Dissertationen zum Thema „Six-dimensional“

In the last years, brane world scenarios have been studied extensively, but most of these studies have been done in the case of five-dimensional spacetime. It is therefore of interest to investigate which of the particular features observed are proper to one extra dimension and which are generic to any number of dimensions. In this thesis, I present an overview of models and solutions to Einstein's equations for six-dimensional brane world scenarios. Solutions for a simple setup with cylindrically symmetric bulk centered about a three-brane are derived and classified. There are two main kinds of topology: either solutions are compactified in a spherical topology, closed up by another three-brane, or they have a disc topology, which must be terminated by a four-brane. One of the particular features of codimension-two branes is demonstrated, namely that their tension, or vacuum energy, induces a deficit angle in the bulk. Solutions for different arrangements of codimension-one and codimension-two branes are also reviewed. Although the review focuses on topological and cosmological properties of the solutions, models using a field theoretical approach to the brane-world scenario, i.e. considering the brane as a topological defect arising from higher dimensional fields, are also considered.

In this thesis we aim to characterize the self-dual strings of six-dimensional superconformal field theories (SCFTs) and develop a variety of techniques to compute their elliptic genera, which provide information about their spectra. All known N = (1, 0) supersymmetric SCFTs in 6d can be obtained by compactifying F-theory on an elliptic Calabi-Yau threefold with singular, noncompact base B. Resolving the singularity in B and wrapping D3 branes on the exceptional curves leads to strings on the tensor branch of the SCFT. The strings become tensionless at the superconformal fixed point and appear to play an important role in the dynamics of the SCFT. For a number of SCFTs we identify two-dimensional N = (0, 4) quiver gauge theories describing bound states of self-dual strings and obtain their elliptic genera by localization. We achieve this for 6d SCFTs describing M5 or D5 branes at a singularity, as well as n M5 branes probing an M9 plane (corresponding to n small E8 instantons). More generally, we relate the elliptic genera of strings of 6d SCFTs to the counting of supersymmetric (BPS) particles that arise upon compactification to 5d. This enables us to compute elliptic genera by topological string techniques. Following this approach we obtain information about the strings associated to SCFTs with a single tensor multiplet and minimal gauge group. Additionally, for SCFTs whose strings arise from M2 branes suspended between M5 or M9 branes we find a quantum mechanical picture in which M5 branes or M9 planes are represented by domain wall operators or states; in this context, elliptic genera are expressed in terms of suitable correlators which we compute. Finally, we find a non-perturbative completion of the topological string partition function that can be employed to compute five-sphere partition functions of 5d SCFTs and superconformal indices of 6d SCFTs. In the latter case, we argue that the superconformal index can be written in terms of elliptic genera of the self-dual strings, providing further evidence of the important role these strings play in the dynamics of 6d SCFTs.
Physics

We review the lore of effective field theories as a background to hierarchy problems in general and the cosmological constant problem in particular. We outline some of the attempted four-dimensional solutions to the cosmological con stant problem and conclude that ones based upon the usual assumptions of four-dimensiona lfield theory typically do not work. We argue that one way to relax the assumptions is to seek solutions to the cosmological constant problem which rely on the presence of extra dimensions. We explicitly exhibit that standard compactification techniques fail to solve the cosmological constant problem because they reduce the problem to a four-dimensional one.
We argue that brave-world models may be helpful in solving the cosmological constant problem because standard model loops contribute to the tension and not to the vacuum energy directly, and can fulfill our stated aim of constructing a model which uses the extra dimensions to mitigate the cosmological constant problem. We identify necessary (not sufficient) properties a theory must possess to successfully use this observation. These properties are: a scaling symmetry encoded in a dilaton-like scalar, and bulk supersymmetry.
We therefore investigate supersymmetric six-dimensional brave-world models. Our models are imbedded within a 6D supergravity that has many of the features of realistic string models. We explicitly show that the compactification of the 6D theory has many of the same features as string compactifications, including flat four-dimensional space, chiral fermions, rnoduli, moduli-stabilisation using fluxes, and gluino condensation. We show that by calculating the non-perturbative correction to the superpotential and loop-corrections to the Kahler function that a meta-stable deSitter vacuum can be found. The vacuum energy can be tuned to be ∼ 10-6 M4Planck .
We find that all solutions of the supergravity equations of motion, under a symmetry ansatz, have flat braves. This implies that this property is independent of some of the details of the braves, such as their tensions. The source of the branes' flatness is the required classical scaling symmetry of the action.
We consider whether this class of models may provide a solution to the cosmological constant problem within the large extra dimensions scenario, in which the radius r ∼ 0.1mm, and in which the standard-model fields are trapped on a 3-brave. We conclude that it may be possible to produce naturally a cosmological constant that is of order r -4 ∼ (10-3eV)4 due to loops because the supersymmetry-breaking scale in the bulk is MSUSY ∼ r-1; although there remains a great deal of work to be done. We comment on recent extensions to cosmological backgrounds.
Further work within these models is outlined, including higher-dimensional models, use of effective field-theory techniques in theories with sharp boundaries, and the treatment of quantum corrections.

We investigate one-dimensional (1D) wave turbulence (WT) systems that are characterised by six-wave interactions. We begin by presenting a brief introduction to WT theory - the study of the non-equilibrium statistical mechanics of nonlinear random waves, by giving a short historical review followed by a discussion on the physical applications. We implement the WT description to a general six-wave Hamiltonian system that contains two invariants, namely, energy and wave action. This enables the subsequent derivations for the evolutions equations of the one-mode amplitude probability density function (PDF) and kinetic equation (KE). Analysis of the stationary solutions of these equations are made with additional checks on their underlying assumptions for validity. Moreover, we derive a differential approximation model (DAM) to the KE for super-local wave interactions and investigate the possible occurrence of a fluctuation relation. We then consider these results in the context of two physical systems - Kelvin waves in quantum turbulence (QT) and optical wave turbulence (OWT). We discuss the role of Kelvin waves in decaying QT, and show that they can be described by six-wave interactions. We explicitly compute the interaction coefficients for the Biot-Savart equation (BSE) Hamiltonian and represent the Kelvin wave dynamics in the form of a KE. The resulting non-equilibrium Kolmogorov-Zakharov (KZ) solutions to the KE are shown to be non-local, thus a new non-local theory for Kelvin wave interactions is discussed. A local equation for the dynamics of Kelvin waves, the local nonlinear equation (LNE), is derived from the BSE in the asymptotic limit of one long Kelvin wave. Numerical computation of the LNE leads to an agreement with the nonlocal Kelvin wave theory. Finally, we consider 1D OWT. We present the first experimental implementation of OWT and provide a comparable decaying numerical simulation for verification. We show that 1D OWT is described by a six-wave process and that the inverse cascade state leads to the development of coherent solitons at large scales. Further investigation is conducted into the behaviour of solitons and their impact to the WT description. Analysis of the fluxes and intensity PDFs lead to the development of a wave turbulence life cycle (WTLC), explaining the coexistence between coherent solitons and incoherent waves. Additional numerical simulations are performed in non-equilibrium stationary regimes to determine if a pure KZ state can be realised.

In this thesis, compactifications of F-theory on six dimensional symmetric toroidalorbifolds are explored. These orbifold geometries have been mathematically classified and it is natural to ask what the physical implications of string theorycompactifications on those geometries are. Since compactifications of string theory to six dimensions describe a sweet spot in terms of developed methods andrich model-building possibilities, it is interesting to investigate the landscape ofthese theories opposed to the swampland of only apparently consistent quantumtheories of gravity. Additionally, superconformal field theories can exist in at mostsix dimensions. These emerge naturally in the considered F-theory constructions. The present work explores effects of compactifications on such orbifolds buildingon the work of [arXiv:1905.00116v1 [hep-th]]. It constitutes a step towards extendingthe geometric classification of these orbifolds to a classification of the physical models. Beyond [arXiv:1905.00116v1 [hep-th]], roto-translations have severe effects on thegeometry and thus the field theory and the spectrum. These effects are discussedin this thesis and include, amongst others, twisted affine folding of gauge groups, the emergence of superconformal points away from intersecting branes as well assuperconformal sectors related to the multiple fibre.
In dieser Thesis werden Kompaktifizierungen von F-Theorie auf sechs dimensionalen symmetrischen, toroidalen Orbifaltigkeiten untersucht. Da diese Orbifaltigkeiten mathematisch klassifiziert wurden, stellt sich auf natürliche Weisedie Frage nach den physikalischen Implikationen von Kompaktifizierungen vonString Theorie auf diesen. In Kompaktifizierungen von String Theorie zu sechs Dimensionen balancieren sich der Fortschritt der Methoden und die Möglichkeitenphysikalische Theorien zu modellieren optimal. Daher ist es wichtig das "Landscape" dieser Theorien zu untersuchen, im Gegensatz zu dem so genannten "Swampland" von vermeintlich konsistenten Quantentheorien der Gravitation. Darüber hinaus stellt sich heraus, dass superkonforme Feldtheorien höchstens insechs Dimensionen existieren können. Die vorliegende Arbeit erkundet die Effekte von Kompaktifizierungen auf solchen Orbifaltigkeiten aufbauend auf der Arbeit von [arXiv:1905.00116v1 [hep-th]]. Sie stellt einen wichtigen Schritt dar auf dem Weg zu einer Ausweitung der geometrischen Klassifikation dieser Orbifaltigkeiten zu einer Klassifikation der physikalischen Modelle. Über [arXiv:1905.00116v1 [hep-th]] hinaus resultieren Roto-Translationen in Effekten auf die Feldtheorie sowie deren Spektrum. Diese Effekte werden in dieser Thesis diskutiert. Beispiele reichen von getwisteten affinen Faltungen von Eichgruppen, zu dem Auftreten von superkonformen Punkten ohne sich schneidende Branen und superkonforme Sektoren in Verbindung mit dem "mehrfach Faser"-Phänomen.

This thesis was conducted under the regulations of Heidelberg University under the joint supervision of Professor Luca Amendola (University of Heidelberg) and Assistant Professor Magdalena Larfors (Uppsala University) during a one-year ERASMUS-exchange.

In this work we investigate the global symmetries of six-dimensional superconformal field theories (6D SCFTs) via their description in F-theory. We provide computer algebra system routines determining global symmetry maxima for all known 6D SCFTs while tracking the singularity types of the associated elliptic fibrations. We tabulate these bounds for many CFTs including every 0-link based theory. The approach we take provides explicit tracking of geometric information which has remained implicit in the classifications of 6D SCFTs to date. We derive a variety of new geometric restrictions on collections of singularity collisions in elliptically fibered Calabi-Yau varieties and collect data from local model analyses of these collisions. The resulting restrictions are sufficient to match the known gauge enhancement structure constraints for all 6D SCFTs without appeal to anomaly cancellation and enable our global symmetry computations for F-theory SCFT models to proceed similarly.

Thesis (Ph.D.)--University of Missouri-Columbia, 2006.
The entire dissertation/thesis text is included in the research.pdf file; the official abstract appears in the short.pdf file (which also appears in the research.pdf); a non-technical general description, or public abstract, appears in the public.pdf file. Title from title screen of research.pdf file viewed on (February 26, 2007) Vita. Includes bibliographical references.

Streuamplituden der Quantenchromodynamik (QCD), N = 4 Super-Yang-Mills-Theorie (SYM-Theorie) und der sechsdimensionalen N = (1, 1) SYM-Theorie werden untersucht, mit einem Fokus auf die Symmetrien und Relationen zwischen den Streuamplituden dieser Eichtheorien auf dem Baum-Niveau. Die Baum-Niveau- und Ein-Schleifen-Farbzerlegung beliebiger QCD-Amplituden in primitive Amplituden wird bestimmt und Identitäten hergeleitet, welche den Nullraum unter den primitiven Amplituden aufspannen. Anschließend wird bewiesen, dass alle farbgeordneten Baum-Niveau-Amplituden der masselosen QCD aus der N = 4 SYM-Theorie erhalten werden können. Analytische Formeln für alle für die QCD relevanten N = 4 SYM-Amplituden werden bestimmt und die Effizienz und Genauigkeit der numerischen Auswertung der analytischen Formeln für farbgeordnete QCD-Baum-Niveau-Amplituden mit einer effizienten numerischen Implementierung der Berends-Giele-Rekursion verglichen. Die Symmetrien der massive Amplituden auf dem Coulomb-Zweig der N = 4 SYM-Theorie werden hergeleitet. Diese können durch eine dimensionale Reduktion der masselosen Baum-Niveau-Amplituden der sechsdimensionalen N = (1, 1) SYM-Theory erhalten werden. Darüber hinaus wird bezeigt, wie es mit Hilfe einer numerischen Implementierung der BCFW-Rekursion möglich ist analytische Formeln für die Baum-Niveau-Superamplituden der N = (1, 1) SYM-Theory zu erhalten und die Möglichkeit eines Uplifts der masselose Baum-Niveau-Amplituden der N = 4 SYM-Theory untersucht. Schließlich wird eine Alternative zur dimensionalen Regularisierung der N = 4 SYM-Theorie untersucht. Die Infrarotdivergenzen werden hierbei durch Massen regularisiert, die durch einen Higgs-Mechanismus erhalten wurden. Die korrespondierende Stringtheorie-Beschreibung deutet auf eine exakte duale konforme Symmetrie der Streuamplituden hin. Durch explizite Rechnungen wird dies bestätigt und Vorteile des Regulators werden demonstriert.
We study scattering amplitudes in quantum chromodynamics (QCD), N = 4 super Yang-Mills (SYM) theory and the six-dimensional N = (1, 1) SYM theory, focusing on the symmetries of and relations between the tree-level scattering amplitudes in these three gauge theories. We derive the tree level and one-loop color decomposition of an arbitrary QCD amplitude into primitive amplitudes. Furthermore, we derive identities spanning the null space among the primitive amplitudes. We prove that every color ordered tree amplitude of massless QCD can be obtained from gluon-gluino amplitudes of N = 4 SYM theory. Furthermore, we derive analytical formulae for all gluon-gluino amplitudes relevant for QCD. We compare the numerical efficiency and accuracy of evaluating these closed analytic formulae for color ordered QCD tree amplitudes to a numerically efficient implementation of the Berends-Giele recursion. We derive the symmetries of massive tree amplitudes on the coulomb branch of N = 4 SYM theory, which in turn can be obtained from N = (1, 1) SYM theory by dimensional reduction. Furthermore, we investigate the tree amplitudes of N = (1, 1) SYM theory and explain how analytical formulae can be obtained from a numerical implementation of the supersymmetric BCFW recursion relation and investigate a potential uplift of the massless tree amplitudes of N = 4 SYM theory. Finally we study an alternative to dimensional regularization of N = 4 SYM theory. The infrared divergences are regulated by masses obtained from a Higgs mechanism. The corresponding string theory set-up suggests that the amplitudes have an exact dual conformal symmetry. We confirm this expectation and illustrate the calculational advantages of the massive regulator by explicit calculations.

Thesis (Ph. D.)--Massachusetts Institute of Technology, Dept. of Physics, 2012.
Cataloged from PDF version of thesis.
Includes bibliographical references (p. 217-232).
Comparing the set of supergravity theories allowed by low-energy consistency conditions with the set of string vacua provides useful insights into quantum gravity and string theory. In fact, such a "landscape analysis" for ten-dimensional supergravity theories was at the core of the exciting series of developments that is now referred to as the first superstring revolution. In this thesis, we discuss the lessons we learn about quantum supergravity and string theory by carrying out such an analysis for the space of six-dimensional supergravity theories with minimal supersymmetry. We first review six-dimensional supergravity theories and explain why the space of these theories is an ideal place to carry out the landscape analysis. We then describe how anomaly constraints bound the space of consistent theories, i.e., we map the space of theories T that satisfy known low-energy consistency conditions. We then go on to describe string constructions that give six-dimensional string vacua with minimal supersymmetry, i.e., we map the space of theories S c T that come from string vacua. Finally, we compare the space of theories T and S and explore its implications. We first find that there is a large discrepancy between T and S. Among the set T - S, we identify some theories that are potentially new string vacua, but also identify many theories that cannot be embedded in any known string vacua. These theories may potentially be ruled out by yet undiscovered low energy constraints. Understanding these theories is an important step in addressing the question of string universality in six dimensions. We also find some surprising equalities that hold for Calabi-Yau threefolds that follow from demanding that F-theory string vacua should be consistent.
by Daniel Sung-Joon Park.
Ph.D.

In this thesis we explore (1,0) supersymmetric theories in six dimensions. The first part of the thesis focuses on the investigation of supersymmetric solutions of (1,0) six dimensional supergravity theory coupled to any number of tensor, vector and scalar multiplets. The methodology used to solve the Killing spinor equations will be based on the spinorial geometry technique. Therefore, we begin by giving details of the spinorial geometry approach in the first chapter. In the chapter that follows six dimensional supergravity coupled to tensor, vector and scalar multiplets is described. Once we have given details of the theory under consideration the solutions to the Killing spinor equations are discussed in some detail. In particular, we find that there are backgrounds preserving 1, 2, 3, 4 and 8 supersymmetries broadly falling into two cases; those with Killing spinors that have compact isotropy groups and those with non-compact isotropy groups. We then discuss the integrability conditions of the Killing spinor equations. In the fourth chapter we analyse the supersymmetric near horizon geometries of (1,0) six dimensional supergravity coupled to arbitrary number of tensor and scalar multiplets. In order to do this we make use of Gaussian null coordinates as well as the solutions of the Killing spinor equations. We find that there are two classes of near horizon geometries. One class is isometric to R1;1 S, where S is a suitable 4-manifold, and the other class is isometric to AdS3 3, where 3 is a homology 3-sphere. In the final chapter we investigate a more recent development, namely (1,0) superconformal theories in six dimensions. In particular we find the BPS solutions of (1,0) superconformal theory in all cases. In addition, we analyse the half supersymmetric solutions to some specic models in detail and give examples of string and 3-brane solutions.

This report discusses a study undertaken to develop, pilot, and tentatively validate a self- regulated learning (SRL) inventory for L2 contexts. This inventory was specifically designed to measure learners' ability to self-regulate their learning. Although there have been a few SRL inventories developed to measure this ability, they do not conform to the six-dimensional SRL model proposed by educational psychologists and backed by extensive research. This warranted the development of a new SRL inventory. The primary focus of this study was that of taking initial steps to develop such an inventory. These steps involved writing and refining items conforming to a six-dimensional SRL model. After selecting 30 items from the initial item pool, the SRL inventory was piloted. Both qualitative and quantitative measures were then employed to provide an initial indication of the inventory's trustworthiness, reliability, and validity.

Thesis (S.B.)--Massachusetts Institute of Technology, Dept. of Mechanical Engineering, 2006.
Includes bibliographical references (leaf 36).
The purpose of this research was to demonstrate the feasibility for creating a three-dimensional monolithic compliant six-axis nanopositioner. Much of this work was based off of the original two-dimensional HexFlex manipulator created by Prof. Martin Culpepper and a three-dimensional design by Samuel Korb. The compliant mechanism was manufactured from a single sheet of 1/8 inch 5052 Aluminum. The mechanism was designed to be fabricated on the non-precision, abrasive water-jet and to be formed using bending processes. The fabrication process was successful. The entire machining process was on the order of one hour. The forming process was repeated multiple times without failure of the mechanism in all cases. The formed mechanism was tested to characterize its ability to manipulate the positioning stage both in- and out-of-plane. The transmission ratio for in-plane was measured at 6.4 while the out out-of-plane ratio was 6.3. The input deflection vs. output deflection curves display a linear relationship, but there was .0003 inches of hysteresis seen in the out-of-plane data after a max deflection of .0009 inches. This amount of hysteresis is undesirable and leaves further testing to determine its causes.
by James Labuz.
S.B.

Cette thèse de doctorat introduit un modèle et un algorithme six-dimensions pour la reconstruction des orientations cristallines locales dans les matériaux polycristallins. Le modèle s’applique actuellement aux données obtenues avec un rayonnement synchrotron (faisceau parallèle et monochromatique), mais il est également possible d’envisager des extensions aux instruments et sources de laboratoire (polychromatique et divergent). Le travail présenté est principalement une extension de la technique connue sous le nom de “Diffraction Contrast Tomography” (DCT) qui permet la reconstruction de la forme et de l’orientation cristalline des grains dans des matériaux polycristallins (avec certaines restrictions concernant la taille et le nombre total de grains ainsi que la mosaicité intragranulaire)
This Ph.D. thesis is about the development and formalization of a six-dimensional tomography method, for the reconstruction of local orientation in poly-crystalline materials. This method is based on a technique known as diffraction contract tomography (DCT), mainly used in synchrotrons, with a monochromatic and parallel high energy X-ray beam. DCT exists since over a decade now, but it was always employed to analyze undeformed or nearly undeformed materials, described by “grains” with a certain average orientation. Because an orientation can be parametrized by the used of only three num- bers, the local orientation in the grains is modelled by a six-dimensional space X6 = R3 ⊗ O3, that is the outer product between a three-dimensional real- space and another three-dimensional orientation-space. This means that for each point of the real-space, there could be a full three-dimensional orientation- space, which however in practice is restricted to a smaller region of interest called “local orientation-space”. The reconstruction problem is then formulated as a global minimisation prob- lem, where the reconstruction of a single grain is the solution that minimizes a functional. There can be different choices for the functionals to use, and they depend on the type of reconstructions one is looking for, and on the type of a priori knowledge is available. All the functionals used include a data fidelity term which ensures that the reconstruction is consistent with the measured diffraction data, and then an additional regularization term is added, like the l1-norm minimization of the solution vector, that tries to limit the number of orientations per real-space voxel, or a Total Variation operator over the sum of the orientation part of the six-dimensional voxels, in order to enforce the homogeneity of the grain volume. When first published, the results on synthetic data from the third chapter high- lighted some key features of the proposed framework, and showed that it was in principle possible to extend DCT to the reconstruction of moderately de- formed materials, but it was unclear whether it could work in practice. The following chapters instead confirm that the proposed framework is viable for reconstructing moderately deformed materials, and that in conjunction with other techniques, it could also overcome the limitations imposed by the grain indexing, and be applied to more challenging textured materials

La present tesi doctoral s’ha centrat en el repte d’aconseguir, mitjançant Fabricació Additiva (FA), models per a assaig quirúrgic, sota la premissa que els equips per fer-los haurien de ser accessibles a l’àmbit hospitalari. L’objectiu és facilitar l’extensió de l’ús dels prototips com a eina de preparació d’operacions quirúrgiques, transformant la pràctica mèdica actual de la mateixa manera que en el seu moment ho van fer tecnologies com les que van facilitar l’ús de radiografies. El motiu d’utilitzar FA, en lloc de tecnologies més tradicionals, és la seva capacitat de materialitzar de forma directa les dades digitals obtingudes de l’anatomia del pacient mitjançant sistemes d’escanejat tridimensional, fent possible l’obtenció de models personalitzats. Els resultats es centren en la generació de nou coneixement sobre com aconseguir equipaments d’impressió 3D multimaterials accessibles que permetin l’obtenció de models mimètics respecte als teixits vius. Per facilitar aquesta buscada extensió de la tecnologia, s’ha focalitzat en les tecnologies de codi obert com la Fabricació per Filament Fos (FFF) i similars basades en líquids catalitzables. La recerca s’alinea dins l’activitat de desenvolupament de la FA al CIM UPC, i en aquest àmbit concret amb la col·laboració amb l’Hospital Sant Joan de Déu de Barcelona (HSJD). El primer bloc de la tesi inclou la descripció de l’estat de l’art, detallant les tecnologies existents i la seva aplicació a l’entorn mèdic. S’han establert per primer cop unes bases de caracterització dels teixits vius -sobretot tous- per donar suport a la selecció de materials que els puguin mimetitzar en un procés de FA, a efectes de millorar l’experiència d’assaig dels cirurgians. El caràcter rígid dels materials majoritàriament usats en impressió 3D els fa poc útils per simular tumors i altres referències anatòmiques. De forma successiva, es tracten paràmetres com la densitat, la viscoelasticitat, la caracterització dels materials tous a la indústria, l’estudi del mòdul elàstic de teixits tous i vasos, la duresa d’aquests, i requeriments com l’esterilització dels models. El segon bloc comença explorant la impressió 3D mitjançant FFF. Es classifiquen les variants del procés des del punt de vista de la multimaterialitat, essencial per fer models d’assaig quirúrgic, diferenciant entre solucions multibroquet i de barreja al capçal. S’ha inclòs l’estudi de materials (filaments i líquids) que serien més útils per mimetitzar teixits tous. Es constata com en els líquids, en comparació amb els filaments, la complexitat del treball en processos de FA és més elevada, i es determinen formes d’imprimir materials molt tous. Per acabar, s’exposen sis casos reals de col·laboració amb l’HJSD, una selecció d’aquells en els que el doctorand ha intervingut en els darrers anys. L’origen es troba en la dificultat de l’abordatge d’operacions de resecció de tumors infantils com el neuroblastoma, i a la iniciativa del Dr. Lucas Krauel. Finalment, el Bloc 3 té per objecte explorar nombrosos conceptes (fins a 8), activitat completada al llarg dels darrers cinc anys amb el suport dels mitjans del CIM UPC i de l’activitat associada a treballs finals d’estudis d’estudiants de la UPC, arribant-se a materialitzar equipaments experimentals per validar-los. La recerca ampla i sistemàtica al respecte fa que s’estigui més a prop de disposar d’una solució d’impressió 3D multimaterial de sobretaula. Es determina que la millor via de progrés és la de disposar d’una pluralitat de capçals independents a fi de capacitar la impressora 3D per integrar diversos conceptes estudiats, materialitzant-se una possible solució. Cloent la tesi, es planteja com seria un equipament d’impressió 3D per a models d’assaig quirúrgic, a fi de servir de base per a futurs desenvolupaments.
La presente tesis doctoral se ha centrado en el reto de conseguir, mediante Fabricación Aditiva (FA), modelos para ensayo quirúrgico, bajo la premisa que los equipos para obtenerlos tendrían que ser accesibles al ámbito hospitalario. El objetivo es facilitar la extensión del uso de modelos como herramienta de preparación de operaciones quirúrgicas, transformando la práctica médica actual de la misma manera que, en su momento, lo hicieron tecnologías como las que facilitaron el uso de radiografías. El motivo de utilizar FA, en lugar de tecnologías más tradicionales, es su capacidad de materializar de forma directa los datos digitales obtenidos de la anatomía del paciente mediante sistemas de escaneado tridimensional, haciendo posible la obtención de modelos personalizados. Los resultados se centran en la generación de nuevo conocimiento para conseguir equipamientos de impresión 3D multimateriales accesibles que permitan la obtención de modelos miméticos respecto a los tejidos vivos. Para facilitar la buscada extensión de la tecnología, se ha focalizado en las tecnologías de código abierto como la Fabricación por Hilo Fundido (FFF) y similares basadas en líquidos catalizables. Esta investigación se alinea dentro de la actividad de desarrollo de la FA en el CIM UPC, y en este ámbito concreto con la colaboración con el Hospital Sant Joan de Déu de Barcelona (HSJD). El primer bloque de la tesis incluye la descripción del estado del arte, detallando las tecnologías existentes y su aplicación al entorno médico. Se han establecido por primera vez unas bases de caracterización de los tejidos vivos – principalmente blandos – para dar apoyo a la selección de materiales que los puedan mimetizar en un proceso de FA, a efectos de mejorar la experiencia de ensayo de los cirujanos. El carácter rígido de los materiales mayoritariamente usados en impresión 3D los hace poco útiles para simular tumores y otras referencias anatómicas. De forma sucesiva, se tratan parámetros como la densidad, la viscoelasticidad, la caracterización de materiales blandos en la industria, el estudio del módulo elástico de tejidos blandos y vasos, la dureza de los mismos, y requerimientos como la esterilización de los modelos. El segundo bloque empieza explorando la impresión 3D mediante FFF. Se clasifican las variantes del proceso desde el punto de vista de la multimaterialidad, esencial para hacer modelos de ensayo quirúrgico, diferenciando entre soluciones multiboquilla y de mezcla en el cabezal. Se ha incluido el estudio de materiales (filamentos y líquidos) que serían más útiles para mimetizar tejidos blandos. Se constata como en los líquidos, en comparación con los filamentos, la complejidad del trabajo en procesos de FA es más elevada, y se determinan formas de imprimir materiales muy blandos. Para acabar, se exponen seis casos reales de colaboración con el HJSD, una selección de aquellos en los que el doctorando ha intervenido en los últimos años. El origen se encuentra en la dificultad del abordaje de operaciones de resección de tumores infantiles como el neuroblastoma, y en la iniciativa del Dr. Lucas Krauel. Finalmente, el Bloque 3 desarrolla numerosos conceptos (hasta 8), actividad completada a lo largo de los últimos cinco años con el apoyo de los medios del CIM UPC y de la actividad asociada a trabajos finales de estudios de estudiantes de la UPC, llegándose a materializar equipamientos experimentales para validarlos. La investigación amplia y sistemática al respecto hace que se esté más cerca de disponer de una solución de impresión 3D multimaterial de sobremesa. Se determina que la mejor vía de progreso es la de disponer de una pluralidad de cabezales independientes, a fin de capacitar la impresora 3D para integrar diversos conceptos estudiados, materializándose una posible solución. Para cerrar la tesis, se plantea cómo sería un equipamiento de impresión 3D para modelos de ensayo quirúrgico, a fin de servir de base para futuros desarrollos.

By formulating the six dimensional (0,2) superconformal field theory X[j] on a Riemann surface decorated with certain codimension two defects, a multitude of four dimensional N=2 supersymmetric field theories can be constructed. In this dissertation, various aspects of this construction are investigated in detail for j=A,D,E. This includes, in particular, an exposition of the various partial descriptions of the codimension two defects that become available under dimensional reductions and the relationships between them. Also investigated is a particular observable of this class of four dimensional theories, namely the partition function on the four sphere and its relationship to correlation functions in a class of two dimensional non-rational conformal field theories called Toda theories. It is pointed out that the scale factor that captures the Euler anomaly of the four dimensional theory has an interpretation in the two dimensional language, thereby adding one of the basic observables of the 4d theory to the 4d/2d dictionary.
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碩士
國立清華大學
物理學系
90
In six dimensional spacetime, we assume that the left-handed neutrinos live on the brane. Because the right-handed neutrino is a Standard-Model gauge singlet, it is allowed to propagate in the 5+1 - dimensional world and accrue an infinite tower of Kaluza -Klein excitations. Besides, we will also demonstrate the orbifold relations by the symmetry of the Lagrangian in six dimensions. Using these orbifold relations, we can write down the general Lagrangian and the neutrino mass matrix can be obtained.

博士
國立成功大學
機械工程學系碩博士班
96
Order, circuit, and branch defects are frequently encountered in the dimensional synthesis of linkages. In order to obtain mechanisms without defects, it is necessary to investigate the causes for occurring dead-center, order defects, circuit defects, and branch defects for each mechanism, and then propose suitable constraint equations for avoiding defects in the dimensional synthesis processes. The main purpose of this work is to propose a unified method for the defect-free dimensional synthesis of four- and six-bar linkages. The proposed method can be applied for the dimensional synthesis of four- and six-bar function generators, path generators, and motion generators. The defect-free four-bar linkages are synthesized by using a geometric method and an optimization method, respectively. Based on an improved geometric method, an identification flowchart is proposed for obtaining feasible regions for the fixed pivot or moving pivot of the driven link of a four-bar linkage for a two-pose problem. For the defect-free optimal synthesis of four-bar linkages, the closed-form solutions for the positions of the output link of the mechanism are used to establish the objective function: the dimensionless average absolute deviations of the angular positions of the output link and/or the coupler point positions between the generated output and required positions. The constraint equations for avoiding order, circuit, and branch defects are included in the optimal synthesis, thus defect-free mechanisms are obtained. For the dyadic six-bar linkages, using the concepts of the coupler curve of a four-bar linkage, the accessible region of a dyad, and the geometric feature of dead-center configurations, procedures are proposed for identifying the different circuits and branches of dyadic six-bar linkages. Using the characteristics of order, circuit, and branch defects, the constraint equations to avoid them are presented. The objective function is also established by using the position closed-form solutions of mechanisms. An optimization approach is then utilized for the defect-free dimensional synthesis of dyadic six-bar linkages. For the nondyadic six-bar linkages, the explicit equations relating the generated output and specified variables are derived by eliminating and transforming angular variables on two loops and by using the specified values of input and output variables. Then, the objective function of the optimal synthesis is obtained. Using the characteristics of order, circuits, branches, and the geometric features of dead-center configurations for nondyadic six-bar linkages, the constraint equations for avoiding order, circuit, and branch defects are proposed for the defect-free optimal synthesis of nondyadic six-bar linkages.

碩士
國立中興大學
機械工程學系所
104
Stamping presses have a place in n traditional manufacturing industry because of its good productivity, stability and low cost. Presses have various types of processing, like stamping, blanking, embossing, bending, drawing and forging, different types of processing needs different characteristics like stroke, working speed, and tonnage. In this research, we synthesize Stephenson III six-bar mechanism by using motion generation with precision point and genetic algorithm. Genetic algorithm is easy to use on optimization problems, and it can avoid using difficult functions like differential function of the object function. We will derive the formulas of Stephenson six-bar mechanism in Cartesian coordinates, and chose the precision point that needed and the parameters that will be use as gene in genetic algorithm, and program the algorithm it in Python for mechanism dimensional synthesis.

碩士
淡江大學
電機工程學系碩士班
104
In this thesis, a trajectory construction method with a three-dimensional model is proposed and actually applied in a laboratory-developed six-axis robot manipulator. First, based on the information point and point-density in a three-dimensional model to stratify the point information. Then an edge mask is applied to find the edge points and the Hermite curve is used to decide some fit points. Finally, a corresponding trajectory is constructed for this considered point information. In the simulation test, points in a single hierarchical level are first used to do the simulation test. The point density, with or without using the Hermite curve method, and the amount of fitting points are respectively used to do the analysis and comparison. From the simulation results, the proposed method can indeed effectively achieve a smoother trajectory. In the simulation of MATLAB, a D-H link table, forward kinematics, and inverse kinematics are considered to construct a virtual environment of this six-axis robot manipulator. And in the virtual environment, a simulation result of a cone drawing by using the proposed method is presented to prove the proposed method is indeed feasible. In the actual test, the proposed method is applied to let this laboratory-developed six-axis robot manipulator can draw the desired results.

碩士
國立台灣工業技術學院
機械工程技術研究所
85
The purpose of this thesis is to investigate the motion characteristics and dimensional synthesis of an impulse type six-link variable-speed drive mechanism. The displacement analysis and the governing equation for computing the limit positions of the output link of the mechanism is first derived by using analytical method. In addition, a graphical method is presented for solving the possible coordinates of the speed control point of the mechanism. Based on this method, an iterative algorithm is derived toconstruct the allowable ranges of the control point, such that an appropriate curve for speed control can be synthesized within the range. A method for synthesizing the dimensions of the links to enlarge the solution range of the control point is also developed. Numerical example shows that this method can effectively reduce the minimum speed ratio and increase the speed variation range.

碩士
國立臺灣科技大學
機械工程系
95
This thesis deals with the optimal dimensional synthesis of a six-bar hard-top convertible roof mechanism. The mechanism investigated in this study is selected from a number of existing patented mechanisms and the kinematic structure of which is of the Watt’s type I six-bar linkage. The constraint equations in between two prescribed positions of the coupler link are first derived from the vector loop closure equations of three triads, from which it is found that the maximum number of design positions that can be specified for this type of mechanisms is eight. An analytical procedure for four-precision-point motion generation is then presented. In addition, a numerical method for eliminating the branching problems of the synthesized mechanism is developed. Finally, the simulated annealing optimization technique is employed for synthesizing the optimal dimensions of the mechanism such that it would not only give the minimum storage space but also have the maximum mechanical advantage along the motion trajectory. The proposed method is verified by two numerical examples.

碩士
國立中正大學
教育學研究所
102
Abstract Achievement goal theory has developed rapidly in recent years. In the beginning, it was a two-dimensional theory. Later on, it developed into a three-dimensional theory, then developed into a four-dimensional theory, and finally developed into a six-dimensional theory. The primary objective of this study is to construct a scale to measure the achievement goals accomplished by the elementary school teachers. Samples were chosen from a population comprising the teachers employed by 2,587 public elementary schools across Taiwan (Penghu County excluded). All cities and counties of Taiwan were divided into four districts, namely, north, central, south, and east districts, using stratified random sampling procedure. To ensure the validity of data and analysis, questionnaires were answered by different teachers in all cities and counties. Different numbers of questionnaires were chosen from four districts according to the ratio of 3:2:2:1. Then, the scale was tested based on the data shown by the questionnaires. 804 questionnaires were sent out; 706 questionnaires returned. Valid return rate was 89.05%. Data was analyzed using structural equation model (SEM) to identify the competition model and the validity criteria. According to the research results, model 1, out of all six-dimensional achievement goal models, has the least index for the competition model. Thus, the first-order six-dimensional model is an ideal tool to measure the elementary school teachers’ achievement goals, and is capable of predicting the positive correlation between creative teaching performance, self-efficacy, and six-dimensional achievement goal. In the final chapter, recommendations are presented for future researches and educators. Key words: achievement goal, goal orientation, model competing, scale testing

碩士
國立高雄應用科技大學
機械工程系
106
In this study, five evolutionary algorithms-a genetic algorithm (GA), particle swarm optimization (PSO), hybrid particle swarm optimization (HPSO), differential evolution (DE), and self-adaptive differential evolution (SaDE)-were used to optimize dimensional synthesis for the path generation mechanisms of four-bar linkages and Watt-II six-bar linkages. The dimensional synthesis was optimized by minimizing the objective function, which was defined as the sum of squares of the distance error between design points and trajectories of coupler-point of generated mechanisms. Through dimensional synthesis performed on eight different coupler-point trajectories for the path generation of four-bar linkages, the comparisons were made for the rate of convergence of all optimization methods, as well as the errors between coupler-point trajectories of synthesized mechanisms. The results indicated that the SaDE algorithm outperformed the other four evolutionary algorithms, as well as the algorithms adopted in previous studies. Accordingly, the SaDE algorithm may be applicable to the dimensional synthesis problem of multi-loop path generation mechanisms. Because Watt-II six-bar linkages have applications in prosthetics and robot feet, this study employed the vector loop method to derive the kinematic relation of the parameters of the mechanism and performed a kinetostatic analysis to yield a dynamic matrix for solving all joint forces. Subsequently, 11 points on the ideal human walking trajectory were used as design points; the five aforementioned evolutionary algorithms were adopted under kinematic and geometric restrictions to perform optimal dimensional synthesis of Watt-II six-bar leg mechanisms. The results of this synthesis suggested that the SaDE algorithm outperformed the other algorithms in determining the optimal dimensions of the mechanisms. Afterwards, a MATLAB program was written to analyze the kinematic properties and all joint forces of the SaDE-derived optimal Watt-II six-bar leg mechanism. Furthermore, ADAMS was used to perform coupler-point trajectories and dynamic analyses, thereby validating the results obtained through the MATLAB program. Finally, the walking mechanism of a four-leg robot was constructed by assembling four identical Watt-II six-bar linkages symmetrically between the left and right sides but in reverse order between the front and back; ADAMS was then used to simulate the trajectory of the robot’s walking motion and perform a dynamic analysis. In summary, this study used a SaDE algorithm for the optimal dimensional synthesis of Watt-II six-bar linkages and confirmed that the SaDE algorithm had a higher rate of convergence and more satisfactory results than the other evolutionary algorithms. The findings are expected to improve the optimization and design of other complex multi-loop linkages.

碩士
國立臺灣科技大學
機械工程系
98
This thesis deals with the displacement analysis and dimensional synthesis of a spatial massaging mechanism. A patent search for the massaging mechanisms currently in use is first conducted and the kinematic structure of six such mechanisms are identified and analyzed. It is found that most of which can be classified as two degree of freedom spatial linkages. Therefore this thesis is focused on the study of this type mechanism. Based on the use of spatial rotation matrix, the loop closure equation of the mechanism is first derived and then reduced to a fourth order polynomial equation in terms of the input and output angles. This indicates that the mechanism can have at most four branches. In addition, the equations for synthesizing the dimensions of the links for generating the kneading and punching motions with respect to the two input angles are derived. A numerical algorithm based on the cyclic coordinate descent method and the Newton-Raphson method for solving these equations is presented. The proposed methods are verified by a numerical example and a solid model representation of the synthesized mechanism is conducted by using Pro/Engineer computer software.

碩士
國立交通大學
電控工程研究所
102
In this thesis, two cascaded electrodynamic shakers are fed to a six-switch-inverter. To enlarge the region of the output voltages, the high-efficiency multi-dimensional feedback quantized modulation is used. The results of the conventional pulse-width modulation (PWM) are also provided for comparison. All the controls are implemented in FPGA to verify the proposed method. Finally, we verify the difference between PI-PWM and PI-MDFQM by simulation and experiment.

碩士
國立高雄應用科技大學
機械與精密工程研究所
102
In this study, we design coupler point of four-bar path generating linkages for trajectory curve and applied Genetic Algorithms (GA), Particle Swarm Optimization (PSO), the Hybrid Particle Swarm Optimization (HPSO), Differential Evolution (DE), Hybrid Differential Evolution (HDE). First, we used optimization design of planar four-bar path generating linkages, used watt six-bar knee joint linkages human ankle joint trajectory of synthetic, can achieve human footsteps design movement, gait and trajectory close to normal human and passed the point of coupler point design trajectory curve. Secondly, we use the minimum squared error value as the objective function of planar linkage and in linkage length, angle of design variables, to solving the fitness function of optimization design and compare the five evolution algorithms convergent efficiency and synthetic trajectory curve, we also added recent years reference to compare, the results show that the differential evolution by convergence algorithm converges more efficient than the other four algorithms, results from synthetic trajectory hybrid differential evolution curve is the closest. Finally, we used of ADAMS / View software to simulate the optimum design of the path curve, and showing that our mechanism design theory is be feasible and effective.

碩士
國立臺灣大學
森林學研究所
92
Abstract The main purpose of this study is to elaborate the effect of plants’ shape, texture and color on landscape through the simulation of computerized three-dimensional modeling. Six native trees (Michelia compressa ，Calocedrus formosana ，Cinnamomum camphora，Liquidambar formosana ，Koelreuteria elegans spp.formosana and Prunus campanulata) are put separately in single-tree design and mixed-tree design around two historically memorial buildings on campus of National Chengchi University to explore the faculty, administrators and students’ visual preference for scenic beauty. Respectively calculating the average value of tree preference of faculty, students and administrators through questionnaires, we found that Liquidambar formosana is the most preferred tree in single-tree design. The result of ANOVA F-test shows a significant difference in participants’ visual preference to the six trees. The Tukey’s pairwise comparison analysis further indicates the preference for Prunus campanulata and Liquidambar formosana is obviously greater than Michelia compressa and Calocedrus formosana. And in mixed-tree design, the preference for deciduous trees is greater than evergreen trees and a mixture of the six trees. However, the difference, analyzed by ANOVA F-test, is not significant. Respectively calculating the preference value of faculty, students and administrators to each single tree, we found that students prefer Prunus campanulata ; faculty and administrators, Liquidambar formosana. ANOVA F-test shows that there is a significant difference in students’ preference to the six trees, but not in the faculty and administrators’. The Tukey’s pairwise comparison analysis further point out that students’ preference for Prunus campanulata is obviously greater than Calocedrus formosana , Michelia compressa and Cinnamomum camphora ; Liquidambar formosana , than Cinnamomum camphora and Calocedrus formosana ; Koelreuteria elegans spp.formosana , than Calocedrus formosana. Analyzing the mixed-tree design (evergreen trees, deciduous trees and a mixture of the six trees) by ANOVA F-test, we found that the participants’ preference for these three kinds of designs has no much difference. This study shows the faculty, students and administrators of Chengchi University prefer deciduous trees (Liquidambar formosana , Koelreuteria elegans spp.formosana and Prunus campanulata) in both single-tree and mixed-tree designs. The reason is that the color of deciduous trees changes with seasons, thus providing varied visual effects. Using the visualized simulation of three-dimensional modeling can further interpret plants’ effect on landscape to an authentic degree.

Yes
Three-dimensional printing (3DP) has demonstrated great potential for multi-material fabrication because of its capability for printing bespoke and spatially separated material conformations. Such a concept could revolutionise the pharmaceutical industry, enabling the production of personalised, multi-layered drug products on demand. Here, we developed a novel stereolithographic (SLA) 3D printing method that, for the first time, can be used to fabricate multi-layer constructs (polypills) with variable drug content and/or shape. Using this technique, six drugs, including paracetamol, cffeine, naproxen, chloramphenicol, prednisolone and aspirin, were printed with dfferent geometries and material compositions. Drug distribution was visualised using Raman microscopy, which showed that whilst separate layers were successfully printed, several of the drugs diffused across the layers depending on their amorphous or crystalline phase. The printed constructs demonstrated excellent physical properties and the different material inclusions enabled distinct drug release profiles of the six actives within dissolution tests. For the first time, this paper demonstrates the feasibility of SLA printing as an innovative platform for multi-drug therapy production, facilitating a new era of personalised polypills.