light, in order to extract the particles to another experiment or to inject them into a different accelerator. The deflection is carried out by the means of two short, opposite phase pulses. The diversion of the particles is exerted by the integrated Lorentz force of the electromagnetic field travelling along the kicker. This Thesis deals with a detailed calculation, manufacturing and test methodology for strip-line kicker devices. The methodology is then applied to two real cases which are fully designed, built, tested and finally installed in the CTF3 accelerator facility at CERN (Geneva). Analytical and numerical calculations, both in 2D and 3D, are detailed starting from the basic specifications in order to obtain a conceptual design. Time domain and frequency domain calculations are developed in the process using different FDM and FEM codes. The following concepts among others are analyzed: scattering parameters, resonating high order modes, the wakefields, etc. Several contributions are presented in the calculation process dealing specifically with strip-line kicker devices fed by electromagnetic pulses. Materials and components typically used for the fabrication of these devices are analyzed in the manufacturing section. Mechanical supports and connexions of electrodes are also detailed, presenting some interesting contributions on these concepts. The electromagnetic and vacuum tests are then analyzed. These tests are required to ensure that the manufactured devices fulfil the specifications. Finally, and only from the analytical point of view, the strip-line kickers are studied together with a pulsed power supply based on solid state power switches (MOSFETs). The solid state technology applied to pulsed power supplies is introduced and several circuit topologies are modelled and simulated to obtain fast and good flat-top pulses.

Análisis y diseño de un patrón de ruido térmico de 10 MHz a 26,5 GHz en tecnología coaxial

Esta Tesis Doctoral presenta las investigaciones y los trabajos desarrollados durante los años 2008 a 2012 para el análisis y diseño de un patrón primario de ruido térmico de banda ancha en tecnología coaxial. Para ubicar esta Tesis en su campo científico es necesario tomar conciencia de que la realización de mediciones fiables y trazables forma parte del sostenimiento del bienestar de una sociedad moderna y juega un papel crítico en apoyo de la competitividad económica, la fabricación y el comercio, así como de la calidad de vida. En el mundo moderno actual, una infraestructura de medición bien desarrollada genera confianza en muchas facetas de nuestra vida diaria, porque nos permite el desarrollo y fabricación de productos fiables, innovadores y de alta calidad; porque sustenta la competitividad de las industrias y su producción sostenible; además de contribuir a la eliminación de barreras técnicas y de dar soporte a un comercio justo, garantizar la seguridad y eficacia de la asistencia sanitaria, y por supuesto, dar respuesta a los grandes retos de la sociedad moderna en temas tan complicados como la energía y el medio ambiente. Con todo esto en mente se ha desarrollado un patrón primario de ruido térmico con el fin de aportar al sistema metrológico español un nuevo patrón primario de referencia capaz de ser usado para desarrollar mediciones fiables y trazables en el campo de la medida y calibración de dispositivos de ruido electromagnético de radiofrecuencia y microondas. Este patrón se ha planteado para que cumpla en el rango de 10 MHz a 26,5 GHz con las siguientes especificaciones: Salida nominal de temperatura de ruido aproximada de ~ 83 K. Incertidumbre de temperatura de ruido menor que ± 1 K en todo su rango de frecuencias. Coeficiente de reflexión en todo su ancho de banda de 0,01 a 26,5 GHz lo más bajo posible. Se ha divido esta Tesis Doctoral en tres partes claramente diferenciadas. La primera de ellas, que comprende los capítulos 1, 2, 3, 4 y 5, presenta todo el proceso de simulaciones y ajustes de los parámetros principales del dispositivo con el fin de dejar definidos los que resultan críticos en su construcción. A continuación viene una segunda parte compuesta por el capítulo 6 en donde se desarrollan los cálculos necesarios para obtener la temperatura de ruido a la salida del dispositivo. La tercera y última parte, capítulo 7, se dedica a la estimación de la incertidumbre de la temperatura de ruido del nuevo patrón primario de ruido obtenida en el capítulo anterior. Más concretamente tenemos que en el capítulo 1 se hace una exhaustiva introducción del entorno científico en donde se desarrolla este trabajo de investigación. Además se detallan los objetivos que se persiguen y se presenta la metodología utilizada para conseguirlos. El capítulo 2 describe la caracterización y selección del material dieléctrico para el anillo del interior de la línea de transmisión del patrón que ponga en contacto térmico los dos conductores del coaxial para igualar las temperaturas entre ambos y mantener la impedancia característica de todo el patrón primario de ruido. Además se estudian las propiedades dieléctricas del nitrógeno líquido para evaluar su influencia en la impedancia final de la línea de transmisión. En el capítulo 3 se analiza el comportamiento de dos cargas y una línea de aire comerciales trabajando en condiciones criogénicas. Se pretende con este estudio obtener la variación que se produce en el coeficiente de reflexión al pasar de temperatura ambiente a criogénica y comprobar si estos dispositivos resultan dañados por trabajar a temperaturas criogénicas; además se estudia si se modifica su comportamiento tras sucesivos ciclos de enfriamiento – calentamiento, obteniendo una cota de la variación para poder así seleccionar la carga que proporcione un menor coeficiente de reflexión y una menor variabilidad. En el capítulo 4 se parte del análisis de la estructura del anillo de material dieléctrico utilizada en la nota técnica NBS 1074 del NIST con el fin de obtener sus parámetros de dispersión que nos servirán para calcular el efecto que produce sobre el coeficiente de reflexión de la estructura coaxial completa. Además se realiza un estudio posterior con el fin de mejorar el diseño de la nota técnica NBS 1074 del NIST, donde se analiza el anillo de material dieléctrico, para posteriormente realizar modificaciones en la geometría de la zona donde se encuentra éste con el fin de reducir la reflexión que produce. Concretamente se estudia el ajuste del radio del conductor interior en la zona del anillo para que presente la misma impedancia característica que la línea. Y para finalizar se obtiene analíticamente la relación entre el radio del conductor interior y el radio de la transición de anillo térmico para garantizar en todo punto de esa transición la misma impedancia característica, manteniendo además criterios de robustez del dispositivo y de fabricación realistas. En el capítulo 5 se analiza el comportamiento térmico del patrón de ruido y su influencia en la conductividad de los materiales metálicos. Se plantean las posibilidades de que el nitrógeno líquido sea exterior a la línea o que éste penetre en su interior. En ambos casos, dada la simetría rotacional del problema, se ha simulado térmicamente una sección de la línea coaxial, es decir, se ha resuelto un problema bidimensional, aunque los resultados son aplicables a la estructura real tridimensional. Para la simulación térmica se ha empleado la herramienta PDE Toolbox de Matlab®. En el capítulo 6 se calcula la temperatura de ruido a la salida del dispositivo. Se parte del estudio de la aportación a la temperatura de ruido final de cada sección que compone el patrón. Además se estudia la influencia de las variaciones de determinados parámetros de los elementos que conforman el patrón de ruido sobre las características fundamentales de éste, esto es, el coeficiente de reflexión a lo largo de todo el dispositivo. Una vez descrito el patrón de ruido electromagnético se procede, en el capítulo 7, a describir los pasos seguidos para estimar la incertidumbre de la temperatura de ruido electromagnético a su salida. Para ello se utilizan dos métodos, el clásico de la guía para la estimación de la incertidumbre [GUM95] y el método de simulación de Monte Carlo. En el capítulo 8 se describen las conclusiones y lo logros conseguidos. Durante el desarrollo de esta Tesis Doctoral se ha obtenido un dispositivo novedoso susceptible de ser patentado, que ha sido registrado en la Oficina Española de Patentes y Marcas (O.E.P.M.) en Madrid, de conformidad con lo establecido en el artículo 20 de la Ley 11/1986, de 20 de Marzo, de Patentes, con el título Patrón Primario de Ruido Térmico de Banda Ancha (Referencia P-101061) con fecha 7 de febrero de 2011. ABSTRACT This Ph. D. work describes a number of investigations that were performed along the years 2008 to 2011, as a preparation for the study and design of a coaxial cryogenic reference noise standard. Reliable and traceable measurement underpins the welfare of a modern society and plays a critical role in supporting economic competitiveness, manufacturing and trade as well as quality of life. In our modern world, a well developed measurement infrastructure gives confidence in many aspects of our daily life, for example by enabling the development and manufacturing of reliable, high quality and innovative products; by supporting industry to be competitive and sustainable in its production; by removing technical barriers to trade and supporting fair trade; by ensuring safety and effectiveness of healthcare; by giving response to the major challenges in key sectors such energy and environment, etc. With all this in mind we have developed a primary standard thermal noise with the aim of providing the Spanish metrology system with a new primary standard for noise reference. This standard will allow development of reliable and traceable measurements in the field of calibration and measurement of electromagnetic noise RF and microwave devices. This standard has been designed to work in the frequency range from 10 MHz to 26.5 GHz, meeting the following specifications: 1. Noise temperature output is to be nominally ~ 83 K. 2. Noise temperature uncertainty less than ± 1 K in the frequency range from 0.01 to 26.5 GHz. 3. Broadband performance requires as low a reflection coefficient as possible from 0.01 to 26.5 GHz. The present Ph. D. work is divided into three clearly differentiated parts. The first one, which comprises Chapters 1 to 5, presents the whole process of simulation and adjustment of the main parameters of the device in order to define those of them which are critical for the manufacturing of the device. Next, the second part consists of Chapter 6 where the necessary computations to obtain the output noise temperature of the device are carried out. The third and last part, Chapter 7, is devoted to the estimation of the uncertainty related to the noise temperature of the noise primary standard as obtained in the preceding chapter. More specifically, Chapter 1 provides a thorough introduction to the scientific and technological environment where this research takes place. It also details the objectives to be achieved and presents the methodology used to achieve them. Chapter 2 describes the characterization and selection of the bead dielectric material inside the transmission line, intended to connect the two coaxial conductors equalizing the temperature between the two of them and thus keeping the characteristic impedance constant for the whole standard. In addition the dielectric properties of liquid nitrogen are analyzed in order to assess their influence on the impedance of the transmission line. Chapter 3 analyzes the behavior of two different loads and of a commercial airline when subjected to cryogenic working conditions. This study is intended to obtain the variation in the reflection coefficient when the temperature changes from room to cryogenic temperature, and to check whether these devices can be damaged as a result of working at cryogenic temperatures. Also we try to see whether the load changes its behavior after successive cycles of cooling / heating, in order to obtain a bound for the allowed variation of the reflection coefficient of the load. Chapter 4 analyzes the ring structure of the dielectric material used in the NBS technical note 1074 of NIST, in order to obtain its scattering parameters that will be used for computation of its effect upon the reflection coefficient of the whole coaxial structure. Subsequently, we perform a further investigation with the aim of improving the design of NBS technical note 1074 of NIST, and modifications are introduced in the geometry of the transition area in order to reduce the reflection it produces. We first analyze the ring, specifically the influence of the radius of inner conductor of the bead, and then make changes in its geometry so that it presents the same characteristic impedance as that of the line. Finally we analytically obtain the relationship between the inner conductor radius and the radius of the transition from ring, in order to ensure the heat flow through the transition thus keeping the same reflection coefficient, and at the same time meeting the robustness requirements and the feasibility of manufacturing. Chapter 5 analyzes the thermal behavior of the noise standard and its influence on the conductivity of metallic materials. Both possibilities are raised that the liquid nitrogen is kept outside the line or that it penetrates inside. In both cases, given the rotational symmetry of the structure, we have simulated a section of coaxial line, i.e. the equivalent two-dimensional problem has been resolved, although the results are applicable to the actual three-dimensional structure. For thermal simulation Matlab™ PDE Toolbox has been used. In Chapter 6 we compute the output noise temperature of the device. The starting point is the analysis of the contribution to the overall noise temperature of each section making up the standard. Moreover the influence of the variations in the parameters of all elements of the standard is analyzed, specifically the variation of the reflection coefficient along the entire device. Once the electromagnetic noise standard has been described and analyzed, in Chapter 7 we describe the steps followed to estimate the uncertainty of the output electromagnetic noise temperature. This is done using two methods, the classic analytical approach following the Guide to the Estimation of Uncertainty [GUM95] and numerical simulations made with the Monte Carlo method. Chapter 8 discusses the conclusions and achievements. During the development of this thesis, a novel device was obtained which was potentially patentable, and which was finally registered through the Spanish Patent and Trademark Office (SPTO) in Madrid, in accordance with the provisions of Article 20 of Law 11/1986 about Patents, dated March 20th, 1986. It was registered under the denomination Broadband Thermal Noise Primary Standard (Reference P-101061) dated February 7th, 2011.

Noninvasive functional optical spectroscopy of human breast tissue

Near infrared diffuse optical spectroscopy and diffuse optical imaging are promising methods that eventually may enhance or replace existing technologies for breast cancer screening and diagnosis. These techniques are based on highly sensitive, quantitative measurements of optical and functional contrast between healthy and diseased tissue. In this study, we examine whether changes in breast physiology caused by exogenous hormones, aging, and fluctuations during the menstrual cycle result in significant alterations in breast tissue optical contrast. A noninvasive quantitative diffuse optical spectroscopy technique, frequency-domain photon migration, was used. Measurements were performed on 14 volunteer subjects by using a hand-held probe. Intrinsic tissue absorption and reduced scattering parameters were calculated from frequency-domain photon migration data. Wavelength-dependent absorption (at 674, 803, 849, and 956 nm) was used to determine tissue concentration of oxyhemoglobin, deoxyhemoglobin, total hemoglobin, tissue hemoglobin oxygen saturation, and bulk water content. Results show significant and dramatic differences in optical properties between menopausal states. Average premenopausal intrinsic tissue absorption and reduced scattering values at each wavelength are 2.5- to 3-fold higher and 16–28% greater, respectively, than absorption and scattering for postmenopausal subjects. Absorption and scattering properties for women using hormone replacement therapy are intermediate between premenopausal and postmenopausal populations. Physiological properties show differences in mean total hemoglobin (7.0 μM, 11.8 μM, and 19.2 μM) and water concentration relative to pure water (10.9%, 15.3%, and 27.3%) for postmenopausal, hormone replacement therapy, and premenopausal subjects, respectively. Because of their unique, quantitative information content, diffuse optical methods may play an important role in breast diagnostics and improving our understanding of breast disease.

Rational Function Interpolation of Electromagnetic Transfer Functions of High-Speed Interconnect Systems from Discrete Time-Domain and Frequency-Domain Data

We present new methodologies to generate rational function approximations of broadband electromagnetic responses of linear and passive networks of high-speed interconnects, and to construct SPICE-compatible, equivalent circuit representations of the generated rational functions. These new methodologies are driven by the desire to improve the computational efficiency of the rational function fitting process, and to ensure enhanced accuracy of the generated rational function interpolation and its equivalent circuit representation. Toward this goal, we propose two new methodologies for rational function approximation of high-speed interconnect network responses. The first one relies on the use of both time-domain and frequency-domain data, obtained either through measurement or numerical simulation, to generate a rational function representation that extrapolates the input, early-time transient response data to late-time response while at the same time providing a means to both interpolate and extrapolate the used frequency-domain data. The aforementioned hybrid methodology can be considered as a generalization of the frequency-domain rational function fitting utilizing frequency-domain response data only, and the time-domain rational function fitting utilizing transient response data only. In this context, a guideline is proposed for estimating the order of the rational function approximation from transient data. The availability of such an estimate expedites the time-domain rational function fitting process. The second approach relies on the extraction of the delay associated with causal electromagnetic responses of interconnect systems to provide for a more stable rational function process utilizing a lower-order rational function interpolation. A distinctive feature of the proposed methodology is its utilization of scattering parameters. For both methodologies, the approach of fitting the electromagnetic network matrix one element at a time is applied. It is shown that, with regard to the computational cost of the rational function fitting process, such an element-by-element rational function fitting is more advantageous than full matrix fitting for systems with a large number of ports. Despite the disadvantage that different sets of poles are used in the rational function of different elements in the network matrix, such an approach provides for improved accuracy in the fitting of network matrices of systems characterized by both strongly coupled and weakly coupled ports. Finally, in order to provide a means for enforcing passivity in the adopted element-by-element rational function fitting approach, the methodology for passivity enforcement via quadratic programming is modified appropriately for this purpose and demonstrated in the context of element-by-element rational function fitting of the admittance matrix of an electromagnetic multiport.