Extreme Observables and Optimal Measurements in Quantum Theory

Optimization of quantum measurement processes has a pivotal role in carrying out better, more accurate or less disrupting, measurements and experiments on a quantum system. Especially, convex optimization, i.e., identifying the extreme points of the convex sets and subsets of quantum measuring devices plays an important part in quantum optimization since the typical figures of merit for measuring processes are affine functionals. In this thesis, we discuss results determining the extreme quantum devices and their relevance, e.g., in quantum-compatibility-related questions. Especially, we see that a compatible device pair where one device is extreme can be joined into a single apparatus essentially in a unique way. Moreover, we show that the question whether a pair of quantum observables can be measured jointly can often be formulated in a weaker form when some of the observables involved are extreme. Another major line of research treated in this thesis deals with convex analysis of special restricted quantum device sets, covariance structures or, in particular, generalized imprimitivity systems. Some results on the structure ofcovariant observables and instruments are listed as well as results identifying the extreme points of covariance structures in quantum theory. As a special case study, not published anywhere before, we study the structure of Euclidean-covariant localization observables for spin-0-particles. We also discuss the general form of Weyl-covariant phase-space instruments. Finally, certain optimality measures originating from convex geometry are introduced for quantum devices, namely, boundariness measuring how ‘close’ to the algebraic boundary of the device set a quantum apparatus is and the robustness of incompatibility quantifying the level of incompatibility for a quantum device pair by measuring the highest amount of noise the pair tolerates without becoming compatible. Boundariness is further associated to minimum-error discrimination of quantum devices, and robustness of incompatibility is shown to behave monotonically under certain compatibility-non-decreasing operations. Moreover, the value of robustness of incompatibility is given for a few special device pairs.

Optimal distance of the light-curing tip for light transmission through the resin composite

Hammaslääketieteessä käytetettävien komposiittien valonläpäisevyys vaihtelee. Samoin LED-valokovettimet eroavat toisistaan valotehonsa ja muotoilunsa perusteella. On yleisesti tiedossa, että valokovettimesta tulevan valon intensiteetti pinta-alayksikköä kohden heikkenee, kun kovettimen etäisyys kasvaa. Toisaalta ei ole tiedossa, miten valokovetettavan kohteen ja valokovettimen kärjen väliin sijoitettu materiaali tarkalleenottaen vaikuttaa valon intensiteettiin eri etäisyyksiä käytettäessä. Tämän tutkimuksen tarkoituksena on selvittää, miten valokovetettavan kohteen ja valokovettimen kärjen väliin asetettava etukäteen polymerisoitu materiaali vaikuttaa valon intensiteettiin eri etäisyyksillä. Tutkimus suoritettiin käyttämällä kahta eri valokovetinta. Jotta etäisyyden vaikutusta valotustehoon voitiin demonstroida, vaihdettiin kovettimen etäisyyttä sensorista 0,2,4,6,8,10mm välillä. Valotehot rekisteröitiin MARC resin calibrator -laitteella. Sensorin ja valokovettimen kärjen väliin asetettavat erilaiset komposiittilevyt olivat valmiiksi kovetettuja,1mm paksuisia, filleripitoisuuksiltaan neljää erilaista muovia. Valotehot rekisteröitiin jokaiselta etäisyydeltä komposiitin ollessa sensorin päällä. Rinnakkaisesti verrattiin myös etäisyyden vaikutusta valotehoon ilman esikovetettua materiaalia kovettimen kärjen ja valoa mittaavan sensorin välissä. Vertailun suorittamiseksi laskettiin intensiteettisuhdeluku muovillisen ja muovittoman arvon välillä aina tietyllä etäisyydellä Valokovettimen kärjen etäisyyden kasvattaminen sensorista (eli valokovetettavasta kohteesta) odotusten mukaisesti pienensi valotehoa. Laittamalla sensorin ja kovettimen väliin komposiittilevy, valoteho pieneni odotetusti vielä enemmän. Tutkittaessa intensiteettisuhdetta (valoteho muovin kanssa : valoteho ilman muovia) kuitenkin huomattiin, että 4-6mm:n kohdalla suhdeluku oli suurempi kuin 0,2,8 ja 10mm kohdalla. Johtopäätöksenä oli, että suurin mahdollinen valokovetusteho saavutetan laittamalla kovetuskärki mahdollisimman lähelle kohdetta. Jos valokovetettavan kohteen ja valokovettimen kärjen välissä oli kiinteä komposiittipalanen, suurin mahdollinen valokovetusteho kohteeseen saavutetaan edelleen laittamalla kovetuskärki kiinni muoviin. Jos etäisyyttä muovin pinnasta sen sijaan kasvatettiin, valokovetusteho ei laskenutkaan niin nopeasti kuin oli odotettu. Tämä voi liittyä siihen, että tehokkaan valokeilan halkaisijan koko on suurempi verrattuna komposiitin sekä sensorin halkaisian kokoon. Toiseksi on arvioitu, että resiinikomposiitin täyteaineet voisivat fokusoida läpi kulkevaa valoa sensoriin. Se, pitääkö tämä ilmiö paikkansa, vaatii kuitenkin enemmän tutkimusta

Optimal Recycling Combination of Ash in South-East Finland

The present world energy production is heavily relying on the combustion of solid fuels like coals, peat, biomass, municipal solid waste, whereas the share of renewable fuels is anticipated to increase in the future to mitigate climate change. In Finland, peat and wood are widely used for energy production. In any case, the combustion of solid fuels results in generation of several types of thermal conversion residues, such as bottom ash, fly ash, and boiler slag. The predominant residue type is determined by the incineration technology applied, while its composition is primarily relevant to the composition of fuels combusted. An extensive research has been conducted on technical suitability of ash for multiple recycling methods. Most of attention was drawn to the recycling of the coal combustion residues, as coal is the primary solid fuel consumed globally. The recycling methods of coal residues include utilization in a cement industry, in concrete manufacturing, and mine backfilling, to name few. Biomass combustion residues were also studied to some extent with forest fertilization, road construction, and road stabilization being the predominant utilization options. Lastly, residues form municipal solid waste incineration attracted more attention recently following the growing number of waste incineration plants globally. The recycling methods of waste incineration residues are the most limited due to its hazardous nature and varying composition, and include, among others, landfill construction, road construction, mine backfilling. In the study, environmental and economic aspects of multiple recycling options of thermal conversion residues generated within a case-study area were studied. The case-study area was South-East Finland. The environmental analysis was performed using an internationally recognized methodology — life cycle assessment. Economic assessment was conducted applying a widely used methodology — cost-benefit analysis. Finally, the results of the analyses were combined to enable easier comparison of the recycling methods. The recycling methods included the use of ash in forest fertilization, road construction, road stabilization, and landfill construction. Ash landfilling was set as a baseline scenario. Quantitative data about the amounts of ash generated and its composition was obtained from companies, their environmental reports, technical reports and other previously published literature. Overall, the amount of ash in the case-study area was 101 700 t. However, the data about 58 400 t of fly ash and 35 100 t of bottom ash and boiler slag were included in the study due to lack of data about leaching of heavy metals in some cases. The recycling methods were modelled according to the scientific studies published previously. Overall, the results of the study indicated that ash utilization for fertilization and neutralization of 17 600 ha of forest was the most economically beneficial method, which resulted in the net present value increase by 58% compared to ash landfilling. Regarding the environmental impact, the use of ash in the construction of 11 km of roads was the most attractive method with decreased environmental impact of 13% compared to ash landfilling. The least preferred method was the use of ash for landfill construction since it only enabled 11% increase of net present value, while inducing additional 1% of negative impact on the environment. Therefore, a following recycling route was proposed in the study. Where possible and legally acceptable, recycle fly and bottom ash for forest fertilization, which has strictest requirements out of all studied methods. If the quality of fly ash is not suitable for forest fertilization, then it should be utilized, first, in paved road construction, second, in road stabilization. Bottom ash not suitable for forest fertilization, as well as boiler slag, should be used in landfill construction. Landfilling should only be practiced when recycling by either of the methods is not possible due to legal requirements or there is not enough demand on the market. Current demand on ash and possible changes in the future were assessed in the study. Currently, the area of forest fertilized in the case-study are is only 451 ha, whereas about 17 600 ha of forest could be fertilized with ash generated in the region. Provided that the average forest fertilizing values in Finland are higher and the area treated with fellings is about 40 000 ha, the amount of ash utilized in forest fertilization could be increased. Regarding road construction, no new projects launched by the Center of Economic Development, Transport and the Environment in the case-study area were identified. A potential application can be found in the construction of private roads. However, no centralized data about such projects is available. The use of ash in stabilization of forest roads is not expected to increased in the future with a current downwards trend in the length of forest roads built. Finally, the use of ash in landfill construction is not a promising option due to the reducing number of landfills in operation in Finland.