The Application of Polynomial Response Surface and Polynomial Chaos Expansion Metamodels within an Augmented Reality Conceptual Design Environment

The engineering design process consists of many stages. In the conceptual phase, potential designs are generated and evaluated without considering specifics. Winning concepts then advance to the detail design and high fidelity simulation stages. At this point in the process, very accurate representations are made for each design and are then subjected to rigorous analysis. With the advancement of computer technology, these last two phases have been very well served by the software community. Engineering software such as computer-aided design (CAD), finite element analysis (FEA), and computational fluid dynamics (CFD) have become an inseparable part of the design process for many engineered products and processes. Conceptual design tools, on the other hand, have not undergone this type of advancement, where much of the work is still done with little to no digital technology. Detail oriented tools require a significant amount of time and training to use effectively. This investment is considered worthwhile when high fidelity models are needed. However, conceptual design has no need for this level of detail. Instead, rapid concept generation and evaluation are the primary goals. Considering the lack of adequate tools to suit these needs, new software was created. This thesis discusses the development of that conceptual design application. Traditional design tools rely on a two dimensional mouse to perform three dimensional actions. While many designers have become familiar with this approach, it is not intuitive to an inexperienced user. In order to enhance the usability of the developed application, a new interaction method was applied. Augmented reality (AR) is a developing research area that combines virtual elements with the real world. This capability was used to create a three dimensional interface for the engineering design application. Using specially tracked interface objects, the user\u27s hands become the primary method of interaction. Within this AR environment, users are able perform many of the basic actions available within a CAD system such as object manipulation, editing, and assembly. The same design environment also provides real time assessment data. Calculations for center of gravity and wheel loading can be done with the click of a few buttons. Results are displayed to the user in the AR scene. In order to support the quantitative analysis tools necessary for conceptual design, additional research was done in the area of metamodeling. Metamodels are capable of providing approximations for more complex analyses. In the case of the wheel loading calculation, the approximation takes the place of a time consuming FEA simulation. Two different metamodeling techniques were studied in this thesis: polynomial response surface (PRS) and polynomial chaos expansion (PCE). While only the wheel loading case study was included in the developed application, an additional design problem was analyzed to assess the capabilities of both methods for conceptual design. In the second study, the maximum stresses and displacements within the support frame of a bucket truck were modeled. The source data for building the approximations was generated via an FEA simulation of digital mockups, since no legacy data was available. With this information, experimental models were constructed by varying several factors, including: the distribution of source and test data, the number of input trials, the inclusion of interaction effects, and the addition of third order terms. Comparisons were also drawn between the two metamodeling techniques. For the wheel loading models, third order models with interaction effects provided a good fit of the data (root mean square error of less than 10%) with as few as thirty input data points. With minimal source data, however, second order models and those without interaction effects outperformed third order counterparts. The PRS and PCE methods performed almost equivalently with sufficient source data. Difference began to appear at the twenty trial case. PRS was more suited to wider distributions of data. The PCE technique better handled smaller distributions and extrapolation to larger test data. The support frame problem represented a more difficult analysis with non-linear responses. While initial third order results from the PCE models were better than those for PRS, both had significantly higher error than in the previous case study. However, with simpler second order models and sufficient input data (more than thirty trials) adequate approximation results were achieved. The less complex responses had error around 10%, and the model predictions for the non-linear response were reduced to around 20%. These results demonstrate that useful approximations can be constructed from minimal data. Such models, despite the uncertainty involved, will be able to provide designers with helpful information at the conceptual stage of a design process

Mathematical Methods, Modelling and Applications

This volume deals with novel high-quality research results of a wide class of mathematical models with applications in engineering, nature, and social sciences. Analytical and numeric, deterministic and uncertain dimensions are treated. Complex and multidisciplinary models are treated, including novel techniques of obtaining observation data and pattern recognition. Among the examples of treated problems, we encounter problems in engineering, social sciences, physics, biology, and health sciences. The novelty arises with respect to the mathematical treatment of the problem. Mathematical models are built, some of them under a deterministic approach, and other ones taking into account the uncertainty of the data, deriving random models. Several resulting mathematical representations of the models are shown as equations and systems of equations of different types: difference equations, ordinary differential equations, partial differential equations, integral equations, and algebraic equations. Across the chapters of the book, a wide class of approaches can be found to solve the displayed mathematical models, from analytical to numeric techniques, such as finite difference schemes, finite volume methods, iteration schemes, and numerical integration methods

Doctor of Philosophy

dissertationThe statistical study of anatomy is one of the primary focuses of medical image analysis. It is well-established that the appropriate mathematical settings for such analyses are Riemannian manifolds and Lie group actions. Statistically defined atlases, in which a mean anatomical image is computed from a collection of static three-dimensional (3D) scans, have become commonplace. Within the past few decades, these efforts, which constitute the field of computational anatomy, have seen great success in enabling quantitative analysis. However, most of the analysis within computational anatomy has focused on collections of static images in population studies. The recent emergence of large-scale longitudinal imaging studies and four-dimensional (4D) imaging technology presents new opportunities for studying dynamic anatomical processes such as motion, growth, and degeneration. In order to make use of this new data, it is imperative that computational anatomy be extended with methods for the statistical analysis of longitudinal and dynamic medical imaging. In this dissertation, the deformable template framework is used for the development of 4D statistical shape analysis, with applications in motion analysis for individualized medicine and the study of growth and disease progression. A new method for estimating organ motion directly from raw imaging data is introduced and tested extensively. Polynomial regression, the staple of curve regression in Euclidean spaces, is extended to the setting of Riemannian manifolds. This polynomial regression framework enables rigorous statistical analysis of longitudinal imaging data. Finally, a new diffeomorphic model of irrotational shape change is presented. This new model presents striking practical advantages over standard diffeomorphic methods, while the study of this new space promises to illuminate aspects of the structure of the diffeomorphism group

Pedestrian head detection using automatic scale selection for feature detection and statistical edge curvature analysis

In this report we focus on pedestrian head detection and tracking in video sequences. The task is not trivial in real and complex scenarios where the deformation induced by the perspective field requires a multi-scale analy- sis. Multi-scale shape models for the human head are considered to identify the correct size of the region of interest. Anisotropic diffusion is used as a pre-processing step and edge detection is performed using an automatic scale selection process. A non parametric statistical description is given for the edge curvature and detection is performed by means of goodness-of-fit tests. The head detector is used as a validation tool in a correlation-based tracker. The local maxima of the correlation matrix are analyzed. Tracking is performed associating the displacement vector of the target with that local maximum which maximizes the goodness-of-fit with the distribution of the edge curvature of the head

Workshop on Harmonic Oscillators

Proceedings of a workshop on Harmonic Oscillators held at the College Park Campus of the University of Maryland on March 25 - 28, 1992 are presented. The harmonic oscillator formalism is playing an important role in many branches of physics. This is the simplest mathematical device which can connect the basic principle of physics with what is observed in the real world. The harmonic oscillator is the bridge between pure and applied physics

The mass composition of massive early-type galaxies

Es ist anzunehmen, dass die Vielfalt der Galaxien im lokalen Universum aus sukzessiven Generationen von Galaxienverschmelzungen hervorgegangen ist. Massereiche Ellipsen stehen dabei an der Spitze der Hierarchie der Galaxienverschmelzungen. Außerdem bergen sie die größten supermassereichen Schwarzen Löcher. Das Szenario der hierarchischen Verschmelzungen kann viele der beobachteten Eigenschaften von Ellipsen erklären. Dennoch bleibt die genaue Zusammensetzung der Massen in diesen Galaxien schleierhaft. Die Massenfunktion lokaler schwarzer Löcher, und insbesondere ihr oberes Ende, sind nicht bekannt. Auch wissen wir nicht, welcher Anteil der Gesamtmasse einer Galaxie den Sternen und welcher der dunklen Materie zuzuschreiben ist, da es hier stets eine unbekannte Fraktion an stellaren Objekten gibt, welche Masse zur Galaxie beitragen, aber kaum oder gar kein Licht. Auf der einen Seite gibt es eine unbekannte Anzahl an lichtschwachen Zwergsternen, und auf der anderen Seite einen unbekannten Bruchteil an Sternen, der zu Relikten kollabiert ist. Die ursprüngliche massen funktion (UMF) der Sterne umfasst diese Information. Verschiedene Studien der UMF haben eine andere UFM in massiven Ellipsen als in weniger massereichen Galaxien wie unserer Milchstraße ermittelt. Doch meistens produzieren verschiedene Methoden widersprüchliche Resultate für dieselben Galaxien. Auf der Messung nicht-parametrischer Sichtliniengeschwindigkeitsverteilungen (SGV) basierende dynamische Modelle können genützt werden, um Galaxienmassen zu messen und in einzelne Komponenten zu zerlegen. In dieser Dissertation messe ich die nicht-parametrischen SGV von 9 + 1 Ellipsen bis zur Fluchtgeschwindigkeit des jeweiligen Potentials mit unserem Code WINGIFT. Darauf basierend konstruiere ich für acht der Galaxien Schwarzschild Orbit-Modelle. Dabei präsentiere ich hier die Entdeckung eines von nur vier bisher dynamisch gemessenen Schwarzen Löchern mit M_BH > 10^10 M⊙, sowie zwei empirische Relationen zwischen M_BH und der zentralen Flächenhelligkeit, sowie zentralen Oberflächendichte massiver Ellipsen. Mit diesen Relationen lässt sich das obere Ende der Massenfunktion lokaler schwarzer Löcher in der Zukunft gezielt erforschen. Für sieben der Galaxien präsentiere ich dynamische Evidenz für interne Gradienten der UMF. Solche intrinsischen Gradienten der UMF könnten die Diskrepanzen bisheriger auf verschiedenen Methoden basierenden Messungen der UMF lösen. Die gefundenen Gradienten suggerieren, dass sich in den Zentren von Ellipsen sehr kompakte Regionen vorfinden ≲ 1 kpc, deren stellare Populationen einen höheren Anteil an entweder lichtschwachen Zwergsternen oder Relikten vorweisen als es für Populationen im Rest des Universums der Fall ist.It is thought that most galaxies in the local universe are the outcome of several generations of hierarchical mergers of progenitor galaxies. Massive early-type galaxies (ETGs) occupy the top ranks of this hierarchy. They also harbour the biggest supermassive black holes (SMBHS) in the local universe. The merger framework can explain many of the observed properties of different kinds of ETGs. However, the exact mass compositions of these objects remains elusive: For once, the local SMBH mass function is poorly understood and barely sampled at the high mass end. We also do not know how much galaxy mass is contributed by stars and how much by dark matter, because an unknown fraction of stars are low-luminosity dwarf stars, and another unknown fraction of more massive stars have turned into remnants – both of these contribute a significant amount of mass to galaxies, but little or no light. The stellar initial mass function (IMF) underlying the stellar population(s) of a galaxy encompasses this information. Different studies, using different methods have claimed that the IMF in massive ETGs is different from that of less massive galaxies like the Milky Way. But these results have thus far remained overwhelmingly contradictory on the level of individual galaxies. Accurate measurements of non-parametric line-of-sight velocity distributions (LOSVDs) in ETGs can be analysed with Schwarzschild orbit models to produce precise galaxy mass decompositions. In this thesis, I measure the full non-parametric shape of LOSVDs all the way to the escape velocity of each galaxy’s gravitation potential for a total of 9 + 1 massive ETGs using our kinematic fitting code WINGFIT. For eight of the galaxies I construct Schwarzschild models based on these kinematics. I present the discovery of one of so far only four SMBHs more massive than 10^10 M⊙ with direct dynamical detections, and two new SMBH-host scaling relations between MBH and the central surface brightness, as well as surface mass-density of massive galaxies. In the future, these empirical relations can be used for a targeted sampling of the high mass end of the local SMBH mass function. For seven of the ETGs, I present dynamical evidence for internal radial gradients of the IMF. Such gradients can potentially explain the contradictions between previous IMF measurements from different methods. These measurements suggest that the centers of ETGs contain very spatially concentrated regions (r ≲ 1 kpc) of stellar populations with an enhanced fraction of either low-luminosity dwarfs or remnants relative to stellar populations in the rest of the universe

Third International Workshop on Squeezed States and Uncertainty Relations

The purpose of these workshops is to bring together an international selection of scientists to discuss the latest developments in Squeezed States in various branches of physics, and in the understanding of the foundations of quantum mechanics. At the third workshop, special attention was given to the influence that quantum optics is having on our understanding of quantum measurement theory. The fourth meeting in this series will be held in the People's Republic of China

Flowing matter

This open access book, published in the Soft and Biological Matter series, presents an introduction to selected research topics in the broad field of flowing matter, including the dynamics of fluids with a complex internal structure -from nematic fluids to soft glasses- as well as active matter and turbulent phenomena.Flowing matter is a subject at the crossroads between physics, mathematics, chemistry, engineering, biology and earth sciences, and relies on a multidisciplinary approach to describe the emergence of the macroscopic behaviours in a system from the coordinated dynamics of its microscopic constituents.Depending on the microscopic interactions, an assembly of molecules or of mesoscopic particles can flow like a simple Newtonian fluid, deform elastically like a solid or behave in a complex manner. When the internal constituents are active, as for biological entities, one generally observes complex large-scale collective motions. Phenomenology is further complicated by the invariable tendency of fluids to display chaos at the large scales or when stirred strongly enough. This volume presents several research topics that address these phenomena encompassing the traditional micro-, meso-, and macro-scales descriptions, and contributes to our understanding of the fundamentals of flowing matter.This book is the legacy of the COST Action MP1305 “Flowing Matter”