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No description available.

Dilute atomic Bose-Einstein condensates support intriguing macroscopic excitations in the form of quantized vortices and dark solitons. In this thesis we present extensive quantitative studies of the dynamics of these phenomena in the limit of zero temperature, performed by numerical simulation of the Gross- Pitaevskii equation. We show that vortices and dark solitons are inherently unstable to acceleration through the condensate, leading to the emission of sound waves. Indeed, for a single vortex/soliton, the power emitted is proportional to the square of the local acceleration. However, due to the finite size of the condensate, the vortex/soliton reinteracts with the emitted sound. This coupling has an important effect on the ensuing dynamics, and we illustrate how it can be engineered to induce net decay, stabilise, or even drive energy into the vortex/soliton. Under the harmonic confinement typically employed to trap the condensates, the acceleration-induced decay is stabilised by reabsorption of the emitted sound. However, by modifying the trap geometry, e.g. by adding an inner dimple in which the soliton resides or an optical lattice potential, it is possible to break this equilibrium and so induce a net decay of the vortex/soliton in a controllable manner. The decay rate can be considerable and should be observable under current experimental conditions. The dynamical stability of quantized vortices is also relevant to the field of turbulence in superfluid Helium, where the motion of the vortices is induced by the surrounding distribution of vortices rather than density. We extend these results to this field, and additionally consider the interactions between two and three vortices, which are also found to involve sound emission. By exciting the sound field of the condensate it is possible to drive parametrically energy into a dark soliton. In a real dissipative environment, this can be used to stabilise the soliton decay. Finally, we illustrate the links between dark solitons and vortices: a dark soliton embedded in a three-dimensional system is prone to decay into vortex rings, while a vortex in a quasi-one-dimensional geometry cannot be supported and exists as a hybrid between a vortex and dark soliton, known as a solitonic vortex.

Various experimental settings that involve drying solutions or suspensions of nanoparticles often called nano-fluids have recently been used to produce structured nanoparticle layers. In addition to the formation of polygonal networks and spinodal-like patterns, the occurrence of branched structures has been reported. After reviewing the experimental results, the work presented in this thesis relies only on simulations. Using a modified version of the Monte Carlo model first introduced by Rabani et al. [95] the study of structure formation in evaporating films of nanoparticle solutions for the case that all structuring is driven by the interplay of evaporating solvent and diffusing nanoparticles is presented. The model has first been used to analyse the influence of the nanoparticles on the basic dewetting behaviour, i.e., on spinodal dewetting and on dewetting by nucleation and growth of holes. We focus, as well, on receding dewetting fronts which are initially straight but develop a transverse fingering instability. One can analyse the dependence of the characteristics of the resulting branching patterns on the driving effective chemical potential, the mobility and concentration of the nanoparticles, and the interaction strength between liquid and nanoparticles. This allows to understand the underlying fingering instability mechanism. We describe briefly how the combination of a Monte Carlo model with a Genetic Algorithm (GA) can be developed and used to tune the evolution of a simulated self-organizing nanoscale system toward a predefined nonequilibrium morphology. This work has presented evolutionary computation as a method for designing target morphologies of self-organising nano-structured systems. Finally, highly localised control of 2D pattern formation in colloidal nanoparticle arrays via surface inhomogeneities created by atomic force microscope (AFM) induced oxidation is presented and some simulations are shown. Furthermore, the model can be extended further, and by including the second type of nanoparticle, the binary mixture behaviour can be captured by simulations. We conclude that Kinetic Monte Carlo simulations have allowed the study of the processes that lead to the production of particular nanoparticle morphologies.

This thesis is concerned with the syntheses of a range of polyfluorinated biphenyl ether derivatives for use as dopants in commercial LC materials, so that overall display performance may be improved. Reactions of hexa– and penta–fluorobenzene with sodium phenoxide in polar aprotic solvents (MeCN, THF) and under mild reaction conditions (45–50 °C, 4–65 h) afford moderate yields of pentafluorophenoxybenzene and 1,2,4,5–tetrafluoro–3–phenoxybenzene, respectively. SNAr reactions of sodium phenoxide with less electrophilic 1,2,3,4–tetra– and 1,2,3,5–tetra–fluorobenzene under microwave irradiation (150 °C, 30 mins) furnish good yields of 1,2,4–trifluoro–3–phenoxybenzene and 1,2,5–trifluoro–3–phenoxybenzene, respectively. Similar SNAr methodology is used to access a series of 1,2,4,5–tetra– and 1,2,4–tri–fluoro–3–(4–n–alkylphenoxy)benzene derivatives in good yield. A two–step SNAr–hydrodebromination procedure to access trifluorophenoxybenzene systems from highly electrophilic dibromotetrafluorobenzene derivatives is also developed, and provides a practical synthetic route to 1,2,4–trifluoro–5–phenoxybenzene. Finally, a three–step SNAr–diazotisation–reductive diazotisation pathway is developed for the syntheses of difluorophenoxybenzene derivatives, which are not accessible by direct SNAr reactions of sodium phenoxide with corresponding trifluorobenzene derivatives. The use of these polyfluorinated biphenyl ether systems as dopants for LC materials is assessed by a range of electro–optical measurements. Highly fluorinated nitrobenzene systems are compatible substrates for palladium–catalysed Suzuki–Miyaura and Heck–type cross–coupling reactions involving C–F bond activation. Cross–coupling reactions of pentafluoronitrobenzene with a range of boronic acids and protected ester equivalents bearing electron–withdrawing or electron–donating substituents in the meta– and para– positions, with respect to the C–B bond, are described. For example, Reaction of pentafluoronitrobenzene with 5,5–dimethyl–2–phenyl–1,3,2–dioxaborinane in the presence of catalytic quantities of Pd(PPh3)4 and using KF/alumina as the preferred base (DMF, 150 °C, 15 mins, μW) affords 2,3,4,5–tetrafluoro–6–nitrobiphenyl in good yield (80 %). The nitro group is crucial to the success of the cross–coupling processes and is believed to facilitate the oxidative addition step by directing the palladium catalyst into the adjacent C–F bond by a predominantly SNAr–type mechanism.

The photophysical changes that take place in Poly(9,9-di-n-alkylfluorenes) upon formation of the beta phase in methylcyclohexane solution are observed by optical spectroscopy. The equilibrium absorption spectra as a function of temperature show that conformational changes occur for all five polymers studied, from the hexyl (PF6) to decyl (PF10) side chains. The spectroscopic indicators of beta phase formation are not observed in PF6, and the trend of beta phase formation efficacy shows an optimal side chain length of 8 carbons. The beta phase formation in PF8, PF9 and PF10 is modelled using a previously reported aggregation model, with limited success. A mechanism for the beta phase formation is proposed, where the interactions between the alkyl side chains provide the chemical energy to overcome the activation energy barrier to planarise the polymer backbone, leading to the extended conjugation length that characterises the beta phase. Excitation spectra show that the beta phase can occur reversibly in dilute solution, most likely by chain folding leading to side chain interactions. The presence of side chain interactions is confirmed by evidence of a PF7-PF9 alternating structure formed in a mixed solution. The same trend of beta phase formation is observed in thin films of these polymers after thermal cycling and warm toluene vapour exposure, showing that side chain interactions are also required for beta phase formation in the solid state. Spectra of PF8 films with controlled keto content show that the energy transfer to the keto sites is mediated by migration, indicating that the beta phase is formed in domains rather than isolated chains, a result which is consistent with the side chain interaction model and other published results. The fraction of beta phase formed is shown to decrease linearly with a greater content of dibenzothiophene (DBT) co-monomer units, up to a cut-off limit of 20%. A statistical model of the distribution of DBT units in the chain is used to find a conjugation length of 9 monomer units, in contrast to a previous estimate but in agreement with the persistence length of PF8 in toluene. These results characterise the beta phase formation mechanism and its effects on the photophysical properties of Poly(9,9-di-n-alkylfluorenes), which is under widespread investigation for more use in efficient blue and white organic LED applications.

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The potential of the instantaneous Fourier transforming ability of optical systems is now being tapped. In particular, optical correlation is more and more becoming the focus of attention by current research groups with its many applications in the fields of machine vision, pattern identification and target tracking. This thesis gives a comprehensive view of the current state of the science of optical correlation and describes the many factors affecting experimental results of typical correlation systems including algorithmical errors and limitations and optical effects such as noise or phase inconsistency. The uses and types of spatial light modulator used in such systems are described and, in particular, the reflective electronically addressed liquid crystal over silicon modulator used in this thesis. Liquid crystal mesophases are examined and their light modulating effects analysed with respect to their applications in optical systems. Current optimisation algorithms and techniques are analysed and an adaptive stochastically self-correcting correlator system is described. Results are presented as computer simulations and sample optical processing architectures are described. These illustrate the benefits of such a technique on physical systems with the capability of cancelling out the effects of imperfections in objects and filters and indeed in the optics themselves.

This thesis extensively outlines the design and performance of the fIrst helium droplet apparatus to be built in the United Kingdom. Helium clusters (6000 atoms) were generated: by adiabatic expansion of research grade (99.9999%) 4He, at a stagnation pressure of 20bar, through a 5flm nozzle, cooled to 12K. The helium droplet beam is collimated by a 0.5mm skimmer (Molecular Beam Dynamics) before entering a 'pick-up' cell (lOcm, length) where the cluster beam interacts with a gaseous species of spectroscopic interest. The droplets 'pick-up' singular or multiple molecules that release their relative kinetic and potential energies to the droplet and become thermalised to the ultra cold environment of the helium bath (0.38K). Helium droplets therefore provide a cold, largely noninteractive medium in which to study the spectroscopy of molecular species. Contained in this thesis is a description: of the experimental challenge to produce a cluster source able to perform at the extreme conditions required to produce helium droplets; the modifIcations of the 'pick-up' system such that a variety of species (gases, liquids and solids) can be studied; the design and construction of a LIF region; the upgrade of a quadrupole mass spectrometer for maximum utility for this application; a description of the laser system and data acquisition methods; a review of cluster and helium droplet research; the theory associated with cluster and especially helium droplet generation; characterisation of the helium droplet beam, 'pickup' and fragmentation of neutral species upon detection; the preliminary results obtained from a study of resonant photon absorption (UV) of benzene solvated by helium droplets and the fIrst evidence of multiphoton ionisation of a molecule in a helium droplet

A continuum model incorporating flow is developed as an extension to the work of Stewart and Momoniat who considered a mechanical soliton travelling through a sample of smectic C* liquid crystal. Here we study a wave front propagating through an infinite sample of ferroelectric liquid crystal in a planar geometry, under the influence of an inclined electric field of constant magnitude. We use the dynamic theory for smectic C liquid crystals of Leslie, Stewart and Nakagawa, appropriately extended to include the spontaneous polarisation and elastic energy terms encountered in smectic C* materials. We incorporate flow terms into our model giving a total of five dynamic equations. The resulting dynamic equations have infinitesimal perturbations imposed upon them. The perturbation equations are linearised and, by exploiting an exact solution in the case where the field is co-planar with the sample, a set of linear perturbation equations are developed. Simplifying assumptions lead to a pair of equations which, when suitable time decaying, spatially dependent perturbations are applied yield an eigenvalue problem. By employing a suitable numerical scheme we examine the resulting stability problem and use the results to identify critical electric field strengths below which we conjecture, travelling waves are not initiated. We also present a novel method for determining wave front profiles for a mechanical soliton in a planar sample of ferroelectric smectic C liquid crystal. We end by looking at numerical method for determining wave speeds in ferroelectric smectic C liquid crystals which employs discretised nonlinear Volterra integral equations of the second kind. The method is completely general in scope, and may in fact be used to tackle wave speed problems for any appropriate reaction-diffusion equation which admits travelling wave solutions.