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A number of different ways of using galaxy clusters to provide information concerning fundamental cosmological parameters are considered. Using the observed local cluster X-ray temperature function in conjunction with the Press-Schechter formalism, the normalisation of a CDM power spectrum is found to be σ(_8) = (0.52 ± 0.04)Ω(_o)(^-0.46+0.10Ωo) if Ʌ(_o) = 0 or σ(_8) = (0.52 ± 0.04)Ω(_o)(^-0.52+0.13Ωo) if Ʌ(_o) = 1 — Ω(_0). This result is employed to provide detailed predictions for the abundance of clusters at high redshift, and the differences between predictions for various cosmologies are emphasised. New tests using available high-redshift cluster data are presented. For the adopted power spectrum normalisation, it is found that an Ω(_o) = 0.3, Ʌ(_o) = 0 cosmology vastly overpredicts the number of clusters that were actually found with 0.4 < z < 0.6 in the Extended Medium Sensitivity Survey. The rapid variation in the expected abundance with both σ(_8) and the assumed scatter in the L(_x) – T_x) relation limits the significance of this result, but this model is still ruled out at the ~ 95% confidence level. Order statistics are utilised to calculate the probability of finding extremely massive clusters at high redshifts. With presently available observations, no interesting upper limit can yet be placed on Ω(_o). Systematic variations in the cluster-cluster correlation length calculated using numerical simulations and resulting from the definition of clusters, the chosen σ(_8), the mean intercluster separation and whether or not redshift space distortions are included, are found to exceed the statistical errors on the measurements. Although the uncertainty in ε(_cc) derived from an ensemble of 10 Standard CDM simulations is not sufficient at large separations to remove the discrepancy between this model and results from the APM Cluster Survey, this does suggest that the level at which such a scenario has previously been rejected using ε(_cc) should be significantly reduced. Details and a few tests of a procedure for improving mass and spatial resolution in cosmological simulations are presented. After showing that a coarse-sampling technique can be used to represent the large-scale forces sufficiently accurately, the method is then used to perform ten simulations of clusters forming in an Ω(_o) = 0.3, Ʌ(_o) = 0.7 CDM cosmology. To incorporate non-radiative gas, an SPH code adapted to work on a GRAPEsupercomputer is used. The resulting clusters are found to have virial radii in good agreement with the predictions of the spherical collapse model, dark matter density profiles well described by the 'NFW formula and isothermal central gas components, with temperatures dropping by a factor of ~ 2 near the virial radius. The evolution of these properties is studied as well as that of the bulk quantities describing the clusters, with particular reference to the β parameters relating cluster gas temperatures with virial mass or velocity dispersion. Slightly greater evolution in the luminosity is seen than in previous Ω(_o) = 1 simulations, suggesting that the improved resolution is important. The β parameter relevant to the normalisation of the mass fluctuation spectrum is found to be 0.98 ± 0.07.

In Gram-negative bacteria, the Outer membrane (OM) acts as a first barrier to screen unwanted compounds whilst enabling ions and very small solutes to diffuse into the cell. Most of nutrients and essential ions are effectively transported across a membrane via the outer membrane proteins (OMPs). The water-filled β- barrel OMPs are called porins. These pores are classified into two groups, non- specific and substrate-specific porins. Each of them has different mechanisms to facilitate its substrate translocation. To reveal the process of substrate permeation and selectivity in microscopic detail, molecular dynamics (MD) simulations and applications were performed in this thesis. The studies in this thesis focus on a series of classical porins. These proteins share similar feature where extracellular loop(s) (generally loop 3 (L3)) is folded into the middle of the pore and act as a constriction site which is important for substrate specificity and selectivity. The studies firstly concentrate on the structural properties and dynamics of the general trimeric porins, OmpC and OmpF whose sequences share 60% identity. OmpC and OmpF are found to have similar mechanism of latching loop (L2) to maintain trimeric stability. The smaller pore size allows OmpC to be more cation-selective than OmpF. Additionally, the major driving force for cation permeation in both porins is not from electrostatic properties. This differs from the phosphate-selective porin, trimeric OprP, where a phosphate diffusion depends on electrostatic interactions with positively charged pore-lining residues. The charge brush-like behavior of interior Arg and Lys residues plays a major role in phosphate selectivity. Also, the free energy profiles (PMF) reveal two key regions that are important for differentiating phosphate from other anions. The brush-like mechanism of OprP were also implanted to the simplified model pores in order to determine the possibility of transferring phosphate-selective properties of OprP to a model which may be useful for future design of nanopores. It is found that the duplication of functional residues and pore cavity can turn a model into the highly phosphate-selective pore. Importantly, the phosphate-binding affinity is dependent on the ability of the pore to interfere and occupy the hydration shell of a translocating phosphate where such ability can be maximized by an increase in sidechain flexibility. In case of uptake of more complex substrates, OpdK also employs a constriction site to select its substrate, aromatic vanillate (VNL) with total charge of -1. Unlike ion-specific porins, the free VNL is attracted by polar and aromatic interactions and sequentially directed through the periplasmic vestibule by charged residues insides the pore. The correct orientation of VNL on arrival is crucial for OpdK to recognize and enable the permeation process.

A experimental study of the two-phase flow inside a lean premixed prevaporised combustor has been carried out in order to evaluate the capabilities of large eddy simulations applied to engineering applications. To this end, a existing LPP design was modified in order to simplify the injection mechanisms involved and gain a optimum optical access if the critical injection region. The liquid and the gas phase inside the LPP module are then characterised with the help of non-invasive laser techniques, namely PDA for the liquid phase, LDA for the airstream and PLIF for the vapour phase. Relevant information regarding droplet sizes, droplet velocity, airstream velocity and fuel placement have thus been collected. The measurements are then evaluated against flow solutions computed by a Eulerian-Lagrangian ite-volume solver. A hybrid RANS/LES modelling strategy has been adopted for the gas phase and the Lagrangian tracking procedure has been updated to predict the influence of the gas turbulence on the droplet dispersion, and the heat penetrating the droplet during its evaporation. This simulation is finally matched against ZD and 3D steady RANS solution in a attempt to demonstrate the superiority of the time dependent approach.

This thesis documents the usefulness and accuracy of uncalibrated simulations to determine for what end-uses these simulations should be used. The study was divided into three segments 1)comparison of the accuracy of two simulation models, massless and advanced, against measured data 2) comparison of the results from two simulations models, simplistic and massless, to determine the sensitivity of envelope shape and details for two weather conditions 3) identification of the parameters that have a significant impact on the simulation output. Five buildings were selected as the test sample. Four of the buildings were multi story commercial buildings. The fifth was a single-family residential house. For the first segment of the study two simulation models were created for all the buildings; the massless model with emphasis on the envelope using massless construction and typical values for system parameters and the advanced model with the inclusion of thermal mass and extensive as-built details of the systems. For the second part of the research the simplistic model was created having a single floor one-zone with glazing and conditioned areas equivalent to the massless model. The sensitivity analysis was done using the massless model and selected variables from the loads and systems as sensitivity parameters. By following the procedure mentioned, it was found that uncalibrated simulation models do not depict the real operating conditions of a building. For some cases the simulated values are higher than the measured data while for others they are significantly lower. The CV (RMSE) between the measured and simulated values ranges from 30 to 150%. From the comparison of the simplistic and massless model, it was concluded that the outer envelope shape and details have an impact on the heating and cooling energy use irrespective of the weather conditions. For internally load dominated buildings this impact is more on the heating loads than on the cooling loads. The conclusions from the sensitivity analysis were that outside air fraction and the total supply air have the most significant impact on the simulation output while thermal mass has a small impact.

A large direct numerical simulation database spanning a wide range of Reynolds and Schmidt number is used to examine fundamental laws governing passive scalar mixing and turbulence structure. Efficient parallel algorithms have been developed to calculate quantities useful in examining the Kolmogorov small-scale phenomenology. These new algorithms are used to analyze data sets with Taylor scale Reynolds numbers as high as 650 with grid-spacing as small as the Kolmogrov length scale. Direct numerical simulation codes using pseudo-spectral methods typically use transpose based three-dimensional (3D) Fast Fourier Transforms (FFT). The ALLTOALL type routines to perform global transposes have a quadratic dependence on message size and typically show limited scaling at very large problem sizes. A hybrid MPI/OpenMP 3D FFT kernel has been developed that divides the work among the threads and schedules them in a pipelined fashion. All threads perform the communication, although not concurrently, with the aim of minimizing thread-idling time and increasing the overlap between communication and computation. The new algorithm is seen to reduce the communication time by as much as 30% at large core-counts, as compared to pure-MPI communication. Turbulent mixing is important in a wide range of fields ranging from combustion to cosmology. Schmidt numbers range from O(1) to O(0.01) in these applications. The Schmidt number dependence of the second-order scalar structure function and the applicability of the so-called Yaglomﾒs relation is examined in isotropic turbulence with a uniform mean scalar gradient. At the moderate Reynolds numbers currently achievable, the dynamics of strongly diffusive scalars is inherently different from moderately diffusive Schmidt numbers. Results at Schmidt number as low as 1/2048 show that the range of scales in the scalar field become quite narrow with the distribution of the small-scales approaching a Gaussian shape. A much weaker alignment between velocity gradients and principal strain rates and a strong departure from Yaglomﾒs relation have also been observed. Evaluation of different terms in the scalar structure function budget equation assuming statistical stationarity in time shows that with decreasing Schmidt number, the production and diffusion terms dominate at the intermediate scales possibly leading to non-universal behavior for the low-to-moderate Peclet number regime considered in this study. One of the few exact, non-trivial results in hydrodynamic theory is the so-called Kolmogorov 4/5th law. Agreement for the third order longitudinal structure function with the 4/5 plateau is used to measure the extent of the inertial range, both in experiments and simulations. Direct numerical simulation techniques to obtain the third order structure structure functions typically use component averaging, combined with time averaging over multiple eddy-turnover times. However, anisotropic large scale effects tend to limit the inertial range with significant variance in the components of the structure functions in the intermediate scale ranges along the Cartesian directions. The net result is that the asymptotic 4/5 plateau is not attained. Motivated by recent theoretical developments we present an efficient parallel algorithm to compute spherical averages in a periodic domain. The spherically averaged third-order structure function is shown to attain the K41 plateau in time-local fashion, which decreases the need for running direct numerical simulations for multiple eddy-turnover times. It is well known that the intermittent character of the energy dissipation rate leads to discrepancies between experiments and theory in calculating higher order moments of velocity increments. As a correction, the use of three-dimensional local averages has been proposed in the literature. Kolmogorov used the local 3D averaged dissipation rate to propose a refined similarity theory. An algorithm to calculate 3D local averages has been developed which is shown to scale well up to 32k cores. The algorithm, computes local averages over overlapping regions in space for a range of separation distances, resulting in N^3 samples of the locally averaged dissipation for each averaging length. In light of this new calculation, the refined similarity theory of Kolmogorov is examined using the 3D local averages at high Reynolds number and/or high resolution.

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