In order to fully understand the functionality of conformal devices, it is critical to develop computational models built from engineered models of 3-dimensional objects. This thesis established a scanning procedure to engineering 3D digital model for whole organs, known as template engineering. The resultant scanning data enabled designing, manufacturing, and modeling of novel organ healthcare devices. Specifically, we applied template engineering and structured-light scanning techniques to capture the 3D topographical information for whole organ systems. Sequentially, we developed multiphysics models for understanding the device functionality, including the function of devices for microfluidic interface and whole organ mechanical stabilization. / Master of Science

Published Article / This paper discusses the results obtained from studies on the performance of different cooling layouts. The conventional method of cooling makes use of straight-line cooling channels. This simple method of cooling does not possess the capability of uniformly cooling down the part produced. In contrast, conformal cooling is a technique that makes use of cooling channels in an injection moulding tool that closely follows the geometry of the part to be produced. The paper presents some experiences gained in a comparative case study of conventional cooling vs conformal cooling using simulation, followed by an experimental validation and statistical analysis of the results.

This thesis is concerned with the properties of 1 + 1 dimensional massive field theories in both infinite and semi-infinite geometries. Chapters 1, 2 and 3 develop the necessary theoretical framework and review existing work by Chim and Zamolodchikov [1] on integrable perturbations of the (bulk) q-state Potts model, the particular model under consideration in this thesis. Chapter 4 consists of a detailed analysis of the bootstrap for this model, during the course of which unexpected behaviour arises. The treatment of 1] has consequently been revised, but further investigation will be necessary before complete understanding of this behaviour can be reached. In the final chapter, attention turns to the imposition of boundary conditions on two dimensional systems. After looking at this from a statistical mechanical point of view, a brief review of boundary conformal held theory and its integrable perturbations is given. This leads once more to a consideration of the q-state Potts model. After summarising [2], where fixed and free boundary conditions are considered, a third and previously untreated boundary condition is discussed.

Thesis (Ph.D.)--Massachusetts Institute of Technology, Dept. of Mathematics, 1981. / MICROFICHE COPY AVAILABLE IN ARCHIVES AND SCIENCE. / Includes bibliographical references. / by Moshe Dubiner. / Ph.D.

Every triangle has a unique point, called the conformal center, from which a random (Brownian motion) path is equally likely to first exit the triangle through each of its three sides. We use concepts from complex analysis, including harmonic measure and the Schwarz-Christoffel map, to locate this point. We could not obtain an elementary closed form expression for the conformal center, but we show some series expressions for its coordinates. These expressions yield some new hypergeometric series identities. Using Maple in conjunction with a homemade Java program, we numerically evaluated these series expressions and compared the conformal center to the known geometric triangle centers. Although the conformal center does not exactly coincide with any of these other centers, it appears to always lie very close to the Second Morley point. We empirically quantify the distance between these points in two different ways. In addition to triangles, certain other special polygons and circles also have conformal centers. We discuss how to determine whether such a center exists, and where it will be found.

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Thesis (doctoral)--Universität Jena, 1915. / Vita. Includes bibliographical references.

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Made available in DSpace on 2016-05-17T16:50:51Z (GMT). No. of bitstreams: 0 Previous issue date: 2006-09-29. Added 1 bitstream(s) on 2016-05-17T16:54:28Z : No. of bitstreams: 1 000855054.pdf: 470877 bytes, checksum: 60b3c5b992ae7d78b6dc013884d65cfa (MD5) / Nesta tese vamos estudar dois aspectos diferentes da física da constante cosmológica: a estrutura algébrica do grupo de de Sitter, e as suas implicações na dinâmica do Universo. Na primeira parte, apresentaremos uma descrição da estrutura geométrica do espaço de de Sitter, bem como uma discussão detalhada da estrutura do grupo de de Sitter. Revisaremos os limites do grupo de de Sitter obtidos por meio do processo de contração de Inönü-Wigner, e estudaremos o limite formal 'lâmbda' 'SETA' 'INFINITO'. Neste limite, obtem-se um espaço-tempo singular, maximalmente simétrico, transitivo sob transformações conformes próprias, e com propriedades termodinâmicas que se ajustam à idéia de uma condição inicial para um Universo com big-bang. Ainda neste contexto, proporemos uma relatividade restrita baseada no grupo de de Sitter. Nesta teoria, a constante cosmológica introduz uma escala de comprimento invariante: o raio de de Sitter. A introdução desta escala invariante não implica numa violação da simetria de Lorentz, mas sim numa mudança na estrutura causal do espaço-tempo, bem como nas definições de momento e energia. Na segunda parte da tese, que trata das aplicações cosmológicas, apresentaremos um modelo dinâmico para a constante cosmológica. Neste modelo, como consequência das equações de Einstein, uma variação em 'lâmbda' deve necessariamente ser compensada pela criação ou destruição de matéria, de modo que a energia total seja mantida constante. Um modelo particular para esta evolução da constante cosmológica é apresentado, o qual está baseado no principio holográfico. Veremos como o modelo pode incorporar simultaneamente a expansão acelerada do Universo, e a coincidência na ordem de grandeza das densidades de energia escura e de matéria / In this thesis we study two different aspects of the physics of the cosmological constant: the algebraic structure of the de Sitter group, and its implications in the large scale dynamics of the Universe. In the first part we present a general description of the geometrical structure of de Sitter space, and a discussion about the structure of de Sitter group. We review the contraction limits of de Sitter group, obtained by means of the Inönü-Wigner procedure, and we study in detail the formal limit 'lâmbda' 'SETA' 'INFINITO'. In this limit, one obtains a maximally-symmetric, singular spacetime, transitive under proper conformal transformations, and with thermodynamic properties that agreee with the idea of an initial condition for a big-bang Universe. In the same context, we propose a special relativity based on the de Sitter group. In this theory, the cosmological constant introduces an invariant length scale: the de Sitter radius. The introduction of this invariant scale does not imply a violation of the Lorentz symmetry, but simply a change in the causal structure of the spacetime, as well as in the basic notions of momentum and energy. In the second part of the thesis, that related with cosmological applications, a dynamic model for the cosmological constant will be presented. In this model, as a consequence of Einstein's equations, a variation in 'lâmbda' must necessarily be compensated by creation or destruction of matterenergy, in such a way that the total energy remains constant. A particular model allowing for the evolution of the cosmological constant is presented, which is based on the holographic principle. We will show how this model can accommodate simultaneously the accelerated expansion of the Universe and the coincidence in the magnitude of matter and dark energy densities

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