Time Discretization of the SST-generalized Navier-Stokes Equations: Positive and Negative Results

In the theory of the Navier-Stokes equations, the proofs of some basic known results, like for example the uniqueness of solutions to the stationary Navier-Stokes equations under smallness assumptions on the data or the stability of certain time discretization schemes, actually only use a small range of properties and are therefore valid in a more general context. This observation leads us to introduce the concept of SST spaces, a generalization of the functional setting for the Navier-Stokes equations. It allows us to prove (by means of counterexamples) that several uniqueness and stability conjectures that are still open in the case of the Navier-Stokes equations have a negative answer in the larger class of SST spaces, thereby showing that proof strategies used for a number of classical results are not sufficient to affirmatively answer these open questions. More precisely, in the larger class of SST spaces, non-uniqueness phenomena can be observed for the implicit Euler scheme, for two nonlinear versions of the Crank-Nicolson scheme, for the fractional step theta scheme, and for the SST-generalized stationary Navier-Stokes equations. As far as stability is concerned, a linear version of the Euler scheme, a nonlinear version of the Crank-Nicolson scheme, and the fractional step theta scheme turn out to be non-stable in the class of SST spaces. The positive results established in this thesis include the generalization of classical uniqueness and stability results to SST spaces, the uniqueness of solutions (under smallness assumptions) to two nonlinear versions of the Euler scheme, two nonlinear versions of the Crank-Nicolson scheme, and the fractional step theta scheme for general SST spaces, the second order convergence of a version of the Crank-Nicolson scheme, and a new proof of the first order convergence of the implicit Euler scheme for the Navier-Stokes equations. For each convergence result, we provide conditions on the data that guarantee the existence of nonstationary solutions satisfying the regularity assumptions needed for the corresponding convergence theorem. In the case of the Crank-Nicolson scheme, this involves a compatibility condition at the corner of the space-time cylinder, which can be satisfied via a suitable prescription of the initial acceleration.

Modulsymbole und Bruhat-Tits-Gebäude der PGL(3) über Funktionenkörpern

Thema der vorliegenden Arbeit ist die Bestimmung von Basen von Räumen spezieller harmonischer 2-Koketten auf Bruhat-Tits-Gebäuden der PGL(3) über Funktionenkörpern. Hierzu wird der Raum der speziellen harmonischen 2-Koketten auf dem Bruhat-Tits-Gebäude der PGL(3) zunächst mit gewissen komplexen Linearkombinationen von 2-Simplizes des Quotientenkomplexes, sogenannten geschlossenen Flächen, identifiziert und anschließend durch verallgemeinerte Modulsymbole beschrieben. Die Darstellung der Gruppe der Modulsymbole durch Erzeuger und Relationen ermöglicht die Bestimmung einer endlichen Basis des Raums der speziellen harmonischen 2-Koketten. Die so gewonnenen Erkenntnisse können zur Untersuchung von Hecke-Operatoren auf speziellen harmonischen 2-Koketten genutzt werden. Mithilfe des hergeleiteten Isomorphismus zwischen dem Raum der speziellen harmonischen 2-Koketten und dem Raum der geschlossenen Flächen wird die Theorie der Hecke-Operatoren auf den Raum der geschlossenen Flächen übertragen. Dies ermöglicht die Berechnung von Abbildungsmatrizen der Hecke-Operatoren auf dem Raum der harmonischen 2-Koketten durch die Auswertung auf den geschlossenen Flächen.

Parallel Methods for Synthesizing Whole-Hand Grasps from Generalized Prototypes

This report addresses the problem of acquiring objects using articulated robotic hands. Standard grasps are used to make the problem tractable, and a technique is developed for generalizing these standard grasps to increase their flexibility to variations in the problem geometry. A generalized grasp description is applied to a new problem situation using a parallel search through hand configuration space, and the result of this operation is a global overview of the space of good solutions. The techniques presented in this report have been implemented, and the results are verified using the Salisbury three-finger robotic hand.

Virtual Model Control of a Biped Walking Robot

The transformation from high level task specification to low level motion control is a fundamental issue in sensorimotor control in animals and robots. This thesis develops a control scheme called virtual model control which addresses this issue. Virtual model control is a motion control language which uses simulations of imagined mechanical components to create forces, which are applied through joint torques, thereby creating the illusion that the components are connected to the robot. Due to the intuitive nature of this technique, designing a virtual model controller requires the same skills as designing the mechanism itself. A high level control system can be cascaded with the low level virtual model controller to modulate the parameters of the virtual mechanisms. Discrete commands from the high level controller would then result in fluid motion. An extension of Gardner's Partitioned Actuator Set Control method is developed. This method allows for the specification of constraints on the generalized forces which each serial path of a parallel mechanism can apply. Virtual model control has been applied to a bipedal walking robot. A simple algorithm utilizing a simple set of virtual components has successfully compelled the robot to walk eight consecutive steps.

Lean Enterprise Transformation: Measuring and Accelerating the transition to lean.

PowerPoint presentation that showcases: • Research Objectives • Strategic Value of the Lean Enterprise • Multi-Stakeholder Value Optimization • Lean Enterprise Self-Assessment Tool (LESAT) • Leading and Lagging Indicators of Lean Enterprise Transformation • Empirical Results in the Aerospace Industry • Accelerating the Lean Transformation - Linking LESAT to Strategic Objectives • Summary and Questions

CITE and educational transformation

Presentation given by Professor Hugh Davis to the University Strategic Research Group for the Digital Economy monthly lunch meeting on Monday 24 September 2012. This session provided an update on the evolution of the University Centre for Innovation in Technologies and Education (CITE) in September 2012.

Legal Sociology Reformulated: the Transformation of Law in Globalization and New Citizenship

This article seeks to demonstrate how Law inter-related with Economy, constitutes in modern societies one of the main instruments for the construction of citizen consensus or the construction of political hegemony in modern societies. If we consider this affirmation —as is argued here— the transformations suffered in recent decades by Law as a consequence of the new phase of capitalistic globalization, have played an important role in the constitution of a new subjectivity (“single thought”) in the population.

Distribución hiperbólica generalizada: una aplicación en la selección de portafolios y en la cuantificación de medidas de riesgo de mercado

En este trabajo se implementa una metodología para incluir momentos de orden superior en la selección de portafolios, haciendo uso de la Distribución Hiperbólica Generalizada, para posteriormente hacer un análisis comparativo frente al modelo de Markowitz.

Diferencias individuales y desarrollo de habilidades de liderazgo : el rol del locus de control

El presente proyecto se ha elaborado con la finalidad de encontrar la relación existente entre el liderazgo y el locus de control, por medio de una revisión documental que permita dar una visión más amplia de estos dos fenómenos. De acuerdo con investigaciones realizadas, existen características individuales que afectan el desarrollo de liderazgo, lo cual a su vez tiene un impacto sobre el comportamiento de los individuos dentro de una sociedad. Uno de estos factores es el locus de control, el cual sesta determinado por características del individuo, y por el ambiente en el cual se desenvuelven las personas. Existen diferentes evidencias que soportan ésta relación entre locus de control y liderazgo. En éste estudio documental se describirán estos hallazgos, identificando las características del individuo y del contexto que influyen sobre ellos. Asimismo se pondrá en contexto a través del trabajo las características principales de los líderes y como se presentan las interacciones entre los lideres y seguidores, teniendo en cuenta que no todas las veces los seguidores desarrollan este papel al seguir a su líder, sino que por otro lado y estos pueden tomar parte fundamental en la interacción, influyendo de manera directa sobre el líder. Se recuerda que a los lideres los hacen sus seguidores y que sin estos no podrían desarrollar el papel de líder.

Determinants of demand for antenatal care in Colombia

Even though antenatal care is universally regarded as important, determinants of demand for antenatal care have not been widely studied. Evidence concerning which and how socioeconomic conditions influence whether a pregnant woman attends or not at least one antenatal consultation or how these factors affect the absences to antenatal consultations is very limited. In order to generate this evidence, a two-stage analysis was performed with data from the Demographic and Health Survey carried out by Profamilia in Colombia during 2005. The first stage was run as a logit model showing the marginal effects on the probability of attending the first visit and an ordinary least squares model was performed for the second stage. It was found that mothers living in the pacific region as well as young mothers seem to have a lower probability of attending the first visit but these factors are not related to the number of absences to antenatal consultation once the first visit has been achieved. The effect of health insurance was surprising because of the differing effects that the health insurers showed. Some familiar and personal conditions such as willingness to have the last children and number of previous children, demonstrated to be important in the determination of demand. The effect of mother’s educational attainment was proved as important whereas the father’s educational achievement was not. This paper provides some elements for policy making in order to increase the demand inducement of antenatal care, as well as stimulating research on demand for specific issues on health.

Edexcel GCSE history A : the making of the modern world. Unit 3A : war and the transformation of british society c. 1903-28. Student book.

Es una de las cuatro unidades del curso de preparación para los exámenes del General Certificate Secondary Education (GCSE). Esta unidad 3 es diferente de las dos unidades anteriores pues sus temas se basan en comprender la importancia de las fuentes en el estudio de la historia y como pueden ser interpretadas de varias maneras, lo que lleva a los historiadores a emitir juicios sobre la utilidad y fiabilidad de la información que proporcionan. Asimismo, se explica que en esta parte del examen del GCSE se conjugan los conocimientos y la información sobre los hechos con los juicios sobre las fuentes históricas.

Edexcel GCSE history A : the making of the modern world. Unit 3B : war and the transformation of british society c. 1931-51. Student book.

Es una de las cuatro unidades del curso de preparación para los exámenes del General Certificate Secondary Education (GCSE). Esta unidad 3 es diferente de las dos unidades anteriores pues sus temas se basan en comprender la importancia de las fuentes en el estudio de la historia y como pueden ser interpretadas de varias maneras, lo que lleva a los historiadores a emitir juicios sobre la utilidad y fiabilidad de la información que proporcionan. Asimismo, se explica que en esta parte del examen del GCSE se conjugan los conocimientos y la información sobre los hechos con los juicios sobre las fuentes históricas.

Adaptation to climate change : from resilience to transformation.

Es un análisis exhaustivo de las dimensiones sociales del cambio climático, pues se considera una prioridad para el desarrollo humano aprender a vivir con sus efectos. Se presentan una serie de opciones que puede afrontar la humanidad en esta tarea estrictamente defensiva de adaptación a los riesgos del calentamiento global de la Tierra. Es una obra de referencia para los estudiantes de pregrado y postgrado interesados en los estudios sobre cambio climático, geografía y desarrollo.

Reflections on the transformation of education for the knowledge age. 'Reflexiones sobre la transformación de la educación para la era del conocimiento'.

Monográfico con el título: 'Aprendizaje y construcción del conocimiento en la red'. Resumen basado en el de la publicación