Mathematical modelling of shoreline evolution under climate change

This study focuses on the impact of potential changes in the wind-wave climate on shoreline change. The `one-line' model for medium to long-term prediction of coastline evolution is employed. New analytical and numerical solutions of this important model are described. Specifically: 1) original semi-analytical solutions are derived that relax the unrealistic assumption of existing analytical work that a constant wave condition drives shoreline change and, 2) a more general form of the one-line model is solved with a novel application of the `Method of Lines'. Model input consists of 30-year nearshore wave climate scenarios, corresponding to the `present' (1961-1990) and the future (2071-2100). Winds from a high resolution, (12km x 12km), regional climate model, obtained offshore of the south-central coast of England at a dense temporal resolution of 3 hours, are used to develop the aforementioned wave climate scenarios, through hindcast and inshore wave transformation. A hypothetical shoreline segment is adopted as a `benchmark' case for comparisons. Monthly and seasonal statistics of output shoreline positions are generated and assessedfo r relative changeso f `significance' between `present' and future. Different degrees of evidence that such changes do exist are found. This study is the first application of such high resolution climate model output to investigate climate change impact on shoreline response. Major findings include: 1) shoreline changes of `significance' are strongly linked to `significant' changes in future wave direction, 2) future changes appear smaller for entire seasons than for individual months, 3) shoreline position variability is often smaller in the future, 4) different climate model experiments produce diverging results; however, general trends are largely similar. The present study, at a fundamental level, offers analytical solutions of the 'oneline' model that are closer to reality and a numerical solution that is of increased effciency.. At a practical level, it contributes to better understanding of the patterns of shoreline response to changing offshore wave climate through: 1) the use of fast and straightforward methods that can accommodate numerous climate scenarios without need for data reduction, and 2) the development of a methodology for using climate model output for coastal climate change impact assessment studies

Regulated rewriting in formal language theory

Thesis (MSc (Mathematical Sciences))--University of Stellenbosch, 2008.Context-free grammars are well-studied and well-behaved in terms of decidability, but many real-world problems cannot be described with context-free grammars. Grammars with regulated rewriting are grammars with mechanisms to regulate the applications of rules, so that certain derivations are avoided. Thus, with context-free rules and regulated rewriting mechanisms, one can often generate languages that are not context-free. In this thesis we study grammars with regulated rewriting mechanisms. We consider problems in which context-free grammars are insufficient and in which more descriptive grammars are required. We compare bag context grammars with other well-known classes of grammars with regulated rewriting mechanisms. We also discuss the relation between bag context grammars and recognizing devices such as counter automata and Petri net automata. We show that regular bag context grammars can generate any recursively enumerable language. We reformulate the pumping lemma for random permitting context languages with context-free rules, as introduced by Ewert and Van der Walt, by using the concept of a string homomorphism. We conclude the thesis with decidability and complexity properties of grammars with regulated rewriting

26. Theorietag Automaten und Formale Sprachen 23. Jahrestagung Logik in der Informatik: Tagungsband

Der Theorietag ist die Jahrestagung der Fachgruppe Automaten und Formale Sprachen der Gesellschaft für Informatik und fand erstmals 1991 in Magdeburg statt. Seit dem Jahr 1996 wird der Theorietag von einem eintägigen Workshop mit eingeladenen Vorträgen begleitet. Die Jahrestagung der Fachgruppe Logik in der Informatik der Gesellschaft für Informatik fand erstmals 1993 in Leipzig statt. Im Laufe beider Jahrestagungen finden auch die jährliche Fachgruppensitzungen statt. In diesem Jahr wird der Theorietag der Fachgruppe Automaten und Formale Sprachen erstmalig zusammen mit der Jahrestagung der Fachgruppe Logik in der Informatik abgehalten. Organisiert wurde die gemeinsame Veranstaltung von der Arbeitsgruppe Zuverlässige Systeme des Instituts für Informatik an der Christian-Albrechts-Universität Kiel vom 4. bis 7. Oktober im Tagungshotel Tannenfelde bei Neumünster. Während des Tre↵ens wird ein Workshop für alle Interessierten statt finden. In Tannenfelde werden • Christoph Löding (Aachen) • Tomás Masopust (Dresden) • Henning Schnoor (Kiel) • Nicole Schweikardt (Berlin) • Georg Zetzsche (Paris) eingeladene Vorträge zu ihrer aktuellen Arbeit halten. Darüber hinaus werden 26 Vorträge von Teilnehmern und Teilnehmerinnen gehalten, 17 auf dem Theorietag Automaten und formale Sprachen und neun auf der Jahrestagung Logik in der Informatik. Der vorliegende Band enthält Kurzfassungen aller Beiträge. Wir danken der Gesellschaft für Informatik, der Christian-Albrechts-Universität zu Kiel und dem Tagungshotel Tannenfelde für die Unterstützung dieses Theorietags. Ein besonderer Dank geht an das Organisationsteam: Maike Bradler, Philipp Sieweck, Joel Day. Kiel, Oktober 2016 Florin Manea, Dirk Nowotka und Thomas Wilk

Electronic transport in nanoelectromechanical systems : noise, back-action, and quantum measurement

The important progress made in nanolitography processes in the last decades has had a profound impact in our daily lives, by making possible the miniaturization of consumer electronics. Unbeknownst to most consumers, it is nowadays possible to fabricate free-standing nanoscale devices, that will naturally vibrate under thermal or external excitation. Over the last decade, a new subfield of physics devoted to studying these objects emerged: nanomechanics. In this thesis, we study electronic transport in such nanostructures where mechanical degrees of freedom play an important role. More precisely, we calculate the full transport properties (e.g. average current, frequency-dependent current noise) of different mesoscopic detectors in the presence of coupling to a nanomechanical oscillator. The objective of our study is twofold. First, there is a strong interest in understanding the effect that the coupling to electronic degrees of freedom has on the state of the mechanical system. We will show that under many conditions the interaction with the detector can be understood in terms of an effective thermal bath, but also discuss the limitations of this effective environment model. A second main aspect of the work presented here is the calculation of the signature of the mechanical object in the transport properties of the detector. As one of the primary goal in the field of nanoelectromechanical systems is to use the output of such electrical detectors to achieve position measurements at the quantum limit, this question obviously is of great relevance to the field. This thesis is organized in 3 main parts, each associated with a different electronic detector. After a short introduction to nanoelectromechanical systems, we focus in Part II on a system composed a single-electron transistor coupled capacitively to a classical mechanical oscillator. We present a complete study of the transport properties of the coupled system, going beyond the usual weak-coupling approximation. In Part III, we discuss the properties of a system where a tunnel junction is coupled to the mechanical object. Looking at this system from the point of view of quantum measurement, we analyze the transport properties of a system composed of two independent tunnel junctions coupled to the same oscillator and demonstrate how, by using the cross correlated output of the two detectors, one can improve the sensitivity of position measurements beyond the usual quantum limit. In this part, we also demonstrate that the current noise of a system composed of two tunnel junctions (one with fixed transmission amplitude, the other with position-dependent transmission amplitude) can contain information about the momentum of the mechanical oscillator. Lastly, in Part IV we study a system composed of a mechanical oscillator coupled to a superconducting single-electron transistor. The coupled dynamics of the oscillator and mesoscopic detector are in this case very complex, and we demonstrate how a numerical approach based on a solution of the Liouville equation can be used to validate results obtained from approximate analytical approaches. We also demonstrate, by looking at the frequency-dependence of the charge fluctuations on the superconducting single-electron transistor, limitations to the model where the effect of the detector back-action on the oscillator is modeled as an effective environment

Mehrfach-limitierte Lindenmayer-Systeme

The theory of L systems originated with the biologist and mathematician Aristide Lindenmayer. His original goal was to provide mathematical models for the simultaneous development of cells in filamentous organisms. Since L systems may be viewed as rewriting systems, their generated languages, i.e., sets of organisms encoded by strings, are also subject to formal language theory, which aims to classify formal languages as well as their generating mechanisms according to various properties, such as generative power, decidability, etc. D. Wätjen introduced and studied k-limited L systems in order to combine the purely sequential mode of rewriting and the purely parallel mode of rewriting in context-free grammars, respectively, L systems. In biology, these systems may be interpreted as organisms, for which the simultaneous growth of cells is restricted by the supply of some resources of food being limited by some finite value k. In this thesis the constraint of a common limit k is relaxed in favor of individual resource limits k(a) for every cell-type a, which yields the new notion of multi-limited L system. The language families generated by such systems are then classified according to their sets of limits k(a). At first, an intuitive approach to the different mechanisms of the L system variants is provided by presenting a method for the graphical interpretation of L systems, the so-called turtle interpretation. Suitable computer programs implementing a turtle interpreter as well as free-programmable simulators for multi-limited, k-limited, and uniformly k-limited L systems, are developed and their source-code is appended. Subsequently, language families generated by multi-limited L systems are compared to each other, to Wätjen's k-limited as well as to non-limited language families, and to the families of the Chomsky Hierarchy. Besides asymptotically comparing the generative power of multi-limited L systems to that of the underlying non-limited L systems, also their closure properties are investigated.Der Biologe und Mathematiker Aristide Lindenmayer begründete die Theorie der L-Systeme. Das ursprüngliche Ziel dieser Theorie ist die Bereitstellung mathematischer Modelle zur Untersuchung des simultanen Zellwachstums fadenartiger Organismen. Da L-Systeme als eine Art von Ersetzungssystemen definiert sind, sind ihre erzeugten Sprachen, d.h. die Mengen der durch Zeichenketten beschriebenen Organismen, ebenfalls Gegenstand der Theorie der formalen Sprachen. Diese Theorie klassifiziert formale Sprachen sowie ihre Erzeugungsmechanismen gemäß ihrer Eigenschaften, wie z.B. Erzeugungsmächtigkeit oder Entscheidbarkeit. Als ein Sprachen-erzeugender Mechanismus, der zwischen der rein sequentiellen Ersetzung kontextfreier Grammatiken und der rein parallelen Ersetzung von L-Systemen liegt, sind k-limitierte L-Systeme von D. Wätjen eingeführt und untersucht worden. In der Biologie können diese Systeme als Organismen interpretiert werden, deren simultanes Zellwachstum beschränkt ist durch individuelle Nahrungsvorräte mit einer einheitlichen endlichen Kapazität k. Die in dieser Arbeit betrachteten mehrfach-limitierten L-Systeme bilden eine Verallgemeinerung der k-limitierten L-Systeme, indem sie für jeden Zelltyp a einen individuellen Nahrungsvorrat mit einer spezifischen Kapazität k(a) anstelle der einheitlichen Kapazität k vorsehen. Diese Arbeit führt mehrfach-limitierte L-Systeme ein und definiert eine geeignete Kategorisierung der von ihnen erzeugten Sprachfamilien anhand der erlaubten Mengen von Limits k(a). Zunächst wird ein intuitiver Zugang zu den verschiedenen Mechanismen der L-System-Varianten ermöglicht, indem eine Methode zur grafischen Interpretation von L-Systemen, die sogenannte Turtle-Interpretation, vorgestellt wird. Hierzu werden geeignete Computer-Programme für einen Turtle-Interpreter sowie für frei programmierbare Simulatoren von mehrfach-limitierten, k-limitierten sowie uniform k-limitierten L-Systemen erstellt und ihr Quell-Code zur Verfügung gestellt. Die von mehrfach-limitierten L-Systemen erzeugten Sprachfamilien werden bzgl. ihrer Inklusionseigenschaften untereinander, mit Wätjens k-limitierten Sprachfamilien, mit den nicht-limitierten Sprachfamilien sowie mit der Chomsky Hierarchie verglichen. Die Erzeugungsmächtigkeit von mehrfach-limitierten L-Systemen wird asymptotisch verglichen mit den jeweils unterliegenden nicht-limitierten L-Systemen. Des weiteren werden die Abschlusseigenschaften der mehrfach-limitierten L-Systeme untersucht

Inklusion von Patternsprachen und verwandte Probleme

A pattern is a word that consists of variables and terminal symbols. The pattern language that is generated by a pattern A is the set of all terminal words that can be obtained from A by uniform replacement of variables with terminal words. For example, the pattern A = a x y a x (where x and y are variables, and the letter a is a terminal symbol) generates the set of all words that have some word a x both as prefix and suffix (where these two occurrences of a x do not overlap). Due to their simple definition, pattern languages have various connections to a wide range of other areas in theoretical computer science and mathematics. Among these areas are combinatorics on words, logic, and the theory of free semigroups. On the other hand, many of the canonical questions in formal language theory are surprisingly difficult. The present thesis discusses various aspects of the inclusion problem of pattern languages. It can be divide in two parts. The first one examines the decidability of pattern languages with a limited number of variables and fixed terminal alphabets. In addition to this, the minimizability of regular expressions with repetition operators is studied. The second part deals with descriptive patterns, the smallest generalizations of arbitrary languages through pattern languages ("smallest" with respect to the inclusion relation). Main questions are the existence and the discoverability of descriptive patterns for arbitrary languages.Ein Pattern ist ein Wort aus Variablen und Terminalsymbolen. Die von einem Pattern A erzeugte Patternsprache ist die Menge aller Terminalwörter, die durch eine uniforme Ersetzung der Variablen in A durch Terminalwörter erzeugt werden können. So beschreibt das Pattern A = a x y a x (wobei x und y Variablen sind und a ein Terminal ist) die Menge aller Wörter, die ein Wort der Form a x sowohl als Präfix, als auch als Suffix haben (ohne dass sich diese beiden Vorkommen von a x überlappen). Wegen ihrer einfachen Definition besitzen Patternsprachen eine Vielzahl von Verbindungen zu verschiedenen anderen Gebieten der theoretischen Informatik und Mathematik, unter anderem zur Wortkombinatorik, Logik und der Theorie freier Halbgruppen. Andererseits führen viele der üblichen sprachtheoretischen Fragestellungen bei Patternsprachen zu kombinatorischen Problemen von überraschender Schwierigkeit. Die vorliegende Dissertation widmet sich verschiedenen Aspekten des Inklusionsproblems von Patternsprachen und kann in zwei Teile unterteilt werden. Der erste Teil untersucht die Entscheidbarkeit des Inklusionsproblems für Sprachen, die von Pattern mit beschränkter Variablenzahl über Terminalalphabeten von beschränkter Größe erzeugt werden. Darüber hinaus werden verschiedene Aspekte der Minimierbarkeit von regulären Ausdrücken mit Rückreferenzen betrachtet. Der zweite Teil der Dissertation handelt von deskriptiven Pattern; d.h. denjenigen Pattern, die die (hinsichtlich der Inklusion) kleinsten Verallgemeinerungen einer gegebenen Sprache erzeugen. Hauptfragen sind hierbei die Existenz und die Auffindbarkeit deskriptiver Pattern für beliebige Sprachen

Optimised Design and Analysis of All-Optical Networks

This PhD thesis presents a suite of methods for optimising design and for analysing blocking probabilities of all-optical networks. It thus contributes methodical knowledge to the field of computer assisted planning of optical networks. A two-stage greenfield optical network design optimiser is developed, based on shortest-path algorithms and a comparatively new metaheuristic called simulated allocation. It is able to handle design of all-optical mesh networks with optical cross-connects, considers duct as well as fibre and node costs, and can also design protected networks. The method is assessed through various experiments and is shown to produce good results and to be able to scale up to networks of realistic sizes. A novel method, subpath wavelength grouping, for routing connections in a multigranular all-optical network where several wavelengths can be grouped and switched at band and fibre level is presented. The method uses an unorthodox routing strategy focusing on common subpaths rather than individual connections, and strives to minimise switch port count as well as fibre usage. It is shown to produce cheaper network designs than previous methods when fibre costs are comparatively high. A new optical network concept, the synchronous optical hierarchy, is proposed, in which wavelengths are subdivided into timeslots to match the traffic granularity. Various theoretical properties of this concept are investigated and compared in simulation studies. An integer linear programming model for optical ring network design is presented. Manually designed real world ring networks are studied and it is found that the model can lead to cheaper network design. Moreover, ring and mesh network architectures are compared using real world costs, and it is found that optical cros..