Parameters Affecting the Extraction of Polycyclic Aromatic Hydrocarbons with Pressurised Hot Water

Pressurised hot water extraction (PHWE) exploits the unique temperature-dependent solvent properties of water minimising the use of harmful organic solvents. Water is environmentally friendly, cheap and easily available extraction medium. The effects of temperature, pressure and extraction time in PHWE have often been studied, but here the emphasis was on other parameters important for the extraction, most notably the dimensions of the extraction vessel and the stability and solubility of the analytes to be extracted. Non-linear data analysis and self-organising maps were employed in the data analysis to obtain correlations between the parameters studied, recoveries and relative errors. First, pressurised hot water extraction (PHWE) was combined on-line with liquid chromatography-gas chromatography (LC-GC), and the system was applied to the extraction and analysis of polycyclic aromatic hydrocarbons (PAHs) in sediment. The method is of superior sensitivity compared with the traditional methods, and only a small 10 mg sample was required for analysis. The commercial extraction vessels were replaced by laboratory-made stainless steel vessels because of some problems that arose. The performance of the laboratory-made vessels was comparable to that of the commercial ones. In an investigation of the effect of thermal desorption in PHWE, it was found that at lower temperatures (200ºC and 250ºC) the effect of thermal desorption is smaller than the effect of the solvating property of hot water. At 300ºC, however, thermal desorption is the main mechanism. The effect of the geometry of the extraction vessel on recoveries was studied with five specially constructed extraction vessels. In addition to the extraction vessel geometry, the sediment packing style and the direction of water flow through the vessel were investigated. The geometry of the vessel was found to have only minor effect on the recoveries, and the same was true of the sediment packing style and the direction of water flow through the vessel. These are good results because these parameters do not have to be carefully optimised before the start of extractions. Liquid-liquid extraction (LLE) and solid-phase extraction (SPE) were compared as trapping techniques for PHWE. LLE was more robust than SPE and it provided better recoveries and repeatabilities than did SPE. Problems related to blocking of the Tenax trap and unrepeatable trapping of the analytes were encountered in SPE. Thus, although LLE is more labour intensive, it can be recommended over SPE. The stabilities of the PAHs in aqueous solutions were measured using a batch-type reaction vessel. Degradation was observed at 300ºC even with the shortest heating time. Ketones and quinones and other oxidation products were observed. Although the conditions of the stability studies differed considerably from the extraction conditions in PHWE, the results indicate that the risk of analyte degradation must be taken into account in PHWE. The aqueous solubilities of acenaphthene, anthracene and pyrene were measured, first below and then above the melting point of the analytes. Measurements below the melting point were made to check that the equipment was working, and the results were compared with those obtained earlier. Good agreement was found between the measured and literature values. A new saturation cell was constructed for the solubility measurements above the melting point of the analytes because the flow-through saturation cell could not be used above the melting point. An exponential relationship was found between the solubilities measured for pyrene and anthracene and temperature.

Stochastic Filtering

The stochastic filtering has been in general an estimation of indirectly observed states given observed data. This means that one is discussing conditional expected values as being one of the most accurate estimation, given the observations in the context of probability space. In my thesis, I have presented the theory of filtering using two different kind of observation process: the first one is a diffusion process which is discussed in the first chapter, while the third chapter introduces the latter which is a counting process. The majority of the fundamental results of the stochastic filtering is stated in form of interesting equations, such the unnormalized Zakai equation that leads to the Kushner-Stratonovich equation. The latter one which is known also by the normalized Zakai equation or equally by Fujisaki-Kallianpur-Kunita (FKK) equation, shows the divergence between the estimate using a diffusion process and a counting process. I have also introduced an example for the linear gaussian case, which is mainly the concept to build the so-called Kalman-Bucy filter. As the unnormalized and the normalized Zakai equations are in terms of the conditional distribution, a density of these distributions will be developed through these equations and stated by Kushner Theorem. However, Kushner Theorem has a form of a stochastic partial differential equation that needs to be verify in the sense of the existence and uniqueness of its solution, which is covered in the second chapter.

Computing the Stochastic Complexity of Simple Probabilistic Graphical Models

Minimum Description Length (MDL) is an information-theoretic principle that can be used for model selection and other statistical inference tasks. There are various ways to use the principle in practice. One theoretically valid way is to use the normalized maximum likelihood (NML) criterion. Due to computational difficulties, this approach has not been used very often. This thesis presents efficient floating-point algorithms that make it possible to compute the NML for multinomial, Naive Bayes and Bayesian forest models. None of the presented algorithms rely on asymptotic analysis and with the first two model classes we also discuss how to compute exact rational number solutions.

Computationally Efficient Methods for MDL-Optimal Density Estimation and Data Clustering

The Minimum Description Length (MDL) principle is a general, well-founded theoretical formalization of statistical modeling. The most important notion of MDL is the stochastic complexity, which can be interpreted as the shortest description length of a given sample of data relative to a model class. The exact definition of the stochastic complexity has gone through several evolutionary steps. The latest instantation is based on the so-called Normalized Maximum Likelihood (NML) distribution which has been shown to possess several important theoretical properties. However, the applications of this modern version of the MDL have been quite rare because of computational complexity problems, i.e., for discrete data, the definition of NML involves an exponential sum, and in the case of continuous data, a multi-dimensional integral usually infeasible to evaluate or even approximate accurately. In this doctoral dissertation, we present mathematical techniques for computing NML efficiently for some model families involving discrete data. We also show how these techniques can be used to apply MDL in two practical applications: histogram density estimation and clustering of multi-dimensional data.

Pricing Index Options with Stochastic Volatility

The objective of this paper is to investigate the pricing accuracy under stochastic volatility where the volatility follows a square root process. The theoretical prices are compared with market price data (the German DAX index options market) by using two different techniques of parameter estimation, the method of moments and implicit estimation by inversion. Standard Black & Scholes pricing is used as a benchmark. The results indicate that the stochastic volatility model with parameters estimated by inversion using the available prices on the preceding day, is the most accurate pricing method of the three in this study and can be considered satisfactory. However, as the same model with parameters estimated using a rolling window (the method of moments) proved to be inferior to the benchmark, the importance of stable and correct estimation of the parameters is evident.

Irradiation effects in graphene and related materials

Nanomaterials with a hexagonally ordered atomic structure, e.g., graphene, carbon and boron nitride nanotubes, and white graphene (a monolayer of hexagonal boron nitride) possess many impressive properties. For example, the mechanical stiffness and strength of these materials are unprecedented. Also, the extraordinary electronic properties of graphene and carbon nanotubes suggest that these materials may serve as building blocks of next generation electronics. However, the properties of pristine materials are not always what is needed in applications, but careful manipulation of their atomic structure, e.g., via particle irradiation can be used to tailor the properties. On the other hand, inadvertently introduced defects can deteriorate the useful properties of these materials in radiation hostile environments, such as outer space. In this thesis, defect production via energetic particle bombardment in the aforementioned materials is investigated. The effects of ion irradiation on multi-walled carbon and boron nitride nanotubes are studied experimentally by first conducting controlled irradiation treatments of the samples using an ion accelerator and subsequently characterizing the induced changes by transmission electron microscopy and Raman spectroscopy. The usefulness of the characterization methods is critically evaluated and a damage grading scale is proposed, based on transmission electron microscopy images. Theoretical predictions are made on defect production in graphene and white graphene under particle bombardment. A stochastic model based on first-principles molecular dynamics simulations is used together with electron irradiation experiments for understanding the formation of peculiar triangular defect structures in white graphene. An extensive set of classical molecular dynamics simulations is conducted, in order to study defect production under ion irradiation in graphene and white graphene. In the experimental studies the response of carbon and boron nitride multi-walled nanotubes to irradiation with a wide range of ion types, energies and fluences is explored. The stabilities of these structures under ion irradiation are investigated, as well as the issue of how the mechanism of energy transfer affects the irradiation-induced damage. An irradiation fluence of 5.5x10^15 ions/cm^2 with 40 keV Ar+ ions is established to be sufficient to amorphize a multi-walled nanotube. In the case of 350 keV He+ ion irradiation, where most of the energy transfer happens through inelastic collisions between the ion and the target electrons, an irradiation fluence of 1.4x10^17 ions/cm^2 heavily damages carbon nanotubes, whereas a larger irradiation fluence of 1.2x10^18 ions/cm^2 leaves a boron nitride nanotube in much better condition, indicating that carbon nanotubes might be more susceptible to damage via electronic excitations than their boron nitride counterparts. An elevated temperature was discovered to considerably reduce the accumulated damage created by energetic ions in both carbon and boron nitride nanotubes, attributed to enhanced defect mobility and efficient recombination at high temperatures. Additionally, cobalt nanorods encapsulated inside multi-walled carbon nanotubes were observed to transform into spherical nanoparticles after ion irradiation at an elevated temperature, which can be explained by the inverse Ostwald ripening effect. The simulation studies on ion irradiation of the hexagonal monolayers yielded quantitative estimates on types and abundances of defects produced within a large range of irradiation parameters. He, Ne, Ar, Kr, Xe, and Ga ions were considered in the simulations with kinetic energies ranging from 35 eV to 10 MeV, and the role of the angle of incidence of the ions was studied in detail. A stochastic model was developed for utilizing the large amount of data produced by the molecular dynamics simulations. It was discovered that a high degree of selectivity over the types and abundances of defects can be achieved by carefully selecting the irradiation parameters, which can be of great use when precise pattering of graphene or white graphene using focused ion beams is planned.