This study gives our calculations for the temperature-pressure and temperature-concentration phase diagrams using the mean field models applied to ammonium halides (NH4Cl, ND4Cl), ammonium sulfate ((NH4)2SO4/H2O), lithium potassium rubidium sulfate (LiK1-xRbxSO4), potassium pyrosulfate-potassium hydrogensulfate (K2S2O7-KHSO4), cholestanyl myristate-cholesteryl myristate (CnM-CrM), cholestanyl myristate-cholesteryl oleate (CnM-CO), benzene (C6H6) and ice. The phase line equations are derived from the free energies expanded in terms of the order parameters and they are fitted to the experimental data. Some thermodynamic quantities are calculated close to phase transitions in these crystalline systems. We also calculate the specific heat CV using the Raman frequency shifts for NH4Br on the basis of an Ising model close to the lambda-phase transition. A linear relationship is obtained between the specific heat CP and the frequency shifts (1/v)(dv/dT)P near the lambda-point in NH4Br.

Wide band gap metal oxides have recently become one of the most investigated materials in surface science. Among these metal oxides especially TiO2 attracts great interest, because of its wide range applications, low cost, biocompatibility and ease of analysis by all experimental techniques. The usage of TiO2 as a component in solar cell technology is one of the most investigated applications of TiO2 . The wide band gap of TiO2 renders it inecient for isolated use in solar cells. TiO2 surface are therefore coated with a dye in order to increase eciency. This type of solar cells are called dye sensitized solar cells . The eciency of dye sensitized solar cells is directly related with the absorbed light portion of the entire solar spectrum by the dye molecule. Inspite of the early dyes, recent dye molcules, which are called wider wavelength response dye molecules, can absorb a larger portion of entire solar spectrum. Thus, the eciency of dye sensitized solar cells is increased by a considerably amount. In this thesis the electronic structure of organic rings, which are the fundamental components of the dye molecules, adsorbed on anatase (001) surface is analyzed using density functionaltheory. The main goal is to obtain a trend in the electronic structure of the system as a function of increasing ring number. Electronic structure analysis is conducted through band structure and density of states calculations. Results are presented and discussed in the framework of dye sensitized solar cells theory.

Time Resolved OSL (TR-OSL) is a technique to record the luminescence decay curve data after a brief stimulation pulse and can possibly be used for the separation of luminescence signals from quartz and feldspars. In this study luminescence emission from quartz and feldspar samples was investigated. TR-OSL signals of these samples were studied for the variations with preheating and annealing temperature, stimulation pulse width and total stimulation time, optical bleaching, radiation dose and measurement temperature. TR-OSL decay lifetime of quartz samples was found as ~40 &micro / s. Na-feldspar and K-feldspar luminescence signals were deconvoluted using a linear sum of three exponential decays with lifetimes about 45 &micro / s, 8 &micro / s and 1 &micro / s and about 35 &micro / s, 7 &micro / s and 0.6 &micro / s, respectively. Since feldspars signals have a component with lifetime similar to that of quartz (~40 &micro / s), luminescence signal separation with TR-OSL seems to be not straightforward.

The standard Kaluza-Klein theory is reviewed and its basic equations are rewritten in an anholonomic basis. A five dimensional Yang-Mills type quadratic and cubic curvature gravity model is introduced. By employing the Palatini variational principle, the field equations and the stress-energy tensors of these models are presented. Unification of gravity with electromagnetism is achieved through the Kaluza-Klein reduction mechanism. Reduced curvature invariants,field equations and stress-energy tensors in four dimensional space-time are obtained. The structure of interactions among the gravitational, electromagnetic and massless scalar fields are demonstrated in detail. It is shown that in addition to a set of generalized Maxwell and Yang-Mills type gravity equations the Lorentz force also emerges from this theory. Solutions of the standard Kaluza-Klein theory are explicitly demonstrated to be intrinsically contained in the quadratic model.

In this work, Schr&ouml / dinger and Dirac equations will be examined in geometries that confine the particles to hypersurfaces. For this purpose, two methods will be considered. The first method is the thin layer method which relies on explicit use of geometrical relations and the squeezing of a certain coordinate of space (or spacetime). The second is Dirac&rsquo / s quantization procedure involving the modification of canonical quantization making use of the geometrical constraints. For the Dirac equation, only the first method will be considered. Lastly, the results of the two methods will be compared and some notes on the differences between the results will be included.

Energy need in transportation and industry is mainly met by fossil fuels. This causes consumption of resources and some environmental problems. Diesel and gasoline engines are developed to consume fuel efficiently in vehicles. Since these engines work in a low fuel to air ratio, it becomes difficult to reduce nitrogen oxide emission. For this reason NO x storage/reduction (NSR) catalysts have been developed. While engines are operating under lean conditions alkaline or alkaline-earth component of NSR catalysts capture nitrogen oxides and during fuel rich period stored nitrates are reduced to nitrogen and oxygen gases. To develop this technology, different system parameters, for example system components and reaction environments have been widely investigated experimentally. To supplement the experimental findings, binding energies and structural properties of NO x on different catalyst components have been investigated theoretically. It has been experimentally observed that adding TiO2 to other conventional support materials increases resistance against sulfur poisoning, which is one of the main problems concerning NSR catalysts. For this reason, in this thesis (001) and (101) anatase surfaces have been investigated. Moreover, the effects of barium oxide units and layers on the electronic properties of the (001) anatase surface have been studied. To observe the effects of TiO2 as a support component, interactions of NO2 and SO2 on the unsupported and anatase supported (100) BaO surfaces have been compared. A clear increase in sulfur resistance has been observed in the presence of TiO2 in the catalyst under certain conditions.

In this work, two particular orthogonal and conformal decompositions of the 3+1 dimensional Einstein equation and Arnowitt-Deser-Misner (ADM) formalism for general relativity are obtained. In order to do these, the 3+1 foliation of the four-dimensional spacetime, the fundamental conformal transformations and the Hamiltonian form of general relativity that leads to the ADM formalism, de

The specific heat Cp has been showed at various temperatures in the literature, which shows a sharp increase labeled as the lambda-transition at the critical temperature. This transition has been observed previously among the phases of solid-nematic-isotropic liquid in p-azoxyanisole (PAA) and anisaldazine (AAD), and among the phases of solid-smectic-cholesteric-isotropic liquid in cholesteryl myristate (CM). In this thesis work, we analyze the experimental data for the temperature dependence of Cp and the thermal expansion alpha_p and also pressure dependence of alpha_p by a power-law formula. From the analysis of pressure dependence of alpha_p, we calculate the temperature dependencies of specific heat Cp and of the isothermal compressibility kappa_T for the phase transitions considered in PAA, AAD and CM. Our calculations for the temperature dependence of the p and kappa_T can be compared with the experimental data when available in the literature. Polarization, tilt angle and the dielectric constant have been reported in the literature at various temperatures close to the solid-smectic C*-smectic A-isotropic liquid transition in the ferroelectric liquid crystals of A7 and C7. The mean field model with the free energy expanded in terms of the order parameters (polarization and tilt angle) has been reported in the literature previously. In this thesis work, we apply the mean field model first time by fitting the expressions derived for the temperature dependence of the polarization, tilt angle and the dielectric constant to the experimental data for A7 and C7 from the literature. Since the mean field model studied here describes adequately the observed behaviour of A7 and C7, the expressions for the temperature dependence of the polarization, tilt angle and the dielectric constant which we derive, can also be applied to some other ferroelectric liquid crystals to explain their observed behaviour.

In this thesis, conformal transformations in d and two dimensions and the results of conformal symmetry in classical and quantum field theories are reviewed. After investigating the conformal group and its algebra, various aspects of conformal invariance in field theories, like conserved charges, correlation functions and the Ward identities are discussed. The central charge and the Virasoro algebra are briefly touched upon.

In this study we investigate the properties of trapped atoms subjected to rapid rotations. The study is divided into two distinct parts, one for fermions, another for bosons. In the case of the degenerate Fermi gas we explore the density structure of non-interacting cold atoms when they are rotated rapidly. On the other hand, for rapidly rotating two component Bose condensate, we search for new lattice structures in the presence of contact and dipolar interactions. First, the density structure of Fermi gases in a rotating trap is investigated. We focus on the anisotropic trap case, in which two distinct regimes, two and one dimensional regimes, depending on rotation frequency and anisotropy are observed. Two regimes can be illustrated by a simple description of maximum number of states between two Landau levels, which is strongly related to the dimensionality of the system. The regimes are separated from each other by a minimum point in this description. For small anisotropy values the density profiles show a step structure where each step is demonstrated by an elliptical plateau. Each plateau represents a Landau level with a constant density. The local density approximation describes the two dimensional regime with a perfect similarity in the structure of fermion density. The case for one dimensional regime is a little different from the two dimensional case. For large anisotropy values the Friedel oscillation is the dominant aspect of the density profiles. The density profiles show gaussian structure along the direction of strong trapping, and a semicircular form with prominent oscillations along the weak confining direction. Again, the system is nicely described by local density approximation in this regime. A smooth crossover between two regimes is observed, with a switching from a step structure profile to a soft edge transition with Friedel oscillations. At finite temperatures, the step structures are smeared out in two dimension. In one dimensional regime the Friedel oscillations are cleaned as soon as the temperature is turned on. The second part of the study is devoted to the investigation of different lattice structures in two component Bose condensates subjected to very fast rotation, this time in the presence of interactions. We explore the existence of new vortex lattice structures for dipolar two component condensates scanning a wide range of interaction strengths. We introduce a phase diagram as a function of intra and inter-component interactions showing different type of vortex lattice structures. New types of lattice structures, overlapped square and overlapped rectangular, emerge as a result of dipolar interactions and s-wave interaction for a two component condensate. The region where the attractive inter-component interactions dominate the repulsive interactions, the overlapped lattices are formed. The intra-component interactions, which defines the behavior of each component inside, result in different type of lattices by changing the strength of interactions. Two different limits of phase diagram reproduce the results of ordinary two component and dipolar one component Bose condensates. The results of calculation are in agreement with the results of previous studies for two regimes.