Dissertations / Theses on the topic 'Non-homogeneous'

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La tesi analitza les dinàmiques no locals i la intermitència en fluids no homogenis i no isotròpics tant en experiments de laboratori com en dades geogràfiques. Després de l'estudi sobre els models que descriuen la intermitència en fluids homogenis i isotròpics, presentem un model per fluids no homogenis i no isotropics. El model es basa en l'anàlisi de la jerarquia de transmissió d'energia. S'utilitza la tècnica de la Extended Self Similarity amb l'objectiu d'estudiar l'escala de lleis de les funcions estructurals de velocitat. Els resultats experimentals de tres tipus de fluids que s'han comparat amb el model per fluids no homogenis i no isotròpics són els següents: turbulència generada per un cilindre en un canal de vent i turbulència generada per una reixa i per un jet en un canal d'aigua. S'analitza la turbulència geogràfica del Delta de l'Ebre i del Knebel Vig i els resultats són comparats amb els del model anteriorment esmentat. La contribució principal és el descobriment d'un paràmetre aparentment relacionat amb la jerarquia de transmissió d'energia en el rang inercial que juga un paper clau en la comprensió de les dinàmiques dels fluids no homogenis.
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The thesis analyze the non-local dynamics and intermittency in non-homogeneous and non-isotropic flows both in the laboratory experiments and geophysical data. After a review on models describing intermittency in homogeneous and isotropic flows, a different model for non-homogeneous and non-isotropic flows is introduced. A model is based on the analysis of the energy transfer hierarchy. The technique of Extended Self Similarity is used to study the scaling laws of the velocity structure functions. Experimental results of three type of flows cylinder wake turbulence in wind tunnel, grid and jet turbulence in water channel are presented and compared with the model. The geophysical turbulence in the Ebro Delta and Knebel Vig are analyzed and the results are compared with the model. The important contribution is the discovery of a new apparently parameter related to the energy transfer hierarchy in the inertial range which plays a key role in the understanding of the dynamics of the non-homogeneous flows.

Modeling ultrasonic transducers is an important aspect of research in nondestructive evaluation and testing. In most nondestructive evaluation applications, the ultrasonic transducers are traditionally modeled as: (1) point sources generating spherical wave fronts (2) line sources generating cylindrical wave fronts, or (3) planar surfaces generating plane wave fronts. In reality, the transducer front face has finite dimensions; it is neither point source nor planar source because the ultrasound that emits from a piezoelectric transducer does not originate from a point or an infinite plane, but instead originates from the finite surface of the piezoelectric element with flat or curved front face. Analytically modeling the fields radiated by ultrasonic transducers is a very difficult task because of the large number of possible transducer types, sizes and configurations that are used in practice. In this study, a semi analytical technique the Distributed Point Source Method (DPSM) is adapted to model ultrasonic transducers. The DPSM discretizes the transducer surface into a finite number of elemental surfaces. As a result, the complexity associated with the discretization of the three-dimensional problem geometry as done in the finite element technique is reduced. In the DPSM technique, the fundamental governing equations for elastic wave propagation in a fluid and in a solid are solved. For this reason, the DPSM technique is called a semi-analytical technique. In this research, computer codes for computing the ultrasonic field in a three dimensional inhomogeneous medium in front of a transducer of finite dimension have been written in MatLab. Two different cases are considered in this study, nonhomogeneous fluid and fluid-solid interface. Both normal and inclined incidence cases are investigated. This investigation shows that DPSM is an efficient technique for modeling ultrasonic transducers in nonhomogeneous media.

Thesis (S.M.)--Massachusetts Institute of Technology, Dept. of Architecture, 2004.
Includes bibliographical references (leaves 104-110).
(cont.) and form development. Through this approach, space can be perceived not as distributed geometries, but rather as a composite graft responding locally to flows of programmatic and environmental parameters.
Digital methodologies have radically shifted our conception of the design process, as well as our understanding of geometry in terms of flexible relationships instead of finite positions in space. However, the material tectonic that digital means imply has not yet been explored on the basis of the new possibilities disclosed by these very same tools. Tectonic investigations have almost exclusively focused on construction techniques and primarily on the optimisation of methods that preceded the appearance of digital tools. I would argue, that computer generated architecture might imply a new understanding of matter and mass. So far, the materialization of formal expressions instigated by such processes are primarily based on techniques of assembly, which do not negotiate the advanced levels of material complexity that the tools put forward. This thesis lies on the premise of investigating modes to address an emergent rather than imposed materiality of distributions, instigated by computer-generated processes. Methodologically, this thesis has a twofold task. The former is to interrogate an alternate prism of construction history, which does not shed emphasis on geometry, but rather on mass and matter, paraphrasing Michel Serres. The atter task is to launch design experiments that respond to an alternate, emerging perception of material densities, constellations and coagulations. Through a series of digital case studies it becomes both a "theoretical" and "technical" probe of a materiality with local differences exploring non-homogeneous ways of distributing matter in space. Three material strategies--thread, component and substance--will be presented in an attempt to address modes of interrogating a reciprocal relationship between material
by Alexandros Tsamis.
S.M.

Thesis (Ph.D. in Mechanical Engineering)--S.M.U.
Title from PDF title page (viewed Mar. 16, 2009). Source: Dissertation Abstracts International, Volume: 69-03, Section: B, page: 1917. Adviser: Jose L. Lage. Includes bibliographical references.

The Bertrand Duopoly model for demand in economics is a well-used model. Although this model has important insights towards pricing strategy, it does not accurately depict true market behaviors. In this paper, we will examine the advantages and disadvantages of the current model and its assumptions.We then take a whole new approach towards modeling this phenomena, using Poisson processes to model the demand of goods. We will discuss why this is a better approach and explain how we can extend this to better understand pricing strategies and market dynamics. We then apply our findings to the newsvendor problem, a commonly used problem in inventory management. Using non-homogeneous Poisson processes we explain how to find an optimal pricing strategy and an optimal inventory level for the newsvendor problem.In this paper we explain how to extend the newsvendor problem to a newsvendor duopoly problem. Again we show how to find the optimal pricing strategies and inventory levels for multiple goods in a market. Having found the optimal pricing strategy and inventory level, we then examine the market dynamics in more details. We explore monopolistic and duopolistic markets where the goods range from complements to substitutes and homogeneous to differentiated goods. We discuss how to model the progression of the inventory probabilities and then explain how to price inventory options.

The problem of sonar detection and underwater communication in the presence of impulsive snapping shrimp noise is considered. Non-Gaussian amplitude and nonhomogeneous Poisson temporal statistical models of shrimp noise are investigated from the perspective of a single hydrophone immersed in shallow waters. New statistical models of the noise are devised and used to both challenge the superiority of existing models, and to provide alternative insights into the underlying physical processes.A heuristic amplitude statistical model of snapping shrimp noise is derived from first principles and compared with the Symmetric-α-stable model. The models are shown to have similar variability through the body of the amplitude probability density functions of real shrimp noise, however the new model is shown to have a superior fit to the extreme tails. Narrow-band detection using locally optimum detectors derived from these models show that the Symmetric-α-stable detector retains it's superiority, despite providing a poorer overall fit to the amplitude probability density functions. The results also confirm the superiority of the Symmetric-α-stable detector for detection of narrowband signals in shrimp noise from Australian waters.The temporal nature of snapping from a field of shrimp is investigated by considering the snapping as a point process in time. Point process analysis techniques are drawn from the fields of optics, neuro-physics, molecular biology, finance and computer science, and applied to the problem of snapping shrimp noise. It is concluded that the snapping is not consistent with a homogeneous Poisson process and that correlations exist in the point process on three different time scales. The cause of short time correlations is identified as surface reflected replicas, and models of medium time correlations are investigated. It is shown that a Cox-Ingersoll-Ross driven doubly-stochastic Poisson model is able to describe the medium time correlations observed from the counting process, but a k[superscript]th-order interval analysis reveals that there is more information contained within the snapping than can be described by the model. Analysis of shrimp snap times over a full day provides evidence of correlation between snap events on long time scales. Simulation of ocean noise is conducted to illustrate the use of such temporal models, and implications for their use in detection algorithms are discussed.

In this work, we deal with the study of some free boundary problems governed by non-homogeneous equations. In particular, we are interested in the regularity of the free boundaries for solutions of one-phase problems associated with non-divergence elliptic operators with variable coefficients.

For a network of G/oo service facilities, the transient joint distribution of the facility populations is found to have a simple Poisson product form with simple explicit formula for the means. In the network it is assumed that: a) each facility has an infinite number of servers; b) the service time distributions are general; c) external traffic is non-homogenous in time; d) arrivals have random or deterministic routes through the network possibly returning to the same facility more than once; e) arrivals use the facilities on their route sequentially or in parallel (as in the case of a circuit switched telecommunication network). The results have relevance to communication networks and manufacturing systems.

Thesis (M.S. in Applied Mathematics)--Naval Postgraduate School, September 2007.
Thesis Advisor(s): Zhou, Hong. "September 2007." Description based on title screen as viewed on October 25, 2007. Includes bibliographical references (p. 47). Also available in print.

The work presented in this thesis is an investigation of the dynamics of unconfined hydrogen-air flames in the presence of buoyant effects and the determination of an ignition criterion for flame propagation between adjacent pockets of reactive gas separated by air. The experimental work was conducted using the soap bubble technique and visualized with high speed schlieren or large scale shadowgraph systems. A study was first conducted to determine the most suitable soap solution additive among glycerol, guar and polyethylene oxide for conducting the experiments, isolating guar as the best candidate. The soap solution was then used to study the dynamics of flames in single or multiple soap bubbles filled with reactive mixtures of different compositions. The soap bubble method was also further improved by designing a soap dispenser that can maintain a bubble indefinitely and a method to burst the soap solution prior to an experiment using timed heated wires. In the experiments with single bubbles, it was found that for sufficiently lean hydrogen-air mixtures, buoyancy effects become important at small scales. The critical radius of hemispherical flames that will rise due to buoyancy was measured and estimated using a model comparing the characteristic burning speed and the rise speed of the flame kernel. Excellent agreement was found between the model predictions and the measured critical flame radii. The experiments with multiple bubbles provided the scaling rules for flame transition between neighboring pockets of hemispherical or spherical shape separated by an inert gas. The test results demonstrated that the separation distance between the bubbles is mainly determined by the expansion ratio when the buoyancy effects are negligible, corresponding to near stoichiometric mixtures. For leaner mixtures with stronger buoyant effects, the critical separation distance was no longer governed by the expansion ratio alone, as buoyancy forces render the flame propagation across the inert gas more difficult. Visualization of the ignition dynamics confirmed that buoyancy forces tend to accelerate the first kernel up before ignition of the second kernel can be achieved.

The aim of this thesis is to determine which 2-tori T makes $G/T$ formal for a compact connected Lie group G of rank 3. We show that the only time there is a possibility of a non-formal homogeneous space $G/T$ is when the Lie algebra E of G is semisimple and contains three simple ideals. In such a case, the Koszul complex is given by$$ (\Lambda(y\sb2,z\sb2,x\sb3,x\sbsp{3}{\prime}, x\sbsp{3}{\prime\prime}),d)$$and$$dx\sb3 = -y\sbsp{2}{2},\ dx\sbsp{3}{\prime} = -z\sbsp{2}{2},\ {\rm and}\ dx\sbsp{3}{\prime\prime} = -(\alpha y\sb2 + \beta z\sb2)\sp2,$$where $\alpha,\beta\in$ Q. We proveTheorem 5.5.4: This minimal c.g.d.a is formal if and only if $\alpha=0$ or $\beta=0.$ This, as we will see, indicates, in the case of non-formality, a special mixing of the 2-torus inside G.

A method due to É. Cartan was used to algebraically classify the possible four-dimensional manifolds that allow a (2, 2)-signature metric with a transitive group action which acts by isometries. These manifolds are classified according to the Lie algebra of the group action. There are six possibilities: four non-parameterized Lie algebras, one discretely parameterized family, and one family parameterized by R.

Cell migration is a behaviour critical to many key biological effects, including wound healing, cancerous cell invasion and morphogenesis, the development of an organism from an embryo. However, given that each of these situations is distinctly different and cells are extremely complicated biological objects, interest lies in more basic experiments which seek to remove conflating factors and present a less complex environment within which cell migration can be experimentally examined. These include in vitro studies like the scratch assay or circle migration assay, and ex vivo studies like the colonisation of the hindgut by neural crest cells. The reduced complexity of these experiments also makes them much more enticing as problems to mathematically model, like done here. The primary goal of the mathematical models used in this thesis is to shed light on which cellular behaviours work to generate the travelling waves of invasion observed in these experiments, and to explore how variations in these behaviours can potentially predict differences in this invasive pattern which are experimentally observed when cell types or chemical environment are changed. Relevant literature has already identified the difficulty of distinguishing between these behaviours when using traditional mathematical biology techniques operating on a macroscopic scale, and so here a sophisticated individual-cell-level model, an extension of the Cellular Potts Model (CPM), is been constructed and used to model a scratch assay experiment. This model includes a novel mechanism for dealing with cell proliferations that allowed for the differing properties of quiescent and proliferative cells to be implemented into their behaviour. This model is considered both for its predictive power and used to make comparisons with the travelling waves which result in more traditional macroscopic simulations. These comparisons demonstrate a surprising amount of agreement between the two modelling frameworks, and suggest further novel modifications to the CPM that would allow it to better model cell migration. Considerations of the model’s behaviour are used to argue that the dominant effect governing cell migration (random motility or signal-driven taxis) likely depends on the sort of invasion demonstrated by cells, as easily seen by microscopic photography. Additionally, a scratch assay simulated on a non-homogeneous domain consisting of a ’fast’ and ’slow’ region is also used to further differentiate between these different potential cell motility behaviours. A heterogeneous domain is a novel situation which has not been considered mathematically in this context, nor has it been constructed experimentally to the best of the candidate’s knowledge. Thus this problem serves as a thought experiment used to test the conclusions arising from the simulations on homogeneous domains, and to suggest what might be observed should this non-homogeneous assay situation be experimentally realised. Non-intuitive cell invasion patterns are predicted for diffusely-invading cells which respond to a cell-consumed signal or nutrient, contrasted with rather expected behaviour in the case of random-motility-driven invasion. The potential experimental observation of these behaviours is demonstrated by the individual-cell-level model used in this thesis, which does agree with the PDE model in predicting these unexpected invasion patterns. In the interest of examining such a case of a non-homogeneous domain experimentally, some brief suggestion is made as to how this could be achieved.

The work undertaken is concerned with looking at how terahertz frequency radiation (here defined as 300 GHz -10 THz) propagates through media which have a random structure ("non-homogeneous materials"). Materials of this type are important in a wide range of applications, but are of particular interest in security and surveillance. Propagation of terahertz radiation through non-homogeneous materials is not well understood: both interference and scattering effects become important in this spectral range, where the wavelength and size and separation of the scattering centres are often commensurable. A simple model, which uses the phase change of a wave to describe its transmission through media having relatively small changes in refractive index is developed and compared with both exact theories and experimentally obtained measurements. Overall, a satisfactory agreement between the experimental data for transmission through arrays of cylinders, textiles and powders is seen. It is well known that pulses of terahertz radiation from optoelectronic sources have a complex shape. Post detection signal processing routines can be used to clean up the experimentally determined signals. The development of such algorithms is described, before they are applied to experimental results to determine: the minimum size of gaps between slabs to mimic voids in media; and the response of various compounds to a sharply terminated input pulse. The investigation of scattering from random structures requires the construction of a spectrometer having the capability to measure THz pulses scattered at different angles. Such a system ideally requires fibre-fed detection schemes to be used. The construction of a scattering spectrometer is described and its performance outlined. Pulses of terahertz which have been scattered by a sample of interest can be reconstructed, using methods from conventional tomography, to produce images of the phantom under test. Such measurements are outlined here. To our knowledge, this is the first time that tomography has been undertaken using a fixed sample and rotating detector arrangement.

AGÊNCIA NACIONAL DE PETRÓLEO
Redes de Bragg em fibras ópticas (RBF) são formadas por modulações periódicas introduzidas no índice de refração do núcleo de fibras ópticas. Estes componentes comportam-se como filtros espectrais de banda passante, ou seja, quando iluminados por um sinal óptico de banda larga, refletem apenas uma fina fatia espectral de luz, cujo centro, o comprimento de onda de Bragg, é proporcional ao período espacial da modulação no índice de refração. As RBF têm encontrado aplicações importantes no sensoriamento das mais diversas grandezas, sendo hoje utilizadas em sistemas de monitoramento para vários segmentos industriais, tais como os setores de petróleo e gás, construção civil e aeroespacial, que, estima-se, respondem em conjunto por cerca de 70% destas aplicações. Em diversas situações o sensoriamento com RBF baseia-se em medidas indiretas da grandeza de interesse, sendo empregados mecanismos de transdução que transformam variações do mensurando em deformações na fibra óptica. Nestes casos, um problema que deve ser tratado com atenção é o acoplamento entre temperatura e deformação, uma vez que as RBF são sensíveis a estas duas variáveis. Não raro, a alternativa é utilizar simultaneamente duas RBF para obter-se a compensação de temperatura na medida de deformação. Este trabalho apresenta um estudo sobre deformações não homogêneas em redes de Bragg e discute aplicações de duas técnicas que podem ser utilizadas como alternativas para eliminar o efeito da temperatura no sensoriamento de deformação com apenas uma RBF. A primeira delas explora a birrefringência óptica induzida na RBF por carregamentos transversais à fibra óptica. A segunda baseia-se nos efeitos sobre o espectro refletido pela rede de Bragg quando submetida a um campo de deformações longitudinais não uniformes ao longo da direção axial da fibra óptica. No trabalho são apresentados protótipos e dispositivos que exploram tais técnicas para a medida simultânea de pressão e temperatura. Esses protótipos foram projetados com auxílio de ferramentas CAD e modelados utilizando-se o método de elementos finitos em conjunto com a teoria de modos acoplados da Rede de Bragg. As previsões obtidas utilizando-se estes modelos mostraram-se bastante próximas dos resultados das implementações experimentais dos protótipos, indicando que a metodologia de modelagem desenvolvida pode ser aplicada nos projetos de transdutores baseados nas duas técnicas estudadas.
Fiber Bragg gratings (FBG) are modulations in the effective refractive index of optical fibers, introduced in a small length along the fiber core. Such components operate as narrow band reflective filters, that is, when illuminated by a broad-band light source, they reflect a narrow spectral band centered at a specific wavelength, the Bragg wavelength. This wavelength is proportional to the spatial period of the refractive index modulation. Fiber Bragg gratings have find an increasing number of applications as sensors for different quantities, and today are being employed as part of permanent, real time monitoring systems in various industrial segments. The oil and gas sector, together with civil infrastructure and aeronautics and aerospace, account for almost 70% of this applications. In a number of situations, FBG sensing is based on indirect measurements of the quantity being monitored, and a transduction mechanism is employed to transform changes in the measured quantity in strain sensed by the optical fiber. Since the FBG is sensitive to strain and temperature, proper temperature compensation is always necessary. Usually, a second grating is employed to simultaneously measure temperature and strain, performing the required compensation. This thesis presents a study on effects due to non- homogeneous strains in the Bragg grating and discusses application of two different techniques, based on these effects, to allow temperature compensated strain measurement using a single FBG. The first technique explores strain induced optical birefringence when the fiber is loaded transversely. The second technique is based on changes in the spectral shape of the light signal reflected by the grating when subjected to non homogeneous axial strain fields. Prototypes of pressure and temperature transducers based on these techniques have been developed. These prototypes have been designed by employing CAD techniques and modeled using the finite element method in conjunction with the theory of coupled modes for fiber Bragg gratings. Comparisons between results provided by theoretical models and experimental realizations of the prototypes are very close, demonstrating that the developed approach can be applied to design transducers based on the discussed techniques. Results obtained with the proposed pressure and temperature sensors are also encouraging indicating that the two techniques are suitable for industrial applications.

6.1 INTRODUCCIÓ Des del 2001, el grup de Química Organometàl¿lica i Catàlisis Homogènia de la Universitat Jaume I, QOMCAT, dirigit pel professor Eduardo Peris, ha centrat els seus esforços en la investigació i desenvolupament de nous lligands de tipus carbè N-heterocíclics (NHCs) per a la preparació de catalitzadors metàl¿lics millorats. La versatilitat dels lligands de tipus NHC, a més de la fàcil preparació dels seus precursors (normalment sals d'azoli), han permès dissenyar una gran varietat de topologies i formes de coordinació. Dins d'aquest context, aquest grup va iniciar algunes línies d'investigació relacionades amb la 'Química Verda'. Així, nous complexos que contenien lligands NHC van ser sintetitzats per a la reducció de CO2 utilitzant iPrOH en lloc de H2, fent el procés més segur i respectuós amb el medi ambient. A més, la funcionalització de lligands NHC amb grups polars va permetre la síntesi de catalitzadors solubles en dissolvents sostenibles (aigua i glicerol),1-6 i també l'ús d'altres eines d'activació de calefacció d'energia alternativa (MW or US).4-5 Més recentment, el grup va reorientar els seus esforços en el disseny d'estructures rígides basades en lligands poli-NHC per a la preparació de catalitzadors homo- i heterometàl¿lics.7-10 Aquest tipus de policarbens poden estar units mitjançant sistemes rígids ¿-conjugats i poden ser capaços de comunicar electrònicament les unitats carbèniques. Aquesta característica dels complexos poli-NHC pot tindre molt d'interès per a la fabricació de dispositius electrònics moleculars a més de les importants millores catalítiques que pot implementar. A continuació s'inclou una breu ressenya sobre els avanços fets durant aquesta tesi doctoral: Disseny de catalitzadors per al desenvolupament de processos verds i síntesi de nous complexos basats en lligands imidazolilidè-piridilidè i poli-NHC. Els processos verds que decidírem estudiar són la reacció Suzuki-Miyaura d'acoblament C-C en aigua i l'alquilació d'amoníac amb alcohols primaris que transcorre a través d'un mecanisme de "préstec d'hidrogen", conegut més habitualment pel terme anglès Borrowing-Hydrogen. Les reaccions d'acoblament C-C catalitzades per metalls de transició són un dels mètodes més utilitzats per a la formació d'enllaços C-C, sent el pal¿ladi el metall més utilitzat per a desenvolupar aquest tipus de reaccions. Entre aquests processos, la reacció d'acoblament Suzuki-Miyaura, és a dir, l'acoblament entre un àcid arilborònic i un halur d'aril,11 és el protocol més utilitzat per a sintetitzar bifenils atesa la bona tolerància davant diferents grups funcionals. Per aquesta raò, trobar una alternativa més respectuosa amb el medi ambient per a dur a terme aquesta reacció és un repte per als investigadors en el camp de la catàlisi homogènia. Els processos catalítics que s'engloben sota el terme "Borrowing-Hydrogen" constitueixen un ampli ventall de reaccions en les que el nexe comú és determinat per la intermediació d'un catalitzador que serveix com a transportador d'hidrogen entre un parell de substrats.12-15 En una reacció típica de Borrowing-Hydrogen es produeix l'oxidació d'un substrat, normalment un alcohol (o una amina), per un catalitzador metàl¿lic que 'agafa com a préstec' dos àtoms d'hidrogen. Depenent si l'alcohol és primari o secundari, es generarà un aldehid o una cetona, respectivament. Aquests compostos de carbonil poden sofrir una àmplia gama de transformacions ja que poden reaccionar in situ per a donar imines, alquens i compostos de carbonil funcionalitzats. El catalitzador metàl¿lic, que havia agafat com a préstec l'hidrogen, el "torna" al nou compost, produint la seua reducció. Aquests processos catalítics compleixen el principi d'economia atòmica ja que, normalment, tots els àtoms dels substrats apareixen en els productes o, com a màxim, l'únic subproducte obtingut és H2O o NH3, per la qual cosa es consideren processos que contribueixen a la química verda. Els lligands de tipus imidazolilidè-piridilidè (C,C¿-imz-pyr) se formen com a conseqüència de la unió d'una unitat d'imidazolilidè i una unitat piridilidè. El primers complexos que presentaven aquest tipus de lligands (C,C¿-imz-pyr) foren descrits per Colbran,16 6.1 en Esquema 6.1. En els últims anys els lligands de tipus poli-NHC han donant lloc a una gran varietat de complexos polimetàl¿lics, amb diferents topologies que condueixen a l'obtenció de propietats catalítiques inusuals17-20 En aquest sentit, el nostre grup d'investigació ha descrit recentment lligands di- i tri-NHC amb sistemes ¿-electrònics conjuminats per a la preparació de compostos polimetàl¿lics millorats.8, 21 En particular, el lligand tri-NHC 6.2 (Esquema 6.2) va donar lloc a compostos que augmentaven la seua capacitat catalítica en comparació amb altres compostos mono metàl¿lics o tri metàl¿lics amb les mateixes característiques esteroelectròniques Hahn i col¿laboradors van ser els primers a descriure una estructura supramolecular metàl¿lica tridimensional que contenia exclusivament enllaços metall-NHC (6.3, Esquema 6.3).22 Aquesta estructura es va sintetitzar per reacció directa de dos lligands hexa-NHC amb Ag2O. En principi, aquest tipus d'estructures poden ser utilitzades com a caixes macromoleculars encercladores de molècules menudes neutres o iòniques i, per tant, funcionar com a detectors químics.23-28 En concret en el compost 6.3 es mostra la presència d¿un ió bromur a l¿interior de la caixa. 6.2 OBJECTIUS L'objectiu general d'aquesta tesi doctoral és la síntesi de catalitzadors homogenis amb propietats esteroelectròniques millorades. En aquest sentit, el treball es centra en la preparació i caracterització de nous complexos metàl¿lics amb diferents lligands de tipus carbè N-heterocíclic (NHC) o lligands anàlegs, l'estudi dels seus patrons de reactivitat i l'exploració de les seues propietats catalítiques. Els objectius concrets que se¿n deriven son els següents: ¿ Síntesi de complexos de pal¿ladi i iridi per al desenvolupament de processos verds. Principalment, s'intentaran realitzar reaccions catalítiques amb les condicions més respectuoses amb el medi ambient, utilitzant dissolvents no tòxics, amb la màxima economia atòmica i sense malbaratament d'energia. ¿ Estudi sistemàtic de la reactivat de lligands imidazolilidè-piridilidè mitjançant la seua coordinació a precursors de rodi i iridi. ¿ Disseny, síntesi i coordinació de lligands poli-NHC per a la preparació de complexos polimetàl¿lics amb estructures inusuals i altament simètriques. Estudi de les seues propietats electròniques. ¿ 6.3 DISCUSSIÓ DE RESULTATS 6.3.1 Síntesi de compostos de Pd(II) hidrofílics amb lligands NHC. Aplicacions catalítiques 6.3.1.1 Síntesi de compostos de Pd(II) hidrofílics amb lligands NHC L'Esquema 6.4, mostra els tres precursors dels lligands NHC, funcionalitzats amb cadenes sulfonatades, que han sigut utilitzats. El compost AH,3 ha sigut prèviament descrit en la bibliografia, mentre que, els compostos BH2 i CH2 s'han sintetitzat i caracteritzat per primera vegada al llarg del treball d'investigació que es presenta. A partir d'aquests lligands s¿han obtingut complexos de Pd(II) en els quals els lligands s'uneixen al metall de forma mono coordinada, quelat i pinça. Hem tractat que l'elecció d'aquest tipus de modes de coordinació donen lloc a un ampli conjunt de topologies de complexos de pal¿ladi NHC que ja han demostrat propietats catalítiques eficients en dissolvents orgànics.29-30 L'estratègia de metal¿lació utilitzada ha sigut l'ús d'una base dèbil incorporada en el precursor de pal¿ladi per a desprotonar els compostos d'imidazolilidè segons es mostra en l'Esquema 6.5. Els compostos d'imidazoli BH2 i CH2 junt amb els catalitzadors 1A-4C descrits en aquesta secció, han sigut sintetitzats per primera vegada al llarg del treball d'investigació que es presenta i han sigut caracteritzats per espectroscòpia d'RMN, espectrometria de masses i per anàlisi elemental. El complex 4C va ser sintetitzat, ja que la introducció d'un lligand piridina ha demostrat millorar l'activitat catalítica dels compostos amb els quals es coordina per efecte "PEPPSI".31-33 6.3.1.2 Aplicacions catalítiques Amb la finalitat d'avaluar les propietats catalítiques dels complexos hidrofílics preparats en l'apartat anterior, decidírem utilitzar-los en la reacció d'acoblament C-C de Suzuki-Miyaura en aigua, on un àcid arilborònic reacciona amb un halur d'aril per a donar un compost biarilat. Així, es va fer reaccionar l'àcid fenilborònic amb vuit halurs d'aril diferents (4-brom, i 4-cloracetofenona; 4-brom, i 4-clorbenzè; 4-brom, i 4-clortoluè; 4-brom, i 4-cloranisol), tal com es mostra en l'Esquema 6.6. Les reaccions es van fer en una mescla d'aigua/iPrOH (1:1) a 110ºC, amb 1 mol% de catalitzador i en presència de K2CO3. Els resultats obtinguts ens van permetre concloure que els compostos 1A i 3C són els més actius, ja que faciliten rendiments molt elevats en temps de reacció curts (4h, per als bromur d'aril i 12h, per als clorur d'aril). Però és el catalitzador 1A amb què obtenim els resultats més espectaculars quan utilitzem 4-bromacetofenona i 4-cloracetofenona, ja que obtenim rendiments superiors al 99% en 4h i 12h, respectivament. Els resultats catalítics obtinguts suggereixen que la presència del lligand piridina en el compost 4C no augmenta l'activitat catalítica d'aquest per efecte "PEPPSI" en comparació al catalitzador 3C. 6.3.2 Síntesi de compostos de Ir(III) amb lligands formamidina. Aplicacions catalítiques 6.3.2.1 Síntesi de compostos de Ir(III) amb lligands formamidina El lligand 1,3-bis(2,4,6-trimetilfenil)formamidina, D, va ser sintetitzat seguint el procediment descrit en la literatura34 i a partir d'aquest vam obtenir dos compostos diferents de 'IrCp*' depenent de la forma de coordinar-se d'aquest. Si el lligand D adopta coordinació monodentada s'obté el compost 5D, però si la coordinació es en forma quelat obtenim el compost 6D (Esquema 6.7). Aquests dos nous compostos, 5D i 6D, han sigut caracteritzats per espectroscòpia d'RMN, espectrometria de masses i per anàlisi elemental. Les estructures moleculars dels dos compostos han sigut confirmades mitjançant Difracció de Raigs X (DRX) sobre monocristall. 6.3.2.2 Aplicacions catalítiques En aquest cas, decidírem comprovar l'activitat catalítica dels compostos 5D i 6D en dues reaccions governades per processos de Borrowing-Hydrogen. En primer lloc començàrem amb la reacció de ß-alquilació d'alcohols secundaris amb alcohols primaris per a després estendre l'estudi de l'activitat catalítica dels dos complexos en una reacció més interessant, com és l'alquilació d'amoníac amb alcohols primaris. a) ß-Alquilació d'alcohols secundaris amb alcohols primaris Aquesta reacció es va dur a terme en condicions de màxima economia atòmica, és a dir, intentant que tots els materials utilitzats com a reactius s'incorporen als productes. Així, tal com es mostra en l'Esquema 6.8, es va fer reaccionar una mescla equimolecular de l'alcohol primari, alcohol secundari i una base (KOH), en presència de 0.1-1 mol% de catalitzador en toluè a 100ºC. La reacció pot donar lloc a dos productes, l'alcohol alquilat i/o la cetona alquilada. La reacció es va dur a terme utilitzant 2-feniletanol com a alcohol secundari i quatre alcohols primaris diferents (bencilalcohol, butanol, 3-clorbencilalcohol i 4-clorbencilalcohol), utilitzant els catalitzadors 5D i 6D. Els resultats obtinguts van permetre concloure que 5D és molt més eficient que 6D, tant en termes de conversió cap als productes finals com en selectivitat cap a l'alcohol ß-alquilat. El catalitzador 5D també és molt actiu fins i tot a concentracions de 0.1 mol%, sobretot quan utilitzem bencilalcohol i 4-clorbencilalcohol. Els resultats catalítics obtinguts suggereixen que el grup NH en el lligand formamidina del complex 5D aporta un 'efecte NH'35-36 cooperatiu fent que aquest compost siga més actiu que 6D. b) Alquilació d'amoníac amb alcohols primaris En primer lloc vam comparar l'activitat catalítica de [IrCp*Cl2]2, el catalitzador d'Shvo i els nous compostos 5D i 6D. Com es mostra en l'Esquema 6.9, per a dur a terme la reacció es va fer reaccionar diferents sals d'amoni amb bencilalcohol a 110 o 130ºC, utilitzat diverses carregues de catalitzador, en presència d'un 3 mol% de NaHCO3 i amb proporcions de bencilalcohol/sal d'amoni de 3:1 o 3.6:1. El complex 5D i el catalitzador d'Shvo mostraren excel¿lents resultats catalítics en l'alquilació de la sal d'amoni NH4OAc per a obtindre trifenilamina, en comparació amb els resultats obtinguts amb [IrCp*Cl2]2 i el complex 6D sota les mateixes condicions de reacció. A més, 5D va ser moderadament actiu en l'alquilació del NH4OH. Tenint en compte les dades anteriors, decidírem ampliar l'abast del catalitzador d'Shvo i el complex 5D, estudiant la seva activitat catalítica davant una varietat d'alcohols primaris. Tal i com es mostra en l'Esquema 6.10, l'alquilació de sals d'amoni amb diferents alcohols primaris es va dur a terme a 130 o140ºC, utilitzant carregues de catalitzador d'1, 3 i 5 mol%, en presència de KOH o sense base i amb proporcions d'alcohol primari/sal d'amoni de 3.6:1 o 6:1. En aquest cas la reacció pot donar lloc a diferents amines, segons l'alcohol primari utilitzat (4-clorbencilalcohol, 3-clorbencilalcohol, 4-metilbencilalcohol, 1-hexanol, 1-butanol i 1-ciclohexanol). Els resultats obtinguts ens van permetre concloure que amb el catalitzador 5D s'obtenen resultats catalítics extraordinaris, sobretot quan utilitzem bencilalcohol, però, la seua eficiència baixa quan utilitzem alcohols alquílics. La activitat del catalitzador d'Shvo és en la majoria del casos més elevada, mostrant així la gran aplicabilitat d'aquest catalitzador exepcional. A la vista dels resultats obtinguts en les dues reaccions governades per processos de Borrowing-Hydrogen, i tal com havíem comentat anteriorment, creiem que la presència del grup NH en el lligand formamidina del complex 5D està incrementant l'activitat catalítica d'aquest davant el complex 6D i [IrCp*Cl2]2. Aquet 'efecte NH' pot estar facilitant la deshidrogenació de l'alcohol primari per a passar a aldehid en el primer pas del cicle catalític,37 d'una manera similar a les observacions descrites per Noyori en les reaccions d'hidrogenació de cetones.35-36 6.3.3 Síntesi de compostos de Rh(III) i Ir(III) basats en lligands imidazolilidè-piridilidè i estudi de la seua reactivitat no convencional Durant aquesta tesi doctoral també ens vam interessar en la síntesi de compostos de rodi i iridi amb lligands imidazolilidè-piridilidè (C,C¿-imz-pyr) coordinats en forma quelat. A més d'obtenir els compostos di-NHC esperats, també es varen sintetitzar una sèrie de compostos amb els lligands reordenats en formes poc convencionals. L'estudi d'aquests nous compostos amb lligands C,C¿-imz-pyr ofereix una bona oportunitat per a comparar les diferències estructurals i de reactivitat d'aquests complexos depenent del tipus de la coordinació del carbè (normal, abnormal o remota), tant del imidazolilidè com del piridilidè. L'Esquema 6.11 mostra les diferents sals precursores dels lligands C,C¿-imz-pyr que han sigut utilitzades. Totes aquestes sals s'han sintetitzat i caracteritzat, per primera vegada, al llarg del treball d'investigació que es presenta. 6.3.3.1 Síntesi i caracterització dels complexos [MI2(C,C'-imz-pyr)(CH3CN)2]+ (M = Rh, Ir) En primer lloc, vam obtenir una sèrie de complexos de tipus [MI2(C,C'-imz-pyr)(CH3CN)2]+ (M = Rh, Ir) (Esquema 6.13). L'estratègia sintètica per a sintetitzar estos compostos va consistir a fer reaccionar la sal d'imidazoli-piridini corresponent, [EH2]I2-[JH2]I2, amb el precursor metàl¿lic [MCl(diolefina)]2 (M = Rh, Ir; diolefina = COD, NBD) i KI en CH3CN a 65ºC durant 12h. Com a exemple la síntesi del compost 7E es mostra en l'Esquema 6.12. Les noves sals d'imidazoli-piridini, [EH2]I2-[JH2]I2, i els nous complexos metàl¿lics de Rh(III) i Ir(III), 7E-16I, descrits en aquesta secció han sigut caracteritzats per espectroscòpia d'RMN, espectrometria de masses i per anàlisi elemental. Les estructures moleculars dels complexos 11F, 14G i 15I han sigut confirmades mitjançant Difracció de Raigs-X sobre monocristall. L'avaluació de l'espectroscòpia de RMN d'aquests complexos revela algunes característiques que interessa mencionar. Pel que fa a l'espectroscòpia 13C RMN d'aquests compostos, es va observar que les freqüències degudes als carbens dels piridilidens decreixen en l'ordre: remot, normal, abnormal, per al rodi, i remot, abnormal per a l'iridi. Rodi: remot (¿c = 183.9) > normal (¿c = 175.7) > abnormal (¿c = 169.3) Iridi: remot (¿c = 164.7) > abnormal (¿c = 160.8) L'anàlisi de les longituds d'enllaç en les estructures moleculars del compostos 11F i 15I (Esquema 6.14) en han permès constatar que els piridilidens aporten una influència trans major que els imidazolilidens, com ja han suggerit altres grups d'investigació.38-39 6.3.3.2 Síntesi i caracterització dels complexos [MCp*I(C,C'-imz-pyr)]+ (M = Rh, Ir) Decidírem estendre la coordinació dels lligands derivats de les sals, [EH2]I2, [GH2]I2 i [IH2]I2, a altres precursors metàl¿lics com són [MCp*Cl2]2 (M = Rh, Ir) i una sèrie de compostos [MCp*I(C,C'-imz-pyr)]+ (M = Rh, Ir) foren sintetitzats (Esquema 6.16). L'estratègia sintètica per a sintetitzar estos compostos és similar a la utilitzada anteriorment, però en aquest es va afegir base i es va calfar a 90ºC durant 12h. Com a exemple la síntesi del compost 17E es mostra en l'Esquema 6.15. Els nous complexos metàl¿lics de Rh(III) i Ir(III), 17E-24I, descrits en aquesta secció han sigut caracteritzats per espectroscòpia d'RMN, espectrometria de masses i per anàlisi elemental. Les estructures moleculars dels complexos 18E, 19E, 20E, 22G i 23I han sigut confirmades mitjançant Difracció de Raigs-X sobre monocristall. Els compostos 20E, 22G i 23I presenten reactivitats molt inusuals. En el cas de 20E, l'imidazolilidè esta coordinat al centre metàl¿lic mentre que el piridilidè esta acoblat a l'anell de Cp*, així s'obté un anell Cp* funcionalitzat amb un imidazolilidè penjant. Pel que fa al compost 22G, a més de l'activació C-H esperada del CH3 del C2 de l'imidazoli un acoblament reductiu entre el Cp* i l'anell de piridini te lloc. Tant en el cas del complex 20E com per a 22G, creiem que aquests dos compostos se generen via la formació d'un intermedi de tetrametilfulvè de rodi. Tal com s'ha descrit per a compostos amb reactivitats similars.40-45 El compost 23I és un dímer d'iridi en el qual l'obertura de l'anell d'imidazoli ha tingut lloc com a conseqüència de la hidròlisi de l'imidazolilidè. La hidròlisi de carbens no és un fet tant estrany i ha sigut descrit en més ocasions.46 En el nostre cas, a banda de l'obertura de l'anell d'imidazolilidè, es produeixen altres reorganitzacions que tenen a veure amb la descarboxilació de l'aldehid per a generar el lligand carbonil i el lligand imino. 6.3.4 Síntesi de compostos de Rh(I) Ag(I) i Au(I) basats en lligands poli-NHC Durant aquesta tesi doctoral, també hem centrat els nostres esforços en sintetitzar compostos que contenen lligands poli-NHC. En primer lloc, varem sintetitzar i coordinar un lligand tri-NHC amb una estructura central basada en un tribenzotriquinacè (TBTQ) i amb simetria C3v a Rh(I). La segona família de compostos es va obtenir a partir de dues sals d'hexa-imidazoli, els lligands derivats d'elles es varen coordinar a Ag(I) obtenint complexos amb sis àtoms de plata en forma cilíndrica. Els compostos d'or anàlegs també es varen obtenir mitjançant transmetal¿lació. 6.3.4.1 Síntesi i caracterització del complex de Rh(I) amb el lligand tri-NHC-TBTQ L'estratègia sintètica per a preparar compostos amb lligands poli-NHC comença amb l'aminació múltiple de Buchwald-Hartwig de molècules poliaromàtiques amb bromurs adjacents. Aquesta metodologia ha sigut utilitzada per Bielawski i col¿laboradors i nosaltres aplicàrem aquesta metodologia a hexabromtribenzotriquinacè 6.547 (Esquema 6.17). D'aquesta manera, tal com es mostra en l'Esquema 6.17, el compost 6.5 reacciona amb tert-butilamina (tBuNH2) en presència de [Pd(OAc)2], IPr¿HCl i NaOtBu en toluè a 115ºC, per a donar hexaaminotribenzotriquinacè, hexaNH2-TBTQ, que posteriorment es ciclat amb trietilortoformat (HC(OEt)3) en presència de HBF4 a 80ºC, obtenint-se la sal [KH3](BF4)3. Aquesta sal es desprotonada amb KHMD en THF a 0ºC, i amb la posterior addició de [RhCl(COD)]2 a temperatura ambient s'obté el complex 25K que es purificat mitjançant cromatografia de columna. Els nous compostos, hexaNH2-TBTQ, [KH3](BF4)3 i 25K, descrits en aquesta secció han sigut caracteritzats per espectroscòpia d'RMN i espectrometria de masses. L'estructura molecular de [KH3](BF4)3 ha sigut confirmada mitjançant Difracció de Raigs-X sobre monocristall. 6.3.4.2 Síntesi i caracterització de complexos de Ag(I) i Au(I) amb lligands hexa-NHC Amb la finalitat d'augmentar el nombre d'estructures supramoleculars generades a partir de lligands poli-NHC, pensàrem que les sals 1,2,3,4,5,6-hexa(N-alquil imidazoli)benzè [LH6](OTf)6 i [MH6](BF4)6 (alquil = Me i Et, respectivament) (Esquema 6.18), podrien ser bones precursores. Aquestes sals s'obtenen a partir de l'alquilació de hexa(imidazol-1-il)benzè amb metil trifluorometasulfonat per a donar [LH6](OTf)6, o amb trietiloxoni tetrafluoroborat per a donar [MH6](BF4)6 (Esquema 6.18). La reacció d'aquestes dues sals amb Ag2O en CH3OH a 50ºC dona lloc als corresponents complexos cilíndrics, 26L i 27M, que contenen sis centres de Ag(I). Els compostos anàlegs d'or, 28L i 29M, s'obtenen mitjançant la reacció de 26L i 27M en CH3OH a 50ºC i en presència de AuCl(SMe2) (Esquema 6.18). Les noves sals, [LH6](OTf)6 i [MH6](BF4)6 i els nous complexos 26L, 27M, 28L i 29M, descrits en aquesta secció han sigut caracteritzats per espectroscòpia d'RMN i espectrometria de masses. L'estructura molecular de 28M ha sigut confirmada mitjançant Difracció de Raigs-X sobre monocristall. ¿ 6.4 CONCLUSIONS En aquesta tesi doctoral s'han obtingut una sèrie de complexos de pal¿ladi amb lligands NHC hidrofílics i complexos d'iridi amb el lligand formamidina. Aquests complexos han sigut avaluats en processos verds com són la reacció Suzuki-Miyaura d'acoblament C-C en aigua i les reaccions governades per processos de Borrowing-Hydrogen: ß-alquilació d'alcohols secundaris amb alcohols primaris i alquilació d'amoníac amb alcohols primaris. El compost 3C ha sigut el més actiu en la reacció Suzuki-Miyaura d'acoblament C-C en aigua i el compost 5D, junt amb el catalitzador d'Shvo, han presentat les millors activitats en les reaccions governades per processos de Borrowing-Hydrogen. Durant aquesta tesi doctoral, també s'han sintetitzat compostos de Rh(III) i Ir(III) amb lligands imidazolilidè-piridilidè que han presentat reactivitats molt inusuals. La comparació entre els diferents compostos obtinguts ens ha permès determinar que els piridilidens ocasionen un major efecte trans que els imidazolilidens. Finalment, s'han sintetitzat dos lligands nous poli-NHC per a la preparació de complexos polimetàl¿lics amb estructures altament simètriques. La possibilitat de preparar complexos homo-polimetàl¿lics suggereix que prompte podrem trobar la via per a sintetitzar espècies hetero-polimetàl¿liques. Per la nostra experiència, aquests complexos solen ser potencialment útils per al disseny de nous processos catalítics tàndem. A més, una de les propostes que ens hem plantejat és la combinació dels lligands piridilidens amb estructures politòpiques que obri una nova línea d'investigació dins del camp dels carbens N-heterocíclics.

Within this composition commentary, I seek to outline my practice for composing for laptop ensembles, as well as the notational approaches I have developed to facilitate composition, direction, rehearsal and ultimately performance within an intentionally non-homogeneous laptop ensemble. Illustrating the requirement to move beyond the current typical ‘application as score and meta-instrument’ paradigm, I outline my own notational approach for laptop ensemble writing and the features it offers to the operation of laptop ensembles. As a consequence of the notational approach I seek to outline the performative coding role of the player and acknowledge the compositional role it extends to the performer. These theoretical considerations are considered within the practical operation of the Huddersfield Experimental Laptop Orchestra (HELO) and its sibling HELOpg. As a consequence of these experiments I present my preference for graph and text based notations for directing the laptop performer.

The ever growing demand for public transportation and the need to integrate effective transport systems into urban life have led to an increase in the planning and construction of new railway systems in many countries around the world. These projects boast immense economic benefits, including high passenger capacity and reduction in commuting times. However, they are strongly opposed from an environmental point of view, not least the noise and vibration that are generated from their operations and subsequently transmitted into nearby buildings. In order to reduce the level of impact of the rail vehicles on the tracks, and subsequently the environment, railway tracks are commonly constructed with resilient elements, e.g. railpads. The dynamic properties of these elements have significant effects on noise generation, track and ground-borne vibration. It is important to develop understanding of the dynamic behaviour of railway tracks, through numerical modelling and/or experimental testing, in order to devise effective vibration countermeasures. To this end, many numerical models have been developed, most of which assumed linear and homogeneous track properties. However, many studies have shown that resilient elements exhibit pronounced nonlinear behaviour and that variability in track properties exists along the length of the track. In this study, novel approaches for incorporating nonhomogeneous and non-linear railpad properties in the modelling of railway track dynamics have been developed. A new method, called the Double Fourier Summation, have been used to account for nonhomogeneity in track foundation properties. To account for nonlinearity, on the other hand, constitutive relationships have been derived for the static and dynamic rail pad properties based on experimental data. These are then included into a time domain finite elements track model in order to study the effects of nonlinearity on track dynamics. The key findings of this research emphasise the necessity of including non-homogeneous and nonlinear behaviour of track resilience into the modelling of track dynamics. Large disparities in the track displacement, reaction-forces and wheel/rail interaction forces (more than 20 dB in some cases), have been observed between simplified linear homogeneous models and the more complex nonhomogeneous and nonlinear models presented in this work.

DE LA TESIS:

El contenido de esta tesis se enmarca dentro del Análisis Real. En particular, trata del estudio de ciertos problemas de la teoría de pesos, (una referencia clásica sobre esta teoría es el libro de J. García-Cuerva y J.L. Rubio de Francia [GR]). Nosotros consideramos, por este orden, tres problemas clásicos diferentes, que abarcan buena parte de la teoría de pesos:

(i) Estudio de las inclusiones para espacios con pesos y acotación de operadores integrales entre estos espacios.

(ii) Estudio de propiedades funcionales de espacios con pesos asociados a una reordenada decreciente de funciones.

(iii) Estudio de la acotación de operadores maximales asociados a regiones de aproximación entre espacios con pesos.

Todos estos problemas han sido tratados extensamente en la literatura. Nuestro enfoque ha sido el de extender estos resultados a espacios con la mínima estructura necesaria. Concretamente, hemos trabajado respectivamente en cada capítulo en los siguientes contextos:

(i) Espacios de medida arbitrarios.

(ii) Árboles.

(iii) Espacios de tipo homogéneo.

Puesto que un árbol puede ser a su vez un espacio de medida, o puesto que su frontera puede ser un espacio de tipo homogéneo, algunos resultados para espacios de medida y espacios de tipo homogéneo han sido aplicados a los árboles (véanse los capítulos primero y tercero). En cambio, en el capítulo segundo trabajamos exclusivamente en árboles.

Los espacios donde hemos desarrollado nuestra teoría no poseen, en general, ningún tipo de estructura algebraica. Por tanto, todos los resultados persiguen un objetivo común: la extensión de la teoría de pesos a espacios no euclidianos.

Dissertation submitted in fulfilment of the requirements for the degreerequirements Master of Technology: Civi Engineering in the Faculty of Engineering at the Cape Peninsula University of Technology Supervisor: APN. Sutherland Co-supervisor: Prof. R. Haldenwang Cape Town October 2013
The reliable prediction of pressure drop versus flow rate for non-Newtonian pipe flow is important in many industrial processes. In laminar flow scale up is straightforward, but transitional velocity and turbulent flow predictions remain a practical problem. Various theoretical models exist, but nothing in literature shows conclusively which of these is the most reliable and consistent, nor is it evident what effect the choice of rheological model has on the predictions. The aim of this work was to i) evaluate the influence of different rheological models when used in existing prediction techniques for non-Newtonian flow ii) characterise each material type using selected (commonly used) rheological models and iii) predict laminar, transitional and turbulent pipe flow characteristics for each material type using existing prediction techniques, for comparison with experimental results. Only time-independent, homogeneous, non-Newtonian fluids in pipe sizes from 13mm to 200mm were investigated. Rheological models and laminar flow predictions used only the power law, Bingham plastic, Herschel-Bulkley, Casson and Hallbom yield plastic models. The techniques used to predict transitional velocity were Ryan & Johnson, Metzner-Reed, Hedström intersection method, Slatter and Hallbom. For turbulent flow the Newtonian approximation, Dodge & Metzner, Wilson & Thomas, Slatter, Hallbom modified Wilson & Thomas and the Bowen correlation methods were used. The study documents the relevant theory and presents an assessment of the influence of rheology on pipe flow predictions, summarised in terms of the practical performance of the various rheological model/prediction method combinations for the different materials. In laminar flow at practical pseudo shear rates (8V/D; taken as 40s-1) the choice of rheological model does not significantly influence pressure drop predictions. For yield-pseudoplastic materials (eg. kaolin) the Hedström intersection and the Slatter Reynolds number method with Bingham plastic or Casson rheology predicted transitional velocity most accurately. For Bingham plastic materials (eg. bentonite) the best predictions were obtained using the Metzner & Reed Reynolds number with Bingham plastic rheology, although similar results were observed for this technique with all rheologies. The transitional velocity for pseudoplastic materials (eg. CMC) was best predicted by the Slatter and Metzner & Reed Reynolds number methods, using power law or Casson rheology. For turbulent flow of yield pseudoplastic materials the Slatter method using the Casson rheology gave the most accurate predictions overall. Turbulent flow of Bingham plastic materials was best predicted by the Slatter, Hallbom pseudo fluid Nikuradse and Dodge & Metzner methods, using Bingham plastic, Casson or yield plastic rheology. For pseudoplastic materials the Slatter and Wilson & Thomas methods were the most accurate, when used with yield plastic or power law rheology. Transitionalal velocity and turbulent flow predictions for materials with a yield stress vary significantly with rheological model. Laminar data should therefore be examined thoroughly and rheological models fitted with care. For pseudoplastic fluids there is little difference in predictions between the various techniques as long as power law rheology is used.

Thesis (MTech (Mechanical Engineering))--Cape Peninsula University of Technology, 2016.
This dissertation presents how material properties (solids densities, particle size distributions, particle shapes and concentration) of gold tailings slurries are related to their rheological parameters, which are yield stress and viscosity. In this particular case Bingham yield stresses and Bingham plastic viscosities. Predictive models were developed from analysing data in a slurry database to predict the Bingham yield stresses and Bingham plastic viscosities from their material properties. The overall goal of this study was to develop a validated set of mathematical models to predict Bingham yield stresses and Bingham plastic viscosities from their material properties. The interaction of the non-Newtonian material properties is very complex at varying mass solids concentrations. The evaluation of these interactions in terms of constitutive equations is almost impossible and the relationship between material properties, mass solids concentration and rheology can only be modelled in a statistical manner. The validity of each model is checked to ensure that predictions and interpretations are unbiased and efficient. This is done by comparing the resulting models to experimental data generated from test work. An in-depth analysis was conducted to see the interrelationship between the material properties and how they affect the yield stress and viscosity values.

Thesis: S.M., Massachusetts Institute of Technology, Department of Aeronautics and Astronautics, 2015.
Cataloged from PDF version of thesis.
Includes bibliographical references (pages 61-64).
This thesis investigates the field of stochastic hybrid estimation. A broad introduction to the framework surrounding estimation, filtering, and multiple model based systems is presented. More specifically, the often made assumption of a constant time-invariant mode transition probability matrix is relaxed. Recent work done in the area of non-Markov jump stochastic hybrid systems is explored, including semi- Markov systems, non-homogeneous transition probability matrices, and continuous-state-dependent mode transitions. Algorithms needed to develop linear multiple model based filters with non-homogeneous transition probabilities are detailed. Finally, a case study for the practical implementation of an extended Kalman filter in the application of attitude heading and reference systems is conducted.
by Michael William Kasperski.
S.M.

Thesis (S.M.)--Massachusetts Institute of Technology, Dept. of Aeronautics and Astronautics, September 2007.
"August 2007."
Includes bibliographical references (leaves 85-87).
The air traffic management system is currently experiencing a significant transformation to provide better quality service and to match the increasing air traffic demand. This transformation requires airlines to retrofit their fleet. However, airlines implement new operating capabilities at different rates resulting in long transition periods in which aircraft with different equipage levels coexist in the same airspace. Mixed equipage environments can increase controller workload and task complexity, limit the operational benefits of new operating capabilities, and deteriorate the overall system performance. This study proposes a three dimensional approach to explore mixed equipage effects: (1) understand cognitive implications for controllers, (2) understand operational implications for users, and (3) understand system level implications. To further investigate mixed equipage effects and to illustrate the proposed approach, this study analyzed the implementation of reduced separation standards in the North Atlantic. An experimental analysis was conducted to study the integration of mixed separation standards. Results show significant human factor concerns. Controllers had higher error rates at very low mixed equipage levels. Results also suggest that a contributing causal factor may have been that participants employed inadequate system abstractions based on their current mental models. Airspace segregation based on equipage levels is recommended in the North Atlantic to alleviate controller cognitive limitations and ensure incentives for equipped aircraft. Segregation can facilitate the transition to reduced separation standards.
(cont.) A preliminary estimation of the operational benefits that segregation could offer to equipped aircraft in the North Atlantic was performed. We developed a simplified model of the jet stream and its operational cost impact and contrasted the results with a statistical analysis of actual North Atlantic flight times. It was found that the model made optimistic predictions of flight time reduction. Based on the statistical analysis, the incentive for equipped aircraft in a segregated environment in the North Atlantic was estimated by a gain of 4 minutes. This figure is a preliminary estimation and further analysis with larger data samples is required to validate it.
by Patricia E. Pina.
S.M.

L’objectif de cette thèse est d’étudier l’aérodynamique d’un dirigeable dans des conditions d’écoulement instationnaires et non homogènes, en décrivant sa dynamique au moyen de modèles simples et d’outils de calcul rapides et efficaces. En raison de leur « légèreté », les dirigeables sont plus sensibles aux perturbations de l’air. Cela a un impact important sur leur contrôlabilité et par conséquent sur le dimensionnement des gouvernes et du système propulsif.Les phénomènes aérodynamiques liés à la notion de masses et inerties ajoutées, qui sont observés pendant les phases de mouvement relatif accéléré du dirigeable, sont un terme supplémentaire à prendre en compte pour l’évaluation des efforts aérodynamiques. Elles dépendent de la densité du fluide, de la géométrie du corps et du repère choisi. Ces contributions sont généralement négligées lors de l’étude de corps « lourds » tels que les avions, car leur densité est nettement supérieure à celle de l’air. Au contraire, pour les dirigeables, ces termes sont du même ordre de grandeur que leur masse et leur moment d’inertie et représentent donc un aspect fondamental à prendre en compte pour décrire correctement leur dynamique.Nos études sur les masses et inerties ajoutées ont été réalisées par des simulations numériques en fluides parfait et visqueux. Un code numérique pour le calcul de ces termes a été développé afin d’obtenir en un temps réduit une estimation très précise sur des configurations complexes (géométries génériques en présence de parois externes).La présence de perturbations et de gradients de vitesse dans l’atmosphère est à l’origine d’efforts aérodynamiques supplémentaires d’importance majeure pour les dirigeables. Ces phénomènes ont été analysés au moyen de simulations numériques CFD instationnaires. Un modèle simplifié de reconstruction des efforts aérodynamiques a été proposé, basé sur des résultats stationnaires, qui permet de prédire avec précision les caractéristiques aérodynamiques du corps.Enfin, nous avons proposé un modèle complet de la dynamique des dirigeables qui, à l’avenir, pourra être analysé et validé par des tests expérimentaux ou numériques sur des configurations génériques de dirigeables dans des écoulements instationnaires et perturbés
The objective of this thesis is to study the aerodynamics of an airship in unsteady and non-homogeneous flow conditions, describing its dynamics through simplified models and fast and efficient computationlal tools.Because of their « lightness », airships are more sensitive to air disturbances. This has a major impact on their controllability and consequently on the sizing of the control surfaces and the propulsion system.Aerodynamic phenomena related to the notion of added masses, which are observed during the relative accelerated motion phases of the airship, are an additional term to be taken into account for the evaluation of the overall aerodynamic stresses. They depend on the density of the fluid, the geometry of the body and the reference frame. Generally, these contributions are neglected in the investigation of « heavy » bodies such as airplanes, since their density is considerably higher that of air. On the contrary, for airships these terms are the same order of magnitude of their mass and their moment of inertia and therefore represent a fundamental aspect to be taken into account to correctly describe their dynamics.Our studies on added masses have been carried out through numerical simulations in potential and viscous flows. A numerical code for the calculation of these terms has been developed in order to obtain in a short time a very accurate estimate on complex configurations (generic body geometries even in the presence of external walls).The presence of perturbations and velocity gradients in the atmosphere causes additional aerodynamic loads that are particularly relevant for airships. These phenomena have been analyzed through unsteady CFD simulations. Subsequently a simplified model, based on stationary results, has been proposed fir the reconstruction of this loads, resulting accurate in prediction the aerodynamic characteristics of the body.Finally, we have proposed a complete model of the airship dynamics that in the future can be analysed and validated through experimental or numerical tests on generic airship configurations in unsteady and perturbed flows

PONTIFÍCIA UNIVERSIDADE CATÓLICA DO RIO DE JANEIRO
COORDENAÇÃO DE APERFEIÇOAMENTO DO PESSOAL DE ENSINO SUPERIOR
CONSELHO NACIONAL DE DESENVOLVIMENTO CIENTÍFICO E TECNOLÓGICO
PROGRAMA DE EXCELENCIA ACADEMICA
Neste trabalho são analisadas junções entre guias coaxiais não homogêneos com perdas. A expansão modal dos campos eletromagnéticos em um guia coaxial com duas camadas radiais é detalhadamente deduzida, e posteriormente a formulação é generalizada para guias com multicamadas radiais. As constantes de propagação para guias com perdas são determinadas pelo método do winding number, garantindo que todos os autovalores possam ser encontrados. O método do casamento de modos é aplicado na análise e projeto de estruturas coaxiais. A formulação é aplicada na otimização de estruturas de acoplamento e cornetas radiantes com carregamento dielétrico não homogêneo. O preenchimento não homogêneo é empregado nas estruturas radiantes a fim de minimizar a perda de retorno, e principalmente controlar e melhorar o formato do diagrama de radiação para operação em banda larga. Adicionalmente, a formulação é utilizada para analisar a propagação eletromagnética em sistemas de telemetria sem fio para poços de petróleo.
In this work, we analyzed junctions between coaxial waveguides heterogeneously filled with lossy dielectrics. The modal expansion of the electromagnetic fields in a coaxial waveguide with two radial layers is derived in detail, and afterward the formulation is generalized for a multilayer waveguide. The propagation constants for lossy waveguides are determined through the method of winding number, ensuring that all eigenvalues can be found. The mode matching technique is applied in the analysis and design of coaxial structures. The formulation is applied in the optimization of coupling structures and radiating horns with heterogeneous dielectric loading. The heterogeneous filling is used in radiating structures in order to reduce the return loss, and especially to control and improve the shape of the radiation pattern for broadband operation. Additionally, the formulation is used to analyze the electromagnetic propagation in wireless telemetry systems for oil wells.

Understanding spatial perspectives on the spread and incidence of a disease is invaluable for public health planning and intervention. Choropleth maps are commonly used to provide an abstraction of disease risk across geographic space. These maps are derived from aggregated population counts that are known to be affected by the small numbers problem. Kernel density estimation methods account for this problem by producing risk estimates that are based on aggregations of approximately equal population sizes. However, the process of aggregation often combines data from areas with non-uniform spatial and population characteristics. This thesis presents a new method to aggregate space in ways that are sensitive to their underlying risk factors. Such maps will enable better public health practice and intervention by enhancing our ability to understand the spatial processes that result in disparate health outcomes.

The applicability and adequacy of three modeling approaches to describe and predict breakthough curves (BTCs) for non-reactive solutes in statistically homogeneous porous media were numerically and experimentally investigated. Modeling approaches were: the convection-dispersion equation (CDE) with scale-dependent dispersivity, mobile-immobile model (MIM), and the fractional convection-dispersion equation (FCDE). In order to test these modeling approaches, a prototype laboratory column system was designed for conducting miscible displacement experiments with a free-inlet boundary. Its performance and operating conditions were rigorously evaluated. When the CDE with scale-dependent dispersivity is solved numerically for generating a BTC at a given location, the scale-dependent dispersivity can be specified in several ways namely, local time-dependent dispersivity, average time-dependent dispersivity, apparent time-dependent dispersivity, apparent distance-dependent dispersivity, and local distance-dependent dispersivity. Theoretical analysis showed that, when dispersion was assumed to be a diffusion-like process, the scale-dependent dispersivity was locally time-dependent. In this case, definitions of the other dispersivities and relationships between them were directly or indirectly derived from local time-dependent dispersivity. Making choice between these dispersivities and relationships depended on the solute transport problem, solute transport conditions, level of accuracy of the calculated BTC, and computational efficiency The distribution of these scale-dependent dispersivities over scales could be described as either as a power-law function, hyperbolic function, log-power function, or as a new scale-dependent dispersivity function (termed as the LIC). The hyperbolic function and the LIC were two potentially applicable functions to adequately describe the scale dependent dispersivity distribution in statistically homogeneous porous media. All of the three modeling approaches described observed BTCs very well. The MIM was the only model that could explain the tailing phenomenon in the experimental BTCs. However, all of them could not accurately predict BTCs at other scales using parameters determined at one observed scale. For the MIM and the FCDE, the predictions might be acceptable only when the scale for prediction was very close to the observed scale. When the distribution of the dispersivity over a range of scales could be reasonably well-defined by observations, the CDE might be the best choice for predicting non-reactive solute transport in statistically homogeneous porous media.
Ph. D.

In this work we study vertical, acoustic propagation in a non-homogeneous media for a spatially-compact, time-harmonic source. An analytical, 2-layer model is developed representing the acoustic pressure disturbance propagating in the atmosphere. The validity of the model spans the distance from the Earth's surface to 30,000 meters. This includes the troposphere (adiabatic), ozone layer (isothermal), and part of the stratosphere (isothermal). The results of the model derivation in the adiabatic region yield pressure solutions as Bessel functions of the First (J) and Second (Y) Kind of order $-\frac{7}{2}$ with an argument of $2 \Omega \tau$ (where $\Omega$ represents a dimensionless frequency and $\tau$ is a dimensionless vertical height in z (vertical coordinate)). For an added second layer (isothermal region), the pressure solution is a decaying sinusoidal, exponential function above the first layer. In particular, the vertical, acoustic propagation is examined for various configurations. These are divided into 2 basic classes. The first class consists of examining the pressure response function when the source is located on boundary interfaces, while the second class consists of situations where the source is arbitrarily located within a finite layer. In all instances, a time-harmonic, compact source is implicitly understood. However, each class requires a different method of solution. The first class conforms to a general boundary value problem, while the second requires the use of Green's functions method. In investigating problems of the first class, 3 different scenarios are examined. In the first case, we apply our model to a semi-infinite medium with a time-harmonic source ($e^{-i \omega t}$) located on the ground. In the next 2 cases, a semi-infinite medium is overlain on the previous medium at a height of z=13,000 meters. Thus, there exist two boundaries: the ground and the layer interface between the 2 media. Sources placed at these interfaces represent the 2nd and 3rd scenarios, respectively. The solutions to all 3 cases are of the form $A \frac{J_{-\frac{7}{2}}(2 \Omega \tau)}{{\tau}^{-\frac{7}{2}}} + B \frac{Y_{-\frac{7}{2}}(2 \Omega \tau)}{{\tau}^{-\frac{7}{2}}}$, where \textit{A} and \textit{B} are constants determined by the boundary conditions. For the 2nd class, we examine the application to a time-harmonic, compact source placed arbitrarily within the 1st layer. The method of Green's functions is used to obtain a particular solution for the model equations. This result is compared with a Fast Field Program (FFP) which was developed to test these solutions. The results show that the response given by the Green's function compares favorably with that of the FFP. Keywords: Linear Acoustics, Inhomogeneous Medium, Layered Atmosphere, Boundary Value Problem, Green's Function Method

The practical application of non-photochemical laser-induced nucleation (NPLIN) to continuous flow was investigated. Supersaturated aqueous solutions were screened with a 5 ns pulsed laser (532 nm 44 MW cm-2) for NPLIN activity. Upon irradiation succinic acid nucleated at S20 = 4.3 and adipic acid at S20 = 2.0 - 3.0. NPLIN activity is reported for the first time in nicotinic acid (S20 = 2.6 - 3.0). No overall pattern was observed of chemical structure on NPLIN activity. From inorganic compounds similarly screened, ammonium chloride (S20 = 1.04 - 1.20) was identified as most suitable for further tests. It was shown to have an increase of NPLIN crystals with higher supersaturation from 13 at S = 1.038 to 252 at S = 1.135. A quadratic increase in number of crystals with increased laser power. The effects of NPLIN upon ammonium chloride are diminished upon filtration through a 0.2 μm poly (ether sulfone) filter, reducing the number of crystals from 350 to 10 per 70 mJ pulse (25 MW cm-2). The use of NPLIN in continuous flow was demonstrated from the first time. A S23 = 1.1 solution of aqueous ammonium chloride in flow produced crystals when irradiated by 10 pulses s-1 of a 1064 nm 6 ns laser. When the laser was stopped, crystals were no longer produced and the system returned to flowing supersaturated solution. Lab scale apparatus for continuous NPLIN experiments was developed. A design involving a re-dissolution step and loop flow was constructed for both laminar and slug-flow regimes. Nucleation of ammonium chloride (S = 1.1) was demonstrated in both systems. Repeatable NPLIN experiments were hindered by spontaneous nucleation. Spontaneous nucleation in flow was observed around areas where supersaturated solution passed from one component to another. Spontaneous nucleation was also observed upon cooling (25 to 10 °C). Filtration was observed to both suppress NPLIN and spontaneous nucleation in flow.

The present thesis is devoted both to the study of strictly hyperbolic operators with low regularity coefficients and of the density-dependent incompressible Euler system. On the one hand, we show a priori estimates for a second order strictly hyperbolic operator whose highest order coefficients satisfy a log-Zygmund continuity condition in time and a log-Lipschitz continuity condition with respect to space. Such an estimate involves a time increasing loss of derivatives. Nevertheless, this is enough to recover well-posedness for the associated Cauchy problem in the space $H^infty$ (for suitably smooth second order coefficients).In a first time, we consider acomplete operator in space dimension $1$, whose first order coefficients were assumed Hölder continuous and that of order $0$only bounded. Then, we deal with the general case of any space dimension, focusing on a homogeneous second order operator: the step to higher dimension requires a really different approach. On the other hand, we consider the density-dependent incompressible Euler system. We show its well-posedness in endpoint Besov spaces embedded in the class of globally Lipschitz functions, producing also lower bounds for the lifespan of the solution in terms of initial data only. This having been done, we prove persistence of geometric structures, such as striated and conormal regularity, for solutions to this system. In contrast with the classical case of constant density, even in dimension $2$ the vorticity is not transported by the velocity field. Hence, a priori one can expect to get only local in time results. For the same reason, we also have to dismiss the vortex patch structure. Littlewood-Paley theory and paradifferential calculus allow us to handle these two different problems .A new version of paradifferential calculus, depending on a parameter $ggeq1$, is also needed in dealing with hyperbolic operators with nonregular coefficients. The general framework is that of Besov spaces, which includes in particular Sobolev and Hölder sets. Intermediate classes of functions, of logaritmic type, come into play as well

This work investigates the material properties and production parameters of carbon infiltrated carbon nanotube structures (CI-CNT's). The impact of non homogeneous infiltration and the porosity of cross section regions, coupled with changes in designed geometry, in this case beam width, on the density and modulus of elasticity are compared. Three potential geometric models of beam cross section are proposed and evaluated. 3-point bending, SEM images, and numerical optimization are used to assess the validity of each model and the implications they have for future CI-CNT material applications. Carbon capping near exterior beam surfaces is observed and determined to be a contributing factor to variations in material properties correlated with changes in designed geometry and infiltration parameters (temperature, time, and hydrogen flow rate). Unexpected relationships between beam width and elastic modulus are partially explained by modeling the carbon-capped beams as C-shaped structural members consisting of a graphitic carbon shell of varying porosity and thickness and uninfiltrated carbon nanotube internal regions with a near negligible stiffness. Findings of previous works on the effects of infiltration parameters and carbon capping on materials properties are confirmed and expanded. Flange and web thickness and porosity of the graphitic carbon shell are identified as potential design parameters for pursuing tunable material properties in high precision geometry MEMS and compliant mechanism applications.

a b s t r a c t A study concerning the propagation of free non-axisymmetric waves in a homogeneous piezoelectric cylinder of transversely isotropic material with axial polarization is carried out on the basis of the linear theory of elasticity and linear electro-mechanical coupling. The solution of the three dimensional equations of motion and quasi-electrostatic equation is given in terms of seven mechanical and three electric potentials. The characteristic equations are obtained by the application of the mechanical and two types of electric boundary conditions at the surface of the piezoelectric cylinder. A novel method of displaying dispersion curves is described in the paper and the resulting dispersion curves are presented for propagating and evanescent waves for PZT-4 and PZT-7A piezoelectric ceramics for circumferential wave numbers m = 1, 2, and 3. It is observed that the dispersion curves are sensitive to the type of the imposed boundary conditions as well as to the measure of the electro-mechanical coupling of the material.