Analysis of different types of fault is an important and complex task in a power system. Accurate fault analysis requires models that determine fault distances in a transmission line. The mathematical models accurately capture behavior of different types of faults and location in a timely manner, and prevents damaging power system from fault energy. The purpose of this thesis is to use two methods for determining fault locations and their distance to the reference end buses connected by the faulted transmission line. The two methods used in this investigation are referred to as impedance-based and traveling wave methods. To analyze both methods, various types of faults were modeled and simulated at various locations on a two-bus transmission system using EMTP program. Application and usefulness of each method is identified and presented in the thesis. It is found that Impedance-based methods are easier and more widely used than traveling-wave methods.

The target of this thesis is to explain the Travelling Salesman Problem and also create a special program, which will be able to make calculations using the heuristics GENIUS. The Travelling Salesman Problem will be described from two different points of view. The first one is the historical description of the idea of the Travelling Salesman Problem and later will be the problem will be described with some of the very wide number of the calculation methods. For the explanation of the methods, in the thesis there has been chosen some of the algorithms which belong to that methods. The heuristics and also the exact algorithms will be explained. The focus of this thesis is on the heuristics called GENIUS and also in the creation of the program which can calculate it. The program works first with the GENI algorithm and after that it works with US post-optimization algorithm. The program will be described from the point of view of the user and the manual will be written as well. The program will be tested on two different examples and will be compared with the exact algorithm.

Despite the increasing sophistication of digital musical instruments, many performers, composer and listeners remain captivated by traditional acoustic instruments. Interest has grown in the past 2 decades in augmenting acoustic instruments with sensor and actuator technology and integrated digital signal processing, expanding the instrument's capabilities while retaining its essential acoustic character. In this thesis we present a technique, travelling wave control, which allows active control of the vibrations of musical strings and yet has been little explored in the musical instrument literature to date. The thesis seeks to demonstrate that travelling wave control is capable of active damping and of modifying the timbre of a musical string in ways that go beyond those available through the more conventional modal control paradigm. However, we show that travelling wave control is highly sensitive to nonlinearity, which in practical settings can lead to harmonic distortion and even instability in the string response. To avoid these problems, we design and build a highly linear optical string displacement sensor, and investigate the use of piezoelectric stacks to actuate the termination point of a string. With these components we design and build a functioning travelling wave control system which is capable of damping the vibrations of a plucked string without adversely affecting its timbre. We go on to show that by deliberately adding nonlinearity into the control system, we are able to modify the timbre of the string in a natural way by affecting the evolution of the modal amplitudes. The results demonstrate the feasibility of the concept and lay the groundwork for future integration of travelling wave control into future actuated musical instruments.

In this thesis, we study a class of multi-stable reaction-diffusion systems used to model competing species. Systems in this class possess uniform stable steady states representing semi-trivial solutions. We start by considering a bistable, interaction, where the interactions are of classic “Lotka-Volterra” type and we consider a particular problem with relevance to applications in population dynamics: essentially, we study under what conditions the interplay of relative motility (diffusion) and competitive strength can cause waves of invasion to be halted and reversed. By establishing rigorous results concerning related degenerate and near-degenerate systems,we build a picture of the dependence of the wave speed on system parameters. Our results lead us to conjecture that this class of competition model has three “zones of response” in which the wave direction is left-moving, reversible and right-moving, respectively and indeed that in all three zones, the wave speed is an increasing function of the relative motility. Moreover, we study the effects of domain size on planar and non-planar interfaces and show that curvature plays an important role in determining competitive outcomes. Finally, we study a 3-species Lotka-Volterra model, where the third species is treated as a bio-control agent or a bio-buffer and investigate under what conditions the third species can alter the existing competition interaction.

Praktische Optimierungsprobleme beinhalten oft mehrere gleichberechtigte, sich jedoch widersprechende Kriterien. Beispielsweise will man bei einer Reise zugleich möglichst schnell ankommen, sie soll aber auch nicht zu teuer sein. Im ersten Teil dieser Arbeit wird die algorithmische Beherrschbarkeit solcher mehrkriterieller Optimierungsprobleme behandelt. Es werden zunächst verschiedene Lösungsbegriffe diskutiert und auf ihre Schwierigkeit hin verglichen. Interessanterweise stellt sich heraus, dass diese Begriffe für ein einkriterielles Problem stets gleich schwer sind, sie sich ab zwei Kriterien allerdings stark unterscheiden könen (außer es gilt P = NP). In diesem Zusammenhang wird auch die Beziehung zwischen Such- und Entscheidungsproblemen im Allgemeinen untersucht. Schließlich werden neue und verbesserte Approximationsalgorithmen für verschieden Varianten des Problems des Handlungsreisenden gefunden. Dabei wird mit Mitteln der Diskrepanztheorie eine Technik entwickelt, die ein grundlegendes Hindernis der Mehrkriteriellen Optimierung aus dem Weg schafft: Gegebene Lösungen so zu kombinieren, dass die neue Lösung in allen Kriterien möglichst ausgewogen ist und gleichzeitig die Struktur der Lösungen nicht zu stark zerstört wird. Der zweite Teil der Arbeit widmet sich verschiedenen Aspekten von Gleichungssystemen für (formale) Sprachen. Einerseits werden konjunktive und Boolesche Grammatiken untersucht. Diese sind Erweiterungen der kontextfreien Grammatiken um explizite Durchschnitts- und Komplementoperationen. Es wird unter anderem gezeigt, dass man bei konjunktiven Grammatiken die Vereinigungsoperation stark einschränken kann, ohne dabei die erzeugte Sprache zu ändern. Außerdem werden bestimmte Schaltkreise untersucht, deren Gatter keine Wahrheitswerte sondern Mengen von Zahlen berechnen. Für diese Schaltkreise wird das Äquivalenzproblem betrachtet, also die Frage ob zwei gegebene Schaltkreise die gleiche Menge berechnen oder nicht. Es stellt sich heraus, dass, abhängig von den erlaubten Gattertypen, die Komplexität des Äquivalenzproblems stark variiert und für verschiedene Komplexitätsklassen vollständig ist, also als (parametrisierter) Vertreter für diese Klassen stehen kann. / Practical optimization problems often comprise several incomparable and conflicting objectives. When booking a trip using several means of transport, for instance, it should be fast and at the same time not too expensive. The first part of this thesis is concerned with the algorithmic solvability of such multiobjective optimization problems. Several solution notions are discussed and compared with respect to their difficulty. Interestingly, these solution notions are always equally difficulty for a single-objective problem and they differ considerably already for two objectives (unless P = NP). In this context, the difference between search and decision problems is also investigated in general. Furthermore, new and improved approximation algorithms for several variants of the traveling salesperson problem are presented. Using tools from discrepancy theory, a general technique is developed that helps to avoid an obstacle that is often hindering in multiobjective approximation: The problem of combining two solutions such that the new solution is balanced in all objectives and also mostly retains the structure of the original solutions. The second part of this thesis is dedicated to several aspects of systems of equations for (formal) languages. Firstly, conjunctive and Boolean grammars are studied, which are extensions of context-free grammars by explicit intersection and complementation operations, respectively. Among other results, it is shown that one can considerably restrict the union operation on conjunctive grammars without changing the generated language. Secondly, certain circuits are investigated whose gates do not compute Boolean values but sets of natural numbers. For these circuits, the equivalence problem is studied, i.\,e.\ the problem of deciding whether two given circuits compute the same set or not. It is shown that, depending on the allowed types of gates, this problem is complete for several different complexity classes and can thus be seen as a parametrized) representative for all those classes.

The first part of this thesis deals with the approximability of the traveling salesman problem. This problem is defined on a complete graph with edge weights, and the task is to find a Hamiltonian cycle of minimum weight that visits each vertex exactly once. We study the most important multiobjective variants of this problem. In the multiobjective case, the edge weights are vectors of natural numbers with one component for each objective, and since weight vectors are typically incomparable, the optimal Hamiltonian cycle does not exist. Instead we consider the Pareto set, which consists of those Hamiltonian cycles that are not dominated by some other, strictly better Hamiltonian cycles. The central goal in multiobjective optimization and in the first part of this thesis in particular is the approximation of such Pareto sets. We first develop improved approximation algorithms for the two-objective metric traveling salesman problem on multigraphs and for related Hamiltonian path problems that are inspired by the single-objective Christofides' heuristic. We further show arguments indicating that our algorithms are difficult to improve. Furthermore we consider multiobjective maximization versions of the traveling salesman problem, where the task is to find Hamiltonian cycles with high weight in each objective. We generalize single-objective techniques to the multiobjective case, where we first compute a cycle cover with high weight and then remove an edge with low weight in each cycle. Since weight vectors are often incomparable, the choice of the edges of low weight is non-trivial. We develop a general lemma that solves this problem and enables us to generalize the single-objective maximization algorithms to the multiobjective case. We obtain improved, randomized approximation algorithms for the multiobjective maximization variants of the traveling salesman problem. We conclude the first part by developing deterministic algorithms for these problems. The second part of this thesis deals with redundancy properties of complete sets. We call a set autoreducible if for every input instance x we can efficiently compute some y that is different from x but that has the same membership to the set. If the set can be split into two equivalent parts, then it is called weakly mitotic, and if the splitting is obtained by an efficiently decidable separator set, then it is called mitotic. For different reducibility notions and complexity classes, we analyze how redundant its complete sets are. Previous research in this field concentrates on polynomial-time computable reducibility notions. The main contribution of this part of the thesis is a systematic study of the redundancy properties of complete sets for typical complexity classes and reducibility notions that are computable in logarithmic space. We use different techniques to show autoreducibility and mitoticity that depend on the size of the complexity class and the strength of the reducibility notion considered. For small complexity classes such as NL and P we use self-reducible, complete sets to show that all complete sets are autoreducible. For large complexity classes such as PSPACE and EXP we apply diagonalization methods to show that all complete sets are even mitotic. For intermediate complexity classes such as NP and the remaining levels of the polynomial-time hierarchy we establish autoreducibility of complete sets by locally checking computational transcripts. In many cases we can show autoreducibility of complete sets, while mitoticity is not known to hold. We conclude the second part by showing that in some cases, autoreducibility of complete sets at least implies weak mitoticity. / Der erste Teil dieser Arbeit widmet sich der Approximierbarkeit des Traveling Salesman Problems, bei welchem man in vollständigen Graphen mit Kantengewichten eine Rundreise mit minimalem Gewicht sucht. Es werden die wichtigsten mehrkriteriellen Varianten dieses Problems betrachtet, bei denen die Kantengewichte aus Vektoren natürlicher Zahlen mit einer Komponente pro Kriterium bestehen. Verschiedene Rundreisen sind bei mehrkriteriellen Kantengewichten häufig unvergleichbar, und dementsprechend existiert oft keine eindeutige optimale Rundreise. Stattdessen fasst man jene Rundreisen, zu denen jeweils keine eindeutig bessere Rundreise existiert, zu der sogenannten Pareto-Menge zusammen. Die Approximation solcher Pareto-Mengen ist die zentrale Aufgabe in der mehrkriteriellen Optimierung und in diesem Teil der Arbeit. Durch Techniken, die sich an Christofides' Heuristik aus der einkriteriellen Approximation orientieren, werden zunächst verbesserte Approximationsalgorithmen für das zweikriterielle metrische Traveling Salesman Problem auf Multigraphen und für analog definierte Hamiltonpfadprobleme entwickelt. Außerdem werden Argumente gegen eine signifikante Verbesserung dieser Algorithmen aufgezeigt. Weiterhin werden mehrkriterielle Maximierungsvarianten des Traveling Salesman Problems betrachtet, bei denen man Rundreisen mit möglichst großem Gewicht in jedem Kriterium sucht. Es werden einkriterielle Techniken auf den mehrkriteriellen Fall übertragen, bei denen man zunächst eine Kreisüberdeckung mit hohem Gewicht berechnet und anschließend pro Kreis die Kante mit dem niedrigsten Gewicht löscht. Die Auswahl einer solchen Kante pro Kreis ist im mehrkriteriellen Fall nicht trivial, weil mehrkriterielle Gewichtsvektoren häufig unvergleichbar sind. Es wird ein allgemeines Lemma entwickelt, welches dieses Problem löst und damit eine Übertragung der einkriteriellen Maximierungsalgorithmen auf den mehrkriteriellen Fall ermöglicht. Dadurch ergeben sich verbesserte, randomisierte Approximationsalgorithmen für die mehrkriteriellen Maximierungsvarianten des Traveling Salesman Problems. Abschließend werden zu diesen Problemvarianten deterministische Algorithmen entwickelt. Der zweite Teil dieser Arbeit widmet sich Redundanzeigenschaften vollständiger Mengen. Eine Menge heißt autoreduzierbar, wenn zu jeder Instanz x eine von x verschiedene Instanz y mit der gleichen Zugehörigkeit zu der Menge effizient berechnet werden kann. Ist die Menge in zwei äquivalente Teile aufspaltbar, so heißt sie schwach mitotisch, und ist diese Aufspaltung durch einen effizient entscheidbaren Separator erreichbar, so heißt sie mitotisch. Zu verschiedenen Reduktionen und Komplexitätsklassen wird die Frage betrachtet, wie redundant ihre vollständigen Mengen sind. Während sich vorherige Forschung in diesem Gebiet hauptsächlich auf Polynomialzeitreduktionen konzentriert, liefert diese Arbeit eine systematische Analyse der Redundanzeigenschaften vollständiger Mengen für typische Komplexitätsklassen und solche Reduktionen, die sich in logarithmischem Raum berechnen lassen. Je nach Größe der Komplexitätsklasse und Stärke der Reduktion werden dabei verschiedene Techniken eingesetzt. Für kleine Komplexitätsklassen wie beispielsweise NL und P werden selbstreduzierbare, vollständige Mengen benutzt, um Autoreduzierbarkeit aller vollständigen Mengen nachzuweisen, während für große Komplexitätsklassen wie beispielsweise PSPACE und EXP Diagonalisierungsmethoden sogar die Mitotizität vollständiger Mengen zeigen. Für dazwischen liegende Komplexitätsklassen wie beispielsweise NP und die übrigen Level der Polynomialzeithierarchie wird Autoreduzierbarkeit vollständiger Mengen über lokales Testen von Berechnungstranskripten gezeigt. Während in vielen Fällen Autoreduzierbarkeit vollständiger Mengen gezeigt werden kann, bleibt häufig die Frage offen, ob diese Mengen auch mitotisch sind. Abschließend wird gezeigt, dass in einigen Fällen Autoreduzierbarkeit vollständiger Mengen zumindest schwache Mitotizität impliziert.

<p> </p><p>The thesis discusses the backpacking culture in Ecuador. It proposes a clarification of the issue and discusses the problem from two perspectives. Questions are raised about the backpacking identity, the backpacking travel style and how they use given facilities in the host country. The work focuses and analyses the strengths and weaknesses of the destination through the lens of a backpacker. The empirical material is taken from intensive interviews conducted in Ecuador.</p><p>A discussion reviews the backpacking identity, how and why backpackers travel; and the backpacker’s opinion about sustainable tourism in South America. In addition, the thesis concentrates on the travellers’ finances and how they prepare for an extended journey.</p><p> </p>

The Ant System is a new meta-heuristic method particularly appropriate to solve hard combinatorial optimization problems. It is a population-based, nature-inspired approach exploiting positive feedback as well as local information and has been applied successfully to a variety of combinatorial optimization problem classes. The Ant System consists of a set of cooperating agents (artificial ants) and a set of rules that determine the generation, update and usage of local and global information in order to find good solutions. As the structure of the Ant System highly suggests a parallel implementation of the algorithm, in this paper two parallelization strategies for an Ant System implementation are developed and evaluated: the synchronous parallel algorithm and the partially asynchronous parallel algorithm. Using the Traveling Salesman Problem a discrete event simulation is performed, and both strategies are evaluated on the criteria "speedup", "efficiency" and "efficacy". Finally further improvements for an advanced parallel implementation are discussed. (author's abstract) / Series: Report Series SFB "Adaptive Information Systems and Modelling in Economics and Management Science"

Travelling-wave distributed amplifiers are providing gain over broad frequency ranges for microwave applications. Similar concepts are applicable to distributed mixers and, with the use of controlled feedback, to a multifunction component simultaneously emulating a mixer, amplifier and an oscillator. The concept of this new travelling-wave frequency converter is introduced and data for a discrete component test circuit is presented. To facilitate the converter operation a new three-port travelling-wave mixer is introduced and characterized. Four-port scattering and wave scattering transformations are derived as a method of analysis of the four-port distributed structure. This enables sequential circuit analysis on a small computer. Practical applications unique to the advanced automatic network analyser, including time domain measurements, are presented to characterize test circuits as well as to develop ancillary equipment such as a transistor test fixture. Automated error corrected transistor measurements and de-embedding are also discussed. A piecewise linear quantum mechanical method of modelling the conduction channel of a short gate field effect transistor is given to aid the extrapolation of the distributed frequency converter concept to submicron and heterojunction structures. / Thesis (Ph.D.)-University of Natal, Durban, 1985.

Over the last 20 to 30 years, the field of structural fire design has shifted from relying on single element fire resistance testing to the consideration of the effects of full-frame behaviour. The change has been driven by the desire to build more advanced structures and reduce costs. It has been facilitated in part due to structural testing, and in part due to development of complex modelling techniques. This thesis considers the modelling of concrete structures, and presents new techniques and methodologies for analysing the performance of structures in fire. The first part of this work traces modelling techniques from fundamental constitutive behaviour through to sectional capacity calculation. Load induced thermal strain and constitutive modelling approaches are investigated and their impact on structural behaviour is considered. A new, general, technique for conducting sectional analysis on concrete elements is also created. The method relies on analysis of the sectional tangent stiffness to efficiently calculate the biaxial bending capacity of a concrete section subject to any heating regime. This approach is more accurate and conservative than current methods and has the potential to be used as a design tool. This work develops a series of new approaches for the design of large structures subject to fire. A rational and quantifiable methodology is developed for assessing the performance of a structure when subject to fire; this new approach addresses the mismatch in complexity between current vi modelling techniques and measures of structural performance. It allows a more precise approach to be taken to the definition of failure; and can be easily used to compare the structure’s response to different design fires. Finally, a new technique for the definition of design fires founded on fundamental fire dynamics is presented. The approach challenges the assumptions typically made when applying temperature-time curves and is based around the observed phenomenon of travelling fires. A concrete framed structure is subject to a number of travelling fires and the response is assessed using both conventional techniques and the new, in depth analysis.