Biotransformation and endocrine disruptive effects of contaminants in ringed seals - implications for monitoring and risk assessment

Marine mammals are exposed to persistent organic pollutants (POPs), which may be biotransformed to metabolites some of which are highly toxic. Both POPs and their metabolites may lead to adverse health effects, which have been studied using various biomarkers. Changes in endocrine homeostasis have been suggested to be sensitive biomarkers for contaminant-related effects. The overall objective of this doctoral thesis was to investigate biotransformation capacity of POPs and their potential endocrine disruptive effects in two contrasting ringed seal populations from the low contaminated Svalbard area and from the highly contaminated Baltic Sea. Biotransformation capacity was studied by determining the relationships between congener-specific patterns and concentrations of polychlorinated biphenyls (PCBs), organochlorine pesticides (OCPs), polybrominated diphenyl ethers (PBDEs) and their hydroxyl (OH)- and/or methylsulfonyl (MeSO₂)-metabolites, and catalytic activities of hepatic xenobiotic-metabolizing phase I and II enzymes. The results suggest that the biotransformation of PCBs, PBDEs and toxaphenes in ringed seals depends on the congener-specific halogen-substitution pattern. Biotransformation products detected in the seals included OH-PCBs, MeSO₂-PCBs and –DDE, pentachlorophenol, 4-OHheptachlorostyrene, and to a minor extent OH-PBDEs. The effects of life history state (moulting and fasting) on contaminant status and potential biomarkers for endocrine disruption, including hormone and vitamin homeostasis, were investigated in the low contaminated ringed seal population from Svalbard. Moulting/fasting status strongly affected thyroid, vitamin A and calcitriol homeostasis, body condition and concentrations of POPs and their OH-metabolites. In contrast, moulting/fasting status was not associated with variations in vitamin E levels. Endocrine disruptive effects on multiple endpoints were investigated in the two contrasting ringed seal populations. The results suggest that thyroid, vitamin A and calcitriol homeostasis may be affected by the exposure of contaminants and/or their metabolites in the Baltic ringed seals. Complex and non-linear relationships were observed between the contaminant levels and the endocrine variables. Positive relationships between circulating free and total thyroid hormone concentration ratios and OH-PCBs suggest that OH-PCBs may mediate the disruption of thyroid hormone transport in plasma. Species differences in thyroid and bone-related effects of contaminants were studied in ringed and grey seals from low contaminated references areas and from the highly contaminated Baltic Sea. The results indicate that these two species living at the same environment approximately at the same trophic level respond in a very different way to contaminant exposure. The results of this thesis suggest that the health status of the Baltic ringed seals has still improved during the last decade. PCB and DDE levels have decreased in these seals and the contaminant-related effects are different today than a decade ago. The health of the Baltic ringed seals is still suggested to be affected by the contaminant exposure. At the present level of the contaminant exposure the Baltic ringed seals seem to be at a zone where their body is able to compensate for the contaminant-mediated endocrine disruption. Based on the results of this thesis, several recommendations that could be applied on monitoring and assessing risk for contaminant effects are provided. Circulating OH-metabolites should be included in monitoring and risk assessment programs due to their high toxic potential. It should be noted that endogenous variables may have complex and highly variable responses to contaminant exposure including non-linear responses. These relationships may be further confounded by life history status. Therefore, it is highly recommended that when using variables related to endocrine homeostasis to investigate/monitor or assess the risk of contaminant effects in seals, the life history status of the animal should be carefully taken into consideration. This applies especially when using thyroid, vitamin A or calcitriolrelated parameters during moulting/fasting period. Extrapolations between species for assessing risk for contaminant effects in phocid seals should be avoided.

Sähköavusteisen polkupyörän energian talteenotto lineaarigeneraattorilla

Sähköavusteisten polkupyörien määrä on kasvussa. Kasvua hidastavana tekijänä voidaan pitää niiden keskimäärin yli 1000 euron hintaa, josta suurin osa johtuu akustosta. Tämän työn tarkoituksena on selvittää lineaarigeneraattorin hyödynnettävyyttä sähköavusteisissa polkupyörissä. Lisäksi työssä kuvataan vaiheittain prototyypin suunnittelu ja rakentaminen. Mikäli lineaarigeneraattori-avusteisella sähköpolkupyörällä saavutetaan huomattava pidennys toimintamatkaan, voidaan pyörät varustaa halvemmilla ja kapasiteetiltään pienemmillä akuilla. Lineaarigeneraattorin hankintaa kannustaisi se, että se maksaisi vähemmän kuin vaihto suurempikapasiteettiseen akustoon.

Laser cladding with scanning optics

Scanning optics create different types of phenomena and limitation to cladding process compared to cladding with static optics. This work concentrates on identifying and explaining the special features of laser cladding with scanning optics. Scanner optics changes cladding process energy input mechanics. Laser energy is introduced into the process through a relatively small laser spot which moves rapidly back and forth, distributing the energy to a relatively large area. The moving laser spot was noticed to cause dynamic movement in the melt pool. Due to different energy input mechanism scanner optic can make cladding process unstable if parameter selection is not done carefully. Especially laser beam intensity and scanning frequency have significant role in the process stability. The laser beam scanning frequency determines how long the laser beam affects with specific place local specific energy input. It was determined that if the scanning frequency in too low, under 40 Hz, scanned beam can start to vaporize material. The intensity in turn determines on how large package this energy is brought and if the intensity of the laser beam was too high, over 191 kW/cm2, laser beam started to vaporize material. If there was vapor formation noticed in the melt pool, the process starts to resample more laser alloying due to deep penetration of laser beam in to the substrate. Scanner optics enables more flexibility to the process than static optics. The numerical adjustment of scanning amplitude enables clad bead width adjustment. In turn scanner power modulation (where laser power is adjusted according to where the scanner is pointing) enables modification of clad bead cross-section geometry when laser power can be adjusted locally and thus affect how much laser beam melts material in each sector. Power modulation is also an important factor in terms of process stability. When a linear scanner is used, oscillating the scanning mirror causes a dwell time in scanning amplitude border area, where the scanning mirror changes the direction of movement. This can cause excessive energy input to this area which in turn can cause vaporization and process instability. This process instability can be avoided by decreasing energy in this region by power modulation. Powder feeding parameters have a significant role in terms of process stability. It was determined that with certain powder feeding parameter combinations powder cloud behavior became unstable, due to the vaporizing powder material in powder cloud. Mainly this was noticed, when either or both the scanning frequency or powder feeding gas flow was low or steep powder feeding angle was used. When powder material vaporization occurred, it created vapor flow, which prevented powder material to reach the melt pool and thus dilution increased. Also powder material vaporization was noticed to produce emission of light at wavelength range of visible light. This emission intensity was noticed to be correlated with the amount of vaporization in the powder cloud.

Feasibility of industrial implementation of laser cutting into paper making machine

Laser cutting implementation possibilities into paper making machine was studied as the main objective of the work. Laser cutting technology application was considered as a replacement tool for conventional cutting methods used in paper making machines for longitudinal cutting such as edge trimming at different paper making process and tambour roll slitting. Laser cutting of paper was tested in 70’s for the first time. Since then, laser cutting and processing has been applied for paper materials with different level of success in industry. Laser cutting can be employed for longitudinal cutting of paper web in machine direction. The most common conventional cutting methods include water jet cutting and rotating slitting blades applied in paper making machines. Cutting with CO2 laser fulfils basic requirements for cutting quality, applicability to material and cutting speeds in all locations where longitudinal cutting is needed. Literature review provided description of advantages, disadvantages and challenges of laser technology when it was applied for cutting of paper material with particular attention to cutting of moving paper web. Based on studied laser cutting capabilities and problem definition of conventional cutting technologies, preliminary selection of the most promising application area was carried out. Laser cutting (trimming) of paper web edges in wet end was estimated to be the most promising area where it can be implemented. This assumption was made on the basis of rate of web breaks occurrence. It was found that up to 64 % of total number of web breaks occurred in wet end, particularly in location of so called open draws where paper web was transferred unsupported by wire or felt. Distribution of web breaks in machine cross direction revealed that defects of paper web edge was the main reason of tearing initiation and consequent web break. The assumption was made that laser cutting was capable of improvement of laser cut edge tensile strength due to high cutting quality and sealing effect of the edge after laser cutting. Studies of laser ablation of cellulose supported this claim. Linear energy needed for cutting was calculated with regard to paper web properties in intended laser cutting location. Calculated linear cutting energy was verified with series of laser cutting. Practically obtained laser energy needed for cutting deviated from calculated values. This could be explained by difference in heat transfer via radiation in laser cutting and different absorption characteristics of dry and moist paper material. Laser cut samples (both dry and moist (dry matter content about 25-40%)) were tested for strength properties. It was shown that tensile strength and strain break of laser cut samples are similar to corresponding values of non-laser cut samples. Chosen method, however, did not address tensile strength of laser cut edge in particular. Thus, the assumption of improving strength properties with laser cutting was not fully proved. Laser cutting effect on possible pollution of mill broke (recycling of trimmed edge) was carried out. Laser cut samples (both dry and moist) were tested on the content of dirt particles. The tests revealed that accumulation of dust particles on the surface of moist samples can take place. This has to be taken into account to prevent contamination of pulp suspension when trim waste is recycled. Material loss due to evaporation during laser cutting and amount of solid residues after cutting were evaluated. Edge trimming with laser would result in 0.25 kg/h of solid residues and 2.5 kg/h of lost material due to evaporation. Schemes of laser cutting implementation and needed laser equipment were discussed. Generally, laser cutting system would require two laser sources (one laser source for each cutting zone), set of beam transfer and focusing optics and cutting heads. In order to increase reliability of system, it was suggested that each laser source would have double capacity. That would allow to perform cutting employing one laser source working at full capacity for both cutting zones. Laser technology is in required level at the moment and do not require additional development. Moreover, capacity of speed increase is high due to availability high power laser sources what can support the tendency of speed increase of paper making machines. Laser cutting system would require special roll to maintain cutting. The scheme of such roll was proposed as well as roll integration into paper making machine. Laser cutting can be done in location of central roll in press section, before so-called open draw where many web breaks occur, where it has potential to improve runability of a paper making machine. Economic performance of laser cutting was done as comparison of laser cutting system and water jet cutting working in the same conditions. It was revealed that laser cutting would still be about two times more expensive compared to water jet cutting. This is mainly due to high investment cost of laser equipment and poor energy efficiency of CO2 lasers. Another factor is that laser cutting causes material loss due to evaporation whereas water jet cutting almost does not cause material loss. Despite difficulties of laser cutting implementation in paper making machine, its implementation can be beneficial. The crucial role in that is possibility to improve cut edge strength properties and consequently reduce number of web breaks. Capacity of laser cutting to maintain cutting speeds which exceed current speeds of paper making machines what is another argument to consider laser cutting technology in design of new high speed paper making machines.

Linear prediction application for modelling the relationships between a large number of stand characteristics of Norway spruce stands

Abstract

Performance Determinants of Renewable Energy Companies

The purpose of this thesis is to identify the Performance Determinants (PD) of Renewable Energy (RE) companies. It analyzes the background of the RE industry while reflecting simultaneous developments in the fossil based industries. I divided the determinants into two groups: market level and firm level and established hypotheses based on the existing literature. Data from public companies was gathered to construct a Panel Data structure. This is then tested by using a Linear Regression with Fixed Effects model. The model specification was efficient at reflecting the analyzed phenomena. My results showed that both market level and firm level determinants are significant in the RE Industry but the firm level determinants had higher explanatory power (R2). The determinants' relationships were found to follow those from the manufacturing industry more than the utilities' industry. Out of the market level determinants Consumer Price Index (CPI), Interest Rates and Oil prices were significant. Out of the firm level determinants Debt to Assets, Net Investments, Cash flows from operations, Sales and Earnings Before Interests and Taxes (EBIT) were significant. I concluded that this information is valuable for key industry players as they can achieve their objectives faster by elaborating better strategies using these results.

Non-Linear Journal Bearing Model for Analysis of Superharmonic Vibrations of Rotor Systems

A rotating machine usually consists of a rotor and bearings that supports it. The nonidealities in these components may excite vibration of the rotating system. The uncontrolled vibrations may lead to excessive wearing of the components of the rotating machine or reduce the process quality. Vibrations may be harmful even when amplitudes are seemingly low, as is usually the case in superharmonic vibration that takes place below the first critical speed of the rotating machine. Superharmonic vibration is excited when the rotational velocity of the machine is a fraction of the natural frequency of the system. In such a situation, a part of the machine’s rotational energy is transformed into vibration energy. The amount of vibration energy should be minimised in the design of rotating machines. The superharmonic vibration phenomena can be studied by analysing the coupled rotor-bearing system employing a multibody simulation approach. This research is focused on the modelling of hydrodynamic journal bearings and rotorbearing systems supported by journal bearings. In particular, the non-idealities affecting the rotor-bearing system and their effect on the superharmonic vibration of the rotating system are analysed. A comparison of computationally efficient journal bearing models is carried out in order to validate one model for further development. The selected bearing model is improved in order to take the waviness of the shaft journal into account. The improved model is implemented and analyzed in a multibody simulation code. A rotor-bearing system that consists of a flexible tube roll, two journal bearings and a supporting structure is analysed employing the multibody simulation technique. The modelled non-idealities are the shell thickness variation in the tube roll and the waviness of the shaft journal in the bearing assembly. Both modelled non-idealities may cause subharmonic resonance in the system. In multibody simulation, the coupled effect of the non-idealities can be captured in the analysis. Additionally one non-ideality is presented that does not excite the vibrations itself but affects the response of the rotorbearing system, namely the waviness of the bearing bushing which is the non-rotating part of the bearing system. The modelled system is verified with measurements performed on a test rig. In the measurements the waviness of bearing bushing was not measured and therefore it’s affect on the response was not verified. In conclusion, the selected modelling approach is an appropriate method when analysing the response of the rotor-bearing system. When comparing the simulated results to the measured ones, the overall agreement between the results is concluded to be good.

Solution Business Model for Energy Efficiency

This study examined solution business models and how they could be applied into energy efficiency business. The target of this study was to find out, what a functional solution business model applied to energy efficiency improvement projects is like. The term “functionality” was used to refer not only to the economic viability but to environmental and legal aspects and also to the implement of Critical Success Factors (CSFs) and the ability to overcome the most important market barriers and risks. This thesis is based on a comprehensive literature study on solution business, business models and energy efficiency business. This literature review was used as a foundation to an energy efficiency solution business model scheme. The created scheme was tested in a case study which studied two different energy efficiency improvement projects, illustrated the functionality of the created business model and evaluated their potential as customer targets. Solution approach was found to be suitable for energy efficiency business. The most important characteristics of a good solution business model were identified to be the relationship between the supplier and customer, a proper network, knowledge on the customer’s process and supreme technological expertise. Thus the energy efficiency solution business was recognized to be particularly suitable for example for energy suppliers or technological equipment suppliers. Because the case study was not executed from a certain company’s point of view, the most important factors such as relationships and the availability of funding could not be evaluated. Although the energy efficiency business is recognized to be economically viable, the most important factors influencing the profitability and the success of energy efficiency solution business model were identified to be the proper risk management, the ability to overcome market barriers and the realization of CSFs.

Structural and operational optimisation : applications in energy systems

In this work mathematical programming models for structural and operational optimisation of energy systems are developed and applied to a selection of energy technology problems. The studied cases are taken from industrial processes and from large regional energy distribution systems. The models are based on Mixed Integer Linear Programming (MILP), Mixed Integer Non-Linear Programming (MINLP) and on a hybrid approach of a combination of Non-Linear Programming (NLP) and Genetic Algorithms (GA). The optimisation of the structure and operation of energy systems in urban regions is treated in the work. Firstly, distributed energy systems (DES) with different energy conversion units and annual variations of consumer heating and electricity demands are considered. Secondly, district cooling systems (DCS) with cooling demands for a large number of consumers are studied, with respect to a long term planning perspective regarding to given predictions of the consumer cooling demand development in a region. The work comprises also the development of applications for heat recovery systems (HRS), where paper machine dryer section HRS is taken as an illustrative example. The heat sources in these systems are moist air streams. Models are developed for different types of equipment price functions. The approach is based on partitioning of the overall temperature range of the system into a number of temperature intervals in order to take into account the strong nonlinearities due to condensation in the heat recovery exchangers. The influence of parameter variations on the solutions of heat recovery systems is analysed firstly by varying cost factors and secondly by varying process parameters. Point-optimal solutions by a fixed parameter approach are compared to robust solutions with given parameter variation ranges. In the work enhanced utilisation of excess heat in heat recovery systems with impingement drying, electricity generation with low grade excess heat and the use of absorption heat transformers to elevate a stream temperature above the excess heat temperature are also studied.

Commercialization of Modern Renewable Energy

The threat of global warming and its consequences are widely recognized, and the question of how to proceed with the long transition towards fossil fuel -neutral economies concerns many nations and people. At the same time the world’s primary energy use is predicted to increase significantly during the next decades as a result of global population and welfare increase. Improved energy efficiency and increased use of renewable energy sources in the world’s energy mix play important roles in the future energy production and consumption. The objective of this thesis is to study how novel renewable energy technologies, such as distributed small-scale bio-fueled combined heat and power production and wind power technologies could be commercialized efficiently. A wide array of attributes may contribute to the diffusion of new products. In general, the bioenergy and wind power technologies are in emerging phases, and the diffusion stage varies from country to country. The effects of firms’ technology choices, collaboration and alliances are studied in this thesis. Furthermore, the roles of national energy infrastructure and energy support schemes in the commercialization of new renewable energy products are explored. The empirical data is based on energy expert interviews, financial and patent data, and literature reviews of different case studies. The thesis comprises two parts. The first part provides an overview of the study, and the second part includes six research publications. The results reveal that small-scale bio-fueled combined heat and power production and wind power technologies are still in emerging phases in their life cycles, and energy support schemes are crucial in the market diffusion. The study contributes to earlier findings in the literature and industry by confirming that adequate energy policies and energy infrastructure are fundamental in the commercialization of novel renewable energy technologies. Firm-specific issues, including business relationships and new business models, and market-related issues will have a more significant role in the market penetration in the future, when the technologies mature and become competitive without political support schemes.

Comparison of Different Concentrated Solar Power Collector Designs and Development of a Linear Fresnel Solar Collector Model

Concentrated solar power (CSP) is a renewable energy technology, which could contribute to overcoming global problems related to pollution emissions and increasing energy demand. CSP utilizes solar irradiation, which is a variable source of energy. In order to utilize CSP technology in energy production and reliably operate a solar field including thermal energy storage system, dynamic simulation tools are needed in order to study the dynamics of the solar field, to optimize production and develop control systems. The object of this Master’s Thesis is to compare different concentrated solar power technologies and configure a dynamic solar field model of one selected CSP field design in the dynamic simulation program Apros, owned by VTT and Fortum. The configured model is based on German Novatec Solar’s linear Fresnel reflector design. Solar collector components including dimensions and performance calculation were developed, as well as a simple solar field control system. The preliminary simulation results of two simulation cases under clear sky conditions were good; the desired and stable superheated steam conditions were maintained in both cases, while, as expected, the amount of steam produced was reduced in the case having lower irradiation conditions. As a result of the model development process, it can be concluded, that the configured model is working successfully and that Apros is a very capable and flexible tool for configuring new solar field models and control systems and simulating solar field dynamic behaviour.

Modeling Energy Futures Returns With Markov Regime Switching Model

Financial time series have a tendency of abruptly changing their behavior and maintain this behavior for several consecutive periods, and commodity futures returns are not an exception. This quality proposes that nonlinear models, as opposed to linear models, can more accurately describe returns and volatility. Markov regime switching models are able to match this behavior and have become a popular way to model financial time series. This study uses Markov regime switching model to describe the behavior of energy futures returns on a commodity level, because studies show that commodity futures are a heterogeneous asset class. The purpose of this thesis is twofold. First, determine how many regimes characterize individual energy commodities’ returns in different return frequencies. Second, study the characteristics of these regimes. We extent the previous studies on the subject in two ways: We allow for the possibility that the number of regimes may exceed two, as well as conduct the research on individual commodities rather than on commodity indices or subgroups of these indices. We use daily, weekly and monthly time series of Brent crude oil, WTI crude oil, natural gas, heating oil and gasoil futures returns over 1994–2014, where available, to carry out the study. We apply the likelihood ratio test to determine the sufficient number of regimes for each commodity and data frequency. Then the time series are modeled with Markov regime switching model to obtain the return distribution characteristics of each regime, as well as the transition probabilities of moving between regimes. The results for the number of regimes suggest that daily energy futures return series consist of three to six regimes, whereas weekly and monthly returns for all energy commodities display only two regimes. When the number of regimes exceeds two, there is a tendency for the time series of energy commodities to form groups of regimes. These groups are usually quite persistent as a whole because probability of a regime switch inside the group is high. However, individual regimes in these groups are not persistent and the process oscillates between these regimes frequently. Regimes that are not part of any group are generally persistent, but show low ergodic probability, i.e. rarely prevail in the market. This study also suggests that energy futures return series characterized with two regimes do not necessarily display persistent bull and bear regimes. In fact, for the majority of time series, bearish regime is considerably less persistent. Rahoituksen aikasarjoilla on taipumus arvaamattomasti muuttaa käyttäytymistään ja jatkaa tätä uutta käyttäytymistä useiden periodien ajan, eivätkä hyödykefutuurien tuotot tee tähän poikkeusta. Tämän ominaisuuden johdosta lineaaristen mallien sijasta epälineaariset mallit pystyvät tarkemmin kuvailemaan esimerkiksi tuottojen jakauman parametreja. Markov regiiminvaihtomallit pystyvät vangitsemaan tämän ominaisuuden ja siksi niistä on tullut suosittuja rahoituksen aikasarjojen mallintamisessa. Tämä tutkimus käyttää Markov regiiminvaihtomallia kuvaamaan yksittäisten energiafutuurien tuottojen käyttäytymistä, sillä tutkimukset osoittavat hyödykefutuurien olevan hyvin heterogeeninen omaisuusluokka. Tutkimuksen tarkoitus on selvittää, kuinka monta regiimiä tarvitaan kuvaamaan energiafutuurien tuottoja eri tuottofrekvensseillä ja mitkä ovat näiden regiimien ominaisuudet. Aiempaa tutkimusta aiheesta laajennetaan määrittämällä regiimien lukumäärä tilastotieteellisen testauksen menetelmin sekä tutkimalla energiafutuureja yksittäin; ei indeksi- tai alaindeksitasolla. Tutkimuksessa käytetään päivä-, viikko- ja kuukausiaikasarjoja Brent-raakaöljyn, WTI-raakaöljyn, maakaasun, lämmitysöljyn ja polttoöljyn tuotoista aikaväliltä 1994–2014, siltä osin kuin aineistoa on saatavilla. Likelihood ratio -testin avulla estimoidaan kaikille aikasarjoille regiimien määrä,jonka jälkeen Markov regiiminvaihtomallia hyödyntäen määritetään yksittäisten regiimientuottojakaumien ominaisuudet sekä regiimien välinen transitiomatriisi. Tulokset regiimien lukumäärän osalta osoittavat, että energiafutuurien päiväkohtaisten tuottojen aikasarjoissa regiimien lukumäärä vaihtelee kolmen ja kuuden välillä. Viikko- ja kuukausituottojen kohdalla kaikkien energiafutuurien prosesseissa regiimien lukumäärä on kaksi. Kun regiimejä on enemmän kuin kaksi, on prosessilla taipumus muodostaa regiimeistä koostuvia ryhmiä. Prosessi pysyy ryhmän sisällä yleensä pitkään, koska todennäköisyys siirtyä ryhmään kuuluvien regiimien välillä on suuri. Yksittäiset regiimit ryhmän sisällä eivät kuitenkaan ole kovin pysyviä. Näin ollen prosessi vaihtelee ryhmän sisäisten regiimien välillä tiuhaan. Regiimit, jotka eivät kuulu ryhmään, ovat yleensä pysyviä, mutta prosessi ajautuu niihin vain harvoin, sillä todennäköisyys siirtyä muista regiimeistä niihin on pieni. Tutkimuksen tulokset osoittavat myös, että prosesseissa, joita ohjaa kaksi regiimiä, nämä regiimit eivät välttämättä ole pysyvät bull- ja bear-markkinatilanteet. Tulokset osoittavat sen sijaan, että bear-markkinatilanne on energiafutuureissa selvästi vähemmän pysyvä.

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.