<p>The overall objective of the current study is to develop a quantitative understanding of the effects of spatial variability in physical and geochemical properties of crystalline rock on the migration of radionuclides along a single fracture in bedrock. A stochastic model was developed to describe the transport of solutes in fractured rock. The model describes the migration of radionuclides along a one-dimensional path and includes the transversal diffusion into the rock matrix and sorption kinetics. By using a Lagrangian method of description we can extend the model to the description of a two-dimensional transport problem in single fractures. </p><p>This study presents the first analysis of the impact of heterogeneous mass transfer on the transport of radionuclides in rock fractures, where most of the relevant rock properties such as aperture, porosity, effective diffusivity, sorption capacity and maximum diffusion depth are defined as being spatially random. The stochastic analysis performed here reflects the uncertainty in our knowledge of the properties associated with a discrete sampling technique in site investigations.</p><p>Geostatistics of the main parameters was determined experimentally on a large number of rock samples taken from the Swedish crystalline basement. The knowledge of the covariance functions of the main rock properties is then used as a basis for a stochastic analysis. By combining the small perturbation approach with the spectral method the problem could be solved in terms of closed form solutions for the central temporal moments of the residence time probability density function. </p><p>In order to be able to distinguish between the effects of various mechanisms from the effects of heterogeneity on the migration of radionuclides, it was necessary to perform independent studies of the effect of the variation of the dispersion coefficient on the aspect ratio of a rectangular flow section and the effect of adsorption kinetics on the migration. </p><p>Finally, the effect of the heterogeneous rock properties on the solute transport observed in a limited number of migration experiments corresponds fairly well to the theoretical effect expected on the basis of the experimentally determined auto-covariance functions. </p>

In time series analysis, most of the models are based on the assumption of covariance stationarity. However, many time series in the applied sciences show a time-varying second-order structure. That is, variance and covariance, or equivalently the spectral structure, are likely to change over time. Examples may be found in a growing number of fields, such as biomedical time series analysis, geophysics, telecommunications, or financial data analysis, to name but a few. In this thesis, we are concerned with the modelling of such nonstationary time series, and with the subsequent questions of how to estimate their second-order structure and how to forecast these processes. We focus on univariate, discrete-time processes with zero-mean arising, for example, when the global trend has been removed from the data. The first chapter presents a simple model for nonstationarity, where only the variance is time-varying. This model follows the approach of "local stationarity" introduced by [1]. We show that our model satisfactorily explains the nonstationary behaviour of several economic data sets, among which are the U.S. stock returns and exchange rates. This chapter is based on [5]. In the second chapter, we study more complex models, where not only the variance is evolutionary. A typical example of these models is given by time-varying ARMA(p,q) processes, which are ARMA(p,q) with time-varying coefficients. Our aim is to fit such semiparametric models to some nonstationary data. Our data-driven estimator is constructed from a minimisation of a penalised contrast function, where the contrast function is an approximation to the Gaussian likelihood of the model. The theoretical performance of the estimator is analysed via non asymptotic risk bounds for the quadratic risk. In our results, we do not assume that the observed data follow the semiparamatric structure, that is our results hold in the misspecified case. The third chapter introduces a fully nonparametric model for local nonstationarity. This model is a wavelet-based model of local stationarity which enlarges the class of models defined by Nason et al. [3]. A notion of time-varying "wavelet spectrum' is uniquely defined as a wavelet-type transform of the autocovariance function with respect to so-called "autocorrelation wavelets'. This leads to a natural representation of the autocovariance which is localised on scales. One particularly interesting subcase arises when this representation is sparse, meaning that the nonstationary autocovariance may be decomposed in the autocorrelation wavelet basis using few coefficients. We present a new test of sparsity for the wavelet spectrum in Chapter 4. It is based on a non-asymptotic result on the deviations of a functional of a periodogram. In this chapter, we also present another application of this result given by the pointwise adaptive estimation of the wavelet spectrum. Chapters 3 and 4 are based on [6] Computational aspects of the test of sparsity and of the pointwise adaptive estimator are considered in Chapter 5. We give a description of a full algorithm, and an application in biostatistics. In this chapter, we also derive a new test of covariance stationarity, applied to another case study in biostatistics. This chapter is based on [7]. Finally, Chapter 6 address the problem how to forecast the general nonstationary process introduced in Chapter 3. We present a new predictor and derive the prediction equations as a generalisation of the Yule-Walker equations. We propose an automatic computational procedure for choosing the parameters of the forecasting algorithm. Then we apply the prediction algorithm to a meteorological data set. This chapter is based on [2,4]. References [1] Dahlhaus, R. (1997). Fitting time series models to nonstationary processes. Ann. Statist., 25, 1-37, 1997. [2] Fryzlewicz, P., Van Bellegem, S. and von Sachs, R. (2003). Forecasting non-stationary time series by wavelet process modelling. Annals of the Institute of Statistical Mathematics. 55, 737-764. [3] Nason, G.P., von Sachs, R. and Kroisandt, G. (2000). Wavelet processes and adaptive estimation of evolutionary wavelet spectra. Journal of the Royal Statistical Society Series B. 62, 271-292. [4] Van Bellegem, S., Fryzlewicz, P. and von Sachs, R. (2003). A wavelet-based model for forecasting non-stationary processes. In J-P. Gazeau, R. Kerner, J-P. Antoine, S. Metens and J-Y. Thibon (Eds.). GROUP 24: Physical and Mathematical Aspects of Symmetries. Bristol: IOP Publishing (in press). [5] Van Bellegem, S. and von Sachs, R. (2003). Forecasting economic time series with unconditional time-varying variance. International Journal of Forecasting (in press). [6] Van Bellegem, S. and von Sachs, R. (2003). Locally adaptive estimation of sparse, evolutionary wavelet spectra (submitted). [7] Van Bellegem, S. and von Sachs, R. (2003). On adaptive estimation for locally stationary wavelet processes and its applications (submitted).

The overall objective of the current study is to develop a quantitative understanding of the effects of spatial variability in physical and geochemical properties of crystalline rock on the migration of radionuclides along a single fracture in bedrock. A stochastic model was developed to describe the transport of solutes in fractured rock. The model describes the migration of radionuclides along a one-dimensional path and includes the transversal diffusion into the rock matrix and sorption kinetics. By using a Lagrangian method of description we can extend the model to the description of a two-dimensional transport problem in single fractures. This study presents the first analysis of the impact of heterogeneous mass transfer on the transport of radionuclides in rock fractures, where most of the relevant rock properties such as aperture, porosity, effective diffusivity, sorption capacity and maximum diffusion depth are defined as being spatially random. The stochastic analysis performed here reflects the uncertainty in our knowledge of the properties associated with a discrete sampling technique in site investigations. Geostatistics of the main parameters was determined experimentally on a large number of rock samples taken from the Swedish crystalline basement. The knowledge of the covariance functions of the main rock properties is then used as a basis for a stochastic analysis. By combining the small perturbation approach with the spectral method the problem could be solved in terms of closed form solutions for the central temporal moments of the residence time probability density function. In order to be able to distinguish between the effects of various mechanisms from the effects of heterogeneity on the migration of radionuclides, it was necessary to perform independent studies of the effect of the variation of the dispersion coefficient on the aspect ratio of a rectangular flow section and the effect of adsorption kinetics on the migration. Finally, the effect of the heterogeneous rock properties on the solute transport observed in a limited number of migration experiments corresponds fairly well to the theoretical effect expected on the basis of the experimentally determined auto-covariance functions.

Heteroscedasticity (or time-dependent volatility) in economic and financial time series has been recognized for decades. Still, heteroscedasticity is surprisingly often neglected by practitioners and researchers. This may lead to inefficient procedures. Much of the work in this thesis is about finding more effective ways to deal with heteroscedasticity in economic and financial data. Paper I suggest a filter that, unlike the Box-Cox transformation, does not assume that the heteroscedasticity is a power of the expected level of the series. This is achieved by dividing the time series by a moving average of its standard deviations smoothed by a Hodrick-Prescott filter. It is shown that the filter does not colour white noise. An appropriate removal of heteroscedasticity allows more effective analyses of heteroscedastic time series. A few examples are presented in Paper II, III and IV of this thesis. Removing the heteroscedasticity using the proposed filter enables efficient estimation of the underlying probability distribution of economic growth. It is shown that the mixed Normal - Asymmetric Laplace (NAL) distributional fit is superior to the alternatives. This distribution represents a Schumpeterian model of growth, the driving mechanism of which is Poisson (Aghion and Howitt, 1992) distributed innovations. This distribution is flexible and has not been used before in this context. Another way of circumventing strong heteroscedasticity in the Dow Jones stock index is to divide the data into volatility groups using the procedure described in Paper III. For each such group, the most accurate probability distribution is searched for and is used in density forecasting. Interestingly, the NAL distribution fits best also here. This could hint at a new analogy between the financial sphere and the real economy, further investigated in Paper IV. These series are typically heteroscedastic, making standard detrending procedures, such as Hodrick-Prescott or Baxter-King, inadequate. Prior to this comovement study, the univariate and bivariate frequency domain results from these filters are compared to the filter proposed in Paper I. The effect of often neglected heteroscedasticity may thus be studied.

Gravity is the main driving force for groundwater flow, and both landscape topography and geology distribute the effects of gravity on groundwater flow.  The groundwater table defines the distribution of the potential energy of the water. In humid regions where the bedrock permeability is relatively low and the soil depth is sufficiently shallow, the groundwater table closely follows the landscape topography and, thus, the topography controls the groundwater circulation in these regions. In this thesis, I investigate multi-scale topography-controlled groundwater flow, with the goal of systematizing the spatial distribution of groundwater flow and assessing geological parameters of importance for groundwater circulation.  Both exact solutions and numerical models are utilized for analyzing topography-controlled groundwater flow. The more complex numerical models are used to explore the importance of various simplifications of the exact solutions. The exact solutions are based on spectral representation of the topography and superpositioning of unit solutions to the groundwater flow field. This approach is an efficient way to analyze multi-scaled topography-controlled groundwater flow because the impact of individual topographic scales on the groundwater flow can be analyzed separately.  The results presented here indicate that topography is fractal and affects groundwater flow cells at wide range of spatial scales. We show that the fractal nature of the land surface produces fractal distributions of the subsurface flow patterns. This underlying similarity in hydrological processes also yields a single scale-independent distribution of subsurface water residence times which have been found in distributions of solute efflux from watersheds. Geological trends modify the topographic control of the groundwater circulation pattern and this thesis presents exact solutions explaining the impact of geological layering, depth-decaying and anisotropic hydraulic conductivity on the groundwater flow field. For instance, layers of Quaternary deposits and decaying permeability with depth both increase the importance of smaller topographic scales and creates groundwater flow fields where a larger portion of the water occupies smaller and shallower circulation cells, in comparison to homogeneous systems. / Gravitationen är den mest betydelsefulla drivkraften för grundvattenströmning. Topografin och geologin fördelar vattnets potentiella energi i landskapet. Grundvattenytans läge definierar vattnets potentiella energi, vilket är ett randvillkor för grundvattnets strömningsfält. I humida områden med en relativt tät berggrund och tillräckligt tunna jordlager, följer grundvattenytan landskapets topografi. Därav följer att grundvattenströmningen är styrd av topografin i dessa områden. I denna avhandling belyser jag den flerskaliga topografistyrda grundvattenströmningen. Min målsättning har varit att kvantitativt bestämma grundvattenströmningens rumsliga fördelning samt att undersöka hur olika geologiska parametrar påverkar grundvattencirkulationen. Jag har använt såväl numeriska modeller som analytiska lösningar, för att undersöka hur topografin styr grundvattenströmningen. De numeriska modellerna är mer komplexa än de analytiska lösningarna och kan därför användas för att undersöka betydelserna av olika förenklingar som finns i de analytiska lösningarna. De analytiska lösningarna är baserade på spektralanalys av topografin, samt superponering av enhetslösningar, där varje enhetslösning beskriver hur en specifik topografisk skala påverkar grundvattnets strömningsfält. Detta är ett effektivt tillvägagångssätt för att undersöka flerskaliga effekter av topografin, eftersom påverkan av varje enskild topografisk skala kan studeras separat. Resultaten som presenteras indikerar att topografin är fraktal och att den ger upphov till cirkulationsceller av varierande storlek som även dessa är av en fraktal natur. Denna grundläggande fördelning i grundvattnets strömningsfält ger upphov till att grundvattnets uppehållstid i marken följer ett självlikformigt mönster och kan förklara uppmätta tidsvariationer av lösta ämnens koncentrationer i vattendrag efter regn. Geologiska trender påverkar hur grundvattenströmningen styrs av topografin. De exakta lösningar som presenteras här, beskriver hur geologiska lager samt djupavtagande och anisotropisk hydraulisk konduktivitet påvekar grundvattnets strömning. Exempelvis är betydelsen av mindre topografiska skalor viktigare i områden med kvartära avlagringar och en berggrund med djupavtagande konduktivitet, än i områden med homogen bergrund utan kvartära avlagringar. Dessutom är en större andel strömmande vatten belägen närmare markytan i de förstnämnda områdena. / QC 20100802

In this thesis, RXTE timing analysis of Galactic Microquasars GRO J1655-40 and GRS 1915+105, the Chandra and RXTE joint spectral analysis of GRS 1915+105 are presented. We have investigated quasi periodic oscillations (QPOs) in the black hole binaries GRO J1655-40 and GRS 1915+105 observed in 99 and 122 observations made by the Proportional Counter Array (PCA) on board Rossi X-Ray Timing Explorer (RXTE) in both low energy band (2-12 keV) and high energy band (13-27 keV), respectively. Four different X-ray states are seen in the combined characteristics of power spectra, light curves extracted by using All Sky Monitor (ASM) and spectra during 1996 and 2005. Timing analysis of RXTE observations of both of two black hole binaries GRO J1655-40 and GRS 1915+105 displays twin high frequency quasi periodic oscillations (QPOs) which are sometimes simultaneous in high energy band. It is also shown that the time averaged 30 ksec Chandra grating spectrum analysis and RXTE spectrum analysis of recent observation of GRS 1915+105 in the very high state are consistent with the parameters which were mentioned before. We briefly discussed our results and the models on black hole spin and mass.

In this thesis, we present the spectral and timing variabilities of anomalous X-ray pulsar 1E 2259+586 observed with European Photon Imaging PN Camera (EPIC PN) on board X-ray Multi Mirror Mission (XMM), Proportional Counter Array (PCA) on board Rossi X-ray Timing Explorer (RXTE) and Advanced CCD Imaging Spectrometer (ACIS) on board Chandra X-ray Observatory. We presented the results of spectral analysis of 2000 January 11 ACIS observation. Pulse phase spectroscopy was performed on two XMM observations before and after the outburst. Pulse profiles of two XMM observations before the outburst and three XMM observations after the outburst were studied. Results are consistent with the those presented by Patel et al. (2001) and Woods et al. (2004). We searched for the spectral variations versus spin rate during the outburst. Long-term spectral, frequency and spin-down rate variations are presented between 1996 and 2006 including 98 RXTE and 4 XMM observations. However, except outburst region (Woods et al. 2004) no significant spectral and spin rate variabilities were seen. Around the outburst region we confirmed the spectral hardening with increasing spin rate and flux.

The laser beam interaction with matter and the plasma generation have been studied for many years. In some applications what is really important is to understand the composition and the temporal evolution of the species in the interested medium. In this thesis, time resolved optical spectroscopy was employed to understand the evolution of the plasma which is produced by interaction of Infrared (1.064 &micro / m) laser beam with air. In this thesis, a new technique is suggested to analyze the time evolution of laser induced breakdown spectroscopy. The suggested method and the instrumentation of the setup are tested with a single gas (He). After the tests, we analyzed time sequence spectra of Laser Induced Air Breakdown. The suggested method is based on triggering the laser and the spectrometer at different time and applying the spectrometer trigger time by adding the time delay (&amp / #916 / t) between them by using the pulse generator. The results show that the decay rates are slowing down microseconds after the excitation of the plasma. The results of the time-resolved measurements of the line spectra show that different component of the air has different decay rate, and lifetime. The lifetime of helium is 20 &micro / s, and the decay start 5 &micro / s after the initiation of plasma. Air has 12 &micro / s lifetime, and the decay start 3 &micro / s after the initiation of the plasma. Also, the decay rate and the lifetime depend on the state. We also calculate Doppler velocity for different component and different emission states. Doppler velocities show that the component which has great mass has small velocity, the component which has small mass has high velocity.

Optical properties of Tl4In3GaSe8, Tl4InGa3Se8, Tl4In3GaS8, Tl2InGaS4 and Tl4InGa3S8 chain and layered crystals were studied by means of photoluminescence (PL) and transmission-reflection experiments. Several emission bands were observed in the PL spectra within the 475-800 nm wavelength region. The results of the temperature- and excitation intensity-dependent PL measurements in 15-300 K and 0.13&times / 10-3-110.34 W cm-2 ranges, respectively, suggested that the observed bands were originated from the recombination of electrons with the holes by realization of donor-acceptor or free-to-bound type transitions. Transmission-reflection measurements in the wavelength range of 400-1100 nm revealed the values of indirect and direct band gap energies of the crystals studied. By the temperature-dependent transmission measurements in 10-300 K range, the rates of change of the indirect band gap of the samples with temperature were found to be negative. The oscillator and dispersion energies, and zero-frequency refractive indices were determined by the analysis of the refractive index dispersion data using the Wemple&ndash / DiDomenico single-effective-oscillator model. Furthermore, the structural parameters of all crystals were defined by the analysis of X-ray powder diffraction data. The determination of the compositional parameters of the studied crystals was done by energy dispersive spectral analysis experiments.

Trapping centres in as-grown TlInS2 layered single crystals have been studied by using a thermally stimulated current (TSC) technique. TSC measurements have been performed in the temperature range of 10-300 K with various heating rates. Experimental evidence has been found for the presence of five trapping centres with activation energies 12, 14, 400, 570 and 650 meV. Their capture cross-sections and concentrations were also determined. It is concluded that in these centres retrapping is negligible as confirmed by the good agreement between the experimental results and the theoretical predictions of the model that assumes slow retrapping. An exponential distribution of traps was revealed from the analysis of the TSC data obtained at different light excitation temperatures. The transmission and reflection spectra of TlInS2 crystals were measured over the spectral region of 400-1100 nm to determine the absorption coefficient and refractive index. The analysis of the room temperature absorption data revealed the coexistence of the indirect and direct transitions. The absorption edge was observed to shift toward the lower energy values as temperature increases from 10 to 300 K. The oscillator and the dispersion energies, and the zero-frequency refractive index were also reported. Furthermore, the chemical composition of TlInS2 crystals was determined from energy dispersive spectroscopic analysis. The parameters of monoclinic unit cell were found by studying the x-ray powder diffraction.