In this thesis, we develop a first principle technique to study linear AC and the nonlinear DC quantum transport in diffusive conductors. Starting from Buttiker's theory for AC and DC transport, the emittance and nonlinear DC conductance are found in terms of the scattering matrix and it's functional derivative. New theoretical tools are developed to compute the functional derivative of the scattering matrix, which would otherwise be unaccessible. These results allows us to compute the linear AC and the nonlinear DC conductance for a diffusive conductor from first principles, for the first time in literature. The sample-to-sample AC conductance fluctuations are computed for a diffusive conductor. In this regime the dynamic response of the conductor can either be capacitive or inductive, depending on impurity configuration. Our results also suggest a crossover for the AC conductance distribution, from a symmetric to a non symmetric distribution function as the number of impurities increases. A degree of generic behavior is discovered, in that the AC fluctuation amplitudes become independent of the strength of the impurities, although it depends on the impurity density. A sample-to-sample analysis of the nonlinear conductance fluctuations, in the diffusive regime, is also reported. In this situation the distribution function is found to be a symmetric Gaussian like function for small disorder and a symmetric exponentially decaying function for large disorder. An interesting result is that the conductance fluctuations increase in an exponential fashion with N, the number of impurities. / We also considered in this thesis the magneto-conductance fluctuations of a quasi-1D quantum wire with artificial impurities (antidots). This problem can only be solved numerically because of the finite size of the artificial impurities. We develop a novel transfer matrix technique to solve the quantum scattering problem by computing the scattering wave function, as a function of the external magnetic field. The Landauer-Buttiker equation is used to compute the magneto-conductance. This work is motivated by the experimental study [1], where several conductance fluctuations anomalies were reported. Our numerical results give good quantitative agreement with the experimental data and confirms the physical picture obtained from the experiment.

Measurements of the spin-lattice relaxation time, T1, and spin-spin relaxation time, T2, of potassium ferricyanide diluted by potassium coba1ticyanide were made by the CW saturation method. Crystals of two concentrations of Fe3+ in K3Co(CN)6 were investigated: 0.5% and 1.0%. The results are the same for both concentrations to within the probable error. The mean relaxation times for the two concentrations are quoted to one significant figure, together with the probable errors: T1 =(1 +- 0.15) x 10-4 sec and T2 = (9 +- 0.4) x 10-9 sec. Calculations have been made to determine the angular dependence of the paramagnetic resonance spectra of potassium ferricyanide. Three graphs have been plotted which may be useful for comparison with future measurements.

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At the interface between a metal and dielectric, it is possible for an electromagnetic wave to couple with the conduction electrons of the metal to create a coupled oscillation known as a surface plasmon. These surface plasmons can exhibit properties which are not shared with their purely electronic or electromagnetic components. Such unique properties include the ability to transmit plasmonic waves through sub-wavelength spaces, opening up the possibility of combining the high data density seen in photonics-based information technologies with the nanometer-scale electronic components of modern integrated circuitry. Other plasmon properties such as the highly resonant nature of plasmon excitation may potentially lend themselves to novel cancer treatments and medical probing techniques. In order to develop such technologies, a deeper understanding of surface plasmons and their relationship with a material’s properties and structure is necessary. In the present work, angle- and energy-resolved optical measurements for a square lattice of circular Fe20Pd80 islands are presented in the form of reflectivity and transmission maps, along with higher resolution reflectivity, transmission, and TMOKE measurements for a few specific wavelengths. A theoretical model describing the connection between plasmonic and magneto-optical behavior is described and compared with the experimental data, showing a very high correlation.

A current-switched superconducting field-cycling NMR spectrometer has been designed and built for studying the role of quantum tunnelling in molecular dynamics. The instrument is designed for work in the solid state with sample temperatures extending from 4K up to 300K. The maximum field-switching rate is 10Ts-1. Among the samples studied in this thesis is the nuclear spin-relaxation and proton tunnelling. Concerted double proton transfer in the hydrogen bonds of carboxylic acid dimers is well established as the model system for translational quantum tunnelling. The model system has been chosen to illustrate the smooth quantum-to-classical transition and at all temperatures the proton transfer is characterised by a single correlation time. Quadrupolar interactions introduce an additional relaxation to the proton spin polarisation. The enhanced relaxation of the proton spin appears as a dip in the proton magnetisation curve. This technique is employed to measure the quadrupolar transition frequency of 14N and 35Cl and determine the structure of heroin hydrochloride. The introduction of a second spin species has a significant effect on the spin-lattice relaxation. Compared with homonuclear systems, the spectral density acquires additional components characterised by the sum and difference Larmor frequencies of the two nuclei. Further, instead of a single relaxation time, there are four elements of a relaxation matrix. Therefore, the magnetisation recovery becomes bi-exponential and the initial polarisation state of the second nucleus strongly affects the magnetisation recovery of the nucleus which is being observed. We shall report on the results of spin-lattice relaxation investigations on 1H-13C, 1H-19F systems. The role of heteronuclear interactions in spin-lattice relaxation and the newly developed methodology of field-cycling relaxometry will be discussed. This represents the first 13C field-cycling NMR experiment and the first to measure the field dependence of the off-diagonal element of the relaxation matrix.

The technique of functional magnetic resonance imaging is rapidly moving from one of technical interest to wide clinical application. However, there are a number of questions regarding the method that need resolution. Some of these are investigated in this thesis. High resolutionf MRI is demonstrated at 3.0 T, using an interleaved echo planar imaging technique to keep image distortion low. The optimum echo time to use in fMRI experiments is investigated using a multiple gradient echo sequence to obtain six images, each with a different echo time, from a single free induction decay. The same data are used to construct T2* maps during functional stimulation. Various techniques for correcting the N/2 ghost are tested for use in fMRI experiments, and a method for removing the image artefact caused by external r. f. interference in a non-linearly sampled matrix is presented. The steps in the analysis of fMRI data are detailed, and two new non-directed analysis techniques, particularly for data from single events, as opposed to epoch based paradigms, are proposed. The theory behind software that has been written for fMRI data analysis is also given. Finally, some of the results from an fMRI study into the initiation of movement are presented, illustrating the power of single event experiments in the separation of cognitive processes.

The aim of this work was to implement a thorough method for quantifying the errors introduced to frame-based neurosurgical stereotactic procedures by the use of MRI. Chang & Fitzpatrick's reversed gradient distortion correction method was used, in combination with a phantom, to measure these errors. Spatial distortion in MR images of between 1 mm and 2 mm was measured. Further analysis showed that this typically introduced an additional error in the coordinate of the actual treatment point of 0.7 mm. The implications of this are discussed. The main source of distortion in the MR images used for stereotaxis was found to be the head ring. A comparison between imaging sequences and MR scanners revealed that the spatial distortion depends mainly on the bandwidth per pixel of the sequence rather than other differences in the imaging sequences. By comparison with a phase map distortion correction technique, the imaging parameters required to allow successful distortion correction with the reversed gradient method were identified. The most important was the use of full Fourier spin echo acquisitions. The reversed gradient correction method was applied to two contemporary EPI techniques. Considerable improvement was seen in the production of ADC maps after the images had been corrected for distortion. The method also was shown to be valid in application to BOLD fMRI data.

Interest in coherent remote sensing systems has stimulated investigations in the properties laser propagation through extended atmospheric turbulence. This thesis investigates the statistics of phase, and phase related, observables using analytical and computational techniques, together with experimental results. The phase screen technique is used to simulate perturbations to the refractive index of a medium through which the radiation propagates. Several different turbulence models (Gaussian correlated noise, Kolmogorov turbulence, Tatarski and Von Karman spectral models) are investigated, and their relative merits for describing experimental conditions and descriptive statistical measures are compared and contrasted. The phase power spectrum is crucial to an understanding of the practical operation of a coherent imaging system, and later part of the thesis is devoted to the investigation of a LIDAR system in particular. Several turbulence regimes are investigated, from an analytical treatment of a weakly turbulent, extended atmosphere, to large 3D computations designed to simulate experimental arrangements. The 3D simulation technique presented herein has been developed to allow for the investigation of temporal statistics. New power law behaviours are found to appear in temporal frequency spectra which differ from the -8/3 power law form that has been accepted in much of the literature. Strongly turbulent regimes result in a -2 power law while the use of a Gaussian beam profile in an extended medium gives a -11/3 power law under weak turbulence conditions. Please note: Pagination in electronic reproduction differs from print original. The print version is the version of record.

This thesis addresses the problem of radiofrequency probe design for Ultra High Frequency Magnetic Resonance Imaging (7T). The signal-to-noise ratio available in Magnetic Resonance Imaging (MRI) is determined by the static magnetic field strength, causing a continued drive toward higher fields to enable faster image acquisition at finer spatial resolution. The resonant frequency increases linearly with static field strength. At 7T the proton resonant frequency is 300MHz, with a wavelength of approximately 13cm in tissue. As this is smaller than the dimensions of the human head, the phase of the radiofrequency (RF) signal varies considerably across the sample, producing field cancellation due to interference. A full wave electromagnetic simulator, using the Transmission Line Matrix (TLM) method, was developed to investigate RF probes at high frequency. A Birdcage probe operating at 64, 128 and 300MHz (corresponding to 1.5, 3 and 7T) was simulated, loaded with an anatomically detailed human head model. A half-wave microstrip was investigated for use as a high frequency probe element. Magnetic and electric fields produced by a single microstrip were simulated, and the strip dimensions varied to investigate the effect on field penetration into the head and Specific Absorption Rate (SAR). A transmit-receive array probe using four microstrip elements was then developed. Bloch simulations were run, using TLM generated magnetic fields, to investigate imaging at short wavelength. Parallel receive probes are demonstrated to offer considerable advantage over volume probes, as signals from receive elements can be combined without interference. There is no transmit equivalent to parallel reception; simultaneous excitation of independent probe elements causes interference in exactly the same manner as a volume probe. A new imaging sequence was developed using a Burst-like encoding to allow sequential excitation of probe elements, without interference, which can be recalled in a single readout. An improvement in image homogeneity was demonstrated, and SENSE acceleration of the new imaging sequence is shown. The sequence was implemented at 3T using a purpose built four element microstrip probe. An RF multiplexer was also built to enable transmit element switching during the imaging sequence. It was demonstrated that images due to different RF excitations, acquired in a single EPI readout, can be separated.

This thesis describes the development and application of quantitative echo planar magnetic resonance imaging techniques to the study of human placental development in normal and compromised pregnancies. Initially, a method of rapidly and accurately measuring the transverse relaxation time is proposed using a multi-echo measurement sequence. The method is described, validated on CUS04 phantoms and applied in the study of the human placenta and gastric dilution. It is shown that the inversion provided by sinc pulsesis insufficient to generate an accurate measurement but using adiabatic refocusing pulses yields a measurement that is comparable with a single spin echo. Subsequently, a rapid magnetisation transfer method is presented that allows the quantification of the relative size of the bound proton pool. An experimental pulse sequence is proposed, along with a theoretical model, that permits the investigation of the bound proton pool's transition towards the steady state. The sequence and model are validated using agar gel phantoms and shown to agree well with literature values. When applied in the study of the human placenta, it is shown that there is no significant variation in the fitted value of the bound proton pool size with increasing gestational age or in compromised pregnancies. Finally, several methods of measuring the oxygenation level of blood within the human placenta are investigated. The signal intensities of cardiac gated T~• and T~ weighted images acquired at various points in the maternal cardiac cycle are explored but no significant variation is shown through the cycle. A pulsed gradient spin echo sequence that utilises anti-symmetric sensitising gradients is validated and then applied in the human placenta. Oxygenation measurements with this technique are shown to be unfeasible but the potential of the sequence to monitor blood flow in the placenta is demonstrated.