<p>Detta examensarbete presenterar en utvärdering av konsekvenser som kan uppstå vid Införandet av Multiplex Power-mättmetoden för att kontrollera FM-deviation vid radiosändningar i Sverige.</p><p>Metoden är beskriven i en publicerad standard från ITU: ITU-R BS.412-9. Metoden, även kallad Multiplex Power, är en begränsningsstandard för analog (terrestrial) FM sändning på VHF band. Skälet att införa Multiplex Power mätning är att man genom metoden både kan minska grannkanalinterferenserna och samtidigt jämna ut de stora variationerna i de upplevda ljudnivåerna som finns mellan de olika FM-stationerna. Denna mätmetod går ut på att man samplar värden på deviation, lagrar samplen och räknar ut ett medelvärde av energin under ett intervall av 60 sekunder. Detta energivärde jämförs med en referensnivå, som i ITU-normen definieras som +/-19kHz toppdeviation vid 400 Hz modulationssignal. Skillnaden detta referensvärde kan anges i dB av instrumentet, som en enskild siffra vilkets värde skrivs dynamiskt över tid.</p><p>För att kunna utvärdera metoden genomfördes ett lyssningsexperiment. I experimentet användes ljudfiler som är processade enligt hur dagens normer tillämpas i Sverige och ljudfiler som är processade för att följa BS.412-9-normen. Som tillvägagångssätt användes ett webbformulär och en databas. Testpersoner kunde utföra lyssningen och notera resultatet som sedan lagrades för vidare beräkningar. Ljudfilerna och tillhörande mätningsvärden från lyssningsexperimentet användes sedan för att utvärdera resultatet.</p> / QC 20100707

<p>In this thesis we study hybrid numerical methods to be used in computational electromagnetics. The purpose is to address a wide frequency range relative to a given geometry. We also focus on efficient and robust numerical algorithms for computing the so called Smooth Surface Diffraction predicted by Geometrical Theory of Diffraction (GTD). We restrict the presentation to frequency domain scattering problems.</p><p>The hybrid methods consist in combinations of Boundary Element Methods and asymptotic methods. Three hybrids will be presented. One of them has been developed from a theoretical idea to an industrial code. The two other hybrids will be presented mainly from a theoretical perspective.</p><p>To be able to compute the Smooth Surface Diffracted field we introduce a numerical method that is to be used with surface curvature sensitive meshing, complemented with auxiliary data taken from a geometry database. By using two geometry representations we can show first order convergence and we then achieve an efficient and robust numerical algorithm. This numerical algorithm may be an essential part of an GTD implementation which in its turn is a component in the hybrid methods.</p><p>As a background to our new techiniques we will also give short introductions to the Boundary Element Method and the Geometrical Theory of Diffraction from a theoretical and implementational point of view.</p>

<p>In this report, we show how to implement direct ray tracing of B´ezier surfaces on graphics processing units (GPUs), in particular bicubic rectangular Bézier surfaces and nonparametric cubic Bézier triangles. We use Newton’s method for the rectangular case and show how to use this method to find the ray-surface intersection. For Newton’s method to work we must build a spatial partitioning hierarchy around each surface patch, and in general, hierarchies are essential to speed up the process of ray tracing. We have chosen to use bounding box hierarchies and show how to implement stackless traversal of such a structure on a GPU. For the nonparametric triangular case, we show how to find the wanted intersection by simply solving a cubic polynomial. Because of the limited precision of current GPUs, we also propose a numerical approach to solve the problem, using a one-dimensional Newton search.</p>

<p> The inverse heat conduction problem also frequently referred as the sideways heat equation, in short SHE, is considered as a mathematical model for a real application, where it is desirable for someone to determine the temperature on the surface of a body. Since the surface itself is inaccessible for measurements, one is restricted to use temperature data from the interior measurements. From a  mathematical point of view, the entire situation leads to a non-characteristic Cauchy problem, where by using recorded temperature one can solve a well-posed nonlinear problem in the finite region for computing heat flux, and consequently obtain the Cauchy data [u, u_x]. Further by using these data and by performing an appropriate method, e.g. a space marching method, one can eventually achieve the desired temperature at x = 0.</p><p>The problem is severely ill-posed in the sense that the solution does not depend continuously on the data. The problem solved by two different methods, and for both cases we stabilize the computations by replacing the time derivative in the heat equation by a bounded operator. The first one, a spectral method based on finite Fourier space is illustrated to supply an analytical approach for approximating the time derivative. In order to get a better accuracy in the numerical computation, we use cubic spline function for approximating the time derivative in the least squares sense.</p><p>The inverse problem we want to solve, by using Cauchy data, is a nonlinear heat conduction problem in one space dimension. Since the temperature data u = g(t) is recorded, e.g. by a thermocouple, it usually contains some perturbation in the data. Thus the solution can be severely ill-posed if the Cauchy data become very noisy. Two experiments are presented to test the proposed approach.</p>

<p>In this work we consider the nonlinear case of Black-Scholes equation and apply it to American options. Also, method of Liao and Khaliq of high order was applied to nonlinear Black-Scholes equation in case of American options. Here, we use this method oh fourth order in time and space to raise American option price accuracy.</p>

<p>The MUSCL-Hancock finite volume method with different slope limiters has been analyzed in the context of a fast transient flow problem. A derivation and analysis of the axial forces inside a pipe system due to a flow transient is also performed. </p><p>The following slope limiters were implemented and compared: MC, van Leer, van Albada, Minmod and Superbee. The comparison was based on the method's ability to calculate the forces due to a flow transient inside a pipe system.</p><p>The tests and comparisons in this thesis show that the MC, van Leer, van Albada and Minmod limiters behave very much the same for the flow transient problem. If one would rank these four limiters with respect to the numerical error, the order would be the one presented above, the MC limiter being the most accurate. The error the four limiters produce is mainly of diffusive nature and it is just the magnitude of the diffusion that seems to differ between the methods. One should also note that the workload rank of the four limiters is the same as the order presented above. The MC limiter being the least efficient of the four and the Minmod limiter the most efficient.</p><p>In most of the tests performed the Superbee limiter display a rather negative unpredictable behavior. For some relatively simple cases this particular approach shows big difficulties maintaining the dynamical properties of the force. However, the upside of the Superbee limiter is its remarkable ability to maintain the maximum value of the forces present in the pipe system, preventing underestimation of the maximum magnitude of the force.</p>

In this thesis we study hybrid numerical methods to be used in computational electromagnetics. The purpose is to address a wide frequency range relative to a given geometry. We also focus on efficient and robust numerical algorithms for computing the so called Smooth Surface Diffraction predicted by Geometrical Theory of Diffraction (GTD). We restrict the presentation to frequency domain scattering problems. The hybrid methods consist in combinations of Boundary Element Methods and asymptotic methods. Three hybrids will be presented. One of them has been developed from a theoretical idea to an industrial code. The two other hybrids will be presented mainly from a theoretical perspective. To be able to compute the Smooth Surface Diffracted field we introduce a numerical method that is to be used with surface curvature sensitive meshing, complemented with auxiliary data taken from a geometry database. By using two geometry representations we can show first order convergence and we then achieve an efficient and robust numerical algorithm. This numerical algorithm may be an essential part of an GTD implementation which in its turn is a component in the hybrid methods. As a background to our new techiniques we will also give short introductions to the Boundary Element Method and the Geometrical Theory of Diffraction from a theoretical and implementational point of view.

The inverse heat conduction problem also frequently referred as the sideways heat equation, in short SHE, is considered as a mathematical model for a real application, where it is desirable for someone to determine the temperature on the surface of a body. Since the surface itself is inaccessible for measurements, one is restricted to use temperature data from the interior measurements. From a  mathematical point of view, the entire situation leads to a non-characteristic Cauchy problem, where by using recorded temperature one can solve a well-posed nonlinear problem in the finite region for computing heat flux, and consequently obtain the Cauchy data [u, ux]. Further by using these data and by performing an appropriate method, e.g. a space marching method, one can eventually achieve the desired temperature at x = 0. The problem is severely ill-posed in the sense that the solution does not depend continuously on the data. The problem solved by two different methods, and for both cases we stabilize the computations by replacing the time derivative in the heat equation by a bounded operator. The first one, a spectral method based on finite Fourier space is illustrated to supply an analytical approach for approximating the time derivative. In order to get a better accuracy in the numerical computation, we use cubic spline function for approximating the time derivative in the least squares sense. The inverse problem we want to solve, by using Cauchy data, is a nonlinear heat conduction problem in one space dimension. Since the temperature data u = g(t) is recorded, e.g. by a thermocouple, it usually contains some perturbation in the data. Thus the solution can be severely ill-posed if the Cauchy data become very noisy. Two experiments are presented to test the proposed approach.

This dissertation is focused on theoretical and experimental studies of optical properties of materials and multilayer structures composing liquid crystal displays (LCDs) and electrochromic (EC) devices. By applying spectroscopic ellipsometry, we have determined the optical constants of thin films of electrochromic tungsten oxide (WOx) and nickel oxide (NiOy), the films’ thickness and roughness. These films, which were obtained at spattering conditions possess high transmittance that is important for achieving good visibility and high contrast in an EC device. Another application of the general spectroscopic ellipsometry relates to the study of a photo-alignment layer of a mixture of azo-dyes SD-1 and SDA-2. We have found the optical constants of this mixture before and after illuminating it by polarized UV light. The results obtained confirm the diffusion model to explain the formation of the photo-induced order in azo-dye films. We have developed new techniques for fast characterization of twisted nematic LC cells in transmissive and reflective modes. Our techniques are based on the characteristics functions that we have introduced for determination of parameters of non-uniform birefringent media. These characteristic functions are found by simple procedures and can be utilised for simultaneous determination of retardation, its wavelength dispersion, and twist angle, as well as for solving associated optimization problems. Cholesteric LCD that possesses some unique properties, such as bistability and good selective scattering, however, has a disadvantage – relatively high driving voltage (tens of volts). The way we propose to reduce the driving voltage consists of applying a stack of thin (~1µm) LC layers. We have studied the ability of a layer of a surface stabilized ferroelectric liquid crystal coupled with several retardation plates for birefringent color generation. We have demonstrated that in order to accomplish good color characteristics and high brightness of the display, one or two retardation plates are sufficient.

QC 20100726