In this thesis, we investigate analytically and numerically the existence and stability of discrete solitons governed by discrete nonlinear Schrödinger (DNLS) equations with two types of nonlinearity, i.e., cubic and saturable nonlinearities. In the cubic-type model we consider stationary discrete solitons under the effect of parametric driving and combined parametric driving and damping, while in the saturable-type model we examine travelling lattice solitons. First, we study fundamental bright and dark discrete solitons in the driven cubic DNLS equation. Analytical calculations of the solitons and their stability are carried out for small coupling constant through a perturbation expansion. We observe that the driving can not only destabilise onsite bright and dark solitons, but also stabilise intersite bright and dark solitons. In addition, we also discuss a particular application of our DNLS model in describing microdevices and nanodevices with integrated electrical and mechanical functionality. By following the idea of the work above, we then consider the cubic DNLS equation with the inclusion of parametric driving and damping. We show that this model admits a number of types of onsite and intersite bright discrete solitons of which some experience saddle-node and pitchfork bifurcations. Most interestingly, we also observe that some solutions undergo Hopf bifurcations from which periodic solitons (limit cycles) emerge. By using the numerical continuation software Matcont, we perform the continuation of the limit cycles and determine the stability of the periodic solitons. Finally, we investigate travelling discrete solitons in the saturable DNLS equation. A numerical scheme based on the discretization of the equation in the moving coordinate frame is derived and implemented using the Newton-Raphson method to find traveling solitons with non-oscillatory tails, i.e., embedded solitons. A variational approximation (VA) is also applied to examine analytically the travelling solitons and their stability, as well as to predict the location of the embedded solitons.

Dynamic laser light scattering spectroscopy is used to study the motion of short chain flexible molecules in the liquid state. Depolarised Rayleigh-Brillouin scattering is used to investigate the isomers of the homologous alkane series n-pentane to n-octane. In addition to the low frequency Lorentzian component, associated with molecular reorientation, a second Lorentzian component is found in the spectra from the liquids 2,2,4-trimethylpentane, 2-methylhexane, 3-methylhexane, 2,2-dimethylpentane, 2,3-dimethylpentane, 2,2,3- trimethylbutane, 2-methylpentane, 3-methylpentane, 2,2-dimethylbutane, n-pentane and 2-methylbutane. The contribution to the spectra of this second Lorentzian, which is broader than the Lorentzian associated with molecular reorientation and distinct from the interaction induced component, reduces as the molecules become more anisotropic and flexible. The origin of this component is associated with local translational order. The correlation times obtained from molecular reorientation are andlysed in terms of a modified Stokes-Einstein-Debye relation. The Stoke~;-;':instein-Debye volumes obtained are interpreted as the quantity (g2/J2)apv, where (g2/J2) is associated with molecular correlation, P and a with molecular shape and V is the molecular volume. Values of a, the stick-slip coefficient, obtained for the nalkanes indicate that the average molecular conformation is approximately midway between a sphere and an extended chain. For all the isomers a is feound to dUCt'(_~ii~;(; de; the molecule be cornea mor-e rigid and more spherical. The liquid 2,2-dimethylbutane is analysed in terms of the theory of Madden [Mol Phys, ~, 365 (1978)J; dipole-induced dipole interactions between pairs of density fluctuations cause intermolecular optical anisotropy. The results indicate that molecular reorientation may not be the predominant relaxation mechanism. Oleic acid was investigated using polarised Rayleigh-Brillouin spectroscopy. The temperature gradient of the hypersonic frequency shift and elastic modulus show anomalous behaviour in the range 14 - 18°C. This suggests that oleic acid undergoes a change of phase to form a locally nematic structure about 5 °C above the melting point. Complementary measurements of viscosity, density and refractive index support this interpretation.

Quantum dynamics and tunnelling of methyl rotors has been studied using field-cycling nuclear magnetic resonance (NMR) spectrometer, in a variety of samples. The characteristic frequency of the tunnelling motion of methyl groups has been investigated using both low-field dipole-dipole driven experiments and tunnel resonance level-crossing experiments. The classical hopping and quantum tunnelling of methyl groups have been studied by making temperature-dependent and field-dependent measurements of the spin-lattice relaxation time T1. The spectral density functions of the dipolar interaction, mediated by the rotation of methyl groups, have been directly plotted, and the correlation times characteristic of the rotational motion have been determined. Electron spin resonance (ESR) tunnel resonance spectra have been studied in samples with unpaired electrons by making resonant contact between the methyl tunnelling reservoir and the electron spins. The phenomenon of dynamic proton polarisation (DNP) has also been investigated in these samples. Experiments demonstrating the cooling of methyl tunnelling reservoir and the diffusion of energy amongst tunnelling reservoirs are presented. In low-field dipole-dipole driven experiments, in order to avoid the tunnelling transition saturation problem, the sideband stirring radiofrequency (rf) irradiation technique has been utilised and the low-field NMR spectra have been observed with enhanced sideband peaks. The rf irradiation time-dependence of the low-field spectra has been investigated. The experimental data is supported by numerical simulations, using appropriate theoretical models.

Glass transition, physical aging and dielectric relaxation in ultra-thin polymer films (< 100 nm) were investigated using complementary techniques (ellipsometry and dielectric spectroscopy). PtBMA films of different thicknesses were prepared and the thickness dependence of the glass transition temperature (Tg(h)) was investigated with ellipsometry. The uncapped films thinner than 40nm showed signicant depression of Tg and this was explained using the enhanced molecular mobility near the free surfaces. Several sets of PtBMA film samples were then prepared and capped by Al layers; the coating procedure is different for each set. The Tg(h) in PtBMA films with evaporated Al capping layers was essentially the same as that of the uncapped PtBMA films, and this suggests evaporated Al capping layers can not remove the free surface effect. Another set of samples was capped with Al layers using a novel '2(h=2)' sample preparation procedure, and was expected to have no free surface effect. These samples exhibit no apparent thickness dependence. These results suggest that the effect of free surfaces are responsible for the altered dynamics in thin polymer films. However great care has to be taken in attempt to remove the free surface effects caused by solid capping layers. The frequency dependence of the thickness dependence of α relaxation temperature (Tα(h)) in ultra-thin PVAc films was measured using dielectric spectroscopy. Films thinner than 80nm exhibit smaller Tα's than the bulk values at a measurement frequency lower than 10Hz, but there is no signicant thickness dependence of Tα at measurement frequencies higher than 10Hz. The results demonstrated that the Tα(h) has an intrinsic dependence on measurement frequency. We also measured the cooling rate dependence of the Tg(h) using the same samples, and compared Tg(h) with Tα(h) for different cooling rates/measurement frequencies. The results help to address the existing controversial reports about the apparent discrepancies observed between measurements that are performed using different techniques. Dielectric spectroscopy in the temperature domain ε"(T) was measured on thin(<486nm) PVAc films. The data were plotted against ln τ and the parameters describing the widening and distortion of the α relaxation peaks are constant for all measurement frequencies. The observed symmetry of the α relaxation peaks in ε"((T)were related to the constant shape parameters of the asymmetric α relaxation peaks in ε"(ln τ). An explanation is given to the observed widening of the α relaxation peaks with increasing measurement frequency in ε"(T). At a lower measurement frequency (<1Hz), the data obtained from thinner PVAc films showed wider α relaxation peaks (in ε"(T)) than the data obtained from thicker films, and at a higher frequency (>1Hz) this thickness dependence doesn't exist. This was explained using the existence of the liquid-like surface layer with enhanced molecular mobility, and using the measurement frequency effects. PS films of different thickness were prepared and physical aging process in these samples was investigated using ellipsometry. On each sample the measurements were performed at different aging temperatures, and a trend of a decreasing aging rate with decreasing aging temperature is found for all samples. In ultra-thin PS films (<100nm thick) a maximum aging rate at ~17K below Tg film is observed, and these observations were explained using the competition of the two factors that affect the aging, that is, the distance to the equilibrium and the fraction of the free volume. A comparison between the thickness dependence of aging rate and the thickness dependence of Tg suggests that the aging rate serves as a more sensitive probe in the study of polymer molecular dynamics than Tg does.

This dissertation describes a proof-of-principle experiment demonstrating a technique for stable isotope enrichment called Magnetically Activated and Guided Isotope Separation (MAGIS) (1). Over the past century a large number of enriched isotopes have become available, thanks largely to electromagnetic separators called calutrons that were developed during World War II. These isotopes have found applications across an array of fields including medicine, basic science, and energy. Due to substantial maintenance and operating costs, the United States decommissioned the last of its calutrons in 1998, leading to demand for alternative methods of isotope separation. Our experiment suggests the promise for MAGIS as a viable alternative for replenishing stockpiles previously provided by calutrons. Our apparatus combines optical pumping with a scalable magnetic field gradient to enrich lithium-7 (Li-7) by suppressing lithium-6 (Li-6) throughput in a lithium atomic beam. We first evaporate lithium metal in a crucible in order to generate thermal, high flux beam. We then perform optical pumping on Li-6 atoms, magnetically polarizing a substantial fraction of Li-6 atoms into the entirely high-field seeking 2²S₁/₂, F = 1/2 ground state. The resultant beam then samples a magnetic field gradient produced by a 1.5 m long array of rare-earth permanent magnets bent over its length by 20 mrad. This geometry prevents high-field seeking lithium atoms from reaching the plane beyond the magnets, while efficiently deflecting low-field seeking atoms. We measured Li-6 suppression – using independent techniques – along the plane after the magnets beyond a factor of 200, corresponding to Li-7 enrichment to better than 99.95%. As apparatus-specific hindrances appeared to limit this suppression, we believe that we should achieve better enrichment on a commercial apparatus. We also measured both the absolute flux beyond the single, 1.5 in tall magnet array and the efficiency for guiding feedstock material to the collection plane. Given the planar configuration for the field gradient, the flux that we measured should scale linearly with both magnet height and the number of arrays surrounding the source. Our measurements therefore indicate that – at source temperatures that we actually investigated – a commercial apparatus fitting within a volume of just several cubic meters should yield hundreds of grams of enriched (to beyond 99.95%) Li-7 per year. In addition, we observed a competitive ratio between collected material and feedstock with greater than 20% of lithium incident upon the magnet array reaching beyond the magnets. Benchmarking our work against the calutron, we demonstrated comparable enrichment in a manner that should scale to the production of similar quantities. In contrast, however, MAGIS should require vastly less energy input. While calutrons required massive currents for maintaining a static magnetic field over a substantial area, the only non-shared energy expense for MAGIS is the cost for running the low power lasers for optical pumping. Via additional analysis, we have supplemented this proof-of-principle experiment with schemes for applying MAGIS to over half of the stable isotopes in the periodic table. Due to the success of this demonstration and the broad applicability of the principles, we believe that MAGIS will play an important role in the future of stable isotope enrichment. / text

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