<p>The quality of cameras is currently increasing very fast meanwhile the price of them is decreasing. The possibilities of using a camera as a measurement and navigation instrument are thus getting bigger all the time. This thesis studies the transformation relations between a camera image and the scene in space that is projected to it. A theoretical derivation of the transform will be presented, and methods and algorithms for applications based on the transform will be developed.</p><p>The above mentioned transform is called the camera matrix, which contains information about the camera attitude, the camera position, and the internal structure of the camera. Useful information for several different applications can be extracted from the camera image with the help of the camera matrix.</p><p>In one of the applications, treated in this Master´s thesis, the camera attitude is estimated when the camera is calibrated and its position is known. Another application is that of absolute target positioning, where a point in a digital map is searched from its position in a camera image. Better accuracy in the measurements can though be obtained with relative target positioning i.e., estimation of distance and angle between two points in the digital map by picking them out in the image. This is because that the errors of the</p><p>absolute target positioning for each of the two points are dependent and thus partly will cancel each other out when their relative position and angle is measured.</p>

<p>Chapter 1 to 4 give a short introduction to superconductivity, microscopic theory, phase transitions, and Monte-Carlo simulations. Chapter 2 is about Cooper pairing in different settings, but I also give a short introduction to the Hofstadter problem of lattice fermions on a square lattice in a perpendicular magnetic field. The purpose is to clarify some points in Paper-I. Chapter 3 is about phase transitions, and introduces the important concepts of spontaneous symmetry breaking, scaling, and renormalization. In the last section I stress some of the main differences between first order and second order phase transitions. Chapter 4 starts with a short elementary introduction to Monte-Carlo simulations and proceeds with the important, but somewhat more advanced topic of reweighting.</p><p>Chapter 5 to 7 are more closely related to the specific projects I have worked on, and are meant to illuminate and clarify some aspects in Paper-II and Paper-III. Chapter 5 introduce the Ginzburg-Landau model in various parametrizations, present some perturbative (mean-field) results, and introduce the concept of topological defects (vortices) and duality.</p><p>Chapter 6 is closely related to Paper-II and introduce the concept of fractal dimension and the relation between the vortex excitations of the original theory and the dual field theory. Chapter 7 is closely related to Paper-III where we studied the order of the metal to superconductor phase transition. To do this we had to do infinite volume and continuum limit extrapolations. We also had to consider ultraviolet renormalization since the Ginzburg-Landau theory is a continuum field theory with no inherent short scale cut-off. To reduce auto-correlation times we added several improvements to the standard Metropolis algorithm in the Monte-Carlo simulations, the most important being an overrelaxation algorithm for the scalar field and a global update of the scalar amplitude.</p>

We propose and test a new adaptive conjoint analysis method that draws on recent polyhedral “interior-point” developments in mathematical programming. The method is designed to offer accurate estimates after relatively few questions in problems involving many parameters. Each respondent’s ques-tions are adapted based upon prior answers by that respondent. The method requires computer support but can operate in both Internet and off-line environments with no noticeable delay between questions. We use Monte Carlo simulations to compare the performance of the method against a broad array of relevant benchmarks. While no method dominates in all situations, polyhedral algorithms appear to hold significant potential when (a) metric profile comparisons are more accurate than the self-explicated importance measures used in benchmark methods, (b) when respondent wear out is a concern, and (c) when product development and/or marketing teams wish to screen many features quickly. We also test hybrid methods that combine polyhedral algorithms with existing conjoint analysis methods. We close with suggestions on how polyhedral methods can be used to address other marketing problems. / Sloan School of Management and the Center for Innovation in Product Development at MIT

In der vorliegenden Arbeit werden die Eigenschaften geschlossener fluider Membranen, sogenannter Vesikeln, bei endlichen Temperaturen untersucht. Dies beinhaltet Betrachtungen zur Form freier Vesikeln, eine Untersuchung des Adhäsionsverhaltens von Vesikeln an planaren Substraten sowie eine Untersuchung der Eigenschaften fluider Vesikeln in eingeschränkten Geometrien. Diese Untersuchungen fanden mit Hilfe von Monte-Carlo-Simulationen einer triangulierten Vesikeloberfläche statt. Die statistischen Eigenschaften der fluktuierenden fluiden Vesikeln wurden zum Teil mittels Freier-Energie-Profile analysiert. In diesem Zusammenhang wurde eine neuartige Histogrammethode entwickelt.<br><BR> Die Form für eine freie fluide Vesikel mit frei veränderlichem Volumen, die das Konfigurationsenergie-Funktional minimiert, ist im Falle verschwindender Temperatur eine Kugel. Mit Hilfe von Monte-Carlo-Simulationen sowie einem analytisch behandelbaren Modellsystem konnte gezeigt werden, daß sich dieses Ergebnis nicht auf endliche Temperaturen verallgemeinern lässt und statt dessen leicht prolate und oblate Vesikelformen gegenüber der Kugelgestalt überwiegen. Dabei ist die Wahrscheinlichkeit für eine prolate Form ein wenig gröoßer als für eine oblate. Diese spontane Asphärizität ist entropischen Ursprungs und tritt nicht bei zweidimensionalen Vesikeln auf. Durch osmotische Drücke in der Vesikel, die größer sind als in der umgebenden Flüssigkeit, lässt sich die Asphärizität reduzieren oder sogar kompensieren. Die Übergänge zwischen den beobachteten prolaten und oblaten Formen erfolgen im Bereich von Millisekunden in Abwesenheit osmotisch aktiver Partikel. Bei Vorhandensein derartiger Partikel ergeben sich Übergangszeiten im Bereich von Sekunden.<br><br> Im Rahmen der Untersuchung des Adhäsionsverhaltens fluider Vesikeln an planaren, homogenen Substraten konnte mit Hilfe von Monte-Carlo-Simulationen festgestellt werden, dass die Eigenschaften der Kontaktfläche der Vesikeln stark davon abhängen, welche Kräfte den Kontakt bewirken. Für eine dominierende attraktive Wechselwirkung zwischen Substrat und Vesikelmembran sowie im Falle eines Massendichteunterschieds der Flüssigkeiten innerhalb und außerhalb der Vesikel, der die Vesikel auf das Substrat sinken lässt, ndet man innerhalb der Kontakt ache eine ortsunabhangige Verteilung des Abstands zwischen Vesikelmembran und Substrat. Drückt die Vesikel ohne Berücksichtigung osmotischer Effekte auf Grund einer Differenz der Massendichten der Membran und der umgebenden Flüssigkeit gegen das Substrat, so erhält man eine Abstandsverteilung zwischen Vesikelmembran und Substrat, die mit dem Abstand vom Rand der Kontaktfläche variiert. Dieser Effekt ist zudem temperaturabhängig.<br><br> Ferner wurde die Adhäsion fluider Vesikeln an chemisch strukturierten planaren Substraten untersucht. Durch das Wechselspiel von entropischen Eekten und Konfigurationsenergien entsteht eine komplexe Abhängigkeit der Vesikelform von Biegesteifigkeit, osmotischen Bedingungen und der Geometrie der attraktiven Domänen.<br><br> Für die Bestimmung der Biegesteifigkeit der Vesikelmembranen liefern die existierenden Verfahren stark voneinander abweichende Ergebnisse. In der vorliegenden Arbeit konnte mittels Monte-Carlo-Simulationen zur Bestimmung der Biegesteifigkeit anhand des Mikropipettenverfahrens von Evans gezeigt werden, dass dieses Verfahren die <i>a priori</i> für die Simulation vorgegebene Biegesteifigkeit im wesentlichen reproduzieren kann.<br><br> Im Hinblick auf medizinisch-pharmazeutische Anwendungen ist der Durchgang fluider Vesikeln durch enge Poren relevant. In Monte-Carlo-Simulationen konnte gezeigt werden, dass ein spontaner Transport der Vesikel durch ein Konzentrationsgefälle osmotisch aktiver Substanzen, das den physiologischen Bedingungen entspricht, induziert werden kann. Es konnten die hierfür notwendigen osmotischen Bedingungen sowie die charakteristischen Zeitskalen abgeschätzt werden. Im realen Experiment sind Eindringzeiten in eine enge Pore im Bereich weniger Minuten zu erwarten. Ferner konnte beobachtet werden, dass bei Vesikeln mit einer homogenen, positiven spontanen Krümmung Deformationen hin zu prolaten Formen leichter erfolgen als bei Vesikeln ohne spontane Krümmung. Mit diesem Effekt ist eine Verringerung der Energiebarriere für das Eindringen in eine Pore verbunden, deren Radius nur wenig kleiner als der Vesikelradius ist. / In this thesis, the properties of closed fluid membranes or vesicles are studied at finite temperatures. The work contains investigations of the shape of free vesicles, studies of the adhesion behavior of vesicles to planar substrates, and investigations of the properties of fluid vesicles in confined geometries. The investigations have been performed with Monte Carlo simulations of triangulated vesicles. The statistical properties of fluctuating vesicles have been analyzed in detail by means of free energy profiles. In this context, a new histogram method was developed. <br><br> The shape of minimum configurational energy for a free vesicle without volume constraint at zero temperature is a sphere. It is shown by means of Monte Carlo simulations and a model which can be analyzed analytically, that this result does not apply to finite temperatures. Instead, prolate and oblate shapes prevail and the probability for a prolate shape is slightly larger than that for an oblate shape. This spontaneous asphericity is of entropic origin and cannot be observed in two dimensions. Osmotic pressures inside the vesicle that are larger than in the surrounding liquid may reduce or even compensate the asphericity. The transitions between the observed prolate and oblate states occur on the time scale of milliseconds in the absence of osmotically active particles and on the time scale of seconds in the presence of osmotically active particles. <br><br> As far as the adhesion behavior of fluid vesicles to planar homogeneous substrates is concerned, Monte Carlo simulations reveal a strong dependence of the properties of the contact area on its driving force. In the case of a dominating attractive interaction between vesicle membran and substrate as well as for a mass density difference of the liquids inside and outside the vesicle, which push the vesicle against the substrate, the distribution of the distance between the vesicle membrane and the substrate is homogenous. If the vesicle is pushed against the substrate by a difference of the mass densities of the membrane and the surrounding liquid, neglecting all osmotic effects, one gets a distance distribution between the vesicle membrane and the substrate which varies with the distance from the rim of the contact area. Moreover, this effect is temperature-dependent. <br><br> Furthermore, the adhesion of fluid vesicles to chemically structured planar substrates has been studied. The interplay between entropic effects and configurational energies causes a complex dependence of the vesicle shape on the bending rigidity, osmotic conditions, and the geometry of the attractive domains. <br><br> There are several experimental methods for measuring the bending rigidity of vesicle membranes which lead to rather different results for the numerical value. Monte Carlo simulations of Evans' micropipette method show that the difference between the measured bending rigidity and the a priori chosen bending rigidity is small. <br><br> The passage of fluid vesicles through narrow pores has some relevance to medical/pharmaceutical applications. In Monte Carlo simulations it is shown that a spontaneous transport of vesicles can be induced by a concentration gradient of osmotically active particles which corresponds to the physiological conditions. The necessary osmotic conditions and the charateristic time scales are calculated. For real experiments, penetration into the pore should occur within a few minutes. Moreover, it was observed that vesicles with a homogeneous positive spontaneous curvature can be deformed more easily into prolate shapes than vesicles with zero spontaneous curvature. This effect leads to a decrease of the energy barrier for the penetration into a wide pore, which has a radius slightly smaller than that of the vesicle.

Chapter 1 to 4 give a short introduction to superconductivity, microscopic theory, phase transitions, and Monte-Carlo simulations. Chapter 2 is about Cooper pairing in different settings, but I also give a short introduction to the Hofstadter problem of lattice fermions on a square lattice in a perpendicular magnetic field. The purpose is to clarify some points in Paper-I. Chapter 3 is about phase transitions, and introduces the important concepts of spontaneous symmetry breaking, scaling, and renormalization. In the last section I stress some of the main differences between first order and second order phase transitions. Chapter 4 starts with a short elementary introduction to Monte-Carlo simulations and proceeds with the important, but somewhat more advanced topic of reweighting. Chapter 5 to 7 are more closely related to the specific projects I have worked on, and are meant to illuminate and clarify some aspects in Paper-II and Paper-III. Chapter 5 introduce the Ginzburg-Landau model in various parametrizations, present some perturbative (mean-field) results, and introduce the concept of topological defects (vortices) and duality. Chapter 6 is closely related to Paper-II and introduce the concept of fractal dimension and the relation between the vortex excitations of the original theory and the dual field theory. Chapter 7 is closely related to Paper-III where we studied the order of the metal to superconductor phase transition. To do this we had to do infinite volume and continuum limit extrapolations. We also had to consider ultraviolet renormalization since the Ginzburg-Landau theory is a continuum field theory with no inherent short scale cut-off. To reduce auto-correlation times we added several improvements to the standard Metropolis algorithm in the Monte-Carlo simulations, the most important being an overrelaxation algorithm for the scalar field and a global update of the scalar amplitude.

In this paper the Heath, Jarrow and Morton (HJM) framework is applied in the programming language Java for the estimation of the future spot rate. The subcase of an exponential model for the diffusion coefficient (volatility) is used for the pricing of interest rate derivatives (caps).

A numerical study aimed at probabilistically assessing the coastal hazard posed by tsunamis induced by one-dimensional submarine rigid landslides that experience translational failure is presented. The numerical model here utilized is the finite-difference recreation of a linear, fully dispersive mild-slope equation model for wave generation and propagation. This recreated model has the capability to simulate submarine landslides that detach into multiple rigid pieces as failure occurs. An ad-hoc formulation describing the combined space-time coherency of the landslide is presented. Monte Carlo simulations are employed, with an emphasis on the shoreward-traveling waves, to construct probability of exceedance curves for the maximum dimensionless wave height from which wave statistics can be extracted. As inputs to the model, eight dimensionless parameters are specified both deterministically in the form of parameter spaces and probabilistically with normal distributions. Based on a sensitivity analysis, the results of this study indicate that submarine landslides with large width to thickness ratios and coherent failure behavior are most effective in generating tsunamis. Failures modes involving numerous slide pieces that fail in a very compact fashion, however, were observed to induce bigger waves than more coherent landslides. Rapid weakening in tsunami generation potential for some of the parameter combinations suggests that the hazard posed by submarine landslide tsunamis is strongly dependent on source features and local conditions and is only of concern for landslides of substantial dimensions.

Thermal fluctuations and disorder strongly influence the behaviour of hightemperature superconductors. In particular the vortices play a key role in determining their properties. In this thesis the main focus lies on phase transitions, both in ultra-thin films and in three-dimensional systems, which are driven by vortex fluctuations. The last paper concerns the influence of antiferromagnetism on superconductivity in a simple model. A brief review of these topics is given in the introductory part. The main results are: The phase transition in ultra-thin superconducting/superfluid films is studied within the two-dimensional Coulomb gas model, which is known to have a Berezinskii-Kosterlitz-Thouless transition at low vortex densities. We construct the phase diagram from grand canonical Monte Carlo simulations on a continuum, without any restrictions on the vortex density. The dynamical universality classes for vortices in superconductors in zero magnetic field are studied by means of Monte Carlo simulations, with particular attention to the role of screening of the vortex interaction. We construct a formula for the k = 0 helicity modulus directly in terms of the vortex line fluctuations, which can serve as a useful way to detect superconducting coherence in model calculations. A method for simulating vortex lines on a continuum is developed, and used to study the melting of the Abrikosov vortex lattice. We study the critical dynamics for vortices in the presence of columnar defects. The linear resistivity and current-voltage characteristics are calculated in Monte Carlo simulations, and the critical behaviour extracted using finite size scaling. We reconsider the scaling properties as the magnetic field is tilted away from the direction of the columns. The influence of antiferromagnetic correlations on the superconducting properties is studied in a simplified lattice fermion model for superconductivity in the presence of an antiferromagnetic background. We find that the superconducting critical temperature is enhanced by antiferromagnetic order, and that a gap with dx2-y2-wave symmetry is the most stable. / QC 20100512

Phase transitions and their critical scaling properties, especially in systems with disorder, are important both for our theoretical understanding of our environment, but also for their practical use in applications and materials in our everyday life. This thesis presents results from finite size scaling analysis of critical phenomena in systems with disorder, using high-precision Monte Carlo simulations and state of the art numerical methods. Specifically, theoretical models suitable for simulations in the presence of uncorrelated or correlated disorder are studied. Uncorrelated strong disorder, as present in the two dimensional gauge glass model to study the vortex glass phase of high temperature superconductors in an applied magnetic field is shown to lack a finite temperature phase transition. Further, results from dynamic quantities, such as resistance and autocorrelation functions, indicate the existence of two distinct diverging correlation times, one associated with local relaxation and one associated with vortex phase slips. Correlated disorder is studied both in the superfluid transition of helium-4 and in the anisotropic critical scaling of a transverse Meissner-like transition in an experimental setup of a high temperature superconductor. For the superfluid helium transition, it is shown that the presence of fractally correlated disorder presumably alters the universality class of the pure model. Also, a comparison with experimental data suggests that the critical scaling theory describing the heat capacity of helium-4 may need to be modified in the presence of the disorder. In the case of superconductors, analyzing experimental data from resistance measurements in a system with columnar defects together with an anisotropy in the applied magnetic field, reveals a fully anisotropic scaling regime. Finally, a data analysis is presented from simulations of a charged particle gas system in three dimensions, where the normal Coulomb interaction between charges is changed into a logarithmic interaction. Previous work indicates the possibility of a transition similar to the Kosterlitz-Thouless transition in certain two dimensional systems. On the contrary, our simulations seem to favor a system whose critical scaling behavior is consistent with a transition occurring only at zero critical temperature. Overall, disorder in the model systems studied leads to important modifications of the critical scaling properties of pure systems, and thereby also to possible changes of the corresponding universality classes. This results in interesting predictions with experimentally relevant consequences. / QC 20100811

The Vlasov technique is used to model the electron cooling force. Limitations of the applicability of the method is obtained by considering the perturbations of the electron plasma. Analytical expressions of the electron cooling force, valid beyond the Coulomb logarithm approximation, are derived and compared to numerical calculations using adaptive Monte Carlo integration. The calculated longitudinal cooling force is verified with measurements in CELSIUS. Transverse damping rates of betatron oscillations for a nonlinear cooling force is explored. Experimental data of the transverse monochromatic instability is used to determine the rms angular spread due to solenoid field imperfections in CELSIUS. The result, θrms= 0.16 ± 0.02 mrad, is in agreement with the longitudinal cooling force measurements. This verifies the internal consistency of the model and shows that the transverse and longitudinal cooling force components have different velocity dependences. Simulations of electron cooling with applications to HESR show that the momentum reso- lution ∆p/p smaller than 10−5 is feasible, as needed for the charmonium spectroscopy in the experimental program of PANDA. By deflecting the electron beam angle to make use of the monochromatic instability, a reasonable overlap between the circulating antiproton beam and the internal target can be maintained. The simulations also indicate that the cooling time is considerably shorter than expected.