A novel approach to the problem of describing interacting magnetic ions has been put forward by Stevens. The work contained herein offers the first major test of the new formalism; applied specifically to binuclear systems in which magnetic Cr3+ ions occur in discrete pairs of D3h symmetry. Each interacting pair is regarded as a unit; wavefunctions suitable for describing the pair are constructed in determinantal form. The wavefunctions of D3h symmetry are used to define the unperturbed Hamiltonian. An effective Hamiltonian is then used to obtain the energy levels in a restricted energy range. (The region of the 2TI levels of the single Cr3+ ion). A set of selection rules is derived. With direct comparison with experimental results the success of theoretical predictions is estimated. Certain interval relations are obtained. There is no first order spin-orbit splitting. Through second order perturbation the maximum values of the spin-orbit coupling constant are found for three materials. The theoretical Zeeman splittings are stated.

This thesis contains details of experiments involving the use of supercritical fluids (SCF) and high pressure liquids acting as antisolvents and transport media. The thesis is divided into six Chapters, each detailing different aspects of SCF technology. Chapter 1: Provides the reader with general information concerning the properties of supercritical fluids. Information is given concerning the use of SCFs as solvents and antisolvents. Reviews of the PCA and GAS processes are also provided. Chapter 2: Describes the initial study of the preparation of C60(gas) intercalation compounds. PCA generates compounds of C₂H₄, C₂H₆, C₃H₆ and C₃H₈, which were characterised by JR. A novel GAS technique is used to allow collection of PXD, SEM and MAS ¹³C NMR data of these compounds. Chapter 3: Details a novel supercritical antisolvent technique which allows the generation of macroscopic crystals of intercalate species C60(C₂H₄) and C60(C₂H₆). Crystallographic data on these compounds is presented. Datasets for the intercalates C60(CO₂), C70(C₂H₆) and C70(CO₂) were also collected. Chapter 4 Contains preliminary information on the formation of ‘nanopeapods', that is, carbon nanotubes filled with C60. A new route to the formation of these materials at room temperature is shown. Chapter 5: Describes the impregnation of mesoporous silica with aluminium containing species using SCF as a solvent. Materials display unprecedented stability to steaming with high retention of structural ordering and surface area. Chapter 6: Describes the extraction of template molecules from mesoporous silica. The possibility of complete removal of surfactant using a SCF is shown. The effect of temperature and pressure effects are also measured. Appendices are available at the back of the thesis to describe the equipment, analytical techniques and some safety principles for use of SCF.

This thesis presents the development of a high resolution wide field speckle illuminated interferometric surface plasmon microscope. This system is based on a Linnik interferometer and uses a high NA oil immersion objective for the excitation of surface plasmons. The confocal response of the microscope and high surface field enhancement due to surface plasmon excitation lead to high resolution and high contrast of weak surface structures and films. The microscope was also demonstrated in two other modes of operation, a sensing mode where the distributions seen in the back focal plane of the sample objective could be used to determine the optical parameters of the sample and a conventional surface plasmon microscope mode where image enhancement was created through the use of polarizers and optical masks. Results are presented that show the microscope as capable of imaging results comparable or better than that in the literature and without the need to scan. Hence the system is shown to be wholly suitable to biological and research fields interested in thin films and surface reactions.

This work is centered on the study of self-organisation and pattern formation in a prototypical nanostructured system, namely colloidal nanoparticle assemblies. The particular system chosen for investigation, Au nanocrystals spin cast onto silicon substrates from a solvent, despite being chemically rather simple exhibits a rich variety of complex patterns. In the majority of experiments discussed in this thesis, far-from-equilibrium conditions are attained by a spin-casting process which drives rapid solvent evaporation. A systematic study was carried out to determine the various factors affecting the morphology of nanoparticle assemblies produced in this manner. These factors include the concentration of the nanoparticle solution, the particular solvent used, and the chemical/ physical nature of the substrate. Changing these variables can affect both the strength of interactions between individual nanoparticles and between nanoparticles and the substrate. The various morphologies of the nanoparticle structures produced were studied using atomic force microscopy (AFM). Particular attention is paid to the role of the substrate's surface chemistry in pattern selection. A range of different substrates are used to gauge the influence of differing surface chemistries. In addition, scanning probe lithography was employed to microscopically pattern surfaces. This facilitated the observation of effects caused by the presence of two radically different surface chemistries in the micron size range. This patterning process provides the experimenter some measure of control over the morphology of the nanoparticle assembly, allowing the enforcement of predefined length scales onto the network. Simulations of drying nanocrystal films produced using code written by Martin et al [1] have been shown to accurately reproduce the experimental results. These simulations are used to develop theoretical explanations of the experimental data in terms of the varying solvent evaporation rate on the substrate and the manner by which the solvent dewets on chemically and topologically differing areas of a surface. A remarkable probe-induced coarsening of nanoparticle assemblies by repetitive scanning with an AFM probe has been studied. Repeated scanning of colloidal nanoparticle systems causes the irreversible growth of nanoparticle assemblies. The size distribution of structures produced by this growth is shown to be self-similar. With the size of the domains growing with a power law dependence on scan time. From a combination of these results the growth of structures is explained using a model of coarsening based on cluster diffusion and coalescence. This model is subtly different from coalescence in a thermally driven system due to the novel nature of the mechanical coarsening process. Electrical transport through different array morphologies produced via the spin-coating process was studied using D. C. electrical measurements and electrostatic force microscopy (EFM). Measurements over temperatures ranging from 4.5K to room temperature were made. Variations in the manner that power law scaling of the conduction behaviour alters for different arrays is linked to the topological characteristics of the arrays.

In this thesis we investigate mathematical models for a number of topics in the field of nonlinear diffusion, using similarity, asymptotic and numerical methods and focussing on the time-asymptotic behaviour in most cases. Firstly, we consider `fast' diffusion in the vicinity of a mask-edge, with application to dopant diffusion into a semiconductor. A variety of approaches are used to determine concentration contours and aspect ratios. Next we consider flow by curvature. Using group analysis, we determine a number of new symmetries for the governing equations in two and three dimensions. By tracking a moving front numerically, we also construct single and double spiral patterns (reminiscent of those observed in the Belousov-Zhabotinskii chemical reaction), and classify the types of behaviour that can occur. Finally, we analyse travelling wave solutions and the behaviour near to extinction for closed loops. We next consider relaxation waves in a system that can be used to model target patterns, also observed in the Belousov-Zhabotinskii reaction. Numerical and asymptotic results are presented, and a number of new cases of front behaviour are obtained. Finally, we investigate a number of systems using an approach based on the WKB method, analysing the motion of invasive fronts and also the form of the pattern left behind. For Fisher's equation, we demonstrate how modulated travelling waves can be obtained by prescribing an oscillatory initial profile. The method is then extended, firstly to Turing systems and then to oscillatory systems, for which we use an additional periodic plane wave argument to determine the unequal front and pattern speeds, as well as the periodicity. Finally, we illustrate how these methods apply to a recently-used `chaotic' model from ecology.

The present constitution of the Republic of Lithuania is one of the Constitutions in Central and Eastern countries adopted at the end of XX century. There is no doubt that its conception had been influenced both by national and international factors: the countries’ constitutional traditions, the scholarly ideas of M. Romeris, proposals submitted by the Lithuanian and foreign researchers, institutes of former regime, democratic provisions of Western Europe, the experience of Central and Eastern European countries. This work is the analysis of a short, but diverse and complicated both in political and legal sense of the Lithuanian constitutionalism during 1988 – 1992, demonstrating the development of the vision of the constitutional regulation, how the creative process of the present Constitution was influenced by the changing political legal reality and the political life of the constitution process. The complex application of historical-legal and causal methods, using the analysis of normative and non-normative documents as well as applying other legal methods brings to the conclusion of the Master thesis that the preparation of the Constitution is a consecutive and purposeful process of creation and search for the most suitable constitutional model. Despite the fact that during the development process of the Constitution a quite heated political debate was taking place, the present Basic Law can be reasonably referred to as the result of the political and legal compromise... [to full text]

The main objective of this body of work is to define and delineate radical activity in Scotland and Ireland c. 1760-1789 and through this to assess the nature and construction of the contemporary British identity. In their various campaigns Scottish and Irish radicals held the restoration of the lustre of the British constitutional system and the promotion of integrity and propriety in the British state as both motives for, and objectives of, their actions. These radicals sought a restoration of what they perceived to be the post-Glorious Revolution constitutional system. Their actions and writings were based on the premise that the propriety of the British constitution had been compromised by Westminister in the years after 1691. Following a near seventy year long gestation period, Scottish and Irish constitutional grievances were galvanised in the years after the end of the Seven Years' War by the North American colonial challenge to Westminster's constitutional vision. Scotsmen and Irishmen impugned the civil, ecclesiastical and political constitution which had been imposed upon them. Each campaign was an assertion of contemporaneous perceptions of the rights of Britons, or perhaps more accurately an assessment of what Britishness was, contrasted to what it they believed it should have been.

Th. univ. : Droit : Nancy : 1932.

Thesis (D. Min.)--Biblical Theological Seminary, 2007. / Includes bibliographical references.

This thesis utilises large deviation methods to study nonequilibrium phenomena in both quantum and classical systems. The dynamical analogues of the ensembles of statistical mechanics are used to explore dynamical phase spaces of systems, quantifying atypical fluctuations that can play a critical role in long term behaviour. A dynamical ensemble based on fixed numbers of dynamical events, allowing trajectory observation time to fluctuate, is introduced. This ensemble, denoted the x-ensemble, is found to be well suited to numerically simulate atypical fluctuations using transition path sampling (TPS). x-ensemble TPS schemes are analysed with reference to existing methods in both quantum and classical stochastic systems, and are found to offer more flexibility and efficiency in a variety of situations. The potential to develop this scheme into a self-optimizing algorithm is discussed with examples. The x-ensemble is then used in three non-equilibrium scenarios. Firstly in plaquette models of glass formers, in an effort to provide insight into the nature of the glass transition. It is shown that a two-dimensional triangular plaquette model (TPM) exhibits both a trajectory phase-transition between dynamical active and inactive phases, and when two replicas are coupled, a thermal phase transition between states of low and high overlap between the replicas. These two transitions are similar to those seen to occur in more realistic glass formers. When the TPM is generalised to a three-dimensional square pyramid plaquette model (SPyM) these dynamical and thermodynamic features of interest remain. It is argued that these models therefore provide an ideal test-bed for competing theories of the glass transition. Secondly the x-ensemble is used to define and analyse the dynamical analogue of the Jarzynski equality, allowing for the computation of dynamical free energy differences with, in principle, arbitrarily fast protocols linking two dynamical states. This relation is tested and found to hold in open quantum systems. Finally the partition sum zeros method of Lee and Yang is used to extract the location of dynamical phase transitions from the high-order, short-time cumulants of the x-ensemble. Results in both classical and open quantum systems are compared with previously studied dynamical ensembles, providing insight into the nature in which dynamical behaviours are encoded by these ensembles.