This thesis addresses the question of how patterning may arise through cell-to-cell communication. It combines quantitative data analysis with computational techniques to understand biological patterning processes. The first section describes an investigation into the robustness of an evolved artificial patterning system. Cellular automata rules were implemented sequentially according to the instructions in a simple `genome'. In this way, a set of target patterns could be evolved using a genetic algorithm. The patterning systems were tested for robustness by perturbing cell states during their development. This exposed how certain types of patterning rule had very different levels of robustness to perturbations. Rules that generated patterns with complex divergent patterns were more likely to amplify the effect of a perturbation. When smaller genomes, comprising less individual rules, were evolved to match certain target patterns, these were shown to be more likely to select complex patterning rules. As a result, the developmental systems based on smaller genomes were less robust than those with larger genome sizes. Section two provides an analysis of the patterning of microchaetes in the epithelial layer of the notum of Drosophila flies. It is shown that the pattern spacing is not sufficiently described by a model of lateral inhibition through Delta-Notch signalling between adjacent cells. A computational model is used to demonstrate the viability of long range signalling through a dynamic network of filopodia, observed in the basal layer of the epithelium. In-vivo experiments conrm that when filopodia lengths are effected by mutations the pattern spacing reduces in accordance with the model. In the final section the behaviour of simple asynchronous cellular automata are analysed. It is shown how these differ to the synchronous cellular automata used in the first section. A set of rules are identified whose emergent behaviour is similar to the lateral inhibition patterning process established by the Delta-Notch signalling system. Among these rules a particular subset are found to produce patterns that adjust their spacing, over the course of their development, towards a more ordered and densely packed state. A re-examination of the Delta-Notch signalling model reveals that this type of packing optimisation could take place with either dynamic filopodial signalling, or as an alternative, transient Delta signalling at each cell. Under certain parameter regimes the patterns become more densely packed over time, whilst maintaining a minimum zone of inhibition around each Delta expressing cell. The asynchronous CA are also used to demonstrate how stripes can be formed by cell-to-cell signalling and optimised, under certain conditions, so that they align in a single direction. This is presented as a possible novel alternative to the reaction-diffusion mechanism that is commonly used to model the patterning of spots and stripes.

My thesis deals with the investigation of the chemical and physical properties of the gas and dust involved in the formation of low mass stars. As the stars form, warm cores (or ‘hot corinos’) are detected in molecular emission. The study of such emissions allows us to get an insight on the physical conditions of low-mass star formation, and trace its various evolutionary stages. Through out this thesis I make use of a chemical model originally developed for the study of high mass star forming regions. I have adapted this model for the study of low mass stars and first applied it to explore the sensitivity of the chemistry of hot corinos to the changes in the physical conditions of the surrounding environment. It is found that the chemical trends of these cores does not qualitatively differ much from that of hot cores (remnant of high mass star formation) leading us to conclude that, at least in some cases, the formation of low-mass stars may be a scaled-down version of that of massive stars. One of the most studied hot corinos is that surrounding IRAS 16293-2422: in order to validate my model, I compare the predicted chemical abundances to the molecular emission from this object and find a relatively good match. Observations of warm cores also revealed that they are rich in deuterium content. I enlarge our chemical network to include all the possible mono-deuterated species, as well as D2CO. In this study, I look into the chemical evolution of the deuterated species, and aim to identify a set of deuterated molecules as evolutionary indicators for the protostellar stage of the core. A very debated issue when validating chemical models is that of whether the initial chemical conditions of the gas affect the chemical evolution of the star forming cores. I investigate this issue by running a large grid of dark and dense cloud models where the initial conditions are varied, in particular I investigate whether a pre-processed gas (e.g. ‘left over’ from a previous star formation event) may affect subsequent star formation processes and find that in general the initial chemical composition of the gas is in fact irrelevant. Finally, I took part of a study, led by Dr Bayet, where the chemistry of deuterated species in extragalactic environments is investigated and in this thesis I highlight my contribution to this work.

In this thesis, three different model metal-oxide semiconductor systems will be discussed. First, the impact of hydroxyl vacancies, OHvac, on the geometry, electronic structure, and mechanical properties of single-walled aluminosilicate, (Al2SiO7H4)N, and aluminogermanate, (Al2GeO7H4)36, nanotubes is investigated. It is found that, with the exception of one OHvac localised on the outer wall of the (Al2GeO7H4)36 tube, these defects induce occupied and empty states in the band gap. Those states are found to be highly localised both in energy and in real space. Different magnetisation states are also found, depending on both the chemical composition and the specific side with respect to the tube cavity. The focus of the thesis then shifts to one of the most important and well-studied metaloxide surfaces, the rutile TiO2(110) surface. The reactivity of the surface is revisited, in view of the discrepancy between theory and experiment on the interaction between molecular oxygen and surface hydroxyls. This discrepancy is resolved by proposing that excess charge, associated with the oxygen vacancy and originating from Ti interstitials, is present on the surface. This surface charge opens new reaction channels not theoretically possible otherwise. The study utilises hybrid Density Functional Theory (DFT) calculations and Scanning Tunneling Microscopy (STM) simulations to provide evidence for the proposed surface charging. The last part of the thesis focuses on another surface of TiO2, the (011) surface. TiO2(011) has recently attracted attention due owing to its reported high photocatalytic activity. Several proposed structures of the surface are inconsistent with each other. Recent developments, based on Surface X-Ray Diffraction (SXRD) data and DFT simulations, now agree on a new structure. In this part a review of the various structures is provided and further evidence is given on the validity of the new proposal by providing further insight on the appearance of the surface on the STM.

The electromagnetic mode density of the vacuum can be dramatically modified by the presence of an optical resonator. In the strong coupling regime, spontaneous emission in a cavity becomes a reversible process and the intracavity photon number undergoes Rabi oscillations. We load up to 200x10^3 ^133Cs atoms into a nearly confocal lossy cavity and reach the collective strong coupling regime. Normal mode splitting, the hallmark of this regime, is observed and cooperativities up to C_coll = (186±5) are measured. In a second experiment we investigate for the first time the multi-mode character of the coupled cavity-atom system. In a confocal cavity the higher-order transverse cavity modes are degenerate in frequency and accessible to the spontaneous emission of the atomic ensemble. We observe an increase of the coupling constant measured via modal decomposed transmission analysis, which could be attributed to the presence of the higher-order modes. Normal mode splitting proportional to the square root of the atom number was visible for all of the different mode components. Furthermore, we observe a redistribution of the relative weights in the modal transmission composition, which scales with the atom number in the cavity mode. In a second set of experiments, ^87Rb atoms were loaded into a dissipative lin ⊥ lin lattice. By driving the lattice with a biharmonic force, transport can be observed when the systems symmetries are broken: the so called ratchet effect. Research in this area is concerned with the appearance of current reversals. We were able to identify dissipation related symmetry breaking as the underlying cause of an observed current reversal, which occurs as a function of the driving frequency. Furthermore, in a second experiment, we use the ratchet effect as a probe of the optical potential depths. We show that an oscillating force with a frequency far above any other system-inherent timescale, can be used to renormalize the optical potential. The ^87Rb atoms experience an average position dependent force, which becomes controllable over the amplitude of the applied driving.

This thesis details the design, construction and alignment of the Dark Energy Survey's optical corrector. The Dark Energy Camera (DECam) is a new wide-field corrector with a 2.2 square degree field of view and five filters covering the visible wavelengths. It has been commissioned as an upgrade for the Blanco telescope at the Cerro Tololo Inter-American Observatory in Chile. The initial discussion in this thesis centres on the verification of the compression modulus of the rubber used in the opto-mechanical design. Experimental results are compared against the theoretical models used in the design of the optical corrector. This leads into the techniques created to ensure the identical reproduction of these rubber pads. The testing of the chemical composition of the cell material is then explored along with its thermal expansion properties in order to determine compliance with the specifications. The discussion on the design of DECam is completed with the metrology of the cells and the mapping of the variations from at and the non-circularity on the alignment surfaces. The thesis then extends to the alignment of the lenses (both prototype and DECam) within their cells and the tolerances to which they are held. Finally the effect of misalignment of the lenses on the weak lensing signal was investigated. Each lens was considered individually and then random misalignments were used to look at multiple lens misalignments. A quantitative system was used to determine the relative importance of the lenses for ensuring the best possible optical performance from the perspective of the weak lensing community.

State-insensitive traps are an important tool for precision spectroscopy. In these traps both the ground and excited state of the relevant atomic transition are shifted by the same amount. To obtain state-insensitive trapping, a specific trapping wavelength - called the "magic wavelength" - must be used. This thesis describes state-insensitive trapping of caesium atoms, as realised by using a trapping laser beam at the magic wavelength of 935.6 nm. Two different experimental setups were realised and characterised. The first set of experiments provided the characterisation of a singlewell state-insensitive trap, produced by using the laser beam from a Tisapphire laser. The trap lifetime was determined as a function of the trap depth, with the largest lifetime of 203 ms measured for a trap depth of 2.4 mK. Further improvement in the trap lifetime was obtained by applying a depumper laser beam, which prepared the atoms in the lower ground state. This suppresses hyperfine changing collisions, and the lifetime was increased to 3.6 s as a result. Ultimately, the lifetime was limited by the pointing instability of the dipole trap beam and the background gas collisions. A second experimental setup was then realised, to reduce the background gas collisions, which is the limitation of lifetime in the first setup. Furthermore, the imaging system was upgraded to reduce the background noise, and a MOPA system was used to produce the state-insensitive trap. In a second set of experiments, a single-well trap and a 1D optical lattice were compared to evaluate the suppression of two-body collisions in the 1D lattice case.

Quantum information theory has attracted much interest in the last decade. The cause of this interest is twofold: the exciting applications that the theory promises, such as the realization of quantum computers, but also the possibility that perhaps the theory will enable us to solve the mysteries of quantum physics. In this thesis we touched a wide variety of topics with the modest motivation that perhaps, at the very least, one could get a little more insight into the conceptual problems. Our motivation led us to carry out the work presented in this thesis. We explore entanglement properties of light in the context of quantum memories. Quantum memories are set to be a crucial component of future quantum computers. In the short and medium term, the development of e ective quantum memories would pave the way for the implementation of a variety of quantum information protocols. For the applications it is important to be able to store entanglement. In this thesis we investigate the storage of two mode Gaussian states of light in a QND feedback quantum memory and we examine the question whether it is better to store the state already entangled or whether is better to store a squeezed state which is only entangled after storage. We then turn to a study of some aspects of the theory of SIC-POVMs (Symmetric Informationally Complete Positive Operator Valued Measures). SIC-POVMs potentially have numerous application in quantum information. They have been constructed mathematically in every dimension 67. But it remains an open question whether they can be constructed in every nite dimension. In this thesis we describe an analogy between coherent states of a continuous variables systems and SIC-POVMs in a discrete system. We then go on to examine the Galois group of the extension eld generated by the components of the SIC-POVM ducial vector. We prove a number of theorems about this group. We then go on to actually calculate the group for a SIC-POVM in dimension 6 and show that it has a number of interesting properties. We speculate that this line of research may make a useful contribution to an eventual proof of the existence of SIC-POVMs. Finally we investigate quantum communication via spin chains. One of the key requirements for a functioning quantum information processor is the ability to transport quantum information from one location to another. Spin chains are a tool which might be used for this purpose. There have been many proposals recently which showed that under fairly general conditions spin chains communicate quantum information with arbitrarily high delity. However, so far there have not been many proposals addressing the problem of communicating as much quantum information as possible. In this thesis we address this problem and describe a method which achieves a high transmission rate for long spin chains.

The main aim of this study is to calculate a high temperature line list for H_2^32S. The results will form an important addition to the databases used for space applications, as well as laboratory investigations and pollution studies. The Dvr3d program suite is used to calculate the bound ro-vibrational energy levels, and dipole moment transition intensities. The most accurate available potential energy surface is empirically determined. This surface is used in our calculations after refining it by fitting to the up-to-date experimental data. For accurate line intensities, an accurate dipole moment surface (DMS) is needed. Constructing an accurate DMS for H_2S is well known to be difficult. A systematic ab initio study for the DMS has been performed. Different methods were tested in conjunctions with different basis sets taking into account the relativistic corrections and core-valence effects. The resulting (ATY2013) line list should be valid from 0 to 9000 cm^−1 and for temperature up to 2000 K. ATY2013 with cut off intensity of order 10^−31 cm^−1/(molecule×cm^−2) contains ∼36×10^6 transitions at 2000 K. In addition, the pure rotational transition frequencies of H_2S in natural abundance in its ground and first excited vibrational states have been recorded at room temperature at 0.005 cm^−1 resolution in the region 45 to 360 cm^−1 with a globar continuum source at SOLEIL synchrotron. 2400 rotational transitions are assigned to ground vibrational state of the four isotopologues H_2^32S, H_2^33S, H_2^34S and H_2^36S where 65% of them are new. 91 rotational transitions of H_2^36S were identified for the first time, as well as 406 rotational lines of H_2^32S and H_2^34S in their first excited bending vibrational state were recorded and analysed for the first time.

One of the surprising discoveries in the field of extrasolar planets is the proliferation of massive planets in small orbits. It is not believed possible for these planets to form in situ. Instead, it is likely that they formed at much greater distances from their parent stars, beyond the radial distance where the disc temperature drops to below the ice condensation temperature. The inevitable migration that is necessary to transport large planets to greatly reduced orbits has been demonstrated as possible through disc-planet simulations. This migration takes the planet through the ‘terrestrial’ planet forming zone during the period when the terrestrial-planet building blocks, planetesimals, swarm the region. The first part of this thesis considers the effects of planet migration on the orbital dynamics of the planetesimals in the terrestrial zone, how the planetesimals are accreted, shepherded and possibly scattered outwards, and whether enough material survives in the terrestrial zone from which to form terrestrial planets. The orbital eccentricity excitation of the planetesimals results in orbits that inevitably cross. The differential velocity component may result in catastrophic collisions between planetesimals, releasing significant amounts of dust back into the disc. The effect of dust replenishment on the ionisation fraction of the disc and the ability to support MHD turbulence requires knowledge of the physical and chemical environment of the disc. The second part of this thesis considers the chemical evolution of a molecular cloud undergoing gravitational collapse and warm-up to derive chemical abundances applicable to disc modelling. The final part of this thesis investigates the possibility of dust replenishment in the disc due to the induced catastrophic collisions between planetesimals. The potential dust replenishment combined with the derived chemical abundances are input into a chemical disc model to assess the influence of a migrating planet on a protoplanetary disc.

The Heisenberg spin-chain and the Quantum Kicked Rotor (QKR) are key models in condensed matter and quantum chaos respectively. The former, consisting of a line of qubits that interact with their neighbours through an exchange interaction, has recently received much attention in the context of quantum information and communication. In particular, it has been shown that a Heisenberg chain can be used as a channel for the transfer quantum states and the sharing of entanglement. The QKR, on the other hand, is a paradigm of quantum chaos. It is one of a valuable collection of quantum systems with a well dened classical limit that shows both regular and chaotic dynamics. This thesis investigates the dynamics of a Heisenberg chain subjected to periodic ±-kicks from a parabolic magnetic eld. It will be shown that, when perturbed in this way, spin-chains can provide realizations of QKR systems. Using this connection, well-known features of the dynamics of kicked rotors can be used to manipulate the evolution of excitations and entanglement in the spin-chain. Conversely, results from the spin-chain analysis can inform our knowledge of the kicked rotor systems. The focus of the rst part of this thesis is the dynamics of singly excited chains. In this case, the kicked Heisenberg chain is shown to be dynamically equivalent to a QKR. Similar correspondences can be found. Two examples, spin-chain realizations of the Double-Kicked Rotor and a double-well kicked rotor, are explored. Later sections are concerned with the dynamics of multiple excitations. These excitations interact - scattering or forming bound states of inverted spins. The kicked chain now corresponds to a system of coupled kicked rotors. It will be shown that by tuning the parameters it is possible to control the time-evolution of correlations in the chain.