This doctoral dissertation is concerned with the study of quantum dynamics where finite dimensional systems (typically two-level `qubits') interact with or through a set of bosonic modes, in various different configurations. Our main focus is on identifying and investigating signatures of quantum coherence emerging between the qubits in such dynamical situations. We first present a toy model where two qubits are encoded in the single-excitation subspace of the global system and study the average fidelity of a controlled-Z (CZ) quantum gate mediated by the bosonic modes. Next, we turn to analytically intractable spin-boson like models, by adopting the Multi-configurational Ehrenfest (MCE) method. We apply MCE to the study of the Choi fidelity of a CZ gate between two distant qubits, mediated by sets of bosonic modes (including sets which represent discretization of bath's continua) under different coupling Hamiltonians. The testing of the MCE method is then pushed further by a comparative analysis with full variational approaches and adiabatic path integral techniques in a case of super-Ohmic spin-boson model. Finally, we determine a general error bound applicable to most approximated treatments of unitary quantum evolutions, and suitable to compare MCE with other numerical techniques for the study of spin-boson dynamics.

In the present work, a beam of monoenergetic positrons has been used to investigate the ionization of atoms and small molecules at energies below 1 keV. The beam was produced from the radioactive decay of a ²²Na source combined with W-mesh moderators and a magnetic guidance system. The first measurements of the cross-sections for excited-state positronium formation from Xe and simultaneous ionization–excitation cross-sections for positron impact on CO₂ and N₂ have been performed. Near-complete characterization of the detection system coupled with the ability to measure several processes simultaneously allowed the collection of data sets which were internally self-consistent. By normalizing the total ionization cross-section, an absolute scale could be applied to all measurements. A number of methods for achieving this were employed, as a check on external consistency. The cross-section for excited-state positronium formation from Xe completed a study (Murtagh et al., 2009) in Ps formation from the noble gases. The measurement has defined a trend of increasing maximal fraction of Ps formed into the 2P state with increasing atomic number. The measurements of ionization–excitation for molecular targets (Cooke et al., 2010a) reveal that this process is enhanced over the equivalent interaction involving electrons. This enhancement arises mainly (or exclusively, in the case of CO₂) from the effect of positronium formation, over and above the corresponding enhancement in the total ionization cross-section. Based on this observation, and the comparative lack of excited-state Ps detected in these targets, a mechanism for the enhancement involving an accidental resonance between a neutral excited molecular state and an ionic state with Ps formation has been proposed. The cross-sections for ionization–excitation were measured contemporaneously with a full suite of ionization cross-sections.

The localisation of excited electrons on defects in ceramic materials has a significant effect on the evolution of damage resulting from irradiation. The localisation of charge on a defect will change the charge state of that defect, which will affect the position of the defect level and change the defect properties. In ceramic materials for encapsulating radioactive waste the alpha decay of the actinide results in the accumulation of helium within the lattice, which will affect the durability of the waste and alter the performance of the waste form. DFT was used to study the structure and mobility of defects in different charge states for two ceramic materials. MgO was used as a model oxide due to the simple crystal structure. It was found that the charge state has a significant effect on the structure and mobility of the oxygen defects. The localisation of a hole onto the O2- interstitial significantly reduces its migration barrier. The effect of charge localisation on a hexa-interstitial cluster was investigated and it was found that the charge state affects the migration barriers, with the singly-charged cluster again having the lowest migration barrier. Zirconolite, a proposed encapsulation matrix for plutonium, was also studied. The monoclinic crystal structure comprises of layers of alternating 5 and 6 coordinated Ti-O polyhedra, separated by layers of alternating Ca and Zr ions. The structures of intrinsic defects, in different charge states, were studied and a significant effect on the defective structure of Zr and Ti vacancies was observed. Ab initio random structure searching was used to identify the lowest energy interstitial site for each species. DFT-D3 was used to study the structure, mobility and binding of a He atom in zirconolite. It was found that the neutral 5-fold coordinated Ti vacancy was the strongest binding site.

A promising platform for quantum information processing is that of silicon impurities, where the quantum states are manipulated by magnetic resonance. Such systems, in abstraction, can be considered as a nucleus of arbitrary spin coupled to an electron of spin one-half via an isotropic hyperfine interaction. We therefore refer to them as nuclear-electronic spin systems. The traditional example, being subject to intensive experimental studies, is that of phosphorus doped silicon (Si:P) which couples a spin one-half electron to a nucleus of the same spin, with a hyperfine strength of 117.5 MHz. More recently, bismuth doped silicon (Si:Bi) has been suggested as an alternative instantiation of nuclear-electronic spin systems, differing from Si:P by its larger nuclear spin and hyperfine strength of 9/2 and 1.4754 GHz respectively. The aim of this thesis has been to develop a model that is capable of predicting the magnetic resonance properties of nuclear-electronic spin systems. The theoretical predictions of this model have been tested against experimental data collected on Si:Bi at 4.044 GHz, and have proven quite successful. Furthermore, the larger nuclear spin and hyperfine strength of Si:Bi, compared with that of Si:P, are predicted to offer advantages for quantum information processing. Most notable amongst these is that magnetic field-dependent two-dimensional decoherence free subspaces, called optimal working points, have been identified to exist in Si:Bi, but not Si:P.

Since physical form and function are intimately linked, mechanisms that maintain cell shape and size within strict limits are likely to be important for a wide variety of biological processes. However, while intrinsic controls have been found to contribute to the relatively well-defined shape of bacteria and yeast cells, the extent to which individual cells from a multicellular animal control their plastic form remains unclear and is the subject of much scientific interest. In this work I studied the regulation of the cell length using micro-patterned lines to limit cell extension to one dimension. In particular, I described a mechanism by which animal cells maintain a characteristic steady-state length independent of their size, pattern-width and cortical actin, but dependant on microtubule dynamics and organization. Population of dynamic microtubules aligned along the long cell axis, as the result of interactions of microtubule plus ends with the lateral cell cortex, drives elongation of cells on micropatterned lines. Furthermore, I described a mathematical model of micropatterned cells based on microtubules dynamics. Notably, the model recapitulates the cell length control mechanism that I observed experimentally. Moreover, I discuss model predictions and related experimental tests validating these predictions and confirming the cell length control hypothesis. In conclusion, my work suggests that microtubules impose unexpected limits on cell geometry that enable cells to regulate their length. Since cells are the building blocks and architects of tissue morphogenesis, such intrinsically-defined limits may be important for development and homeostasis in multicellular eukaryotes. Finally, preliminary in-vivo experiments confirmed the biological relevance of the homeostasis cell length control in zebra fish.

We describe and apply a microscopic model for the calculation of gas diffusion rates in several proteins, including [NiFe]-hydrogenases, [FeFe]-hydrogenases, and carbon monoxide dehydrogenases. These proteins share a common feature that their substrate gas molecules have to diffuse through the protein matrix before they can reach the active site and be catalysed. For hydrogenases, H₂ serves as a substrate but O₂ and CO are strong inhibitors. For dehydrogenases, CO₂ is the substrate and CO is the product. How they manage to control transport of different gas molecules inside the protein remains a question. In our model, the diffusive hopping of gas molecules in the protein interior is coarse grained using a master equation approach with transition rates estimated from equilibrium and non-equilibrium pulling simulations. Propagating the rate matrix in time, we find that the probability for a gas molecule to reach the enzyme active site follows a mono-exponential increase. Fits to a phenomenological rate law gives an effective diffusion rate constant for gas molecules that is in very good agreement with experimental measurements. This method enables us to characterise gas diffusion in proteins not only qualitatively but also, more importantly, in a quantitative manner. Based on the findings we explore, we can provide insights into how proteins can filter different gas molecules without being affected in their enzymatic activity and further suggest specific amino acid side chains for future mutation experiments in order to protein-engineer a more robust and efficient enzyme.

We aim to explain the reason why Jupiter's upper atmosphere is hotter than initial theories predicted by employing a coupled magnetosphere, ionosphere and thermosphere model. We use this coupled model to study how changes in upstream solar wind dynamic pressure affect Jupiter's thermospheric dynamics, energy balance, aurora and magnetosphere-ionosphere coupling currents. The variation in solar wind pressure is investigated on long (_50 Jovian days) and short (3 hours) time scales, which we respectively refer to as steady state and transient state. We vary the solar wind pressure by changing the size of the magnetosphere, as these two parameters are inversely correlated. In steady state, three different configurations are used: compressed, average and expanded magnetospheres. We find that the power dissipated by Joule heating and ion drag increases by —190% from a compressed to expanded magnetosphere. For transient modelling, the magnetosphere is compressed and expanded in a period of 3 hours. Compressions cause a reversal in momentum transfer between the thermosphere and magnetosphere. Compressions and expansions lead to at least a factor-of-two increase in ion drag and Joule heating, resulting in a —2000 TW increase in total power dissipated in the thermosphere and local temperature variations 25 K. Compressions also cause a —450% increase in auroral UV emission whilst expansions increase UV emission modestly by —37%. While these analyses do not provide a definitive answer to the elevated Jovian thermospheric temperature, they show that, in moving from a steady-state to a time-dependent paradigm, the thermospheric response to magnetospheric reconfiguration is characterised by dramatically different distributions of temperature and wind. In particular, magnetospheric compressions produce extensive cells of equatorward flow emanating from the auroral zone, suggesting that a Jovian-like magnetosphere subject to adequately frequent, repeated episodes of contraction/expansion may possess elevated thermospheric temperatures, perhaps even at the level of those observed.

Solar eruptive events are the most energetic events in the solar system which are driven by the reconfiguration of solar magnetic field. They are catagorised into two groups: Solar flares or Coronal Mass Ejections (CME). The released energy is ejected both downward towards the solar surface and its interior and outward into the interplanetary space. The work presented in this thesis represents a contribution towards better understanding the impact of solar eruptive events on the solar surface and lower atmospheric layers. This thesis uses observations from a wide range of multi-wavelength data set involving SDO/HMI, SDO/AIA, Hinode, TRACE, SOHO/MDI, SOHO/EIT, RHESSI, and GONG to investigate the nature of solar flares induced seismic waves and the formation of "dimming regions" following the eruption of some CMEs. Observational signatures and consequences of Hard X-ray (HXR) and White Light (WL) emission were analysed for two sets of acoustically -active and —quiet solar flares. The rate of energy deposition and the area over which the energy is being deposited suggested that in general acoustically active flares are associated with larger and more impulsive deposition of electron energy. However, this does not always correspond to a higher WL contrast. Dimming regions formed during some CME events and their relation to the topology of magnetic fields embedded in the dimming areas were investigated. Analysis of the magnetic field strength and its associated tilt angle together with the intensity variation of the dimming regions revealed that reconfiguration and stretching of the magnetic field lines results in formation of the dimming regions. However, the study was not conclusive for weaker CMEs.

We have carried out a series of ab initio R-matrix calculations at the static exchange and close-coupling levels of approximation on molecules of astrophysical interest. These include the polar triatomics HCN and HNC (hydrogen isocyanide) and their isotopologues DCN and DNC, the diatomics CS (carbon monosulphide) and SiO (silicon monoxide), the weakly polar CO molecule and the non-polar CH4 molecule. With the exception of CO, all the calculations presented here were carried out using the software ‘Quantemol-N’ which provides an intuitive user-friendly interface to the UK polyatomic R-matrix codes. A chapter is devoted to the discussion on the software: how to prepare an R-matrix calculation using it, its present capabilities and future development. The ultimate aim of this thesis is to demonstrate the need to account for electron-induced chemistry in any astrophysical model. We seek to show that in the case of polar molecules, namely, those molecules with large dipole moments, electron collisions are the dominant mechanism of rotational excitation in comets and other astrophysical bodies. Specifically, we will show that electron-impact excitation rate coefficients are several orders of magnitude higher than the corresponding atom-molecule ones. The thesis concludes with a summary of the key findings and opportunities (and where necessary improvements) that may arise from them. All the scattering equations presented here used atomic units.

Biological systems typically consist of large numbers of interacting components and involve processes at a variety of spatial, temporal and biological scales. Systems biology aims to understand such systems by integrating information from all functional levels into a single cohesive model. Mathematical and computational modelling is a key part of the systems biology approach and can be used to produce composite models which describe systems across multiple scales. One of the major diculties in constructing models of biological systems is the lack of precise parameter values which are often associated with a high degree of uncertainty. This uncertainty in parameter values can be incorporated into the modelling process using sensitivity analysis, the systematic investigation of the relationship between uncertain model inputs and the resulting variation in the model outputs. This thesis discusses the use of global sensitivity analysis in systems biology modelling and addresses two main problem areas: the application of sensitivity analysis to time dependent model outputs and the analysis of multi-scale models. An approach to the analysis of time dependent model outputs which makes use of principal component analysis to extract the key modes of variation from the data, is presented. The analysis of multi-scale models is addressed using group-based sensitivity analysis which enables the identication of the most important sub-processes in the model. Together these methods provide a new methodology for sensitivity analysis in multi-scale systems biology modelling. The methodology is applied to a composite model of blood glucose homeostasis that combines models of processes at the sub-cellular, cellular and organ level to describe the physiological system. The results of the analysis suggest three main points about the system: the mobilisation of calcium by glucagon plays a minor role in the regulation of glycogen metabolism; auto-regulation of hepatic glucose production by glucose is important in regulating blood glucose levels; time-delays between changes in blood glucose levels, the release of insulin by the pancreas and the eect of the hormone on hepatic glucose production are important in the possible onset of ultradian glucose oscillations. These results suggest possible directions for further study into the regulation of blood glucose.