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 role of nuclear and other conventional power plants in the flexible energy system

This thesis reviews the role of nuclear and conventional power plants in the future energy system. The review is done by utilizing freely accesible publications in addition to generating load duration and ramping curves for Nordic energy system. As the aim of the future energy system is to reduce GHG-emissions and avoid further global warming, the need for flexible power generation increases with the increased share of intermittent renewables. The goal of this thesis is to offer extensive understanding of possibilities and restrictions that nuclear power and conventional power plants have regarding flexible and sustainable generation. As a conclusion, nuclear power is the only technology that is able to provide large scale GHG-free power output variations with good ramping values. Most of the currently operating plants are able to take part in load following as the requirement to do so is already required to be included in the plant design. Load duration and ramping curves produced prove that nuclear power is able to cover most of the annual generation variation and ramping needs in the Nordic energy system. From the conventional power generation methods, only biomass combustion can be considered GHG-free because biomass is considered carbon neutral. CFB combusted biomass has good load follow capabilities in good ramping and turndown ratios. All the other conventional power generation technologies generate GHG-emissions and therefore the use of these technologies should be reduced.

Performance Degradation Modelling and Techno-Economic Analysis of Lithium-Ion Battery Energy Storage Systems

Transmission system operators and distribution system operators are experiencing new challenges in terms of reliability, power quality, and cost efficiency. Although the potential of energy storages to face those challenges is recognized, the economic implications are still obscure, which introduce the risk into the business models. This thesis aims to investigate the technical and economic value indicators of lithium-ion battery energy storage systems (BESS) in grid-scale applications. In order to do that, a comprehensive performance lithium-ion BESS model with degradation effects estimation is developed. The model development process implies literature review on lifetime modelling, use, and modification of previous study progress, building the additional system parts and integrating it into a complete tool. The constructed model is capable of describing the dynamic behavior of the BESS voltage, state of charge, temperature and capacity loss. Five control strategies for BESS unit providing primary frequency regulation are implemented, in addition to the model. The questions related to BESS dimensioning and the end of life (EoL) criterion are addressed. Simulations are performed with one-month real frequency data acquired from Fingrid. The lifetime and cost-benefit analysis of the simulation results allow to compare and determine the preferable control strategy. Finally, the study performs the sensitivity analysis of economic profitability with variable size, EoL and system price. The research reports that BESS can be profitable in certain cases and presents the recommendations.

Orientation of Non-Native 2-Monosubstituted and 2,3-Disubstituted 1,4-Naphthoquinones in the A1 binding site of PSI and the effect on the rate of electron transfer : an electron paramagnetic resonance spectroscopy study

The proce-ss ofoxygenic photosynthesis is vital to life on Earth. the central event in photosynthesis is light induced electron transfer that converts light into energy for growth. Ofparticular significance is the membrane bound multisubunit protein known as Photosystem I (PSI). PSI is a reaction centre that is responsible for the transfer of electrons across the membrane to reduce NADP+ to NADPH. The recent publication ofa high resolution X-ray structure of PSI has shown new information about the structure, in particular the electron transfer cofactors, which allows us to study it in more detail. In PSI, the secondary acceptor is crucial for forward electron transfer. In this thesis, the effect of removing the native acceptor phylloquinone and replacing it with a series of structurally related quinones was investigated via transient electron paramagnetic resonance (EPR) experiments. The orientation of non native quinones in the binding site and their ability to function in the electron transfer process was determined. It was found that PSI will readily accept alkyl naphthoquinones and anthraquinone. Q band EPR experiments revealed that the non-native quinones are incorporated into the binding site with the same orientation of the headgroup as in the native system. X band EPR spectra and deuteration experiments indicate that monosubstituted naphthoquinones are bound to the Al site with their side group in the position occupied by the methyl group in native PSI (meta to the hydrogen bonded carbonyl oxygen). X band EPR experiments show that 2, 3- disubstituted methyl naphthoquinones are also incorporated into the Al site in the same orientation as phylloquinone, even with the presence of a halogen- or sulfur-containing side chain in the position normally occupied by the phytyl tail ofphylloquinone. The exception to this is 2-bromo-3-methyl --.- _. -. - -- - - 4 _._ _ _ - _ _ naphthoquinone which has a poorly resolved spectrum, making determination of the orientation difficuh. All of the non-native quinones studied act as efficient electron acceptors. However, forward electron transfer past the quinone could only be demonstrated for anthraquinone, which has a more negative midpoint potential than phylloquinone. In the case of anthraquinone, an increased rate of forward electron transfer compared to native PSI was found. From these results we can conclude that the rate ofelectron transfer from Al to Fx in native PSI lies in the normal region ofthe Marcus Curve.

The Association of Energy Intake with Body Mass in Children With and Without Probable Developmental Coordination Disorder

Objective To determine if there is an association between energy intake (EI) and overweight or obesity status (OWOB) in children with and without probable developmental coordination disorder (p-DCD). Methods 1905 children were included. The Bruininks-Oseretsky Test of Motor Proficiency was used to assess p-DCD, body mass index for OWOB, and the Harvard Food Frequency Questionnaire for EI. Comparative tests and logistic regressions were performed. Results Reported EI was similar between p-DCD and non-DCD children among boys (2291 vs. 2281 kcal/day, p=0.917), but much lower in p-DCD compared to non-DCD girls (1745 vs.. 2068 kcal/day, p=0.007). EI was negatively associated with OWOB in girls only (OR: 0.82 (0.68, 0.98)). Conclusions Girls with p-DCD have a lower reported EI compared to their non-DCD peers. EI is negatively associated with OWOB in girls with p-DCD. Future research is needed to assess longitudinally the potential impact of EI on OWOB in this population.

Support for renewable energy and WTO Law : the actionability of Ontario and Québec renewable energy support mechanisms

Le Traité de Marrakech stipule que le commerce et le développement économique devraient être orientés de manière à permettre l’utilisation optimale des ressources mondiales, conformément à l’objectif de développement durable. Combiné aux dispositions du Protocole de Kyoto et du Traité de Copenhague, les gouvernements poursuivent de politiques nationales favorisant les producteurs nationaux au détriment des étrangers. Cette mémoire propose une analyse des règles de l’OMC, dans le but de déterminer les mesures disciplinaires possibles contre le Canada à l'égard de ses mécanismes de support de l’énergie renouvelable. Une analyse des règles énoncées dans le GATT, l’Accord sur les subventions et les mesures compensatoires et divers accords multilatéraux conclus dans le cadre de l’OMC permet de déterminer si elles pourraient s’appliquer aux mécanismes de support de l’énergie renouvelable. Une analyse des programmes du Québec et de l’Ontario permet une prise de position quant à leur conformité aux règles commerciales de l’OMC.

Effect of Improving Energy Efficiency on System Reliability

In the present scenario of energy demand overtaking energy supply top priority is given for energy conservation programs and policies. Most of the process plants are operated on continuous basis and consumes large quantities of energy. Efficient management of process system can lead to energy savings, improved process efficiency, lesser operating and maintenance cost, and greater environmental safety. Reliability and maintainability of the system are usually considered at the design stage and is dependent on the system configuration. However, with the growing need for energy conservation, most of the existing process systems are either modified or are in a state of modification with a view for improving energy efficiency. Often these modifications result in a change in system configuration there by affecting the system reliability. It is important that system modifications for improving energy efficiency should not be at the cost of reliability. Any new proposal for improving the energy efficiency of the process or equipments should prove itself to be economically feasible for gaining acceptance for implementation. In order to arrive at the economic feasibility of the new proposal, the general trend is to compare the benefits that can be derived over the lifetime as well as the operating and maintenance costs with the investment to be made. Quite often it happens that the reliability aspects (or loss due to unavailability) are not taken into consideration. Plant availability is a critical factor for the economic performance evaluation of any process plant.The focus of the present work is to study the effect of system modification for improving energy efficiency on system reliability. A generalized model for the valuation of process system incorporating reliability is developed, which is used as a tool for the analysis. It can provide an awareness of the potential performance improvements of the process system and can be used to arrive at the change in process system value resulting from system modification. The model also arrives at the pay back of the modified system by taking reliability aspects also into consideration. It is also used to study the effect of various operating parameters on system value. The concept of breakeven availability is introduced and an algorithm for allocation of component reliabilities of the modified process system based on the breakeven system availability is also developed. The model was applied to various industrial situations.

Enhanced shape anisotropy and magneto-optical birefringence by high energy ball milling in NixFe1−xFe2O4 ferrofluids

Ferrofluids belonging to the series NixFe1 xFe2O4 were synthesised by two different procedures—one by standard co-precipitation techniques, the other by co-precipitation for synthesis of particles and dispersion aided by high-energy ball milling with a view to understand the effect of strain and size anisotropy on the magneto-optical properties of ferrofluids. The birefringence measurements were carried out using a standard ellipsometer. The birefringence signal obtained for chemically synthesised samples was satisfactorily fitted to the standard second Langevin function. The ball-milled ferrofluids showed a deviation and their birefringence was enhanced by an order. This large enhancement in the birefringence value cannot be attributed to the increase in grain size of the samples, considering that the grain sizes of sample synthesised by both modes are comparable; instead, it can be attributed to the lattice strain-induced shape anisotropy(oblation) arising from the high-energy ball-milling process. Thus magnetic-optical (MO) signals can be tuned by ball-milling process, which can find potential applications.

The role of energy correlations on Coulomb suppression in ballistic conductors contacted to degenerate reservoirs

Coulomb suppression of shot noise in a ballistic diode connected to degenerate ideal contacts is analyzed in terms of the correlations taking place between current fluctuations due to carriers injected with different energies. By using Monte Carlo simulations we show that at low frequencies the origin of Coulomb suppression can be traced back to the negative correlations existing between electrons injected with an energy close to that of the potential barrier present in the diode active region and all other carriers injected with higher energies. Correlations between electrons with energy above the potential barrier with the rest of electrons are found to influence significantly the spectra at high frequency in the cutoff region.

Shot-noise spectroscopy of energy resolved ballistic currents

We investigate the shot noise of nonequilibrium carriers injected into a ballistic conductor and interacting via long-range Coulomb forces. Coulomb interactions are shown to act as an energy analyzer of the profile of injected electrons by means of the fluctuations of the potential barrier at the emitter contact. We show that the details in the energy profile can be extracted from shot-noise measurements in the Coulomb interaction regime, but cannot be obtained from time-averaged quantities or shot-noise measurements in the absence of interactions.

Average ground-state energy of finite Fermi systems

Semiclassical theories such as the Thomas-Fermi and Wigner-Kirkwood methods give a good description of the smooth average part of the total energy of a Fermi gas in some external potential when the chemical potential is varied. However, in systems with a fixed number of particles N, these methods overbind the actual average of the quantum energy as N is varied. We describe a theory that accounts for this effect. Numerical illustrations are discussed for fermions trapped in a harmonic oscillator potential and in a hard-wall cavity, and for self-consistent calculations of atomic nuclei. In the latter case, the influence of deformations on the average behavior of the energy is also considered.

Enhanced shape anisotropy and magneto-optical birefringence by high energy ball milling in NixFe1 xFe2O4 ferrofluids

Ferrofluids belonging to the series NixFe1 xFe2O4 were synthesised by two different procedures—one by standard co-precipitation techniques, the other by co-precipitation for synthesis of particles and dispersion aided by high-energy ball milling with a view to understand the effect of strain and size anisotropy on the magneto-optical properties of ferrofluids. The birefringence measurements were carried out using a standard ellipsometer. The birefringence signal obtained for chemically synthesised samples was satisfactorily fitted to the standard second Langevin function. The ball-milled ferrofluids showed a deviation and their birefringence was enhanced by an order. This large enhancement in the birefringence value cannot be attributed to the increase in grain size of the samples, considering that the grain sizes of sample synthesised by both modes are comparable; instead, it can be attributed to the lattice strain-induced shape anisotropy(oblation) arising from the high-energy ball-milling process. Thus magnetic-optical (MO) signals can be tuned by ball-milling process, which can find potential applications

Investigations on TiO2 Based Nanocomposites as Potential Photonic Materials

This Study overviews the basics of TiO2with respect to its structure, properties and applications. A brief account of its structural, electronic and optical properties is provided. Various emerging technological applications utilising TiO2 is also discussed.Till now, exceptionally large number of fundamental studies and application-oriented research and developments has been carried out by many researchers worldwide in TiO2 with its low-dimensional nanomaterial form due to its various novel properties. These nanostructured materials have shown many favourable properties for potential applications, including pollutant photocatalytic decomposition, photovoltaic cells, sensors and so on. This thesis aims to make an in-depth investigation on different linear and nonlinear optical and structural characteristics of different phases of TiO2. Correspondingly, extensive challenges to synthesise different high quality TiO2 nanostructure derivatives such as nanotubes, nanospheres, nanoflowers etc. are continuing. Here, different nanostructures of anatase TiO2 were synthesised and analysed. Morphologically different nanostructures were found to have different impact on their physical and electronic properties such as varied surface area, dissimilar quantum confinement and hence diverged suitability for different applications. In view of the advantages of TiO2, it can act as an excellent matrix for nanoparticle composite films. These composite films may lead to several advantageous functional optical characteristics. Detailed investigations of these kinds of nanocomposites were also performed, only to find that these nanocomposites showed higher adeptness than their parent material. Fine tuning of these parameters helps researchers to achieve high proficiency in their respective applications. These innumerable opportunities aims to encompass the new progress in studies related to TiO2 for an efficient utilization in photo-catalytic or photo-voltaic applications under visible light, accentuate the future trends of TiO2-research in the environment as well as energy related fields serving promising applications benefitting the mankind. The last section of the thesis discusses the applicability of analysed nanomaterials for dye sensitised solar cells followed by future suggestions.

Entwicklung der Windenergietechnik in Deutschland und der Einfluss staatlicher Förderpolitik - Technikentwicklung in den 90er Jahren zwischen Markt und Forschungsförderung

Seit gut zehn Jahren erlebt die Windenergienutzung in Deutschland einen in der Mitte der 80er Jahre nicht für möglich gehaltenen Aufschwung. Anlagenanzahl und installierte Leistung haben in diesem Zeitraum mit durchschnittlichen jährlichen Wachstumsraten von mehr als 30 Prozent zugenommen, die mittlere installierte Leistung pro neu errichteter Anlage stieg dabei um das Zehnfache und die technische Verfügbarkeit der Anlagen liegt mittlerweile bei über 98 Prozent. Mit größer werdenden Anlagen zeigt sich weiterhin ein klarer Trend zu Blattwinkel verstellbaren Konzepten, mit zunehmend drehzahlvariabler Betriebsweise. Vor dem von Vielen für die kommenden drei bis sechs Jahre prognostizierten Einstieg in die großtechnische Offshore- Windenergienutzung mit den damit verbundenen immensen technologischen und strukturellen Herausforderungen erscheint es sinnvoll, einen kritischen Blick zurückzuwerfen auf die 90er Jahre mit den ihnen zugrunde liegenden förderpolitischen Rahmenbedingungen. Dabei soll die Frage beantwortet werden, welchen konkreten Einfluss die staatlichen Forschungs- und Förderprogramme, besonders das "250 MW Wind"-Programm, auf die Entwicklung der Windenergienutzung hatten, das heißt, unter welchen Bedingungen sich bestimmte Techniklinien durchsetzten, wie der Einfluss eines geschützten Marktes durch gesetzlich garantierte Einspeisetarife auf diese Entwicklung zu bewerten ist und schließlich, welche Fehlentwicklungen möglicher Weise eingetreten sind. Dazu wird mit Hilfe von Lernkurven gezeigt, welche Kostenreduktionen insgesamt erzielt wurden, wie hoch die dazu notwendigen staatlichen Finanzmittel waren und welche Schlussfolgerungen daraus für die Zukunft abgeleitet werden können. Die Arbeit soll insgesamt dazu beitragen, die erreichten technischen Entwicklungsschritte vor dem Hintergrund der förderpolitischen Gegebenheiten besser zu verstehen, Chancen für gezielte Änderungen in der Förderpraxis zu ergreifen und Hinweise auf die Ausgestaltung von zukünftigen Forschungsprogrammen und Entwicklungsschwerpunkten im Bereich der Windenergie zu geben, um weitere Kostensenkungspotenziale auszuschöpfen. Dabei wird sich die zukünftige Schwerpunktsetzung in der programmatischen Ausrichtung der Forschung stärker auf die drei wichtigsten Anwendungsfelder für Windenergieanlagen konzentrieren müssen, die großtechnische Offshore- Anwendung, die netzgebundene, dezentrale Energieversorgung sowie auf Windenergieanlagen zur ländlichen Elektrifizierung in autonomen Versorgungssystemen für Schwellen- und Entwicklungsländer.

Delocalization of a hole in van der Waals clusters: Ionization potential of rare-gas and small Hg_n clusters

The size dependence of the ionization potential I_p(n) of van der Waals (vdW) bound clusters has been calculated by using a model Hamiltonian, which includes electron hopping, vdW interactions, and charge-dipole interactions. The charge-density and dipole-density distributions for both neutral and ionized n-atom clusters are determined self-consistently. The competition between the polarization energy of the neutral atoms surrounding a partially localized hole and the tendency toward hole delocalization in the ionized clusters is found to dominate the size dependence of I_p(n). To test our theory, we culculate I_p(Xe_n) and I_p(Kr_n) for n \le 300. Good quantitative agreement with experiment is obtained. The theory is also applied to calculate I_p(Hg_n). Comparison with experiments suggests that in Hg_n^+ clusters with n \le 20 the positive charge is mainly distributed within a trimer which is situated at the center of the cluster and which polarizes the n - 3 surrounding neutral atoms.