Modern electron microscopes are fitted with ever larger charge-coupled device (CCD) cameras capable of faster acquisition rates which in turn drives a concomitant increase in the bandwidth of data that is being collected and the amount of information in our datasets. At the same time, current increases in computational performance are largely being delivered through the addition of parallel execution units rather than explicit increases in the speed of single processors, this means techniques that cannot exploit their inherent parallelism are seeing little performance benefit from the generational improvements in computer processors. Many techniques used in electron microscopy to process these large datasets have not been adapted to utilise the modern methods available for parallel data processing which can lead to lengthy offline data processing techniques which could otherwise be performed in near real-time. Reimagining these methods to suit highly parallel computational architectures such as graphics processing units (GPUs) can offer improved performance orders of magnitude higher than their central processing unit (CPU) counterparts. In this thesis I have looked specifically at the case of transmission electron microscopy (TEM) image simulation via the multislice procedure, and exit wave reconstruction (EWR), which can both potentially see huge benefits by adapting these algorithms to exploit their parallelism. Software has been developed for performing multislice simulations using GPU computation where the increase in computational power also allows for modifications to be made which can increase the accuracy of the simulations at the expense of simulation time. The multislice software developed here has no minimum slice thickness limitations and the slice thickness no longer has to be coupled to the structure being simulated to ensure accuracy. The CCD detector characteristics and electron dose have also been incorporated within the simulation process. The use of GPUs has allowed these simulations to be performed in vastly less time than CPUs based equivalent simulations. Software has also been developed for performing EWR on either multicore CPUs or GPUs which lowers the time required to perform EWR sufficiently that real-time reconstruction at typical CCD frame-rates is a distinct possibility. This EWR software additionally features mutual information (MI) based image alignment which can handle accurate image alignment in cases where other methods are prone to failure. These software are used to aid in the investigation of fluorinated graphene conformation via multislice simulation and EWR, and in the study of self-assembled block co-polymer assemblies also by EWR.

This thesis is a report on experimental investigations of magnetotransport, structural and optical properties of p-type modulation doped (MOD) heterostructures with Sit-xGex channel of high Ge content (0.6<x<l) grown on Sit_yGey/Si(OOI) virtual substrate (VS). The active layers of MOD heterostructures were grown by solid source molecular beam epitaxy (SSMBE). The VSs were grown either by SS-MBE or low-pressure chemical vapour deposition (LP-CVD). The influence of thermal annealing on magnetotransport, structural and optical properties of Sit-xGexlSit-yGey heterostructures was studied by performing the post growth furnace thermal annealing (FTA) treatments in the temperature range of 600-900C for 30min and rapid thermal annealing (RTA) treatments at temperature 750C for 30sec. Structural and optical analysis of p-type MOD Sit-xGex!Si1-yGey heterostructures involved the techniques of cross-sectional transmission electron microscopy, ultra low energy secondary ion mass spectrometry, photoluminescence spectroscopy, micro-Raman spectroscopy and scanning white-light interferometry. From the combinations of experimental results obtained by these techniques the Ge composition in the SiGe heteroepilayers, their thicknesses, state of strain in the heteroepilayers and dislocations microstructure in VSs were obtained. After post growth thermal annealing treatments were observed broadening of the Si1-xGex channel accompanied with the reduction of Ge content in the channel and smearing of Sit-xGex/Sit_yGey interfaces. The Sio.7Geo.3 on low-temperature Si butTer VSs with very good structural properties were designed and grown by SS-MBE. These include: relatively thin 850nm total thickness of VS, 4-6nm Peak-to-Valley values of surface roughness, less than lOscm-2 threading dislocations density and more than 95% degree of relaxation in the top layers of VS. The Hall mobility and sheet carrier density of as-grown and annealed p-type MOD Sit-xGex/Sil-yGey heterostructures were obtained by a combination of resistivity and Hall etTect measurements in the temperature range of 9-300K. The FTA at 600C for 30min was seen to have a negligible etTect on the Hall mobility and sheet carrier density. Increasing the annealing temperature resulted in pronounced successive increases of Hall mobility accompanied by the opposite behaviour of sheet carrier density. Each sample had the optimum FTA temperature corresponded to the maximum Hall mobility. After RTA at 750C for 30sec the increase of Hall mobility for researched samples was observed as well. The highest mobility (at sheet carrier density) of 2DHG measured at 9K was observed for sample containing Ge channel grown on thick Sio.4Geo.6 linearly graded VS and corresponds to 14855cm2.y-I·s-l (2.87. 10 1 2cm-2). The highest Hall mobility (at sheet carrier density) measured at 293K was observed for Sio.2Geo.slSio.6sGeo.3s heterostructure after FT A at 750C for 30min and corresponds to 1776cm2.y-I·s-t (2.37·1013cm-2). To extract the drift mobility and sheet carrier density of 2DHG at temperatures up to 300K, magnetotransport measurements in magnetic fields up to II T were performed on several heterostructures. The data were analyzed by technique of Maximum-Entropy Mobility Spectrum Analysis. The highest drift mobility (at sheet carrier density) of2DHG at 290K was obtained for the Sio.2Geo.slSio.6sGeo.3s heterostructure after FTA at 750C and corresponds to 3607 cm2·V- I·s-1 (4.94.1012cm-2). Low temperature magnetotransport measurements down to 350 mK and at magnetic fields up to 11 T were carried out on several heterostructures. From the temperature dependence of the Shubnikov-de Haas oscillations observed at temperatures below 20K were extracted followed parameters of 2DHG, etTective mass, sheet carrier density, transport and quantum scattering times, and related parameters. For the Sio.osGeo.9s1Sio.37Geo.63 heterostructure was obtained the lowest hole etTective mass m*=O.l5·mo and the highest transport to quantum scattering times ratio a=2.18.

Results for the first measurement of the inclusive branching and CP asymmetry of the charmless 3-body decay B+ -> K+π0π0 are presented. The analysis uses a data sample with an integrated luminosity of 429.0 fb−1, recorded by the BABAR detector at the PEP-II asymmetric B Factory. This sample corresponds to 470.9 ± 2.8 million BB pairs. Measurements of the branching fractions (B) and CP asymmetries (ACP) of some of the intermediate resonances in the K+π0π0 Dalitz plot are also presented. The results are summarised here: # B (B+ -> K+π0π0) = (16.2 ± 1.2 ± 1.4) × 10−6 # B (B+ -> K*(892)+π0;K*0(892) -> K+π0) = (2.72 ± 0.50 ± 0.34) × 10−6 # B (B+ -> f0(980)K+; f0(980) -> π0π0) = (2.77 ± 0.56 ± 0.43) × 10−6 # B (B+ -> Xc0K+; Xc0 -> π0π0) = (0.51 ± 0.22 ± 0.09) # ACP (B+ -> K+π0π0) = (−6 ± 6 ± 4)% # ACP (B+ -> K*(892)+π0) = (−4 ± 26 ± 4)% # ACP (B+ -> f0(980)K+) = (17 ± 18 ± 4)% # ACP (B+ -> Xc0K+) = (−89 ± 37 ± 4)%.

An extensive qualitative and quantitative study of Rossby wave, drift wave and zonal flow turbulence in the Charney-Hasegawa-Mima model is presented. This includes details of two generation mechanisms of the zonal flows, evidence of the nonlocal nature of this turbulence and of the energy exchange between the small and large scales. The modulational instability study shows that for strong primary waves the most unstable modes are perpendicular to the primary wave, which corresponds to the generation of a zonal flow if the primary wave is purely meridional. For weak waves, the maximum growth occurs for off-zonal modulations that are close to being in three-wave resonance with the primary wave. Nonlinear jet pinching is observed for all nonlinearity levels but the subsequent dynamics differ between strong and weak primary waves. The jets of the former further roll up into Kármán-like vortex streets and saturate, while for the latter, the growth of the unstable mode reverses and the system oscillates between a dominant jet and a dominant primary wave. A critical level of nonlinearity is defined which separates the two regimes. Some of these characteristics are captured by truncated models. Numerical proof of the extra invariant in Rossby and drift wave turbulence is presented. While the theoretical derivations of this invariant stem from the wave kinetic equation which assumes weak wave amplitudes, it is shown to be relatively-well conserved for higher nonlinearities also. Together with the energy and enstrophy, these three invariants cascade into anisotropic sectors in the k-space as predicted by the Fjørtoft argument. The cascades are characterised by the zonostrophy pushing the energy to the zonal scales. A small scale instability forcing applied to the model has demonstrated the wellknown drift wave - zonal flow feedback loop. The drift wave turbulence is generated from this primary instability. The zonal flows are then excited by either one of the generation mechanisms, extracting energy from the drift waves as they grow. Eventually the turbulence is completely suppressed and the zonal flows saturate. The turbulence spectrum is shown to diffuse in a manner which has been mathematically predicted. The insights gained from this simple model could provide a basis for equivalent studies in more sophisticated plasma and geophysical fluid dynamics models in an effort to fully understand the zonal flow generation, the turbulent transport suppression and the zonal flow saturation processes in both the plasma and geophysical contexts.

The wide reaching nature of plasma physics will be studied here, with the applications of both the large scale, of solar plasma physics and then decreasing by many orders of magnitude to the laboratory plasma, of magnetically confined fusion experiments. Part I The nonlinear evolution of magnetoacoustic waves in a nonadiabatic plasma are investigated analytically. The effect of plasma activity due to linear and quadratic heating and radiative cooling on propagating magnetoacoustic waves in a uniform plasma are considered. A non-linear evolution equation is derived and stationary solutions are looked for the various combination of signs of the linear and quadratic heating-cooling terms, which determine the thermal activity of the plasma. It is shown that self-organizing magnetoacoustic waves (autowaves) exist in an active plasma. These wave have amplitudes that are independent from the initial conditions and function of plasma properties only. Their potential diagnostic purposes are discussed. Furthermore, magnetoacoustic auto-solitary waves are shown to exist. They have been modelled using a novel perturbative technique which allows to determine their propagation speed and shape. Part II Equilibria of MAST-like plasmas with transonic toroidal flows are calculated numerically in the framework of two-fluid theory [Thyagaraja and McClements, 2006] using a fixedboundary equilibrium solver, GRASS.In the non-dissipative limit, with momentum sources neglected, two-fluid analysis leads to interdependence between the rotation, temperature and density profiles, and the possibility of a departure from rigid-body rotation of flux surfaces. The effects of toroidal flows on the position of the magnetic axis, the plasma safety factor profile and the density profile are determined for a range of scenarios, including rigid body rotation. The electron temperature and ion temperature are assumed to be flux functions, with profiles that are broadly consistent with measurements from MAST. This thesis will also highlight the differences, or indeed similarities, of plasma from the astrophysical to the laboratory world.

The continued scaling of Si metal oxide semiconductor field effect transistor (MOSFET) devices to enhance performance is reaching its fundamental limits and the need for new device architecture and/or new materials is driving research and development within the semiconductor industry. Germanium, with its much higher intrinsic carrier mobilities, has a considerable advantage over Si as a channel material and its compatibility with current complementary metal oxide semiconductor (CMOS) technology makes it a very promising candidate. There is currently significant technological interest in the epitaxial growth of high quality relaxed Ge layers directly on Si substrates for potential applications including: high-mobility metal-oxide-semiconductor field-effect-transistors (MOSFETs), infrared photodetectors, solar cells and III-V integration. The crystallographic orientation of the substrate also influences the inversion layer mobility in transistors; compared to (100) orientation, Ge grown on (111) and (110) substrates can considerably enhance the carrier mobilities for electrons and holes. The 4.2% mismatch between Ge and Si is, however, a major drawback for the growth of high quality epitaxial layers, as 3-dimensional islanding, surface roughening and the generation of a high density of defects can occur which are all detrimental to performance of prospective devices. In particular, epitaxial growth on (110) and (111) surfaces is more susceptible to the formation of extended stacking faults as the gliding sequence of the dissociated 30° and 90° partial dislocations is reversed with respect to that for the (100) surface. This means that the concept of a thick graded buffer for gradual strain relaxation is not as easily applicable in the case of (111) and (110) substrates. In this work, we have investigated the growth of relaxed Ge films on (111) and (110) Si substrates by reduced-pressure chemical vapour deposition (RP-CVD) in an ASM Epsilon 2000 reactor using the high temperature/ low temperature growth technique, which comprises of a thin low temperature (LT) Ge seed, a thick high temperature (HT) Ge layer and subsequent in-situ high temperature H2 anneal. We will show how the growth conditions influence both the presence and nature of defects within the Ge layers, their surface morphology and also the state of relaxation using transmission electron microscopy (TEM), atomic force microscopy (AFM) and X-ray diffraction (XRD) techniques. Formation of islands in the 10 nm Ge seed layer has led to a significant enhancement in the quality of the buffer by providing a effective way to relax the layers, reducing the densities of stacking faults and threading dislocations by at least a decade compared to previous studies and also producing a smooth surface around 2 nm rms.

T2K is a long baseline neutrino oscillation experiment located in Japan, with a 295km baseline and peak neutrino energy of 0:6 GeV. It is the first off-axis neutrino experiment where the beam is directed approximately 2.5° away from the detectors in order to produce a narrow-band neutrino beam. The experiment was designed to measure the mixing angle θ13 by measuring the neutrino oscillation process vμ -> ve. This measurement relies on the detection of electrons at the far detector from oscillations, and so it is vital to understand the size of the intrinsic ve component of the beam. A measurement of the intrinsic ve component of the T2K beam was performed using the ND280. An analysis that used all of the data taken by the ND280 from February 2010 until March 2011, a total of 1.09 x 10 20 POT, measured 67.7 +- 12.9(stat) +- 5.2(syst) CC ve interactions. The number of events corresponds to a ratio between data and simulation of 0.983+-0.191(stat)+-0.076(syst) and provides strong evidence that the neutrino flux is well simulated. The simulation from the intrinsic ve measurement was then combined with an analysis of vμ interactions in the ND280 to constrain the neutrino flux uncertainties. An idealised study that considered only statistical and flux systematic uncertainties concluded that the intrinsic ve analysis improved the constraint on the flux uncertainties compared to considering only the ND280 vμ analyses, with the effect most prominent at neutrino energies greater than 1 GeV.

The first observation of the decay mode B0 -> D0K+K- is presented using 0.62 fb-1 of data collected by the LHCb detector in 2011. The branching fraction is measured with respect to the topologically similar decay mode, B0 -> D0π+π-. The ratio of branching fractions is measured to be B(B0 -> D0K+K-) / B(B0 -> D0π+π-) = 0.056 ± 0.011 ± 0.007, where the first uncertainty is statistical and the second is systematic. Using the world average value for the denominator yields B(B0 -> D0K+K-) = (4.7 ± 0.9 ± 0.6 ± 0.5) x 10-5, where the third uncertainty is from B(B0 -> D0π+π-). Secondly, evidence for the B0s -> D0K+K- decay mode is presented. The branching fraction ratio with respect to B0 -> D0K+K- is found to be B(B0s -> D0K+K-) / B(B0 -> D0K+K-) = 0.90 ± 0.27 ± 0.20, where the first uncertainty is statistical and the second is systematic.

Understanding surface erosion in tokamaks due to contact with hot plasma is critical in designing new high power devices. The propagation of the plasma through the scrape off layer (SOL) ultimately defines the spatio-temporal characteristics of this erosion, hence modelling of this region is an important area of research. Transport in the SOL is attributed to advective motions of plasma blobs, for which the advective velocity is estimated in the literature. A new paradigm for comparing the theory of plasma blobs with experimental data is developed, which treats density and velocity data as sets of coherent structures via a peak detection algorithm. The phase difference of plasma density and radial velocity peaks take values depending on the dominating physics of the blob motion. Values of this phase difference are predicted in the interchange and drift wave cases for a strongly nonlinear plasma. Analysis of MAST data reveals interchange activity in the edge and SOL, and a phase structure typical of sheath limited models in the SOL. A further application of the paradigm examines the blob velocity-density scaling v ∝ nα. A new sheath limited model for blob advection with divertor density nt constant gives α = 1. Predictions in the zero parallel current case depend on the blob nonlinearity; we examine the dependency of α on the nonlinearity by solving the time independent equation of blob motion for a range of density profiles, finding α ∼ 0.3 for MAST nonlinearity strength. The α parameter is estimated statistically from MAST data, and it found to peak at α ∼ 1 near the last closed flux surface (LCFS) and fall to zero further from the plasma. The scaling behaviour is further examined using the TOKER code. A numerical model, hTOKER, is developed. A subgrid model is employed that terminates the plasma at a chosen scale with defined spectral properties, which allows a physically accurate way to reduce resolution and computational burden. We examine sheath potential drop (SPD) and finite ion temperature (FTI) effects on SOL transport in the cases of constant (CTI) and flute (SI) nt boundary conditions. For the advection of individual blobs, SPD effects that are stable in the SI case are found to be unstable in the CTI case, and FTI effects are found to be stabilising in all cases. SOL plasma simulations are used to examine the differences in particleenergy flux and peak phase difference using floating or plasma potential. Floating potential overestimates flux by a factor 2, and shifts phase differences from 0◦ to ∼ −30◦. FTI effects are without cancellation from the gyro-viscous counterparts.

Turbulence is a highly non-linear process ubiquitous in Nature. The nonlinearity is responsible for the coupling of many degrees of freedom leading to an unpredictable dynamical evolution of a turbulent system. Nevertheless, experimental observations strongly support the idea that turbulence at small scales achieves a statistically stationary state. This has motivated scientists to adopt a statistical approach for the study of turbulence. In both hydrodynamics (HD) and magnetohydrodynamics (MHD), fluctuations of bulk quantities that describe turbulent flows exhibit the property of statistical scale invariance, which is a form of self-similarity. For fully evolved turbulence in an infinite medium, one interesting consequence of this scale invariance is the power law dependence of the physical observables of the flow such that, for instance, the velocity field fluctuations along a given direction show power law power spectra and multiscaling for the various orders of the structure function within a certain range of scales, known as the inertial range. The characterization of such scaling is crucial in turbulence since it would fully quantify the process itself, distinguishing the latter from a wider class of scaling processes (e.g., stochastic self-similar processes). Experimentally, it has been observed that turbulent systems exhibit an extended self-similarity when either turbulence is not completely evolved or the system has finite size. As consequence of this, the moments of the structure function exhibit a generalized scaling, which points to a universal feature of finite range MHD turbulent ows and, more generally, of scale invariant processes that have finite cut-offs of the fields or parameters. However, the underling physics of this generalized similarity is still an open question. This thesis focuses on the quantification of statistical scaling in turbulent systems of finite size. We apply statistical analyses to the spatio-temporal fluctuations associated with line of sight intensity measurements of a solar quiescent prominence and data of the reconnecting fields in simulations of magnetic reconnection. We find that in both environments these fluctuations exhibit the hallmarks of finite range turbulence. In particular, an extended self-similarity is observed to hold the inertial range of turbulence, which is consistent with a generalized scaling for the structure function. Importantly, this generalized scaling is found to be multifractal in character as a signature of intermittency in the turbulence cascade. The generalized scaling recovered for finite range turbulence exhibits dependence on a function, the generalized function, which contains important information about the bounded turbulent flow such as some characteristics scale of the flow, the crossover from the small scale to the outer scale of turbulence and perhaps some characteristic features of the boundaries (future work). The quantification of the generalized scaling is performed thank to the application of statistical tools, some of which have been here introduced for the first time, which allow to identify the statistical properties of a wide class of scaling processes. Importantly, these techniques are powerful methodologies for testing fractal/multifractal scaling in self-similar and quasi self-similar systems, allowing us to distinguish turbulence from other processes that show statistical scaling.