A summary of the work done in the field of analytic differentiation by computer is presented. It is shown that there exists a need for an analytic differentiation routine whose output can be processed by a regular algebraic compiler. An algorithm is presented which will transform a FORTRAN FUNCTION subprogram into a FORTRAN SUBROUTINE subprogram that evaluates both the original function and its first derivative with respect to one independent variable. Implementation of this algorithm and possible extensions to it are discussed. / Science, Faculty of / Computer Science, Department of / Graduate

A method is presented for linear control system design using functional relations between system parameters and system response. The functional relations are obtained by frequency domain evaluation of an integral performance criterion. The performance criterion is defined as a correlation measure between the responses of a known reference system and the system to be designed. A method is also presented for obtaining algebraic expressions relating the time-domain response of linear and piece-wise linear systems with system parameters. By means of a rational fraction approximation to the exponential e and through use of a known technique for evaluating time-domain convolution integrals, it becomes possible to obtain the time-domain response without the necessity of first having to determine the poles of the system. The time-domain response is obtained as a ratio of polynomials in t with the coefficients as algebraic functions of the system parameters. The extension of the linear design theory to cover non-linear and multivariable systems is given. Several examples are given to illustrate the usefulness of the proposed techniques. / Applied Science, Faculty of / Electrical and Computer Engineering, Department of / Graduate

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Berggren, O. (2014) COMSOL Multiphysics – Ett energitekniskt analysverktyg vid numerisk simulering av köldbryggor och analys av fukt i konstruktionsdetaljer. Examensuppsats i ämnet energiteknik. Institutionen för tillämpad elektronik och fysik vid Umeå Universitet. Konsultföretaget Tyréns har vid sitt kontor i Umeå önskat att utvärdera tillämpningen av programvaran COMSOL Multiphysics. Arbetet bestod av att på nytt simulera och analysera en energiteknisk problemställning, som sedan tidigare ska ha genomförts vid Tyréns. Det valda projektet kallas i detta arbete för referensprojektet och är en del av projekteringen av kulturhuset Väven i Umeå. I referensprojektet behandlas analyserna av köldbryggor och fuktkondensation för flertalet konstruktionsdetaljer, där en av analyserna valdes ut för vidare utvärdering i detta arbete. Målet med utvärderingen var att undersöka om resultaten från arbetet var jämförbara med referensprojektets resultat. I detta ingick det även en presentation av en översiktlig kostnadskalkyl för programvaran COMSOL Multiphysics. Resultaten från analysen av köldbryggan och kondensationen av fukt i konstruktionsdetaljen var i jämförelse med resultaten från referensprojektet något förhöjda, i snitt 20 %. Det genomförda arbetet påvisar att det är möjligt att återskapa de tidigare utförda simuleringarna från referensprojektet i enlighet med det krav och standarder som ställs. De erhållna resultaten är, trots en viss skillnad, jämförbara med de från referensprojektet och är giltiga för att användas vid en verklig projektering. Det slutsatser som kan dras utifrån de erhållna resultaten är att utfall av kondens kan undvikas och att den genomsnittliga värmegenomgångskoefficienten, , indikerar att entrétorgets energiprestanda ej kommer att nå upp till kraven i BBR. Detta trots att -värdet kan antas uppfylla kraven. Då simuleringarna har utförts utan problem i COMSOL Multiphysics och tillgodosett detta arbete med giltiga resultat, anses programvaran vara ett lämpligt simuleringsverktyg hos Tyréns. Kostnaden är dock för en flytande licens av Flixo, i jämförelse till COMSOL Multiphysics mycket lägre. COMSOL Multiphysics är vid utredningstillfället drygt fyra gånger så kostsamt. Fördelen med COMSOL Multiphysics är dock att det kan behandla flera olika typer av fysikaliska problemställningar i en-, två- och tredimensioner med endast grundprogrammet. För att användningen av COMSOL Multiphysics ska vara ekonomisk försvarbart, krävs det att programvaran också används vid tillämpningar utöver simuleringar kring köldbryggor och kondensation av fukt. / Berggren, O. (2014) COMSOL Multiphysics – An analysis tool for energy applications when conducting numerical simulations on thermal bridges and analysis of moisture in construction details. Master thesis in Energy Engineering. Department of Applied Physics and Electronics at Umeå University. The consultant company Tyréns has at its office in Umeå decided to evaluate the application of the software COMSOL Multiphysics.  The evaluation consisted of a simulation on an energy engineering problem with its origin from a project at Tyréns, performed in COMSOL Multiphysics. The chosen project for this task was a part of the design plans of the culture house Väven in Umeå. These design plans includes the analysis of a thermal bridge and moisture on a variety of construction details, where one of them was selected to be investigated further. The main purpose of the investigation was to analyze if the results obtained from the simulations performed in COMSOL Multiphysics were equivalent compared to the results from the design plans. The investigation also included the presentation of an overall cost estimation for the software COMSOL Multiphysics. The obtained results from the analysis of the thermal bridge and moisture in the construction were in both cases slightly raised compared to the results from the design plans, in average an increase of 20 %. The work undertaken concludes that there is fully possible to recreate the previously executed simulations extracted from the design plans in accordance to the requirements and standards that are set. The obtained results are equivalent, even though a minor difference, compared with the results from the design plans and are valid too be used in a real life scenario. The obtained conclusions are that it is possible to prevent moisture in the construction detail. However, the overall U-value, , indicates that the energy efficiency of the entrance square is not good enough to reach the requirements of the SNBBP (Swedish National Board of Housing, Building and Planning). Even though the U-value for the construction detail, , can be assumed to meet the criteria’s of the SNBBP. Due to the fact that the simulations were conducted with COMSOL Multiphysics without any major problems and provided valid results, it is considered that the software is an appropriate tool to perform simulations at Tyréns. However, the cost for a floating license of the software Flixo is much less then for COMSOL Multiphysics. COMSOL Multiphysics is at the time of this study four times as expensive as Flixo. COMSOL Multiphysics has though an advantage because it can treat problems with a multiphysical nature in one, two and three dimensions with the use of only its standard edition. To ensure that the use of COMSOL Multiphysics can be economical viable, it is necessary that the software is used in multiple applications besides performing simulations on thermal bridges and moisture in construction details.

Thesis (Ph. D.)--Oregon Graduate Institute of Science and Technology, 1997.

The numerical solutions of many types of problems are generally obtained by solving approximating linear algebraic systems. Moreover, in solving a nonlinear problem, one may replace it by a sequence of linear systems providing progressively improved approximations. For the study of these linear systems of equations a geometric terminology with the compact symbolism of vectors and matrices is useful. A resume of the basic principles of higher algebra necessary for the development of the material to follow is therefore included. / "A Paper." / "Submitted to the Graduate Council of Florida State University in partial fulfillment of the requirements for the degree of Master of Science." / Advisor: Paul J. McCarthy, Professor Directing Paper. / "May, 1958." / At head of title: Florida State University. / Typescript. / Includes bibliographical references.

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One of the most central concepts in condensed matter physics is the electronic band structure. Although band theory was established more than 80 years ago, recent developments have led to new insights that are formulated in the framework of topological band theory. In this thesis a subset of topological band theory is presented, with particular focus on topological supercon- ductors and accompanying Majorana fermions. While simple models are used to introduce basic concepts, a physically more realistic model is also studied intensely in the papers. Through self- consistent tight-binding calculations it is confirmed that Majorana fermions appear in vortex cores and at wire end points when the superconductor is in the topologically non-trivial phase. Many other properties such as the topological invariant, experimental signatures in the local density of states and spectral function, unconventional and odd-frequency pairing, the precense of spin-polarized currents and spin-polarization of the Majorana fermions, and a local π-phase shift in the order parameter at magnetic impurities are also investigated.

In the design of digital signal processing systems, where single-precision results are required, the power dissipation and area of parallel multipliers can be significantly reduced by truncating the less significant columns and compensating to produce an approximate rounded product. This dissertation presents the design of truncated multiplications of signed inputs utilizing a new number system, the negative fractional two's complement number system which solves an inherent problem of the conventional two's complement number system. This research also presents a new truncated multiplication method to reduce the errors with only slightly more hardware. Error, area, delay and dynamic power estimates are performed at the structural HDL level. The new method is also applied to various conventional number systems. For division, which is the slowest and most complex of the arithmetic operations, a new truncated division method is described that yields the same errors as those of true rounding without additional execution time that is normally required for true rounding. The new method is also applied to various conventional number systems.

The views expressed in this thesis are those of the author and do not reflect the official policy or position of the Department of Defense or the U.S. Government. / The numerical experiments, carried out through the use of a pressure-velocity coupled method to solve the Favre Averaged Navier-Stokes equations, on steady and sinusoidally oscillating flows at five different Keluegan-Carpenter numbers, and three periodicity levels are described. A second-order in time, second-order in space, second-level predictor-corrector finite difference scheme has been used. The solutions were solved by the CFD-ACE program from the CFD Research Corporation. The analysis has produced in-line force coefficients comparable to those obtained experimentally for sinusoidally-oscillating flows.