Orbit-based theoretical approaches to modelling strong eld phenomena allow physical intuition to be extracted from complex multi-dimensional quantum processes. Highorder harmonic generation (HHG) has been interpreted relatively successfully for almost two decades as a three step process in which an ionized electron is accelerated by the eld and recombines with its parent ion, resulting in high-order multiples of the laser frequency. This process is often modelled within the strong-eld approximation (SFA), where the eect of the Coulomb potential on the electron is neglected while the electron is accelerated by the eld, and the single-active electron (SAE) approximation. The SFA provides an appealing interpretation of HHG in terms of interfering electron trajectories. Although successful in reproducing experimental observables in atomic systems, in recent years the importance of multi-electron eects, molecular orbital symmetry and the Coulomb potential in atoms and diatomic molecules have been seen experimentally and theoretically. These eects, neglected by the original SFA formulation, mean that either modications to the original SFA, or new trajectory based theories, are essential for a more complete physical understanding of the HHG phenomenon. This thesis investigates these eects in HHG from homonuclear and heteronuclear diatomic molecules in strong elds. We model and assess the importance of multiple molecular orbital contributions, molecular orbital geometry and two-centre interference on the HHG spectrum. These problems are approached within a semi-analytical, SFA, framework and with a static core. It is found that these eects can be seen in the HHG spectrum. By predicting novel features in the spectrum arising from such eects we obtain not only a better understanding and interpretation of current experimental results, but also new insight and applicability to molecular imaging. In addition to these modications, a new theoretical approach, the coupled coherent state (CCS) method is used to model Hydrogen in an intense eld, although it can be extended to multi-electron systems and diatomic molecules. In the CCS method, the Coulomb potential is fully included at all stages in the HHG process, and most notably, during the electron propagation, where it is neglected by the SFA. The CCS method has favourable scaling with dimensionality, compared to other numerical approaches, as well as being fully quantum. It is trajectory based, facilitating comparison with the three step model and the strong eld approximation. Therefore we benet from the physical intuition of semi-classical approaches but within a fully quantum framework and without the approximations of semi-analytical methods.

Observations of star forming molecular clouds reveal clumpiness on all scales, both in the spectra of molecules and thermal continuum emission from the solid component of the interstellar medium, the dust. Recent, high resolution maps have allowed us to probe down to extremely small scales at which we see clumps of radii just several hundredths of a parsec. A good knowledge of the structure of these regions, and of the chemical processes occurring within, is crucial if we want to properly understand the early stages of star formation and the resulting stellar population. However, observations of cold, dense environments are challenging. Molecules emit at long wavelengths which are notoriously difficult to observe. A comparison with models is also complicated by the fact that in these conditions molecules will freeze-out onto dust grain surfaces forming icy mantles. We know little about the rate at which this process occurs in interstellar conditions, or the chemical reactions that happen on the grain surfaces. In this thesis we present two alternative methods by which to investigate the underlying clumpy nature of a molecular cloud and consider freeze-out in such an environment. Small, quiescent regions of enhanced emission in several molecules (including ammonia and HCO+) have been observed near to Herbig-Haro objects (HHOs) in star forming clouds. It was suggested that these could be due to molecules in small dense clumps being liberated from the dust grain surface by radiation from the shock front. Chemical modelling later proved this theory to be viable, and it was further supported by observational surveys and more detailed modelling of specific regions. In chapter 2 we simulate a dense clump near to an HHO, adapting the chemical code used in the original models to allow the shock front to move past the clump, providing a more realistic description of the effect of the radiation field. Chapter 3 describes how the outputs from these models can be used to simulate observations of part of a molecular cloud made up of small, transient density enhancements irradiated by a passing shock front. We briefly compare our synthetic maps with HCO+ spectra in regions surrounding HHOs. Commonly, researchers use decomposition algorithms on 2D and 3D maps to pick out clumps of emission and evaluate their properties. The mass functions of these objects often appear to emulate the stellar initial mass function, which has led researchers to conclude that the stellar mass is set at a very early stage, prior to the switch on of the protostar. In Chapter 4 we introduce the Gould Belt clouds for which we have HARP CO and SCUBA data (the HARP maps are presented in Appendix B). It is these on which we perform the analysis described in the final 3 Chapters. In Chapter 5 we investigate four popular clumpfinding algorithms, testing them on both synthetic and real (HARP) data, and explore the impact of user defined input parameters on derived properties. We choose one algorithm, with one set of input parameters, and use this to analyse the distribution of CO clumps in five nearby molecular clouds. The results of this study are outlined in Chapter 6. Chapter 7 focuses on the process by which CO freezes-out (depletes) onto the surfaces of dust grains in dark clouds. A single value for the depletion of a particular molecule is difficult to achieve because of its strong dependence on environmental factors and the past evolution of a region. However, we have a consistent data set across a range of environments and so are able to perform a statistical study in which we compare hydrogen densities derived from dust emission with those calculated using the CO maps. We look for missing CO in the gas phase which we then assume to be the result of depletion.

The astonishing success story of microelectronics cannot go on indefinitely. In fact, once devices reach the few-atom scale (nanoelectronics), transient quantum effects are expected to impair their behaviour. Fault tolerant techniques will then be required. The aim of this thesis is to investigate the problem of transient errors in nanoelectronic devices. Transient error rates for a selection of nanoelectronic gates, based upon quantum cellular automata and single electron devices, in which the electrostatic interaction between electrons is used to create Boolean circuits, are estimated. On the bases of such results, various fault tolerant solutions are proposed, for both logic and memory nanochips. As for logic chips, traditional techniques are found to be unsuitable. A new technique, in which the voting approach of triple modular redundancy (TMR) is extended by cascading TMR units composed of nanogate clusters, is proposed and generalised to other voting approaches. For memory chips, an error correcting code approach is found to be suitable. Various codes are considered and a lookup table approach is proposed for encoding and decoding. We are then able to give estimations for the redundancy level to be provided on nanochips, so as to make their mean time between failures acceptable. It is found that, for logic chips, space redundancies up to a few tens are required, if mean times between failures have to be of the order of a few years. Space redundancy can also be traded for time redundancy. As for memory chips, mean times between failures of the order of a few years are found to imply both space and time redundancies of the order of ten.

As interest in biophysics and biophysical modelling has grown in the cell and developmental biology communities, a variety of techniques have been developed to measure the mechanical properties of single cells. Atomic Force Microscopy (AFM) has become one of the preferred methods for these measurements primarily due to its ease of operation and commercial availability. However, measurements on soft cells with a variable surface topography require an additional level of care so that the predicted contact area with the cell surface is accurately estimated. Using combined AFM and confocal microscopy I have shown that with pyramidal tipped cantilevers the cell body can easily deform to the shape of the tip but can also touch the underside of the AFM cantilever beam causing an overestimation of elasticity. Such artefactual increases in contact area could be avoided by using spherical tipped cantilevers or tips with a high aspect ratio. I examined the role of the cytoskeleton and cell contractility in setting single cell stiffness with AFM. With techniques such as AFM, the rheology of single cells is becoming increasingly well characterised. The next logical step in furthering our understanding of organ and embryo mechanics is to scale up investigations to simple tissues such as on cell thick monolayers. I have developed methods to measure the mechanical properties of MDCK epithelial cell monolayers under AFM indentation or planar extension. Using deep indentation of monolayers cultured on soft gels I have measured the evolution of mechanical properties upon the establishment of cell-cell junctions. The relative mechanical stiffnesses of monolayer-gel composites evolve as cell contacts are established and required the formation of mature contractile adherens junctions. To measure the planar mechanical properties of cell monolayers I designed a system to create monolayers freely suspended from their susbstrate between two test rods. Cell monolayers have a higher stiffness than their cellular constituents due to the organisation of the cell cytoskeleton upon the formation of matured intercellular junctions.

The goal of this dissertation is to study the infrared absorption spectrum of the C 3 (carbon three) molecule. In particular, the aim is to investigate its ground electronic state up to 12:500 cm-1, as this affects the atmospheres of cool C-rich stars. The linear C 3 molecule shows very unusual properties for a linear molecule: a high degree of floppiness, no permanent dipole moment and a strong bentstretch interaction. Consequently, the C 3 spectrum presents particular features such as overtones, hot bands, and, as has been recently detected in Carbon stars and molecular clouds, a quite low fundamental bending frequency (63 cm-1) when in the ground electronic state. This dissertation aims to address each of these features. The first section discusses the context for this work: the stars. It provides a brief introduction about the Astrophysics related to this research project. A review at the recent literature is provided and the experimental results which provide the goal for the results of the theoretical work in the rest of the dissertation are set out. The second section introduces the C 3 molecule and outlines its properties. Previous C 3 studies are discussed and the theoretical approach used to study ro-vibrational spectra of triatomic molecules is set out. Preparatory tests and calculations are carried out to allow a theoretical reproduction of C 3 roto vibrational spectrum in the infrared region to be produced. The third part of the thesis expands on the nuclear motion calculations of section 2 and presents the results of the large scale calculations performed using the DVR3D suit programs written by Tennyson et al. [1]. This program allows the calculation of energy levels, wave-functions, expectation values and Einstein Coefficients. It takes as input the Potential Energy Surface (PES) and a Dipole Moment Surface (DMS) constructed a priori (in section 2) by solving the electronic problem within the Born-Oppenheimer's approximation. Because the quality of the PES sets the accuracy of the ro-vibrational calculations tests on different C 3 PESs and DMSs are performed. To reproduce accurate spectra of cool stars atmosphere in the temperature range of 2000 - 4000 K it was necessary perform calculations with high rotational quantum number. For this reason, tests with J>>0 were necessary to optimize the DVR3DRJZ parameters in order to guarantee a certain degree of accuracy and energy levels convergence. The results of these calculations and associated C 3 line-lists should be very useful to support the observations and model atmospheric studies. This work was generously supported by the QUASAAR Marie Curie Network.

Coronal mass ejections (CMEs) are large-scale explosions on the Sun that expel plasma and magnetic field into the heliosphere. The interplanetary counterparts of CMEs, termed interplanetary CMEs (ICMEs), are often directly observed by spacecraft located in the near-Earth environment, and this thesis focuses on understanding the evolution of these structures as the propagate away from the Sun and into the heliosphere. This work contributes to the understanding of space weather in the near-Earth environment, which is known to affect the technological systems at Earth upon which we increasingly rely. A subset of ICMEs, termed magnetic clouds, in which a flux rope structure can often be identified, form the primary focus of these studies. The process by which a magnetic cloud observed directly in interplanetary space may be linked with its associated CME, through the combined study of remote observations of the Sun and in situ observations near-Earth, is discussed. A comparison of the magnetic topology of the erupting structure at both the Sun and in interplanetary space allows us to infer the process by which it erupts, and better understand its evolution as it propagates through the heliosphere. A subset of magnetic clouds, in which we directly observe unusual internal substructure, is identified. We examine the physical nature of this substructure, characterising the observed behaviour of both the magnetic field and plasma in these regions. To improve our understanding of the external physical processes that influence the evolution of a magnetic cloud in interplanetary space, we investigate, and ultimately evaluate, a number of physical mechanisms that may lead to the formation of unusual magnetic cloud topology.

The thesis is concerned with the study of the massless Dirac equation. In the first part we study the massless Dirac equation in dimension 1+3 in the stationary setting, i.e. when the spinor field oscillates harmonically in time. We suggest a new geometric interpretation for this equation. We think of our 3-dimensional space as an elastic continuum and assume that material points can experience no displacements, only rotations. This framework is a special case of the Cosserat theory of elasticity. Rotations of material points are described mathematically by attaching to each geometric point an orthonormal basis which gives a field of orthonormal bases called the coframe. As the dynamical variables we choose the coframe and a density. We choose a particular potential energy which is conformally invariant and then incorporate time into our action by subtracting kinetic energy. We prove that in the stationary setting our model is equivalent to a pair of massless Dirac equations. In the second part we consider an elliptic self-adjoint first order pseudodifferential operator acting on columns of m complex-valued half-densities over a compact n-dimensional manifold. The eigenvalues of the principal symbol are assumed to be simple but no assumptions are made on their sign, so the operator is not necessarily semi-bounded. We study the spectral function and derive a two-term asymptotic formula. We then restrict our study to the case when m=2, n=3, the operator is differential and has trace-free principal symbol, and address the question: is our operator a massless Dirac operator? We prove that it is a massless Dirac operator if and only if, at every point, a) the subprincipal symbol is proportional to the identity matrix and b) the second asymptotic coefficient of the spectral function is zero.

Skin cancer diagnosis often requires invasive biopsies. These can be time-consuming and cause discomfort to the patient. Optical coherence tomography is a non-invasive tool capable of imaging skin on the micron scale. However, the modality’s contrast sensitivity limits its ability to distinguish between healthy and diseased tissue in some non-melanoma skin cancers. In this thesis, optical coherence elastography is explored as a means of contrast enhancement through the analysis of a sample’s mechanical, rather than optical, properties. An analysis of OCT imaging performance is used to design a suitable elastography phantom. Experimental measurements are also used to optimise the image tracking software. A well-defined, controlled actuation is applied to a tissue phantom and imaged using optical coherence elastography. A stiff inclusion is subsequently discerned from the surrounding material, even though conventional image contrast is low. Elastographic detail is also depicted in tissue. Finally, enhancements in axial displacement sensitivity are acquired through the acquisition of phase data and alternative actuation techniques are explored. The optical coherence elastography technique was sensitive to a Young’s modulus ratio of 7 from a 56 μm actuation. The possibility of detecting smaller changes in mechanical properties was also investigated. Axial phase displacement sensitivity was 50 nm, with an order of magnitude increase in strain sensitivity. This demonstrates the technique’s potential usefulness in discriminating between cancerous and healthy tissues.

This thesis describes the neutron scattering studies of three model magnetic systems; the coupled spin dimer compound TlCuCl3, the frustrated spin ladder material BiCu2PO6 and the impurity-doped spin ladder material BiCu_2(1-x)Zn2xPO6. TlCuCl3 is a realisation of a continuously tunable model magnet, where applied hydrostatic pressure can drive the system from a state of disorder into long-range magnetic order with the emergence of an excitation at the quantum critical point that corresponds to longitudinal fluctuations of the ordered moment. The study of the excitations in TlCuCl3 is now extended to finite temperatures. The results are summarised in Chapter 4, where similarities are reported between the quantum phase and thermal phase transitions. Spin ladder systems provide an exciting opportunity to study aspects of low-dimensional physics. With model magnets previously constrained to the limits of `strong' exchange (~ 100 meV) in the cuprates and `weak' exchange (~1 meV) in the metal-organics, the new spin ladder BiCu2PO6 offers the opportunity for study of spin ladder physics in the `intermediate' exchange regime (~ 10 meV). Inelastic neutron scattering studies of this system are presented in Chapter 5, where the magnon dispersion, exchange geometry and anisotropy are deduced from analysis of the excitation energies. Substitution of the Cu2+ sites in BiCu2PO6 with non-magnetic impurities Zn2+ results in the creation of BiCu2(1-x)Zn2xPO6, where a single S = 1/2 moment is liberated for each impurity. These moments are shown to demonstrate long-range correlations and magnetic ordering below a characteristic temperature, TN. Single crystal samples with x = 0.01, 0.03 and 0.05 have been investigated and structural studies of each are reported in Chapter 6. The field and temperature dependence of the observed long-range order is reported as well as a magnetic structure determination and studies of the impurity dependence of the coherence of the magnetic order.

The present work focuses on the investigation of two types of new materials, phosphorescent and near-infrared, for the fabrication of solution-processible Organic Light-Emitting Diodes (OLEDs). After the introduction of the theoretical background in the first part, the second part concentrates on phosphorescent OLEDs based on copper transition metal complexes. The photophysical properties of the copper complexes, the phosphorescent host and the interlayers were studied before the fabrication of phosphorescent OLEDs. Despite the various colours exhibited by the metal complexes all devices emit white light. The possible formation of an exciplex at the guest/host interface was thus investigated. Finally the influence of the solvent on the morphologies of the films and the performances of the devices were studied. The third part focuses on near-infrared OLEDs obtained by using two different strategies. First by using a near-infrared copolymer emitting at 880 nm and incorporating it in green and red hosts and second by the creation of what is believed to be an exciplex at the interface between a hole injection layer and twisted organic molecules that emit at 515 and 540 nm. In both cases pure infra-red light above 800 nm was achieved.