Towards input/output-free modelling of linear infinite-dimensional systems in continuous time

This dissertation describes a networking approach to infinite-dimensional systems theory, where there is a minimal distinction between inputs and outputs. We introduce and study two closely related classes of systems, namely the state/signal systems and the port-Hamiltonian systems, and describe how they relate to each other. Some basic theory for these two classes of systems and the interconnections of such systems is provided. The main emphasis lies on passive and conservative systems, and the theoretical concepts are illustrated using the example of a lossless transfer line. Much remains to be done in this field and we point to some directions for future studies as well.

The solutions and tunneling properties for a linear potential and an inverted harmonic oscillator in an infinite well

In this work we look at two different 1-dimensional quantum systems. The potentials for these systems are a linear potential in an infinite well and an inverted harmonic oscillator in an infinite well. We will solve the Schrödinger equation for both of these systems and get the energy eigenvalues and eigenfunctions. The solutions are obtained by using the boundary conditions and numerical methods. The motivation for our study comes from experimental background. For the linear potential we have two different boundary conditions. The first one is the so called normal boundary condition in which the wave function goes to zero on the edge of the well. The second condition is called derivative boundary condition in which the derivative of the wave function goes to zero on the edge of the well. The actual solutions are Airy functions. In the case of the inverted oscillator the solutions are parabolic cylinder functions and they are solved only using the normal boundary condition. Both of the potentials are compared with the particle in a box solutions. We will also present figures and tables from which we can see how the solutions look like. The similarities and differences with the particle in a box solution are also shown visually. The figures and calculations are done using mathematical software. We will also compare the linear potential to a case where the infinite wall is only on the left side. For this case we will also show graphical information of the different properties. With the inverted harmonic oscillator we will take a closer look at the quantum mechanical tunneling. We present some of the history of the quantum tunneling theory, its developers and finally we show the Feynman path integral theory. This theory enables us to get the instanton solutions. The instanton solutions are a way to look at the tunneling properties of the quantum system. The results are compared with the solutions of the double-well potential which is very similar to our case as a quantum system. The solutions are obtained using the same methods which makes the comparison relatively easy. All in all we consider and go through some of the stages of the quantum theory. We also look at the different ways to interpret the theory. We also present the special functions that are needed in our solutions, and look at the properties and different relations to other special functions. It is essential to notice that it is possible to use different mathematical formalisms to get the desired result. The quantum theory has been built for over one hundred years and it has different approaches. Different aspects make it possible to look at different things.

The solutions and tunneling properties for a linear potential and an inverted harmonic oscillator in an infinite well

In this work we look at two different 1-dimensional quantum systems. The potentials for these systems are a linear potential in an infinite well and an inverted harmonic oscillator in an infinite well. We will solve the Schrödinger equation for both of these systems and get the energy eigenvalues and eigenfunctions. The solutions are obtained by using the boundary conditions and numerical methods. The motivation for our study comes from experimental background. For the linear potential we have two different boundary conditions. The first one is the so called normal boundary condition in which the wave function goes to zero on the edge of the well. The second condition is called derivative boundary condition in which the derivative of the wave function goes to zero on the edge of the well. The actual solutions are Airy functions. In the case of the inverted oscillator the solutions are parabolic cylinder functions and they are solved only using the normal boundary condition. Both of the potentials are compared with the particle in a box solutions. We will also present figures and tables from which we can see how the solutions look like. The similarities and differences with the particle in a box solution are also shown visually. The figures and calculations are done using mathematical software. We will also compare the linear potential to a case where the infinite wall is only on the left side. For this case we will also show graphical information of the different properties. With the inverted harmonic oscillator we will take a closer look at the quantum mechanical tunneling. We present some of the history of the quantum tunneling theory, its developers and finally we show the Feynman path integral theory. This theory enables us to get the instanton solutions. The instanton solutions are a way to look at the tunneling properties of the quantum system. The results are compared with the solutions of the double-well potential which is very similar to our case as a quantum system. The solutions are obtained using the same methods which makes the comparison relatively easy. All in all we consider and go through some of the stages of the quantum theory. We also look at the different ways to interpret the theory. We also present the special functions that are needed in our solutions, and look at the properties and different relations to other special functions. It is essential to notice that it is possible to use different mathematical formalisms to get the desired result. The quantum theory has been built for over one hundred years and it has different approaches. Different aspects make it possible to look at different things.

Methods for the analysis of two dimensional measurement data of paper web

This work is devoted to the problem of reconstructing the basis weight structure at paper web with black{box techniques. The data that is analyzed comes from a real paper machine and is collected by an o®-line scanner. The principal mathematical tool used in this work is Autoregressive Moving Average (ARMA) modelling. When coupled with the Discrete Fourier Transform (DFT), it gives a very flexible and interesting tool for analyzing properties of the paper web. Both ARMA and DFT are independently used to represent the given signal in a simplified version of our algorithm, but the final goal is to combine the two together. Ljung-Box Q-statistic lack-of-fit test combined with the Root Mean Squared Error coefficient gives a tool to separate significant signals from noise.

Three-dimensional model of bubbling fluidized bed combustion

 Diplomityön tarkoituksena on kehittää kolmiulotteinen malli kerrosleijupoltolle. Työn kirjallisuusosa sisältää seuraavat perusteet kerrosleijupolton tekniikasta: yleistiedot, leijutus- ja palamisilmiöt, kiinteän aineen ja kaasun sekoittuminen, päästöt ja lämmönsiirto. Lisäksi palamissysteemin mallinnuksen perusteet ja ratkaisumenetelmät ovat esitelty. Työn mallinnusosassa kehitetty koodi on ohjelmoitu Fortran-ohjelmointikielellä. Kehitetty malli perustuu olemassa olevaan malliin kiertoleijupoltosta. Yhtälö kiintoainekonsentraatioprofiilille on vaihdettu ja kiertovirta on poistettu koodista. Mallilla on tehty herkkyystarkasteluja polttoaineen ja kaasun sekoittumisen sekä reaktiokertoimen vaikutukselle. Visualisointi on tehty ohjelmassa Tecplot 360 ja mallinnustuloksia on vertailtu mitattuihin tuloksiin. Mallin laskemattulokset vastaavat hyvin mittaustuloksia ja kokemusperäisiä tietoja; monissa tapauksissa malli pystyy kvantitatiivisesti kuvaamaan parametrien variointia ja kaikissa tapauksissa malli antaa ainakin kvalitatiivisesti oikeita tuloksia. Työhön liittyvän kehityksen ja mallinnuskokemuksen perusteella on tehty ehdotukset mallin tulevaa kehitystä ja mittauksia varten.

A three dimensional study of heat transfer in a supercritical circulating fluidized bed combustor

From the boiler design point of view, it is imperative to know and understand the operation of the boiler. Since comprehensive measurement of a large furnace is impossible, the furnace can be modeled in order to study its behavior and phenomena. This requires the used model to be validated to correspond with the physical furnace behavior. In this thesis, a three dimensional furnace model is validated to match a bituminous coal utilizing, supercritical once-through circulating fluidized bed combustor based on measurement data. The validated model is used for analyzing the furnace heat transfer. Other heat transfer analysis methods are energy balance method based on tube surface temperature measurements and a method based on measured temperature difference between the tube crest and the fin. The latter method was developed in the thesis using Fluent-software. In the theory part, literature is reviewed and the fundamental aspects of circulating fluidized bed are discussed. These aspects are solid particle behavior in fluidization known as hydrodynamics, behavior of fuel and combustion and heat transfer. Fundamental aspects of modeling are also presented.

The effect of microfibrillated cellulose addition on drying shrinkage and dimensional stability of wood-free paper

Microfibrillated cellulose (MFC) is known to enhance strength properties of paper. Improved strength usually means increased bonding which is strongly connected to dimensional instability of paper. Dimensional instability is due to changes in moisture content of paper; when paper is moistened it expands and when dried, it shrinks. Hygroexpansion is linked to end-use problems and excessive drying shrinkage consumes strength potential. Effective use of materials requires controlling of these phenomena. There isn’t yet data concerning dimensional stability of papers containing MFC which restricts wider use of MFC. Main objective of the work was to evaluate dimensional stability of wood-free paper containing different amounts of MFC. Sheets were dried with different methods to see how drying strains effected on drying shrinkage and hygroexpansion. Also tensile strength was measured to find out the effect of MFC. Results were compared to sheets containing kraft fines and in some test points cationic starch was used alongside with MFC. MFC increased the dimensional instability of freely dried sheets. As the amounts of MFC increased the effects on dimensional stability became more severe. However the fineness of MFC didn’t play any important role. Both hygroexpansion and drying shrinkage were decreased with cationic starch addition. Prevention of drying shrinkage over powered the effects of additives on hygroexpansion. Tensile strength improved up till 7 % addition amount which could be set as the upper limit of MFC addition when paper preparation and tensile strength are concerned.

On Undecidable Dynamical Properties of Reversible One-Dimensional Cellular Automata

Cellular automata are models for massively parallel computation. A cellular automaton consists of cells which are arranged in some kind of regular lattice and a local update rule which updates the state of each cell according to the states of the cell's neighbors on each step of the computation. This work focuses on reversible one-dimensional cellular automata in which the cells are arranged in a two-way in_nite line and the computation is reversible, that is, the previous states of the cells can be derived from the current ones. In this work it is shown that several properties of reversible one-dimensional cellular automata are algorithmically undecidable, that is, there exists no algorithm that would tell whether a given cellular automaton has the property or not. It is shown that the tiling problem of Wang tiles remains undecidable even in some very restricted special cases. It follows that it is undecidable whether some given states will always appear in computations by the given cellular automaton. It also follows that a weaker form of expansivity, which is a concept of dynamical systems, is an undecidable property for reversible one-dimensional cellular automata. It is shown that several properties of dynamical systems are undecidable for reversible one-dimensional cellular automata. It shown that sensitivity to initial conditions and topological mixing are undecidable properties. Furthermore, non-sensitive and mixing cellular automata are recursively inseparable. It follows that also chaotic behavior is an undecidable property for reversible one-dimensional cellular automata.

A Development and Application of a Three-Dimensional Model for a CFB Gasifier

The developing energy markets and rising energy system costs have sparked the need to find new forms of energy production and increase the self-sufficiency of energy production. One alternative is gasification, whose principles have been known for decades, but it is only recently when the technology has become a true alternative. However, in order to meet the requirements of modern energy production methods, it is necessary to study the phenomenon thoroughly. In order to understand the gasification process better and optimize it from the viewpoint of ecology and energy efficiency, it is necessary to develop effective and reliable modeling tools for gasifiers. The main aims of this work have been to understand gasification as a process and furthermore to develop an existing three-dimensional circulating fluidized bed modeling tool for modeling of gasification. The model is applied to two gasification processes of 12 and 50 MWth. The results of modeling and measurements have been compared and subsequently reviewed. The work was done in co-operation with Lappeenranta University of Technology and Foster Wheeler Energia Oy.

New computer software for defining the three-dimensional geometry for a centrifu- gal compressor impeller

In this thesis, a computer software for defining the geometry for a centrifugal compressor impeller is designed and implemented. The project is done under the supervision of Laboratory of Fluid Dynamics in Lappeenranta University of Technology. This thesis is similar to the thesis written by Tomi Putus (2009) in which a centrifugal compressor impeller flow channel is researched and commonly used design practices are reviewed. Putus wrote a computer software which can be used to define impeller’s three-dimensional geometry based on the basic geometrical dimensions given by a preliminary design. The software designed in this thesis is almost similar but it uses a different programming language (C++) and a different way to define the shape of the impeller meridional projection.

Some defects in two-dimensional spin-1/2 Heisenberg antiferromagnets: a numerical study of magnetic effects

En del av de intressantaste fenomenen inom dagens materialfysik uppstår ur ett intrikat samspel mellan myriader av elektroner. Högtemperatursupraledare är det mest berömda exemplet. Varken klassiska teorier eller modeller där elektronerna är oberoende av varandra kan förklara de häpnadsväckande effekterna i de starkt korrelerade elektronsystemen. I vissa kopparoxider, till exempel La2CuO4, är det känt att valenselektronerna till följd av en stark ömsesidig växelverkan lokaliseras en och en till kopparatomerna i föreningens CuO2 plan. Laddningarnas inneboende magnetiska moment—spinnet—får då en avgörande roll för materialets elektriska och magnetiska egenskaper, vilka i exemplets fall kan beskrivas med Heisenbergmodellen som är den grundläggande teoretiska modellen för mikroskopisk magnetism. Men exakt varför föreningarna kan bli supraledande då de dopas med överskottsladdningar är än så länge en obesvarad fråga. Min avhandling undersöker orenheters inverkan på Heisenbergmodellens magnetiska egenskaper—ett problem av både experimentell och teoretisk relevans. En etablerad numerisk metod har använts—en kvantmekanisk Monte Carlo teknik—för att utföra omfattande datorsimuleringar av den matematiska modellen på två dedikerade Linux datorkluster. Arbetet hör till området beräkningsfysik. De teoretiska modellerna för starkt korrelerade elektronsystem, däribland Heisenbergmodellen, är ytterst invecklade matematiskt sett och de kan inte lösas exakt. Analytiska utredningar bygger för det mesta på antaganden och förenklingar vars inverkningar på slutresultatet är ofta oklara. I det avseende kan numeriska studier vara exakta, det vill säga de kan behandla modellerna som de är. Oftast behövs bägge tillvägagångssätten. Den röda tråden i arbetet har varit att numeriskt testa vissa högaktuella analytiska förutsägelser rörande effekterna av orenheter i Heisenbergmodellen. En del av dem har vi på basen av mycket noggranna data kunnat bekräfta. Men våra resultat har också påvisat felaktigheter i de analytiska prognoserna som sedermera delvis reviderats. En del av avhandlingens numeriska upptäckter har i sin tur stimulerat till helt nya teoretiska studier.

Leptogenesis as the origin of matter-antimatter asymmetry in extra dimensional and supersymmetric models

The Standard Model of particle physics is currently the best description of fundamental particles and their interactions. All particles save the Higgs boson have been observed in particle accelerator experiments over the years. Despite the predictive power the Standard Model there are many phenomena that the scenario does not predict or explain. Among the most prominent dilemmas is matter-antimatter asymmetry, and much effort has been made in formulating scenarios that accurately predict the correct amount of matter-antimatter asymmetry in the universe. One of the most appealing explanations is baryogenesis via leptogenesis which not only serves as a mechanism of producing excess matter over antimatter but can also explain why neutrinos have very small non-zero masses. Interesting leptogenesis scenarios arise when other possible candidates of theories beyond the Standard Model are brought into the picture. In this thesis, we have studied leptogenesis in an extra dimensional framework and in a modified version of supersymmetric Standard Model. The first chapters of this thesis introduce the standard cosmological model, observations made on the photon to baryon ratio and necessary preconditions for successful baryogenesis. Baryogenesis via leptogenesis is then introduced and its connection to neutrino physics is illuminated. The final chapters concentrate on extra dimensional theories and supersymmetric models and their ability to accommodate leptogenesis. There, the results of our research are also presented.

Modelling of combustion and sorbent reactions in three-dimensional flow environment of a circulating fluidized bed furnace

This thesis presents a three-dimensional, semi-empirical, steady state model for simulating the combustion, gasification, and formation of emissions in circulating fluidized bed (CFB) processes. In a large-scale CFB furnace, the local feeding of fuel, air, and other input materials, as well as the limited mixing rate of different reactants produce inhomogeneous process conditions. To simulate the real conditions, the furnace should be modelled three-dimensionally or the three-dimensional effects should be taken into account. The only available methods for simulating the large CFB furnaces three-dimensionally are semi-empirical models, which apply a relatively coarse calculation mesh and a combination of fundamental conservation equations, theoretical models and empirical correlations. The number of such models is extremely small. The main objective of this work was to achieve a model which can be applied to calculating industrial scale CFB boilers and which can simulate all the essential sub-phenomena: fluid dynamics, reactions, the attrition of particles, and heat transfer. The core of the work was to develop the model frame and the required sub-models for determining the combustion and sorbent reactions. The objective was reached, and the developed model was successfully used for studying various industrial scale CFB boilers combusting different types of fuel. The model for sorbent reactions, which includes the main reactions for calcitic limestones, was applied for studying the new possible phenomena occurring in the oxygen-fired combustion. The presented combustion and sorbent models and principles can be utilized in other model approaches as well, including other empirical and semi-empirical model approaches, and CFD based simulations. The main achievement is the overall model frame which can be utilized for the further development and testing of new sub-models and theories, and for concentrating the knowledge gathered from the experimental work carried out at bench scale, pilot scale and industrial scale apparatus, and from the computational work performed by other modelling methods.