A hybrid molecular dynamics/multiparticle collision dynamics algorithm was constructed to model the pressure-driven flow of a compressible fluid through a nanoscopic channel of square cross-sectional area, as well as the effect of this flow on the configuration of a polymer chain that was tethered to the surface of this nanochannel. In the process of simulating channel flow, a new adiabatic partial slip boundary condition was created as well as a modified source/sink inlet and outlet boundary condition that could maintain a specified pressure gradient across the channel without the large entrance effects typically associated with these algorithms. The results of the flow simulations were contrasted with the results from a series solution to the Navier-Stokes equation for isothermal compressible flow, and showed excellent agreement with the results from the series solution when slip-boundary conditions were applied. A finitely extendible non-linear elastic spring and bead polymer chain was used to simulate the effect of flow on the polymer chain configuration under poor solvent and θ solvent conditions. Under θ solvent conditions, the cyclical dynamics that have been previousy observed for tethered polymer chains in pure shear flows were noted, however they were restricted to the end of the polymer chain. Under poor solvent conditions, the polymer adopted a metastable helix configuration as it collapsed to a globule state. The study also examined interchain and intrachain entanglements in polymers using the granny knot and overhand knot. The mechanisms by which these tangles untied themselves were determined. At low flow rates, the tangles unravelled by the end of the chain migrating through the loops of the tangle. At high flow rates, the tangles behaved like an entrained object as they reptated towards the end of the chain.

A hybrid molecular dynamics/multiparticle collision dynamics algorithm was constructed to model the pressure-driven flow of a compressible fluid through a nanoscopic channel of square cross-sectional area, as well as the effect of this flow on the configuration of a polymer chain that was tethered to the surface of this nanochannel. In the process of simulating channel flow, a new adiabatic partial slip boundary condition was created as well as a modified source/sink inlet and outlet boundary condition that could maintain a specified pressure gradient across the channel without the large entrance effects typically associated with these algorithms. The results of the flow simulations were contrasted with the results from a series solution to the Navier-Stokes equation for isothermal compressible flow, and showed excellent agreement with the results from the series solution when slip-boundary conditions were applied. A finitely extendible non-linear elastic spring and bead polymer chain was used to simulate the effect of flow on the polymer chain configuration under poor solvent and θ solvent conditions. Under θ solvent conditions, the cyclical dynamics that have been previousy observed for tethered polymer chains in pure shear flows were noted, however they were restricted to the end of the polymer chain. Under poor solvent conditions, the polymer adopted a metastable helix configuration as it collapsed to a globule state. The study also examined interchain and intrachain entanglements in polymers using the granny knot and overhand knot. The mechanisms by which these tangles untied themselves were determined. At low flow rates, the tangles unravelled by the end of the chain migrating through the loops of the tangle. At high flow rates, the tangles behaved like an entrained object as they reptated towards the end of the chain.

<p> This dissertation describes an extention of fluid mechanical data for flow around blunt objects in the intermediate Reynolds Number regime using the digital computer. The aim was to develop fluid mechanical models to predict the flow phenomena around a blunt object in an infinite fluid and a multiparticle system. </p> <p> The dissertation is divided into two self-contained parts. Part I describes the flow around a blunt object in an infinite fluid media. The flow around a solid sphere in steady flow, a solid sphere in accelerating flow and a spherical liquid drop in steady flow are described. The study demonstrates that the actual drag becomes asymptotic with the Oseen drag relation as the Reynold Number approaches zero. Secondly, the study demonstrates that acceleration from rest of a sphere under the influence of gravity can be predicted precisely by solving the fluid mechanical equations. Finally the flow in and around a circulating spherical raindrop is presented. </p> <p> Part II describes the extension of the cell model for multiparticle systems in the creeping flow regime to the intermediate Reynolds Number regime. Three cases were studied: beds of solid spheres, cylinder bundles in cross-flow and gas bubble swarms. Theoretical predictions of pressure drop through the assemblage and material or heat transport were obtained. Comparison of these predictions with experimental data has shown that the approach provides an excel lent first approximation for predicting multiparticle phenomena. </p> / Thesis / Doctor of Philosophy (PhD)

Thesis (MSc (Physics))--University of Stellenbosch, 2009. / Hanbury Brown-Twiss interferometry is a correlation technique by which the size and shape of the emission function of identical particles created during collisions of high-energy leptons, hadrons or nuclei can be determined. Accurate experimental datasets of three-dimensional correlation functions in momentum space now exist; these are sometimes almost Gaussian in form, but may also show strong deviations from Gaussian shapes. We investigate the suitability of expressing these correlation functions in terms of statistical quantities beyond the normal Gaussian description. Beyond means and the covariance matrix, higher-order moments and cumulants describe the form and di erence between the measured correlation function and a Gaussian distribution. The corresponding series expansion is the Gram- Charlier series and in particular the Gram-Charlier Type A expansion found in the literature, which is based on a Gaussian reference distribution. We investigate both the Gram-Charlier Type A series as well as generalised forms based on non-Gaussian reference distributions, as well as the related Edgeworth expansion. For testing purposes, experimental data is initially represented by a suite of one-dimensional analytic non-Gaussian distributions. We conclude that the accuracy of these expansions can be improved dramatically through a better choice of reference distribution, suggested by the sign and size of the kurtosis of the experimental distribution. We further extend our investigation to simulated samples of such test distributions and simplify the theoretical expressions for unbiased estimators (k-statistics) for the case of symmetric distributions.