This report discusses two examples of the use of Poincare disc models and their different relationships to Euclidean geometry. The topics include light reflection in hyperbolic geometry and the Hyperbolic Pythagorean Theorem; all in relation to the Poincare unit disc and Poincare upper half plane model. / text

Numerical simulations of the Navier-Stokes equations are performed to achieve a better understanding of the behaviour of wakes generated by wind turbines. The simulations are performed by combining the in-house developed computer code EllipSys3D with the actuator line and disc methodologies. In the actuator line and disc methods the blades are represented by a line or a disc on which body forces representing the loading are introduced. The body forces are determined by computing local angles of attack and using tabulated aerofoil coefficients. The advantage of using the actuator disc technique is that it is not necessary to resolve blade boundary layers. Instead the computational resources are devoted to simulating the dynamics of the flow structures. In the present study both the actuator line and disc methods are used. Between approximately six to fourteen million mesh points are used to resolve the wake structure in a range from a single turbine wake to wake interaction in a farm containing 80 turbines. These 80 turbines are however represented by 20 actuator discs due to periodicity because of numerical limitations. In step one of this project the objective was to find a numerical method suitable to study both the flow structures in the wake behind a single wind turbine and to simulate complicated interaction between a number of turbines. The study resulted in an increased comprehension of basic flow features in the wake, but more importantly in the use of a numerical method very suitable for the upcoming purpose. The second objective of the project was to study the basic mechanisms controlling the length of the wake to obtain better understanding of the stability properties of wakes generated by wind turbine rotors. The numerical model was based on large eddy simulations of the Navier-Stokes equations using the actuator line method to generate the wake and the tip vortices. To determine critical frequencies the flow is disturbed by inserting a harmonic perturbation. The results showed that instability is dispersive and that growth occurs only for specific frequencies and mode types. The study also provides evidence of a relationship between the turbulence intensity and the length of the wake. The relationship however needs to be calibrated with measurements. In the last project objective, full wake interaction in large wind turbine farms was studied and verified to measurements. Large eddy simulations of the Navier-Stokes equations are performed to simulate the Horns Rev off-shore wind farm 15 km outside the Danish west coast. The aim is to achieve a better understanding of the wake interaction inside the farm. The simulations are performed by using the actuator disc methodology. Approximately 13.6 million mesh points are used to resolve the wake structure in the park containing 80 turbines. Since it is not possible to simulate all turbines, the 2 central columns of turbines have been simulated with periodic boundary conditions. This corresponds to an infinitely wide farm with 10 turbines in downstream direction. Simulations were performed within plus/minus 15 degrees of the turbine alignment. The infinitely wide farm approximation is thus reasonable. The results from the CFD simulations are evaluated and the downstream evolution of the velocity field is depicted. Special interest is given to what extent production is dependent on the inflow angle and turbulence level. The study shows that the applied method captures the main production variation within the wind farm. The result further demonstrates that levels of production correlate well with measurements. However, in some cases the variation of the measurement data is caused by the different measurement conditions during different inflow angles. / QC 20100720

As wind industry is developing steadily oshore, the wind turbine spacing remainsa key element for maximizing revenues and reducing loading from turbineswake interaction. In the case of relatively close to shore oshore wind farms, orlarge arrays onshore, the turbulence intensity coming from dierent sectors canhave an eect on wake growth and decay. In an attempt to obtain wind featuresat site, some boundary conditions for micro-siting simulation are found, using acommercial RANS ow solver CFD software was used. The approach in this workcould be described more practical than theoretical and could be more useful fordevelopers than pure CFD specialists.By simulating with three dierent roughness length for open sea, with theappropriate and contextual assumptions, for the oshore Lillgrund wind farm,vertical proles and turbulence intensity were extracted from the WindSim softwareat the meteorological mast position and enabled measurement comparison.In a second attempt to compare the eect of the wind and turbulence prolespreviously obtained, a sector of interest is simulated with the actuator disc model.In general, the site conditions over the large-scale domain evaluated by thecommercial software are satisfactory after adjusting the roughness length for theopen sea. The turbulence intensity trend for various in ow angle is capturedby the simulations and computed wind proles are for the most part adequately.A comparison of spring and winter ltered measurements enable discussion uponsome sectors disagreement. As for the small-scale actuator disc model using thedeveloped site conditions, the result is over-estimated by the simulations, especiallyfor the second row downstream.

Vi har i vår forskningsöversikt inte hittat någon beskrivning på hur ledarskap kan anpassas tillmedarbetares olika personlighetstyper. Vårt syfte med studien var således att ta reda på hurolika typer av ledarskap kan anpassas till anställdas olika personlighetstyper för att uppnåstörsta möjlighet till utveckling av deras motivation. Vilket är en bidragande faktor till ettföretags utveckling och bör därför ligga i ledarens intresse. Med hjälp av två olikapersonlighetsklassificeringsmodeller, teorier om ledarskap och motivation samt empiri hämtatfrån ledare i arbetslivet har vi studerat vad för typ av ledarskap som fungerar för modellernasolika personlighetstyper. Med hjälp av kvalitativ forskningsstrategi har vi använt oss avtvärsnittsdesign samt en öppen och sex semistrukturerade intervjuer för att uppnå studienssyfte.Genom vår studie kan vi på ett tydligt sätt visa på att de personligheter vi utgått ifrån kräverolika typ av ledarskap, motiveras av olika faktorer och att situationen kan ha stor inverkan pånär ett visst ledarskap passar. Resultatet av vår studie har utformats till två tabeller utifrån depersonlighetsklassificeringsmodeller vi använt oss av. Tabellerna presenterar vilkenledarskapsteori som passar till vilken personlighetstyp. Studien resulterade även i ettkonstaterande att ledare bör använda sig av relationsinriktat ledarskap i grunden ochkomplettera det med uppgiftsinriktat ledarskap, för att finna de anställdas motivation och ledadem på ett framgångsrikt sätt. / In the research of this study we found a gap regarding information on how to adapt leadershipto employees of various personalities. Our purpose was now to fill that research gap. In ourstudy on personality-adapted leadership, we found that all kinds of personalities have variouspreferences to be led. Using two different personality classification models, theories ofleadership and motivation as well as empirical evidence drawn from Business leaders, wehave studied which kind of leadership that works best for models of different personalitytypes. With the help of a cross-section design, qualitative methods together with semistructuredinterviews we were able to combine the theories we used with the empiricalevidence. Accordingly, our purpose is to acknowledge how leadership can be adapted todifferent personalities to achieve the greatest opportunity for the development of theirmotivation. This is a contributing factor to the development of a company and shouldtherefore be in the leader’s interest.As a conclusion our study shows how different personalities demand certain kinds ofleadership, that they get motivated by a wide range of factors and that various situations canhave a big effect where a certain leadership is most suitable. The result of our study has led totwo tables based on the personality classification models, which show which leadershiptheory fits the different kinds of personality types. The study also shows that leaders shouldadapt a relationship-oriented leadership and complement it with a task-oriented one in order tofind their employees motivation and be able to lead them in a successful way.

This research was aimed at the development, implementation and evaluation of an empowerment programme for parents with children in their middle childhood, focused on temperament analysis. The motivation for this study stemmed from the absence of relevant programmes in the field of social work concerning different temperaments and needs of children that parents does not understand or meet. Intervention research was applied. A two-phase research approach was undertaken. In phase 1, a qualitative research was used to do a need assessment. The need assessment was done by means of two focus group discussions with ten parents in each group. The following research question was formulated for this phase: What is the needs of parents related to a programme that focus on temperament analysis for children in there middle childhood. This data complemented the literature study which was undertaken and provided information that established the contents of the empowerment programme. The research question could therefore be answered. The qualitative approach was used in phase 2 as the single-system design. The following research hypothesis was formulated for this phase: If an empowerment programme that includes a temperament analysis is attempted with parents, a significant change in their knowledge in handling and understanding of their children should realise. The empowerment programme for parents with children in their middle childhood consisted of six sessions and was implemented over a period of two weeks. Four parents and one single parent undertook the empowerment programme. A group assessment was undertaken with the five children of the parents who attended the empowerment programme. The focus of the group assessment was to determine a tendency to respond. The self-designed questionnaire was completed prior to the empowerment programme and thereafter. This instrument of measurement confirmed the hypothesis. Conclusions and recommendations for the utilization of the programme in future research were formulated as a result of the research study. / Thesis (PhD (Human Movement Science))--University of Pretoria, 2007. / Social Work and Criminology / unrestricted