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The technique of detecting EPR spectra and measuring spin-bath relaxation times by the megneto-optical Faraday rotation has been applied to carefully grown crystals of praseodymium ethylsulphate (PrES). This method has been successfully applied to neodymium ethylsulphate by Rieckhoff and Griffiths. PrES was chosen because Pr³⁺ is an ion having an even number of unpaired hf electrons and thus possesses a non-degenerate ground state, the removal of any degeneracy in zero magnetic field being due to low symmetry components of the crystalline electric field. All experiments were done' at liquid helium temperatures (1.4 ≤ T ≤ 4.2°K) and in external magnetic fields up to 12 kilogauss. Successful measurements were made with the optic axis of the crystal aligned parallel to the polarized light beam and the external magnetic field. It was necessary to orient the magnetic field component of-the microwave power parallel to the external magnetic field in order to induce spin transitions. Theory shows that the magnitude of the Faraday rotation is proportional to the difference in population of the ground state doublet. The EPR spectrum and spin-bath relaxation times were measured in terms of saturation, the saturation being defined by s = [formula omitted], where Θ and Θ₀ are the rotation in the presence and absence of microwave power. The EPR spectrum at X band of undiluted PrES is a broad band Extending over several kilogauss with no evidence of hyperfine structure. The band decreases at 8400 φ and covers 800 φ from its maximum to half power point. Pr¹⁴¹ has nuclear spin 1 = [formula omitted] and the absence of any hyperfine structure indicates that crystal field distortion is the main source of line broadening. This result agrees with work done by Baker and Bleaney who in examining the low field side of this spectrum at K band found no trace of hyperfine structure. The empirical dependence of saturation on the relative microwave power is found to be s = [formula omitted]. This relationship cannot be explained theoretically. Since homogeneous line broadening predicts s = [formula omitted], we conclude that the resonance line is inhomogeneously broadened. The relaxation times measured as a function of temperature over the ranee 1.4 to 2.18°K and at 4.22°K and as a function of the external magnetic field, range from 0.1 to 10 msec. For 1.40 ≤ T ≤ 1.80°K, T decreases from 0.4 to 0.15 msec; is proportional to T[symbol omitted] and is consiaered to be the phonon-bath relaxation time. Values of T show a scatter within 0.20 ± 0.02 msec for 1.80 ≤ T ≤ 1.95°K. As the λ -point is approached (1.95 ≤ T ≤ 2.18°K), T exhibits a very rapid increase, having a value of 0.20 msec at 2.155°K and 0.85 msec at 2.165°K. This behaviour appears to be related to the energy exchange between the crystal and helium bath. Measurements of T at 2.18°K and 4.22°K indicate that the return to thermal equilibrium of the spin-phonon system is limited by the thermal conductivity of the liquid helium bath. The magnetic field dependence of T is interpreted in terms of phonon scattering by the paramagnetic Pr³⁺ ions. The effect is strongest at the lowest temperatures (i.e. ~ 1.4°K) where there is an increase in T from 0.5 to 2.0 msec for the magnetic field H increasing from 3.5 to 11.5 kilogauss. The effect of the magnetic field on T decreases with increasing temperature and at 2.15°K T appears to be independent of field. An unsuccessful attempt to detect electron spin resonance in neodymium ethylsulphate oriented with its optic axis .perpendicular to the light path (and external magnetic field) is described. / Science, Faculty of / Physics and Astronomy, Department of / Graduate

The objective of this study is to elucidate as much as possible the theory and analysis of BOURDON tubes. Both thick-walled and thin-walled tubes are considered. Three papers, representative of the state-of-the-art of BOURDON tube analysis, are reviewed (References 1, 2, and 6): <p> 1. Wuest, W. "Theory of High-Pressure BOURDON Tubes". </p><p> 2. Andreeva, L. E>, "Elastic Elements of Instruments" </p> <p> 3. Dressler, R., "Elastic Shell-Theory Formulation for BOURDON Tubes" </p><p> Reanalysis of (3) above, with a different approach (Appendix A) checked and completed the general formulation by Dressler. The final forms of all necessary equations, boundary conditions, etc. to the solution of the three governing equations of the BOURDON tube with an elliptical cross-section are given. </p><p> Comparison of results of Andreeva's sensitivity equation with test data of Kardos, Mason and Exline (References 3, 4 and 5) using a qualitative approach as set out by Kardos (References 3 and 17) showed good correlation. </p><p> The study concludes with recommendations for the approach of future research and preliminary design procedures for BOURDON tubes. </p> / Thesis / Master of Engineering (ME)

A quarter of the world's population experience wheezing. These sounds have been used for diagnosis since the time of the Ebers Papyrus (ca. 1500 BC), but the underlying physical mechanism responsible for the sounds is still poorly understood. The main purpose of this thesis is to change this, developing a theory for the onset of wheezing using both experimental and analytical approaches, with implications for both scientific understanding and clinical diagnosis. Wheezing is caused by a fluid structure interaction between the airways and the air flowing through them. We have developed the first systematic set of experiments of direct relevance to this physical phenomena. We have also developed new tools in shell theory using geometric algebra to improve our physical understanding of the self-excited oscillations observed when air flows through flexible tubes. In shell theory, the use of rotors from geometric algebra has enabled us to develop improved physical understanding of how changes of curvature, which are of direct importance to constitutive laws, come about. This has enabled a scaling analysis to be applied to the self-excited oscillations of flexible tubes, showing for the first time that bending energy is dominated by strain energy. We made novel use of multiple camera reconstruction to validate this scaling analysis by directly measuring the bending and strain energies during oscillations. The dominance of strain energy allows a simplification of the governing shell equations. We have developed the first theory for the onset of self-excited oscillations of flexible tubes based on a flutter instability. This has been validated with our experimental work, and provides a predictive tool that can be used to understand wheezing in the airways of the lung. Our theory for the onset of wheezing relates the frequency of oscillation to the airway geometry and material properties. This will allow diagnoses based on wheezing sounds to become more specific, which will allow the stethoscope, which has changed little in the last 200 years, to be brought into the 21st century.

This thesis presents four investigations into mechanical aspects of soft thin structures, focusing on the effects of stochastic and thermal fluctuations and of material inhomogeneities. First, we study the self-organization of arrays of high-aspect ratio elastic micropillars into highly regular patterns via capillary forces. We develop a model of capillary mediated clustering of the micropillars, characterize the model using computer simulations, and quantitatively compare it to experimental realizations of the self-organized patterns. The extent of spatial regularity of the patterns depends on the interplay between cooperative enhancement and history-dependent stochastic disruption of order during the clustering process. Next, we investigate the influence of thermal fluctuations on the mechanics of homogeneous, elastic spherical shells. We show that thermal fluctuations give rise to temperature- and size-dependent corrections to shell theory predictions for the mechanical response of spherical shells. These corrections diverge as the ratio of shell radius to shell thickness becomes large, pointing to a drastic breakdown of classical shell theory due to thermal fluctuations for extremely thin shells. Finally, we present two studies of the mechanical properties of thin spherical shells with structural inhomogeneities in their walls. The first study investigates the effect of a localized reduction in shell thickness—a soft spot—whereas the second studies shells with a smoothly varying thickness. In both cases, the inhomogeneity significantly alters the response of the shell to a uniform external pressure, revealing new ways to control the strength and shape of initially spherical elastic capsules. / Engineering and Applied Sciences

The influence of dent imperfections on the elastic stress behavior of cylindrical shells is explored. This problem is of central importance to the prediction of fatigue failure due to dents in petroleum pipelines. Using an approximate technique called the Equivalent Load Method, a semi-analytical model of two-dimensional dent stress behavior is developed. In the three-dimensional situation, decreased dent localization, in particular dent length, and increased dent depth are confirmed to cause dent stress concentration behavior to shift from having a single peak at the dent center to having peaks at the dent periphery. It is demonstrated that the equivalent load method does not predict this shift in stress behavior and cannot be relied upon to analyze relatively small, deep imperfections. The two stress modes of dents are associated with two modes of dent fatigue behavior that have significantly different fatigue lives. A method for distinguishing longer lived Mode P dents from shorter lived Mode C dents based on two measured features of dent geometry is developed and validated. An approach for implementing this analysis in the evaluation of real dents is also suggested.