Thesis (Ph. D.)--Virginia Polytechnic Institute and State University, 1993. / Vita. Abstract. Includes bibliographical references (leaves 106-108). Also available via the Internet.

Thesis (M.S.)--Brigham Young University. Dept of Mathematics, 2007. / Includes bibliographical references (p. 100-102).

L'étude de stabilité des systèmes différentiels issus des équations de Navier-Stokes consiste à analyser la réponse du système linéarisé à une perturbation en onde plane. Elle ne peut pas rendre compte de tous les mécanismes possibles d'instabilité non linéaire. De telles analyses de stabilité non linéaire ont été abordées pour des discrétisations en différences finies de l'équation scalaire non visqueuse de Burgers. Elles sont basées sur l'analyse en ondes résonantes, en considérant un ensemble d'ondes qui forment un groupe fermé pour l'équation discrétisée. Une conclusion importante de ces travaux est que quelques mécanismes non linéaires instables existent qui échappent à l'analyse linéaire, comme le mécanisme de focalisation étudié et expliqué à l'aide des modes de side band, introduits pour amorcer les instabilités. Cette approche d'ondes résonantes est étendue à l'analyse non linéaire de stabilité pour les méthodes LBM (Lattice Boltzmann Method). Nous présentons pour la première fois une équation vectorielle à la place de l' équation scalaire de Burgers, car la méthode LBM considère une fonction de distribution par vitesses discrètes. L'application du principe des ondes résonantes aux équations de Boltzmann sur réseau pour un écoulement monodimensionnel, compressible et isotherme dans un schéma D1Q3 donne des cartes d'instabilité, dans le cas de 1 ou plusieurs modes résonants, très dépendantes des conditions initiales. Le phénomène de focalisation n'a pas été obtenu dans la formulation LBM. Des croissances transitoires dues à la non-normalité des opérateurs peuvent exister. Elles sont calculées par une méthode d'optimisation Lagrangienne utilisant les équations adjointes de LBM. L'application du principe des ondes résonantes est étendue à un modèle 2D. On montre que les instabilités deviennent prépondérantes. / The stability study of differential systems derived from the Navier- Stokes equations consists in analysing the response of the planar linearized system from a disturbance on a flat wave. It cannot account for all possible mechanisms of nonlinear instability. Such non-linear stability analyses were discussed for finite difference of the scalar non-viscous Burger equation. They are based on the analysis in resonant waves, considering a set of waves that form a closed group for the discretized equation. An important conclusion of this work is that some unstable nonlinear mechanisms exist that are beyond the linear analysis, as the focusing mechanism studied and explained using the methods of side band, introduced to initiate instabilities. This approach of resonant waves is extended to non-linear stability analysis for LBM (Lattice Boltzmann Method) methods. We report for the first time a vector equation instead of the scalar Burgers equation, because the LBM method considers a distribution function by discrete speeds. The principle of resonant waves to lattice Boltzmann equations for one-dimensional flow in a compressible and isothermal D1Q3 scheme gives instability maps, in the case of one or more resonant modes , highly dependent upon the initial conditions. The phenomenon of focus has not been obtained in the LBM formulation. Transient growth due to non-normality of operators may exist. They are calculated by a Lagrangian optimization method combined with LBM equations. The principle of resonant waves is extended to a 2D model. We show that the instabilities become dominant.

This dissertation investigates the need for a change in popular perception of what an institutional building should and could look and feel like. This is achieved through the exploration of ways to create a therapeutic environment that houses a sub-acute facility which provides operational after care for patients discharged from Louis Pasteur Private Hospital in the Pretoria CBD. As well as providing for certain functional requirements, the architectural exploration aims to enrich and encourage the healing process of patients within the city with a rich mixture of stimulating and therapeutic experiences and qualities. Through the exploration and incorporation of various theories, these aims are set as an end goal not only throughout the design process, but are also used to guide the technical development and solutions that are used within the finalization of the facility. With a constant concept of creating a space for healing within the city of Pretoria, a Centre for Healing is created which holds these ideals at the core of its existence. / Dissertation (MArch(Prof))--University of Pretoria, 2010. / Architecture / unrestricted

In his thesis, Mother bird hovering over the city: space, spirituality and a community-based urban praxis, the promovendus adopted a trans-disciplinary, praxis-approach to consider participatory, critical and liberationist planning and city-building processes. His journey was about the soul of the city, embodied in its spaces and its people. It reflected on unfolding urban spaces, tracing dynamics in the Berea-Burgers Park neighbourhood of Tshwane’s inner city between 1993 and 2016. The narratives emerging from this neighbourhood was brought into conversation with a range of other narratives, hoping to discern and propose a vision for a community-based urban praxis. The journey originated from a deliberate option for the city’s most vulnerable people, hoping to contribute towards a city characterised by radical forms of inclusion, sustainability and justice. It recognised that space is not neutral and spatial constructs are shaped by deep value frameworks that are prejudiced, exclusive and oppressive, or equalising, inclusive, and life-affirming. What the promovendus sought to discern and outline was a spirituality that can infuse planning praxis and spatial thinking: making spaces that will mediate dignity, justice and well-being. Part I of the study considered a new epistemology, identity and methodology, expressed in the metaphor of “becoming like children”, requiring a new selfunderstanding for those involved in planning, city-building or place-making, but also amongst urban citizens and vulnerable urban dwellers: to reclaim their own voice and agency in processes of city-making. In Part II of the study, after describing and deconstructing urban spaces and discourses in a contextual-narrative way, a spirituality and ethic of urban space are developed. It argues for a radical shift from planning as bureaucracy and technocracy, to planning as immersed, participatory artistry: opening up to the “genius” or (S)pirit of space – the Mother bird – hovering over urban spaces, responsive to urban cries, of humans and earth alike, and inviting us to be co-constructors of new and surprising spaces, mending and making whole. / Thesis (PhD)--University of Pretoria, 2017. / Town and Regional Planning / PhD / Unrestricted

El siguiente proyecto de hamburguesas hechas a base de ingredientes orgánicos y naturales como la quinua, lentejas y Cushuro muestra su viabilidad en base a una investigación realizada a jóvenes y adultos entre los 18 a 55 años de los niveles socioeconómicos A y B. De este modo, la investigación ha permitido identificar a un grupo de consumidores que tienen dificultades para conseguir productos saludables que cumplan con los requerimientos fundamentales para ser considerados como orgánicos, y también se busca fortalecer el consumo de un producto peruano que contiene gran variedad de nutrientes que requieren las personas diariamente. De igual forma, se determinó que hay una disponibilidad alta de compra por adquirir este tipo de productos que ayuden a ahorrar tiempo y permitan variar sus comidas diarias. Por último, el público objetivo ha mostrado interés por los ingredientes de las hamburguesas, dado esto esta situación el interés de compra y la disponibilidad de recibirlo en casa ha incrementado. De acuerdo con lo señalado anteriormente, se ha optado por desarrollar el proyecto utilizando métodos de investigación de mercados donde se ha analizado la industria, al consumidor, competidores y proveedores. Para lograr un buen desarrollo empresarial se han planteado objetivos estratégicos que serán guiados a partir de planes estratégicos. Finalmente, se han obtenido resultados como: las utilidades netas serán de S/. 36,628,39 para el primer año, de S/. 30,423,92 para el segundo año y de S/. 119,812,28 para el tercer año. / The following hamburger project based on organic and natural ingredients such as quinoa, lentils and Cushuro shows its viability based on research carried out on young people and adults between 18 and 55 years of socioeconomic levels A and B. Thus, the research has allowed to identify a group of consumers who have difficulties in obtaining healthy products that meet the fundamental requirements to be considered organic, and also seeks to strengthen the consumption of a Peruvian product that contains a variety of nutrients that require people daily. Likewise, it was determined that there is a high availability of purchase by acquiring these types of products that help save time and allow you to vary your daily meals. Finally, the target audience has shown interest in the ingredients of hamburgers, given this situation the purchase interest and the availability of receiving it at home has increased. In accordance with the above, it has been decided to develop the project using market research methods where the industry, the consumer, competitors and suppliers have been analyzed. To achieve a good business development, strategic objectives have been set that will be guided by strategic plans. Finally, results have been obtained such as: the net profits will S/. 36,628,39 for the first year, S/. 30,423,92 for the second year and S/. 119,812,28 for the third year. / Trabajo de investigación

In this thesis a numerical study of the one dimensional viscous Burgers equation is conducted. The discretization techniques Finite Differences, Finite Element Method and Group Finite Elements are applied and their impact on model reduction techniques, namely Proper Orthogonal Decomposition (POD), Group POD and the Discrete Empirical Interpolation Method (DEIM), is studied. This study is facilitated by examination of several common ODE solvers. Embedded in this process, some results on the structure of the POD basis and an alternative algorithm to compute the POD subspace are presented. Various numerical studies are conducted to compare the different methods and the to study the interaction of the spatial discretization on the ROM through the basis functions. Moreover, the results are used to investigate the impact of Reduced Order Models (ROM) on Optimal Control Problems. To this end, the ROM is embedded in a Trust Region Framework and the convergence results of Arian et al. (2000) is extended to POD-DEIM. Based on the convergence theorem and the results of the numerical studies, the emphasis is on implementation strategies for numerical speedup. / Master of Science

The Burgers equation, and related partial differential equations (PDEs), can be numerically challenging for small values of the viscosity parameter. For example, these equations can develop discontinuous solutions (or solutions with large gradients) from smooth initial data. Aside from numerical stability issues, standard numerical methods can also give rise to spurious oscillations near these discontinuities. In this study, we consider an equivalent form of the Burgers equation given by Constantin and Iyer, whose solution can be written as the expected value of a stochastic differential equation. This equivalence is used to develop a numerical method for approximating solutions to Burgers equation. Our preliminary analysis of the algorithm reveals that it is a natural generalization of the method of characteristics and that it produces approximate solutions that actually improve as the viscosity parameter vanishes. We present three examples that compare our algorithm to a recently published reference method as well as the vanishing viscosity/entropy solution for decreasing values of the viscosity. / Master of Science / Burgers equation is a Partial Differential Equation (PDE) used to model how fluids evolve in time based on some initial condition and viscosity parameter. This viscosity parameter helps describe how the energy in a fluid dissipates. When studying partial differential equations, it is often hard to find a closed form solution to the problem, so we often approximate the solution with numerical methods. As our viscosity parameter approaches 0, many numerical methods develop problems and may no longer accurately compute the solution. Using random variables, we develop an approximation algorithm and test our numerical method on various types of initial conditions with small viscosity coefficients.

The problem of establishing local existence and uniqueness of solutions to systems of differential equations is well understood and has a long history. However, the problem of proving global existence and uniqueness is more difficult and fails even for some very simple ordinary differential equations. It is still not known if the 3D Navier-Stokes equation have global unique solutions and this open problem is one of the Millennium Prize Problems. However, many of these mathematical models are extremely useful in the understanding of complex physical systems. For years people have considered methods for modifying these equations in order to obtain models that still capture the observed fundamental physics, but for which one can rigorously establish global results. In this thesis we focus on a taming method to achieve this goal and apply taming to modeling and numerical problems. The method is also applied to a class of nonlinear differential equations with conservative nonlinearities and to Burgers’ Equation with Neumann boundary conditions. Numerical results are presented to illustrate the ideas. / Master of Science

We study the Korteweg-de Vries-Burgers equation. With a deep investigation into the spectral and smoothing properties of the linearized system, it is shown by applying Banach Contraction Principle and Gronwall's Inequality to the integral equation based on the variation of parameters formula and explicit representation of the operator semigroup associated with the linearized equation that, under appropriate assumption appropriate assumption on initial states w(x, 0), the nonlinear system is well-posed and its solutions decay exponentially to the mean value of the initial state in H1(O, 1) as t -> +". / Ph. D.