In spectral methods for numerical PDEs, when the solutions are periodical, the Fourier functions may be used. However, when the solutions are non-periodical, the Legendre and Chebyshev polynomials are recommended, reported in many papers and books. There seems to exist few reports for the study of non-periodical solutions by spectral Fourier methods under the Dirichlet conditions and other boundary conditions. In this paper, we will explore the spectral Fourier methods(SFM) and collocation Fourier methods(CFM) for elliptic and eigenvalue problems. The CFM is simple and easy for computation, thus for saving a great deal of the CPU time. The collocation Fourier methods (CFM) can be regarded as the spectral Fourier methods (SFM) partly with the trapezoidal rule. Furthermore, the error bounds are derived for both the CFM and the SFM. When there exist no errors for the trapezoidal rule, the accuracy of the solutions from the CFM is as accurate as the spectral method using Legendre and Chebyshev polynomials. However, once there exists the truncation errors of the trapezoidal rule, the errors of the elliptic solutions and the leading eigenvalues the CFM are reduced to O(h^2), where h is the mesh length of uniform collocation grids, which are just equivalent to those by the linear elements and the finite difference method (FDM). The O(h^2) and even the superconvergence O(h4) are found numerically. The traditional condition number of the CFM is O(N^2), which is smaller than O(N^3) and O(N^4) of the collocation spectral methods using the Legendre and Chebyshev polynomials. Also the effective condition number is only O(1). Numerical experiments are reported for 1D elliptic and eigenvalue problems, to support the analysis made. The simplicity of algorithms and the promising numerical computation with O(h^4) may grant the CFM to be competent in application in numerical physics, chemistry, engineering, etc., see [7].

<p>This thesis is based on studies of the deregulated electricity markets located in the United States of America. The problem statement of the thesis evolved continuously throughout our initial period of research. Focus was finally put on monitoring and detection of potential market power caused by congestion in the transmission network. The existence of market power is a serious concern in today’s electric energy markets. A system that monitors the trading is needed and much research and many proposals on how to deal with this problem have been introduced over the years. We focus on some of these approaches and develop an approach of our own, which we call “Monopolistic Energy Calculation”. We adopt the idea to identify participants with the ability to raise prices without losing market share. An ability that should not be present on a competitive market. We take this idea further by identifying participants with the ability to make considerable price raises without losing all market shares. We propose a way to calculate the remaining market shares (Monopolistic Energy Levels) after a large price raise. These calculated levels of energy, that are only deliverable by a certain participant or by a certain group of participants, are caused by the active congestions in the network.</p><p>The approach detects the amounts of these energy levels and the location in the network at which they are present. This is a prospective method if used with a prediction of the following day’s demand, which is regularly available with high accuracy. The method can also be used for monitoring purposes to identify critical situations in real-time. The method is implemented and two sets of simulations are done in which we explain and evaluate the approach. The results are promising and the correlation between “Monopolistic Energy” and market power is confirmed.</p> / <p>Detta examensarbete är baserat på studier av de deregulerade electricitsmarknaderna i USA. Problemformuleringen var i början av detta arbete inte definitiv, utan utvecklades under en längre inledande fas av forskningsarbete. Slutligen kunde vi faställa att detektion av potentiell marknadskraft på elektricitetsmarknaden, orsakat av överbelastningar i transmissionnätverket, var av särskilt intresse. Ett system som övervakar handeln och förekomster av orättvisor orsakat av detta är nödvändigt. Det har de senaste åren gjorts mycket forskning inom detta område. Baserat på denna forskning utvecklades sedan ett eget förslag, som vi kallar ”Monopolistic Energy Calculations”. Vissa tidigare förslag på hur problemet kan angripas blev av särskilt intresse. En idé från dessa var att identifiera marknadsaktörer med förmågan att höja priser utan att förlora marknadsandelar, en icke önskvärd egenskap hos aktörer då en konkurrenskraftig marknad är eftertraktad.</p><p>Vi tar denna idé ett steg längre genom att identifiera marknadsaktörer med förmågan att höja priser signifikant utan att förlora alla marknadsandelar. Vi föreslår ett sätt att beräkna dessa energinivåer som endast är möjliga att levereras av en eller ett fåtal särskilda aktörer, som direkt följd av de aktiva stockningarna i nätverket, under antagandet av en inelastisk efterfrågan. Vi föreslår ett sätt att beräkna de återstående marknadsandelarna (Monopolistic Energy Levels) efter en stor prishöjning. Vår metod beräknar mängden av denna energi och var i nätverket dessa mängder förekommer. Denna metod kan sia om framtida problem om en estimering av morgondagens efterfråga används. Sådana estimeringar görs idag</p><p>regelbundet med hög träffsäkerhet. Metoden kan även användas i realtid för upptäckt av kritiska marknadssituationer. Simuleringar av detta görs som förklarar vår lösning och utvärderar den. Resultaten är lovande och korrelationen mellan ”Monopolistisk Energi” och marknadskraft är bekräftade.</p>

This thesis is based on studies of the deregulated electricity markets located in the United States of America. The problem statement of the thesis evolved continuously throughout our initial period of research. Focus was finally put on monitoring and detection of potential market power caused by congestion in the transmission network. The existence of market power is a serious concern in today’s electric energy markets. A system that monitors the trading is needed and much research and many proposals on how to deal with this problem have been introduced over the years. We focus on some of these approaches and develop an approach of our own, which we call “Monopolistic Energy Calculation”. We adopt the idea to identify participants with the ability to raise prices without losing market share. An ability that should not be present on a competitive market. We take this idea further by identifying participants with the ability to make considerable price raises without losing all market shares. We propose a way to calculate the remaining market shares (Monopolistic Energy Levels) after a large price raise. These calculated levels of energy, that are only deliverable by a certain participant or by a certain group of participants, are caused by the active congestions in the network. The approach detects the amounts of these energy levels and the location in the network at which they are present. This is a prospective method if used with a prediction of the following day’s demand, which is regularly available with high accuracy. The method can also be used for monitoring purposes to identify critical situations in real-time. The method is implemented and two sets of simulations are done in which we explain and evaluate the approach. The results are promising and the correlation between “Monopolistic Energy” and market power is confirmed. / Detta examensarbete är baserat på studier av de deregulerade electricitsmarknaderna i USA. Problemformuleringen var i början av detta arbete inte definitiv, utan utvecklades under en längre inledande fas av forskningsarbete. Slutligen kunde vi faställa att detektion av potentiell marknadskraft på elektricitetsmarknaden, orsakat av överbelastningar i transmissionnätverket, var av särskilt intresse. Ett system som övervakar handeln och förekomster av orättvisor orsakat av detta är nödvändigt. Det har de senaste åren gjorts mycket forskning inom detta område. Baserat på denna forskning utvecklades sedan ett eget förslag, som vi kallar ”Monopolistic Energy Calculations”. Vissa tidigare förslag på hur problemet kan angripas blev av särskilt intresse. En idé från dessa var att identifiera marknadsaktörer med förmågan att höja priser utan att förlora marknadsandelar, en icke önskvärd egenskap hos aktörer då en konkurrenskraftig marknad är eftertraktad. Vi tar denna idé ett steg längre genom att identifiera marknadsaktörer med förmågan att höja priser signifikant utan att förlora alla marknadsandelar. Vi föreslår ett sätt att beräkna dessa energinivåer som endast är möjliga att levereras av en eller ett fåtal särskilda aktörer, som direkt följd av de aktiva stockningarna i nätverket, under antagandet av en inelastisk efterfrågan. Vi föreslår ett sätt att beräkna de återstående marknadsandelarna (Monopolistic Energy Levels) efter en stor prishöjning. Vår metod beräknar mängden av denna energi och var i nätverket dessa mängder förekommer. Denna metod kan sia om framtida problem om en estimering av morgondagens efterfråga används. Sådana estimeringar görs idag regelbundet med hög träffsäkerhet. Metoden kan även användas i realtid för upptäckt av kritiska marknadssituationer. Simuleringar av detta görs som förklarar vår lösning och utvärderar den. Resultaten är lovande och korrelationen mellan ”Monopolistisk Energi” och marknadskraft är bekräftade.

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Functional heterojunctions in organic electronic devices are interfaces formed either between a conducting electrode and an organic semiconductor or between two different organic semiconductors in blended and multilayered structures. This thesis is primarily concerned with the energy level alignment and the interfacial electronic structures at functional heterojunctions encountered in electronic devices made with solution-processable semiconducting polymers. Investigations on the electronic structures across these heterointerfaces are performed with the combined use of electromodulation and photoemission spectroscopic techniques. Electromodulation and ultraviolet photoemission spectroscopic techniques enable direct determination of the surface work functions of electrodes at the electrode/semiconducting polymer interfaces. We overcame the inherent problems faced by electromodulation spectroscopy, which undermine accurate determination of interfacial electronic structures, by performing electroabsorption (EA) measurements at reduced temperatures. We showed in this thesis that low-temperature EA spectroscopy is a surface sensitive technique that can determine the interface electronic structures in electrode/polymer semiconductor/electrode diodes. Using this technique, we demonstrated that the energy level alignments in these solution-processed organic electronic devices are determined by the surface work functions of passivated metals rather than by those of clean metals encountered in ultrahigh vacuum. This thesis also discloses our studies on the electronic structures in polymeric diodes with type II donor-acceptor heterojunctions using the EA spectroscopy. We showed that minimising meausurement temperature and attenuating EA illumination intensity enable accurate determinations of the electronic structures in these devices. We demonstrated that the electronic structures and the performance characteristics of multilayered polymer light-emitting diodes are also determined by the surface work functions of passivated metals. Our investigations confirm that electronic doping of the organic active layers, rather than minimisation of the Schottky barriers at electrode/polymer contacts, holds the key in realising high-performance organic light-emitting devices.

No description available.

Organic and hybrid organic-inorganic photovoltaic (PV) devices have the potential to provide low-cost, large scale renewable energy. Despite the tremendous progress that has been made in this field, device efficiencies remain low. This low efficiency can be partly attributed to the low open-circuit voltages (Voc) generated by organic and hybrid organic-inorganic PV devices. The Voc is critically determined by the energy-level alignment at the interface between the materials forming the device. In this thesis we use first-principles methods to explore the energy-level alignment at the interfaces between the conjugated polymer poly(3-hexylthiophene) (P3HT) and three electron acceptors, zinc oxide (ZnO), gallium arsenide (GaAs) and graphene. We find that Voc reported in the literature for ZnO/P3HT devices is significantly lower than the theoretical maximum and that the interfacial electrostatic dipole plays an important role in the physics underlying the charge transfer at the heterojunction. We note significant charge transfer from the polymer to the semiconductor at GaAs/P3HT interfaces, and use this result to help interpret experimental data. Our findings support the conclusion that charge transferred from P3HT to GaAs nanowires can passivate the surface defect states of the latter and, as a result, account for the observed decrease in photoluminescence lifetimes. Finally, we explore the energy-level alignment at the graphene/P3HT interface and find that Voc reported for experimental devices is in line with the theoretical maximum. The effect of functionalised graphene is also examined, leading to the suggestion that functionalisation might have important consequences for device optimisation.

No description available.

No description available.