Method of the Riemann-Hilbert Problem for the Solution of the Helmholtz Equation in a Semi-infinite Strip

In this dissertation, a new method is developed to study BVPs of the modified Helmholtz and Helmholtz equations in a semi-infinite strip subject to the Poincare type, impedance and higher order boundary conditions. The main machinery used here is the theory of Riemann Hilbert problems, the residue theory of complex variables and the theory of integral transforms. A special kind of interconnected Laplace transforms are introduced whose parameters are related through branch of a multi-valued function. In the chapter 1 a brief review of the unified transform method used to solve BVPs of linear and non-linear integrable PDEs in convex polygons is given. Then unified transform method is applied to the BVP of the modified Helmholtz equation in a semi-infinite strip subject to the Poincare type and impedance boundary conditions. In the case of BVP of the modified Helmholtz equation in a semi-infinite strip subject to the impedance boundary conditions, two scalar RHPs are derived, then the closed form solutions of the given BVP are derived. The difficulty in application of the unified transform method to BVP of the Helmholtz equation in a semi infinite strip is discussed later on. The chapter 2 contains application of the finite integral transform (FIT) method to study the BVP for the Helmholtz equation in a semi-infinite strip subject to the Poincare type and impedance boundary conditions. In the case of the impedance boundary conditions, a series representation of the solution of the BVP for the Helmholtz equation in a semi-infinite strip is derived. The Burniston-Siewert method to find integral representations of a certain transcendental equation is presented. The roots of this equation are required for both methods, the FIT method and the RHP based method. To implement the Burniston-Siewert method, we solve a scalar RHP on several segments of the real axis. In chapter 3, we have applied the new method to study the Poincare type and impedance BVPs for the Helmholtz equation in a semi-infinite strip. In the case of the Poincare type boundary conditions an order two vector RHP is derived. In general, it is not possible to find closed form solution of an order two vector RHP. In the case of the impedance boundary conditions two scalar RHPs are derived whose closed form solutions are found. Then the series representation for solution of the BVP of the Helmholtz equation in a semi-infinite strip subject to the impedance boundary conditions, is recovered using the inverse transform operator, and the residue theory of complex variables. The numerical results are presented for various values of the parameters involved. It is observed that the FIT method and the new method generate exactly the same solution of the BVP of the Helmholtz equation in a semi-infinite strip subject to the impedance boundary conditions. In chapter 4, we have applied the new method to study the acoustic scattering from a semi-infinite strip subject to higher order boundary conditions. Two scalar RHPs are derived whose closed form solutions are found. A unique solution of the problem is obtained

The development and applications of a system designed to quantify coronary arterial stenosis

The objective analysis of coronary artery stenosis is required for the assessment of interventions in the management of Coronary Artery Disease (CAD). This thesis presents a microcomputer-based system designed to meet this requirement which is easy to use and relatively cheap. The hardware consists of a standard 35 mm cine-projector (International General Electric Company), a rear projection graphics tablet (GTCO Corporation) and microcomputer (Vector Graphic Limited) with printer (Epson Limited). The graphics tablet and projector are mounted into a steel framework which allows an arteriographic image to be cast from the rear of the projector and focused, parallax free, onto the centre of the tablet. The tablet in turn communicates with the computer via a RS232 link. [Continues.

Designing sound : procedural audio research based on the book by Andy Farnell

In procedural media, data normally acquired by measuring something, commonly described as sampling, is replaced by a set of computational rules (procedure) that defines the typical structure and/or behaviour of that thing. Here, a general approach to sound as a definable process, rather than a recording, is developed. By analysis of their physical and perceptual qualities, natural objects or processes that produce sound are modelled by digital Sounding Objects for use in arts and entertainments. This Thesis discusses different aspects of Procedural Audio introducing several new approaches and solutions to this emerging field of Sound Design.Em Media Procedimental, os dados os dados normalmente adquiridos através da medição de algo habitualmente designado como amostragem, são substituídos por um conjunto de regras computacionais (procedimento) que definem a estrutura típica, ou comportamento, desse elemento. Neste caso é desenvolvida uma abordagem ao som definível como um procedimento em vez de uma gravação. Através da análise das suas características físicas e perceptuais , objetos naturais ou processos que produzem som, são modelados como objetos sonoros digitais para utilização nas Artes e Entretenimento. Nesta Tese são discutidos diferentes aspectos de Áudio Procedimental, sendo introduzidas várias novas abordagens e soluções para o campo emergente do Design Sonoro

NASA thesaurus. Volume 3: Definitions

Publication of NASA Thesaurus definitions began with Supplement 1 to the 1985 NASA Thesaurus. The definitions given here represent the complete file of over 3,200 definitions, complimented by nearly 1,000 use references. Definitions of more common or general scientific terms are given a NASA slant if one exists. Certain terms are not defined as a matter of policy: common names, chemical elements, specific models of computers, and nontechnical terms. The NASA Thesaurus predates by a number of years the systematic effort to define terms, therefore not all Thesaurus terms have been defined. Nevertheless, definitions of older terms are continually being added. The following data are provided for each entry: term in uppercase/lowercase form, definition, source, and year the term (not the definition) was added to the NASA Thesaurus. The NASA History Office is the authority for capitalization in satellite and spacecraft names. Definitions with no source given were constructed by lexicographers at the NASA Scientific and Technical Information (STI) Facility who rely on the following sources for their information: experts in the field, literature searches from the NASA STI database, and specialized references

THE DEVELOPMENT OF A HOLISTIC EXPERT SYSTEM FOR INTEGRATED COASTAL ZONE MANAGEMENT

Coastal data and information comprise a massive and complex resource, which is vital to the practice of Integrated Coastal Zone Management (ICZM), an increasingly important application. ICZM is just as complex, but uses the holistic paradigm to deal with the sophistication. The application domain and its resource require a tool of matching characteristics, which is facilitated by the current wide availability of high performance computing. An object-oriented expert system, COAMES, has been constructed to prove this concept. The application of expert systems to ICZM in particular has been flagged as a viable challenge and yet very few have taken it up. COAMES uses the Dempster- Shafer theory of evidence to reason with uncertainty and importantly introduces the power of ignorance and integration to model the holistic approach. In addition, object orientation enables a modular approach, embodied in the inference engine - knowledge base separation. Two case studies have been developed to test COAMES. In both case studies, knowledge has been successfully used to drive data and actions using metadata. Thus a holism of data, information and knowledge has been achieved. Also, a technological holism has been proved through the effective classification of landforms on the rapidly eroding Holderness coast. A holism across disciplines and CZM institutions has been effected by intelligent metadata management of a Fal Estuary dataset. Finally, the differing spatial and temporal scales that the two case studies operate at implicitly demonstrate a holism of scale, though explicit means of managing scale were suggested. In all cases the same knowledge structure was used to effectively manage and disseminate coastal data, information and knowledge

The role of computer-aided design in the learning of practical 3D-descriptive geometry: a case study

There are a number of problems surrounding the teaching of practical 3-D descriptive geometry to children in secondary education, notably the difficulty pupils have with visualising an object's form from orthographic views, and the interpretation of an object's geometric attributes into the descriptive geometry representation. The purpose of the current research is to evaluate the use of computer-aided design in this area of the curriculum and is based upon work undertaken in a North London comprehensive school. The school and its context is described and evaluated. Theories of child development and educational psychology of relevance to the study are reviewed, notably the work of Piaget, Bryant, Gagne, and Freeman. The history and nature of 3-D descriptive geometry is reviewed in practice and in education, with special reference to various methods employed in instruction. Dr. J. Vince's PICASO SYSTEM of computer subroutines and functions written in FORTRAN for graphic applications is explained as a means of teaching the subject, with special reference to the researcher's own instructional material and computer programs. The use and effectiveness of these teaching materials are related and evaluated in the light of students' performance and results. The research concludes that the special benefits of computer graphics in this field are: the economic production of appropriate didactic material under the direct control of the teacher, increased pupil motivation due to the use of better illustration and the interest generated by computer-aided design project work. and an opportunity to employ analytic geometry to support learning. Its limitations include: the high cost of the computer and peripheral devices, and the lack of a facility for modelling objects by the removal of solid volumes in the existing software. Further research is recommended in the areas of computer graphics, descriptive geometry, and psychology

Modeling EMI Resulting from a Signal Via Transition Through Power/Ground Layers

Signal transitioning through layers on vias are very common in multi-layer printed circuit board (PCB) design. For a signal via transitioning through the internal power and ground planes, the return current must switch from one reference plane to another reference plane. The discontinuity of the return current at the via excites the power and ground planes, and results in noise on the power bus that can lead to signal integrity, as well as EMI problems. Numerical methods, such as the finite-difference time-domain (FDTD), Moment of Methods (MoM), and partial element equivalent circuit (PEEC) method, were employed herein to study this problem. The modeled results are supported by measurements. In addition, a common EMI mitigation approach of adding a decoupling capacitor was investigated with the FDTD method

Data security in photonic information systems using quantum based approaches

The last two decades has seen a revolution in how information is stored and transmitted across the world. In this digital age, it is vital for banking systems, governments and businesses that this information can be transmitted to authorised receivers quickly and efficiently. Current classical cryptosystems rely on the computational difficulty of calculating certain mathematical functions but with the advent of quantum computers, implementing efficient quantum algorithms, these systems could be rendered insecure overnight. Quantum mechanics thankfully also provides the solution, in which information is transmitted on single-photons called qubits and any attempt by an adversary to gain information on these qubits is limited by the laws of quantum mechanics. This thesis looks at three distinct different quantum information experiments. Two of the systems describe the implementation of distributing quantum keys, in which the presence of an eavesdropper introduces unavoidable errors by the laws of quantum mechanics. The first scheme used a quantum dot in a micropillar cavity as a singlephoton source. A polarisation encoding scheme was used for implementing the BB84, quantum cryptographic protocol, which operated at a wavelength of 905 nm and a clock frequency of 40 MHz. A second system implemented phase encoding using asymmetric unbalanced Mach-Zehnder interferometers, with a weak coherent source, operating at a wavelength of 850 nm and pulsed at a clock rate of 1 GHz. The system used depolarised light propagating in the fibre quantum channel. This helps to eliminate the random evolution of the state of polarisation of photons, as a result of stress induced changes in the intrinsic birefringence of the fibre. The system operated completely autonomously, using custom software to compensate for path length fluctuations in the arms of the interferometer and used a variety of different single-photon detector technologies. The final quantum information scheme looked at quantum digital signatures, which allows a sender, Alice, to distribute quantum signatures to two parties, Bob and Charlie, such that they are able to authenticate that the message originated from Alice and that the message was not altered in transmission