Analysis discrete function theory

There is a recent trend to describe physical phenomena without the use of infinitesimals or infinites. This has been accomplished replacing differential calculus by the finite difference theory. Discrete function theory was first introduced in l94l. This theory is concerned with a study of functions defined on a discrete set of points in the complex plane. The theory was extensively developed for functions defined on a Gaussian lattice. In 1972 a very suitable lattice H: {Ci qmxO,I qnyo), X0) 0, X3) 0, O < q < l, m, n 5 Z} was found and discrete analytic function theory was developed. Very recently some work has been done in discrete monodiffric function theory for functions defined on H. The theory of pseudoanalytic functions is a generalisation of the theory of analytic functions. When the generator becomes the identity, ie., (l, i) the theory of pseudoanalytic functions reduces to the theory of analytic functions. Theugh the theory of pseudoanalytic functions plays an important role in analysis, no discrete theory is available in literature. This thesis is an attempt in that direction. A discrete pseudoanalytic theory is derived for functions defined on H.

Speech sample estimation from composite zerocrossings and encoding via adaptive switching of transforms

This thesis investigates the potential use of zerocrossing information for speech sample estimation. It provides 21 new method tn) estimate speech samples using composite zerocrossings. A simple linear interpolation technique is developed for this purpose. By using this method the A/D converter can be avoided in a speech coder. The newly proposed zerocrossing sampling theory is supported with results of computer simulations using real speech data. The thesis also presents two methods for voiced/ unvoiced classification. One of these methods is based on a distance measure which is a function of short time zerocrossing rate and short time energy of the signal. The other one is based on the attractor dimension and entropy of the signal. Among these two methods the first one is simple and reguires only very few computations compared to the other. This method is used imtea later chapter to design an enhanced Adaptive Transform Coder. The later part of the thesis addresses a few problems in Adaptive Transform Coding and presents an improved ATC. Transform coefficient with maximum amplitude is considered as ‘side information’. This. enables more accurate tfiiz assignment enui step—size computation. A new bit reassignment scheme is also introduced in this work. Finally, sum ATC which applies switching between luiscrete Cosine Transform and Discrete Walsh-Hadamard Transform for voiced and unvoiced speech segments respectively is presented. Simulation results are provided to show the improved performance of the coder

Chaotic dynamics of electric-field domains in periodically driven superlattices

Self-sustained time-dependent current oscillations under dc voltage bias have been observed in recent experiments on n-doped semiconductor superlattices with sequential resonant tunneling. The current oscillations are caused by the motion and recycling of the domain wall separating low- and high-electric-field regions of the superlattice, as the analysis of a discrete drift model shows and experimental evidence supports. Numerical simulation shows that different nonlinear dynamical regimes of the domain wall appear when an external microwave signal is superimposed on the dc bias and its driving frequency and driving amplitude vary. On the frequency-amplitude parameter plane, there are regions of entrainment and quasiperiodicity forming Arnold tongues. Chaos is demonstrated to appear at the boundaries of the tongues and in the regions where they overlap. Coexistence of up to four electric-field domains randomly nucleated in space is detected under ac+dc driving.

Some bivariate life time models in discrete time"

The term reliability of an equipment or device is often meant to indicate the probability that it carries out the functions expected of it adequately or without failure and within specified performance limits at a given age for a desired mission time when put to use under the designated application and operating environmental stress. A broad classification of the approaches employed in relation to reliability studies can be made as probabilistic and deterministic, where the main interest in the former is to device tools and methods to identify the random mechanism governing the failure process through a proper statistical frame work, while the latter addresses the question of finding the causes of failure and steps to reduce individual failures thereby enhancing reliability. In the probabilistic attitude to which the present study subscribes to, the concept of life distribution, a mathematical idealisation that describes the failure times, is fundamental and a basic question a reliability analyst has to settle is the form of the life distribution. It is for no other reason that a major share of the literature on the mathematical theory of reliability is focussed on methods of arriving at reasonable models of failure times and in showing the failure patterns that induce such models. The application of the methodology of life time distributions is not confined to the assesment of endurance of equipments and systems only, but ranges over a wide variety of scientific investigations where the word life time may not refer to the length of life in the literal sense, but can be concieved in its most general form as a non-negative random variable. Thus the tools developed in connection with modelling life time data have found applications in other areas of research such as actuarial science, engineering, biomedical sciences, economics, extreme value theory etc.

Numerical Simulation of Two-Part Underwater Towing System

The motion instability is an important issue that occurs during the operation of towed underwater vehicles (TUV), which considerably affects the accuracy of high precision acoustic instrumentations housed inside the same. Out of the various parameters responsible for this, the disturbances from the tow-ship are the most significant one. The present study focus on the motion dynamics of an underwater towing system with ship induced disturbances as the input. The study focus on an innovative system called two-part towing. The methodology involves numerical modeling of the tow system, which consists of modeling of the tow-cables and vehicles formulation. Previous study in this direction used a segmental approach for the modeling of the cable. Even though, the model was successful in predicting the heave response of the tow-body, instabilities were observed in the numerical solution. The present study devises a simple approach called lumped mass spring model (LMSM) for the cable formulation. In this work, the traditional LMSM has been modified in two ways. First, by implementing advanced time integration procedures and secondly, use of a modified beam model which uses only translational degrees of freedoms for solving beam equation. A number of time integration procedures, such as Euler, Houbolt, Newmark and HHT-α were implemented in the traditional LMSM and the strength and weakness of each scheme were numerically estimated. In most of the previous studies, hydrodynamic forces acting on the tow-system such as drag and lift etc. are approximated as analytical expression of velocities. This approach restricts these models to use simple cylindrical shaped towed bodies and may not be applicable modern tow systems which are diversed in shape and complexity. Hence, this particular study, hydrodynamic parameters such as drag and lift of the tow-system are estimated using CFD techniques. To achieve this, a RANS based CFD code has been developed. Further, a new convection interpolation scheme for CFD simulation, called BNCUS, which is blend of cell based and node based formulation, was proposed in the study and numerically tested. To account for the fact that simulation takes considerable time in solving fluid dynamic equations, a dedicated parallel computing setup has been developed. Two types of computational parallelisms are explored in the current study, viz; the model for shared memory processors and distributed memory processors. In the present study, shared memory model was used for structural dynamic analysis of towing system, distributed memory one was devised in solving fluid dynamic equations.

Agent Based Simulation of Street Robbery

Routine activity theory introduced by Cohen& Felson in 1979 states that criminal acts are caused due to the presenceof criminals, vic-timsand the absence of guardians in time and place. As the number of collision of these elements in place and time increases, criminal acts will also increase even if the number of criminals or civilians remains the same within the vicinity of a city. Street robbery is a typical example of routine ac-tivity theory and the occurrence of which can be predicted using routine activity theory. Agent-based models allow simulation of diversity among individuals. Therefore agent based simulation of street robbery can be used to visualize how chronological aspects of human activity influence the incidence of street robbery.The conceptual model identifies three classes of people-criminals, civilians and police with certain activity areas for each. Police exist only as agents of formal guardianship. Criminals with a tendency for crime will be in the search for their victims. Civilians without criminal tendencycan be either victims or guardians. In addition to criminal tendency, each civilian in the model has a unique set of characteristicslike wealth, employment status, ability for guardianship etc. These agents are subjected to random walk through a street environment guided by a Q –learning module and the possible outcomes are analyzed

Agent Based Evacuation Simulation Using Leader-Follower Model

Agent based simulation is a widely developing area in artificial intelligence.The simulation studies are extensively used in different areas of disaster management. This work deals with the study of an agent based evacuation simulation which is being done to handle the various evacuation behaviors.Various emergent behaviors of agents are addressed here. Dynamic grouping behaviors of agents are studied. Collision detection and obstacle avoidances are also incorporated in this approach.Evacuation is studied with single exits and multiple exits and efficiency is measured in terms of evacuation rate, collision rate etc.Net logo is the tool used which helps in the efficient modeling of scenarios in evacuation

Discrete wavelet transform de-noising in eukaryotic gene splicing

This paper compares the most common digital signal processing methods of exon prediction in eukaryotes, and also proposes a technique for noise suppression in exon prediction. The specimen used here which has relevance in medical research, has been taken from the public genomic database - GenBank.Here exon prediction has been done using the digital signal processing methods viz. binary method, EIIP (electron-ion interaction psuedopotential) method and filter methods. Under filter method two filter designs, and two approaches using these two designs have been tried. The discrete wavelet transform has been used for de-noising of the exon plots.Results of exon prediction based on the methods mentioned above, which give values closest to the ones found in the NCBI database are given here. The exon plot de-noised using discrete wavelet transform is also given.Alterations to the proven methods as done by the authors, improves performance of exon prediction algorithms. Also it has been proven that the discrete wavelet transform is an effective tool for de-noising which can be used with exon prediction algorithms

Some Aspects of Domain Specific Conceptual Modeling for Simulation of Logistic Terminal Operations

When simulation modeling is used for performance improvement studies of complex systems such as transport terminals, domain specific conceptual modeling constructs could be used by modelers to create structured models. A two stage procedure which includes identification of the problem characteristics/cluster - ‘knowledge acquisition’ and identification of standard models for the problem cluster – ‘model abstraction’ was found to be effective in creating structured models when applied to certain logistic terminal systems. In this paper we discuss some methods and examples related the knowledge acquisition and model abstraction stages for the development of three different types of model categories of terminal systems

Modelling and simulation of a photovoltaic fuel cell hybrid system

A stand-alone power system is an autonomous system that supplies electricity to the user load without being connected to the electric grid. This kind of decentralized system is frequently located in remote and inaccessible areas. It is essential for about one third of the world population which are living in developed or isolated regions and have no access to an electricity utility grid. The most people live in remote and rural areas, with low population density, lacking even the basic infrastructure. The utility grid extension to these locations is not a cost effective option and sometimes technically not feasible. The purpose of this thesis is the modelling and simulation of a stand-alone hybrid power system, referred to as “hydrogen Photovoltaic-Fuel Cell (PVFC) hybrid system”. It couples a photovoltaic generator (PV), an alkaline water electrolyser, a storage gas tank, a proton exchange membrane fuel cell (PEMFC), and power conditioning units (PCU) to give different system topologies. The system is intended to be an environmentally friendly solution since it tries maximising the use of a renewable energy source. Electricity is produced by a PV generator to meet the requirements of a user load. Whenever there is enough solar radiation, the user load can be powered totally by the PV electricity. During periods of low solar radiation, auxiliary electricity is required. An alkaline high pressure water electrolyser is powered by the excess energy from the PV generator to produce hydrogen and oxygen at a pressure of maximum 30bar. Gases are stored without compression for short- (hourly or daily) and long- (seasonal) term. A proton exchange membrane (PEM) fuel cell is used to keep the system’s reliability at the same level as for the conventional system while decreasing the environmental impact of the whole system. The PEM fuel cell consumes gases which are produced by an electrolyser to meet the user load demand when the PV generator energy is deficient, so that it works as an auxiliary generator. Power conditioning units are appropriate for the conversion and dispatch the energy between the components of the system. No batteries are used in this system since they represent the weakest when used in PV systems due to their need for sophisticated control and their short lifetime. The model library, ISET Alternative Power Library (ISET-APL), is designed by the Institute of Solar Energy supply Technology (ISET) and used for the simulation of the hybrid system. The physical, analytical and/or empirical equations of each component are programmed and implemented separately in this library for the simulation software program Simplorer by C++ language. The model parameters are derived from manufacturer’s performance data sheets or measurements obtained from literature. The identification and validation of the major hydrogen PVFC hybrid system component models are evaluated according to the measured data of the components, from the manufacturer’s data sheet or from actual system operation. Then, the overall system is simulated, at intervals of one hour each, by using solar radiation as the primary energy input and hydrogen as energy storage for one year operation. A comparison between different topologies, such as DC or AC coupled systems, is carried out on the basis of energy point of view at two locations with different geographical latitudes, in Kassel/Germany (Europe) and in Cairo/Egypt (North Africa). The main conclusion in this work is that the simulation method of the system study under different conditions could successfully be used to give good visualization and comparison between those topologies for the overall performance of the system. The operational performance of the system is not only depending on component efficiency but also on system design and consumption behaviour. The worst case of this system is the low efficiency of the storage subsystem made of the electrolyser, the gas storage tank, and the fuel cell as it is around 25-34% at Cairo and 29-37% at Kassel. Therefore, the research for this system should be concentrated in the subsystem components development especially the fuel cell.

Räumliche Modellierung der Dynamik von Landnutzung in Hessen und ihrer Wirkung auf die biologische Kohlenstoffspeicherung - Entwicklung eines GIS-basierten Modellsystems

Die gegenwärtige Entwicklung der internationalen Klimapolitik verlangt von Deutschland eine Reduktion seiner Treibhausgasemissionen. Wichtigstes Treibhausgas ist Kohlendioxid, das durch die Verbrennung fossiler Energieträger in die Atmosphäre freigesetzt wird. Die Reduktionsziele können prinzipiell durch eine Verminderung der Emissionen sowie durch die Schaffung von Kohlenstoffsenken erreicht werden. Senken beschreiben dabei die biologische Speicherung von Kohlenstoff in Böden und Wäldern. Eine wichtige Einflussgröße auf diese Prozesse stellt die räumliche Dynamik der Landnutzung einer Region dar. In dieser Arbeit wird das Modellsystem HILLS entwickelt und zur Simulation dieser komplexen Wirkbeziehungen im Bundesland Hessen genutzt. Ziel ist es, mit HILLS über eine Analyse des aktuellen Zustands hinaus auch Szenarien über Wege der zukünftigen regionalen Entwicklung von Landnutzung und ihrer Wirkung auf den Kohlenstoffhaushalt bis 2020 zu untersuchen. Für die Abbildung der räumlichen und zeitlichen Dynamik von Landnutzung in Hessen wird das Modell LUCHesse entwickelt. Seine Aufgabe ist die Simulation der relevanten Prozesse auf einem 1 km2 Raster, wobei die Raten der Änderung exogen als Flächentrends auf Ebene der hessischen Landkreise vorgegeben werden. LUCHesse besteht aus Teilmodellen für die Prozesse: (A) Ausbreitung von Siedlungs- und Gewerbefläche, (B) Strukturwandel im Agrarsektor sowie (C) Neuanlage von Waldflächen (Aufforstung). Jedes Teilmodell umfasst Methoden zur Bewertung der Standorteignung der Rasterzellen für unterschiedliche Landnutzungsklassen und zur Zuordnung der Trendvorgaben zu solchen Rasterzellen, die jeweils am besten für eine Landnutzungsklasse geeignet sind. Eine Validierung der Teilmodelle erfolgt anhand von statistischen Daten für den Zeitraum von 1990 bis 2000. Als Ergebnis eines Simulationslaufs werden für diskrete Zeitschritte digitale Karten der Landnutzugsverteilung in Hessen erzeugt. Zur Simulation der Kohlenstoffspeicherung wird eine modifizierte Version des Ökosystemmodells Century entwickelt (GIS-Century). Sie erlaubt einen gesteuerten Simulationslauf in Jahresschritten und unterstützt die Integration des Modells als Komponente in das HILLS Modellsystem. Es werden verschiedene Anwendungsschemata für GIS-Century entwickelt, mit denen die Wirkung der Stilllegung von Ackerflächen, der Aufforstung sowie der Bewirtschaftung bereits bestehender Wälder auf die Kohlenstoffspeicherung untersucht werden kann. Eine Validierung des Modells und der Anwendungsschemata erfolgt anhand von Feld- und Literaturdaten. HILLS implementiert eine sequentielle Kopplung von LUCHesse mit GIS-Century. Die räumliche Kopplung geschieht dabei auf dem 1 km2 Raster, die zeitliche Kopplung über die Einführung eines Landnutzungsvektors, der die Beschreibung der Landnutzungsänderung einer Rasterzelle während des Simulationszeitraums enthält. Außerdem integriert HILLS beide Modelle über ein dienste- und datenbankorientiertes Konzept in ein Geografisches Informationssystem (GIS). Auf diesem Wege können die GIS-Funktionen zur räumlichen Datenhaltung und Datenverarbeitung genutzt werden. Als Anwendung des Modellsystems wird ein Referenzszenario für Hessen mit dem Zeithorizont 2020 berechnet. Das Szenario setzt im Agrarsektor eine Umsetzung der AGENDA 2000 Politik voraus, die in großem Maße zu Stilllegung von Ackerflächen führt, während für den Bereich Siedlung und Gewerbe sowie Aufforstung die aktuellen Trends der Flächenausdehnung fortgeschrieben werden. Mit HILLS ist es nun möglich, die Wirkung dieser Landnutzungsänderungen auf die biologische Kohlenstoffspeicherung zu quantifizieren. Während die Ausdehnung von Siedlungsflächen als Kohlenstoffquelle identifiziert werden kann (37 kt C/a), findet sich die wichtigste Senke in der Bewirtschaftung bestehender Waldflächen (794 kt C/a). Weiterhin führen die Stilllegung von Ackerfläche (26 kt C/a) sowie Aufforstung (29 kt C/a) zu einer zusätzlichen Speicherung von Kohlenstoff. Für die Kohlenstoffspeicherung in Böden zeigen die Simulationsexperimente sehr klar, dass diese Senke nur von beschränkter Dauer ist.

Anisotropic adaptive resolution of boundary layers for heat conduction problems

We deal with the numerical solution of heat conduction problems featuring steep gradients. In order to solve the associated partial differential equation a finite volume technique is used and unstructured grids are employed. A discrete maximum principle for triangulations of a Delaunay type is developed. To capture thin boundary layers incorporating steep gradients an anisotropic mesh adaptation technique is implemented. Computational tests are performed for an academic problem where the exact solution is known as well as for a real world problem of a computer simulation of the thermoregulation of premature infants.

Modellierung und numerische Simulation der Thermoregulation von Früh- und Neugeborenen

Bei frühgeborenen Säuglingen spielt die Thermoregulation zur Aufrechterhaltung einer überlebenswichtigen Körpertemperatur durch Wärmeproduktion, -abgabe bzw. -aufnahme eine entscheidende Rolle. Der Einsatz moderner Inkubatoren soll die körpereigenen Thermoregulatoren unterstützen, und es ist im Hinblick auf verschiedene medizinische Fragestellungen wünschenswert, diesen Prozess modellieren zu können. Wir stellen ein einfaches Modell auf der Basis von partiellen Differentialgleichungen vor und beschreiben detailliert die numerische Simulation mit Hilfe einer Finite-Volumen-Methode. Dazu wird ein zweidimensionales Modell eines Frühgeborenen trianguliert und das Modell diskretisiert. Zahlreiche numerische Resultate zeigen die Qualität unseres Modells.

Stability of preconditioned finite volume schemes at low Mach numbers

In [4], Guillard and Viozat propose a finite volume method for the simulation of inviscid steady as well as unsteady flows at low Mach numbers, based on a preconditioning technique. The scheme satisfies the results of a single scale asymptotic analysis in a discrete sense and comprises the advantage that this can be derived by a slight modification of the dissipation term within the numerical flux function. Unfortunately, it can be observed by numerical experiments that the preconditioned approach combined with an explicit time integration scheme turns out to be unstable if the time step Dt does not satisfy the requirement to be O(M2) as the Mach number M tends to zero, whereas the corresponding standard method remains stable up to Dt=O(M), M to 0, which results from the well-known CFL-condition. We present a comprehensive mathematical substantiation of this numerical phenomenon by means of a von Neumann stability analysis, which reveals that in contrast to the standard approach, the dissipation matrix of the preconditioned numerical flux function possesses an eigenvalue growing like M-2 as M tends to zero, thus causing the diminishment of the stability region of the explicit scheme. Thereby, we present statements for both the standard preconditioner used by Guillard and Viozat [4] and the more general one due to Turkel [21]. The theoretical results are after wards confirmed by numerical experiments.

Ein Beitrag zur Modellierung und Simulation von elektromechanischen Systemen

Die in dieser Arbeit durchgeführten Untersuchungen zeigen, daß es möglich ist, komplexe thermische Systeme, unter Verwendung der thermisch-, elektrischen Analogien, mit PSpice zu simulieren. Im Mittelpunkt der Untersuchungen standen hierbei Strangkühlkörper zur Kühlung von elektronischen Bauelementen. Es konnte gezeigt werden,daß alle Wärmeübertragungsarten, (Wärmeleitung, Konvektion und Wärmestrahlung) in der Simulation berücksichtigt werden können. Für die Berechnung der Konvektion wurden verschiedene Methoden hergeleitet. Diese gelten zum einen für verschiedene Kühlkörpergeometrien, wie z.B. ebene Flächen und Kühlrippenzwischenräume, andererseits unterscheiden sie sich, je nachdem, ob freie oder erzwungene Konvektion betrachtet wird. Für die Wärmestrahlung zwischen den Kühlrippen wurden verschiedenen Berechnungsmethoden entwickelt. Für die Simulation mit PSpice wurde die Berechnung der Wärmestrahlung zwischen den Kühlrippen vereinfacht. Es konnte gezeigt werden, daß die Fehler, die durch die Vereinfachung entstehen, vernachlässigbar klein sind. Für das thermische Verhalten einer zu kühlenden Wärmequelle wurde ein allgemeines Modell entworfen. Zur Bestimmung der Modellparameter wurden verschiedene Meßverfahren entwickelt. Für eine im Fachgebiet Elektromechanik entwickelte Wärmequelle zum Test von Kühlvorrichtungen wurde mit Hilfe dieser Meßverfahren eine Parameterbestimmung durchgeführt. Die Erstellung des thermischen Modells eines Kühlkörpers für die Simulation in PSpice erfordert die Analyse der Kühlkörpergeometrie. Damit diese Analyse weitestgehend automatisiert werden kann, wurden verschiedene Algorithmen unter Matlab entwickelt. Es wurde ein Algorithmus entwickelt, der es ermöglicht, den Kühlkörper in Elementarzellen zu zerlegen, die für die Erstellung des Simulationsmodells benötigt werden. Desweiteren ist es für die Simulation notwendig zu wissen, welche der Elementarzellen am Rand des Kühlkörpers liegen, welche der Elementarzellen an einem Kühlrippenzwischenraum liegen und welche Kühlkörperkanten schräg verlaufen. Auch zur Lösung dieser Aufgaben wurden verschiedene Algorithmen entwickelt. Diese Algorithmen wurden zu einem Programm zusammengefaßt, das es gestattet, unterschiedliche Strangkühlkörper zu simulieren und die Simulationsergebnisse in Form der Temperaturverteilung auf der Montagefläche des Kühlkörpers grafisch darzustellen. Es können stationäre und transiente Simulationen durchgeführt werden. Desweiteren kann der thermische Widerstand des Kühlkörpers RthK als Funktion der Verlustleistung der Wärmequelle dargestellt werden. Zur Verifikation der Simulationsergebnisse wurden Temperaturmessungen an Kühlkörpern durchgeführt und mit den Simulationsergebnissen verglichen. Diese Vergleiche zeigen, daß die Abweichungen im Bereich der Streuung der Temperaturmessung liegen. Das hier entwickelte Verfahren zur thermischen Simulation von Strangkühlkörpern kann somit als gut bewertet werden.