<p>We begin by recalling some basic definitions from Lie algebra theory to motivate our subsequent transition to the more general setting of category theory. Next, we develop a relatively self-contained introduction to those areas of category theory needed for an understanding of what follows. Here we also motivate and introduce the graphical calculus notations. We then state the definitions of a braided commutator algebra, a braided Lie algebra, and a braided commutator Lie algebra. We proceed to show that color Lie algebras and Lie superalgebras are examples of braided Lie algebras. Thus, we are interested in examining color Lie algebras and Lie superalgebras in the generalized setting of braided Lie algebras. So we end by examining the representation theory of braided Lie algebras and braided commutator Lie algebras. In paricular, we find analogues of the adjoint representation, the tensor product representation, and the contragredient representation.</p>

<p>The Yankee cylinder is used in most of Metso Paper's machines. It is used in the drying and creping process. Since the outcome of these processes largely affect the paper's final quality it is important that the Yankee cylinder behaves in a controlled fashion. One important parameter affecting the behaviour of the Yankee cylinder is its surface temperature.</p><p>The objective of this thesis was to search for and evaluate methods for measuring the surface temperature of a Yankee cylinder during operation. Metso Paper is looking for a method having an accuracy of ΔT = 1°C, a response time of t<10 ms, and being portable.</p><p>Three different instruments were tested during the thesis:</p><ul><li>Thermophone, a contact measurement device currently used by Metso Paper.</li><li>RAYNGER MX4, a pyrometer from Raytek.</li><li>FLIR P640, a thermographic camera with a 640x480 focal plane array from FLIR.</li></ul><p>The instruments were tested by performing measurements on Metso Paper's pilot machine in Karlstad during operation. The measurements revealed drawbacks for all three instruments. The biggest drawbacks of the Thermophone was its response time, t~5 min, and its dependence on the frictional heating of the teflon cup. The frictional heating causes the measured temperature to increase even after 15 min making it hard to know when to stop the measurement. How much the frictional heating affects the measured temperature was difficult to analyse, making it a suggestion for future studies.</p><p>The biggest drawback of the pyrometer and the thermographic camera is the measurement error due to emissivity errors. Since the Yankee cylinder have a varying surface finish the emissivity varies a lot along the surface introducing temperature errors as large as ΔT=30°C.</p><p>Two methods that claim to be emissivity independent were investigated; double-band and gold cup pyrometers. Double-band pyrometers require the target to be a grey body and for it to have large temperatures, T>300°C, making this method unsuitable for measuring the surface temperature of the Yankee cylinder.</p><p>Gold cup pyrometers require the gold hemisphere to have a reflectance of ρ=1. Because of the environment surrounding the Yankee cylinder it would be difficult keeping the gold hemisphere as clean as required making this method unsuitable as well.</p>

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Denna avhandling innefattar såväl experimentella som numeriska studier av laserkylda atomer i optiska kristallgitter. Bland annat har laserkylningsprocesser studerats, där atomers rörelser i optiska kristallgitter har uppvisat andra typer av bakomliggande mekanismer än de som tidigare förutsågs genom “Sisyfoskylningsmodellen”. Sedan atomer kylda till några mikrokelvin först realiserades (sent 60-tal) så har Sisyfoskylningsmodellen varit hörnstenen för förståelsen av laserkylda och lokaliserade atomer i dissipativa optiska kristallgitter. I dissipativa optiska kristallgitter finns det en balans mellan den uppvärmande diffusionen och den kylande friktionen. Studier i denna avhandling visar att laserkylningsprocesser är mer komplexa än vad denna modell innefattar. Både experimentella och numeriska resultat visar att atomer i optiska kristallgitter har två hastighetsfördelningar där en “kallare” och en “varmare” mod av atomer omfördelas mellan moderna. Speciellt så visar det sig att varma atomer dels värms och diffunderar ut ur gittret, men samtidigt populeras den kalla moden med en tidsutveckling som inte förändrar dess temperatur nämnvärt. I detta arbete presenteras också resultat från den första realiserade tredimensionella Brownska motorn baserad på ljus-atom-växelverkan. Det unika med denna Brownska motor är att den är kontrollerbar både vad gäller dess hastighet som dess riktning. Den underliggande principen för denna Brownska motor är tämligen generell och den kan därför vara applicerbar inom andra vetenskapliga discipliner såsom nanoteknik, biologi, kemi och elektronik. Generellt så är förståelsen av Brownska motorer viktigt eftersom de återfinns i vår omgivning, från exempelvis härkomsten av muskelsammandragningar och materialtransporter i levande celler till rörelsen hos bakterier och mindre organismer. Det flesta av de experimentella resultaten presenterade i denna avhandling har varit möjliga genom utveckling och förbättringar av den experimentella uppställningen. Framförallt så har kvaliten och reproducerbarheten vid de olika mätningar som gjorts blivit avsevärt förbättrade jämfört med tidigare vilket utgör en bra grund för framtida studier av ultrakalla atomer. / In this thesis, detailed experimental studies and numerical simulations are presented of laser cooling mechanisms in dissipative optical lattices and results of the first realized three dimensional Brownian motor in optical lattices. A dissipative optical lattice is a periodic light shift potential, created in the interference patterns of laser beams. In this, atoms can be both cooled and trapped, and the most important relaxation mechanism is generally considered to be “Sisyphus cooling”. However, careful experimental and theoretical investigations indicate the presence of other cooling processes as well. This is studied by varying different parameters such as irradiance and frequency of the lattice light. The time evolution of atoms in optical lattices show strong evidence of a bimodal velocity distribution, where a population transfer between one mode containing “hot” atoms and one mode containing “cold” atoms is evident. The normal diffusion of atoms in optical lattices is characterized by isotrop random fluctuations and exhibit the nature of Brownian motion. We have realized a technique where this motion is rectified and controlled. This is done in a three dimensional double optical lattice. This Brownian motor has control properties for both its speed and its direction in three dimensions. Our three dimensional double optical lattice is created by using laser light, exploiting two transitions, in the D2 line of cesium. Two three dimensional optical lattices are spatially overlapped; each optical lattice traps atoms in one of two hyperfine ground states. The controllability comes about by inducing phase shifts in the lattice laser beams, which displace the lattices relative to each other. This type of highly controlled Brownian motor is of fundamental interest since Brownian motion is present in almost all systems and for the role they play in protein motors and the function of living cells, and for the potential applications in nanotechnology. Brownian motors of this kind also open the way to possible studies of quantum Brownian motors and quantum resonances that are predicted for atomic ratchets. Optical lattices, and especially double optical lattices, have also been suggested as a platform for quantum state manipulations due to the good isolation from environment and ambient effects. Most of the work in this thesis is a first step towards the implementation of quantum manipulation schemes in a double optical lattice.

Light scattering in turbid media is essential for such diverse application areas as paper and print, computer rendering, optical tomography, astrophysics and remote sensing. This thesis investigates angular variations of light reflected from plane-parallel turbid media using both mathematical models and reflectance measurements, and deals with several applications. The model of most widespread use in industry is the Kubelka-Munk model, which neglects angular variations in the reflected light. This thesis employs a numerical solution of the angle resolved radiative transfer problem to better understand how the angular variations are related to medium properties. It is found that the light is reflected anisotropically from all media encountered in practice, and that the angular variations depend on the medium absorption and transmittance and on the angular distribution of the incident light. If near-surface bulk scattering dominates, as in strongly absorbing or highly transmitting media or obliquely illuminated media, relatively more light is reflected in large polar (grazing) angles. These results are confirmed by measurements using a set of paper samples. The only situation with isotropic reflectance is when a non-transmitting, non-absorbing medium is illuminated diffusely. This is the only situation where the Kubelka-Munk model is exactly valid. The results also show that there is no such thing as an ideal bulk scattering diffusor, and these findings can affect calibration and measurement procedures defined in international standards.The implications of the presented results are studied for a set of applications including reflectance measurements, angle resolved color and point spreading. It is seen that differences in instrument detection and illumination geometry can result in measurement differences. The differences are small and if other sources of error - such as fluorescence and gloss - are not eliminated, the differences related to instrument geometry become difficult to discern. Furthermore, the angle resolved color of a set of paper samples is assessed both theoretically and experimentally. The chroma decreases and the lightness increases as the observation polar angle increases. The observed differences are clearly large, and it is an open issue how angle resolved color should be handled. Finally, the dependence of point spreading in turbid media on the medium parameters is studied. The asymmetry factor is varied while maintaining constant the optical response in a standardized measurement geometry. It is seen that the point spreading increases as forward scattering becomes more dominant, and that the effect is larger if the medium is low-absorbing with large mean free path. A generic model of point spreading must therefore capture the dependence on all of these medium parameters.This thesis shows that turbid media reflect light anisotropically, and angle resolved radiative transfer models are therefore necessary to capture this. Using simplified models can introduce errors in an uncontrolled manner. The results presented potentially have consequences for all applications dealing with light scattering, some of which are studied here.

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This thesis presents a comprehensive review of research into students’ depictions of quantum mechanics. A taxonomy to describe and compare quantum mechanics education research is presented, and this taxonomy is used to highlight the foci of prior research. A brief history of quantum mechanics education research is also presented. Research implications of the review are discussed, and several areas for future research are proposed. In particular, this thesis highlights the need for investigations into what interpretations of quantum mechanics are employed in teaching, and that classical physics – in particular the classical particle model – appears to be a common theme in students’ inappropriate depictions of quantum mechanics. Two future research projects are presented in detail: one concerning interpretations of quantum mechanics, the other concerning students’ depictions of the quantum mechanical wave function.This thesis also discusses teaching implications of the review. This is done both through a discussion on how Paper 1 can be used as a resource for lecturers and through a number of teaching suggestions based on a merging of the contents of the review and personal teaching experience.

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