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Darbo tikslas - išnagrinėti dvimatės parabolinio tipo lygties su nelokaliąja integraline sąlyga sprendimą baigtinių skirtumų metodu. Išnagrinėtas kintamųjų krypčių metodo algoritmas tokiam uždaviniui spręsti. Išnagrinėtas dvimatės parabolinės lygties su keliomis nelokaliosiomis integralinėmis kraštinėmis sąlygomis sprendimas kintamųjų krypčių metodu. Uždavinio sprendinys randamas papildomai išsprendžiant neaukštos eilės algebrinę tiesinių lygčių sistemą, kuri sudaroma panaudojant nelokaliąsias integralines sąlygas. Išanalizuota skirtuminio operatoriaus su nelokaliosiomis sąlygomis spektro struktūra. Spektro struktūra išanalizuota tuo tikslu, kad galima būtų išnagrinėti dvimačio parabolinio uždavinio su viena nelokaliąja integraline sąlyga sprendžiamo kintamųjų krypčių ar lokaliai vienmačiu metodu, stabilumą. Nustatyta nelokaliosios sąlygos įtaka spektro struktūrai. Sudarytas elipsinio uždavinio su papildoma nelokaliąja sąlyga sprendimo algoritmas. / The aim of the work is to analyze the finite difference method for solving two-dimensional parabolic equation with an integral boundary condition. The alternating direction method for solving the problem of this kind is analyzed. This method is applied the alternating direction method for solving two-dimensional parabolic equation with two nonlocal integral condition is analyzed. Solution of the problem is found by resolving an additional linear system of equations of lower order . Structure of the spectrum for difference operator with nonlocal condition is analyzed. In order to analyze stability of two-dimensional parabolic equation with one integral condition the structure of spectrum is analyzed. Influence of nonlocal condition for structure of the spectrum is determined. The finite difference method for elliptic problem is constructed.

The aim of the work is to analyze the finite difference method for solving two-dimensional parabolic equation with an integral boundary condition. The alternating direction method for solving the problem of this kind is analyzed. This method is applied the alternating direction method for solving two-dimensional parabolic equation with two nonlocal integral condition is analyzed. Solution of the problem is found by resolving an additional linear system of equations of lower order . Structure of the spectrum for difference operator with nonlocal condition is analyzed. In order to analyze stability of two-dimensional parabolic equation with one integral condition the structure of spectrum is analyzed. Influence of nonlocal condition for structure of the spectrum is determined. The finite difference method for elliptic problem is constructed. / Darbo tikslas - išnagrinėti dvimatės parabolinio tipo lygties su nelokaliąja integraline sąlyga sprendimą baigtinių skirtumų metodu. Išnagrinėtas kintamųjų krypčių metodo algoritmas tokiam uždaviniui spręsti. Išnagrinėtas dvimatės parabolinės lygties su keliomis nelokaliosiomis integralinėmis kraštinėmis sąlygomis sprendimas kintamųjų krypčių metodu. Uždavinio sprendinys randamas papildomai išsprendžiant neaukštos eilės algebrinę tiesinių lygčių sistemą, kuri sudaroma panaudojant nelokaliąsias integralines sąlygas. Išanalizuota skirtuminio operatoriaus su nelokaliosiomis sąlygomis spektro struktūra. Spektro struktūra išanalizuota tuo tikslu, kad galima būtų išnagrinėti dvimačio parabolinio uždavinio su viena nelokaliąja integraline sąlyga sprendžiamo kintamųjų krypčių ar lokaliai vienmačiu metodu, stabilumą. Nustatyta nelokaliosios sąlygos įtaka spektro struktūrai. Sudarytas elipsinio uždavinio su papildoma nelokaliąja sąlyga sprendimo algoritmas.

The weather dynamics are significantly determined by the motion of the atmosphere and the ocean. This motion is often turbulent, characterized by fluctuations of the flow velocity over wide spatial and temporal scales. This fact, besides limited observability and inaccurate models, impedes the predictability of quantities such as the velocity of winds, which are relevant for the everyday life. One is always interested in improving such predictions - by employing better models or obtaining more information about the system. The Crooks fluctuation theorem is a relation from nonequilibrium thermodynamics, which has its typical applications in nanoscale systems. It quantifies the distribution of imposed work in a process, where the system is pushed out of thermal equilibrium. This distribution is broadened due to the fluctuations of the microscopic degrees of freedom in the system. The fluctuations of the velocity field in turbulent flow suggest the derivation of an analogy of Crooks' theorem for this macroscopic system. The knowledge about the validity of such a relation is additional information, which one in reverse could use to improve predictions about the system. In this thesis both issues are addressed: the derivation of the theorem, and the improvement of predictions. We illustrate the application of Crooks' theorem to hydrodynamic flow within a model of a two-dimensional inviscid and incompressible fluid field, when pushed out of dynamical equilibrium. The flow on a rectangular domain is approximated by the two-dimensional vorticity equation with spectral truncation. In this setting, the equilibrium statistics of the flow can be described through a canonical ensemble with two conserved quantities, kinetic energy and enstrophy. To perturb the system out of equilibrium, we change the shape of the domain according to a protocol, which changes the kinetic energy but leaves the enstrophy constant. This is interpreted as doing work to the system. Evolving along a forward and its corresponding backward process, we find that the distributions of the work performed in these processes satisfy the Crooks relation with parameters derived from the canonical ensembles. We address the issue of prediction in this thesis in a concrete setting: There are examples where the distributions of a variable in the forward and the backward process collapse into one, hence Crooks' theorem relates the distribution of one variable with itself. For a finite data set drawn from such a distribution, we are interested in an estimate of this variable to exceed a certain threshold. We demonstrate that, using the knowledge about Crooks' relation, forecast schemes can be proposed which improve compared to a pure frequency estimate on the data set. The findings are illustrated in three examples, studies of parameters such as exceedance threshold and data set size are presented.

The electrical and thermal conductance and the Seebeck coefficient are calculated for one-dimensional systems, and their behavior as a function of temperature and chemical potential is investigated. It is shown that the conductances are proportional to an average of the transmission probability around the Fermi level with the average taken for the thermal conductance being over a wider range. This has the effect of creating less well-defined plateaus for thermal-conductance quantization experiments. For weak non-linearities, the charge and entropy currents across a quantum point contact are expanded as a series in powers of the applied bias voltage and the temperature difference. After that, the expansions of the Seebeck voltage in temperature difference and the Peltier heat in current are obtained. Also, it is shown that the linear thermal conductance of a quantum point contact displays a half-plateau structure, almost flat regions appearing around half-integer multiples of the conductance quantum. This structure is investigated for the saddle-potential model.

An enantioselective heart-cut two-dimensional liquid chromatography-atmospheric pressure photoionization-tandem mass spectrometry method was developed for the analysis of 25 methylsulfonyl polychlorinated biphenyl metabolites in tissue extracts. Enantioseparation was achieved for 9 out of the 10 chiral analytes in less than 91 minutes, improving upon previous gas chromatography-based methods. Use of a pyrenyl-ethyl silica column in the first dimension enabled separation of all but two pairs of isobaric analytes. Limits of detection of 0.01 to 1.73 ng on-column were achieved. The precision and accuracy were within acceptable limits, but poor sensitivity was achieved for several meta-methylsulfonyl-substituted congeners. Despite this limitation, the method was successfully applied to the analysis of Greenland sledge dog (Canis familiaris) plasma and adipose tissue extracts. Concentration and enantiomer fraction data are presented. None of the target analytes were detected in Norwegian glaucous gull (Larus hyperboreus) plasma extracts.

In this thesis we used ESR to investigate magnetic properties of low D vandium and copper oxides in which small quantum spins are arranged in 1D chains and 2D layers. The thesis covers five different low dimensional spin systems. They turned out to be experimental reliazation of some of the most intersiting theoritical models in the field of quantum magnetism.

The use of short columns, higher carrier gas velocity and fast temperature programs in Comprehensive Two-Dimensional Gas Chromatography coupled to Time-of- Flight Mass Spectrometry (GC x GC/TOFMS) technique is expected to increase the speed of analysis up to several orders of magnitude when compared to conventional gas chromatography (GC) or gas chromatography/mass spectrometry (GC/MS). A systematic evaluation of the GC x GC/TOFMS configuration for high-speed applications has received little attention in the literature. The feasibility of High Speed Comprehensive Two-Dimensional Gas Chromatography coupled to Mass Spectrometry (High speed GC x GC/MS) for complex mixtures has been investigated in this thesis. A particular focus was placed on comparing conventional scanning quadrupole mass spectrometry (qMS) with a newly available non-scanning time-of-flight instruments (TOFMS). Experiments were carried out using GC/qMS, GC x GC/qMS, GC/TOFMS and GC x GC/TOFMS both in normal (slow) and fast temperature rates coupled with high frequency modulation in GC x GC. Initially a complex mixture consists of 24 semivolatile compounds was used as the analyte for the above purpose. In the initial experiments parameters like acquisition rate and duty cycle for qMS were determined to evaluate the effectiveness of the instrument for fast analysis. The practical duty cycle value obtained for the qMS was only about 18 % for single ion and one compound at a dwell time of 10 ms in SIM mode. In both high-speed GC/qMS and high-speed GC x GC/qMS techniques only about 40 % of the components in the complex mixture were found to be well separated. The acquisition rate of scanning instruments like qMS is incompatible for fast eluting peaks in high speed GC. TOFMS that has an acquisition rate of several hundred spectra per second offer the potential to define the fast GC peaks accurately. The high quality spectra from TOFMS also enable deconvolution of coeluting peaks in the complex mixtures. The advantage of the automated spectral deconvolution is demonstrated for the identification of the coeluting peaks in the complex mixtures. Coelution of peaks is also observed with highspeed GC/TOFMS technique. The high-speed GC x GC/TOFMS was also tested with two different analyte system ??? A pesticide mixture and platformate (an aromatic mixture) to evaluate the suitability for high-speed analysis of complex mixtures. A poor resolution was observed for the pesticide mixture in the two-dimensional plane and it appeared, as there was nearly no orthogonal separation in the second dimension. The platformate mixture displayed a better two-dimensional separation. Chromatographic peak resolution is not really a primary requirement for locating and identifying the coeluting compounds in high-speed GC x GC/TOFMS technique. However, it was observed that the high-speed GC x GC/TOFMS too faced problem to unscramble the mass spectra of those compounds with similar structure and sharing the same unique masses.

The fate and behaviour of hydrophobic organic compounds (e.g. pesticides) in soils are largely controlled by sorption processes. Recent findings suggest that the chemical properties of soil organic carbon (OC) significantly control the extent of sorption of such compounds in soil systems. However, currently there is no practical tool to integrate the effects of OC chemistry into sorption predictions. Therefore, the K [subscript]oc model, which relies on the soil OC content (foc), is used for predicting soil sorption coefficients (K[subscript]d) of pesticides. The K[subscript]oc model can be expressed as K[subscript]d = K[subscript]oc × foc, where K[subscript]oc is the OC-normalized sorption coefficient for the compound. Hence, there is a need for a prediction tool that can effectively capture the role of both the chemical structural variation of OC as well as foc in the prediction approach. Infrared (IR) spectroscopy offers a potential alternative to the K[subscript]oc approach because IR spectra contain information on the amount and nature of both organic and mineral soil components. The potential of mid-infrared (MIR) spectroscopy for predicting K[subscript]d values of a moderately hydrophobic pesticide, diuron, was investigated. A calibration set of 101 surface soils from South Australia was characterized for reference sorption data (K[subscript]d and K[subscript]oc) and foc as well as IR spectra. Partial least squares (PLS) regression was employed to harness the apparent complexity of IR spectra by reducing the dimensionality of the data. The MIR-PLS model was developed and validated by dividing the initial data set into corresponding calibration and validation sets. The developed model showed promising performance in predicting K[subscript]d values for diuron and proved to be a more efficacious than the K[subscript]oc model. The significant statistical superiority of the MIR-PLS model over the K[subscript]oc model was caused by some calcareous soils which were outliers for the K[subscript]oc model. Apart from these samples, the performance of the two compared models was essentially similar. The existence of carbonate peaks in the MIR-PLS loadings of the MIR based model suggested that carbonate minerals may interfere or affect the sorption. This requires further investigation. Some other concurrent studies suggested excellent quality of prediction of soil properties by NIR spectroscopy when applied to homogenous samples. Next, therefore, the performance of visible near-infrared (VNIR) and MIR spectroscopy was thoroughly compared for predicting both foc and diuron K[subscript]d values in soils. Some eleven calcareous soils were added to the initial calibration set for an attempt to further investigate the effect of carbonate minerals on sorption. MIR spectroscopy was clearly a more accurate predictor of foc and K[subscript]d in soils than VNIR spectroscopy. Close inspection of spectra showed that MIR spectra contain more relevant and straightforward information regarding the chemistry of OC and minerals than VNIR and thus useful in modelling sorption and OC content. Moreover, MIR spectroscopy provided a better (though still not great) estimation of sorption in calcareous soils than either VNIR spectroscopy or the K[subscript]oc model. Separate research is recommended to fully explore the unusual sorption behaviour of diuron in calcareous soils. In the last experiment, two dimensional (2D) nuclear magnetic resonance/infrared heterospectral correlation analyses revealed that MIR spectra contain specific and clear signals related to most of the major NMR-derived carbon types whereas NIR spectra contain only a few broad and overlapped peaks weakly associated with aliphatic carbons. 2D heterospectral correlation analysis facilitated accurate band assignments in the MIR and NIR spectra to the NMR-derived carbon types in isolated SOM. In conclusion, the greatest advantage of the MIR-PLS model is the direct estimation of Kd based on integrated properties of organic and mineral components. In addition, MIR spectroscopy is being used increasingly in predicting various soil properties including foc, and therefore, its simultaneous use for K[subscript]d estimation is a resource-effective and attractive practice. Moreover, it has the advantage of being fast and inexpensive with a high repeatability, and unlike the K[subscript]oc approach, MIR-PLS shows a better potential for extrapolating applications in data-poor regions. Where available, MIR spectroscopy is highly recommended over NIR spectroscopy. 2D correlation spectroscopy showed promising potential for providing rich insight and clarification into the thorough study of soil IR spectra. / http://proxy.library.adelaide.edu.au/login?url= http://library.adelaide.edu.au/cgi-bin/Pwebrecon.cgi?BBID=1415416 / Thesis (Ph.D.) - University of Adelaide, School of Earth and Environmental Sciences, 2009

The fate and behaviour of hydrophobic organic compounds (e.g. pesticides) in soils are largely controlled by sorption processes. Recent findings suggest that the chemical properties of soil organic carbon (OC) significantly control the extent of sorption of such compounds in soil systems. However, currently there is no practical tool to integrate the effects of OC chemistry into sorption predictions. Therefore, the K [subscript]oc model, which relies on the soil OC content (foc), is used for predicting soil sorption coefficients (K[subscript]d) of pesticides. The K[subscript]oc model can be expressed as K[subscript]d = K[subscript]oc × foc, where K[subscript]oc is the OC-normalized sorption coefficient for the compound. Hence, there is a need for a prediction tool that can effectively capture the role of both the chemical structural variation of OC as well as foc in the prediction approach. Infrared (IR) spectroscopy offers a potential alternative to the K[subscript]oc approach because IR spectra contain information on the amount and nature of both organic and mineral soil components. The potential of mid-infrared (MIR) spectroscopy for predicting K[subscript]d values of a moderately hydrophobic pesticide, diuron, was investigated. A calibration set of 101 surface soils from South Australia was characterized for reference sorption data (K[subscript]d and K[subscript]oc) and foc as well as IR spectra. Partial least squares (PLS) regression was employed to harness the apparent complexity of IR spectra by reducing the dimensionality of the data. The MIR-PLS model was developed and validated by dividing the initial data set into corresponding calibration and validation sets. The developed model showed promising performance in predicting K[subscript]d values for diuron and proved to be a more efficacious than the K[subscript]oc model. The significant statistical superiority of the MIR-PLS model over the K[subscript]oc model was caused by some calcareous soils which were outliers for the K[subscript]oc model. Apart from these samples, the performance of the two compared models was essentially similar. The existence of carbonate peaks in the MIR-PLS loadings of the MIR based model suggested that carbonate minerals may interfere or affect the sorption. This requires further investigation. Some other concurrent studies suggested excellent quality of prediction of soil properties by NIR spectroscopy when applied to homogenous samples. Next, therefore, the performance of visible near-infrared (VNIR) and MIR spectroscopy was thoroughly compared for predicting both foc and diuron K[subscript]d values in soils. Some eleven calcareous soils were added to the initial calibration set for an attempt to further investigate the effect of carbonate minerals on sorption. MIR spectroscopy was clearly a more accurate predictor of foc and K[subscript]d in soils than VNIR spectroscopy. Close inspection of spectra showed that MIR spectra contain more relevant and straightforward information regarding the chemistry of OC and minerals than VNIR and thus useful in modelling sorption and OC content. Moreover, MIR spectroscopy provided a better (though still not great) estimation of sorption in calcareous soils than either VNIR spectroscopy or the K[subscript]oc model. Separate research is recommended to fully explore the unusual sorption behaviour of diuron in calcareous soils. In the last experiment, two dimensional (2D) nuclear magnetic resonance/infrared heterospectral correlation analyses revealed that MIR spectra contain specific and clear signals related to most of the major NMR-derived carbon types whereas NIR spectra contain only a few broad and overlapped peaks weakly associated with aliphatic carbons. 2D heterospectral correlation analysis facilitated accurate band assignments in the MIR and NIR spectra to the NMR-derived carbon types in isolated SOM. In conclusion, the greatest advantage of the MIR-PLS model is the direct estimation of Kd based on integrated properties of organic and mineral components. In addition, MIR spectroscopy is being used increasingly in predicting various soil properties including foc, and therefore, its simultaneous use for K[subscript]d estimation is a resource-effective and attractive practice. Moreover, it has the advantage of being fast and inexpensive with a high repeatability, and unlike the K[subscript]oc approach, MIR-PLS shows a better potential for extrapolating applications in data-poor regions. Where available, MIR spectroscopy is highly recommended over NIR spectroscopy. 2D correlation spectroscopy showed promising potential for providing rich insight and clarification into the thorough study of soil IR spectra. / http://proxy.library.adelaide.edu.au/login?url= http://library.adelaide.edu.au/cgi-bin/Pwebrecon.cgi?BBID=1415416 / Thesis (Ph.D.) - University of Adelaide, School of Earth and Environmental Sciences, 2009