In the present study, the influence of geometric scale, unit orientation (alternatively, flow direction), and the dimensionless Reynolds and Keulegan-Carpenter quantities on the hydrodynamic loading of Core-Loc armour units is explored through a series of physical modelling tests under unsteady and oscillatory flow conditions.

Every cell contains several millions of diffusing and reacting biological molecules. The interactions between these molecules ultimately manifest themselves in all aspects of life, from the smallest bacterium to the largest whale. One of the greatest open scientific challenges is to understand how the microscopic chemistry determines the macroscopic biology. Key to this challenge is the development of mathematical and computational models of biochemistry with molecule-level detail, but which are sufficiently coarse to enable the study of large systems at the cell or organism scale. Two such models are in common usage: the reaction-diffusion master equation, and Brownian dynamics. These models are utterly different in both their history and in their approaches to chemical reactions and diffusion, but they both seek to address the same reaction-diffusion question. Here we make an in-depth study into the physical validity of these models under various biological conditions, determining when they can reliably be used. Taking each model in turn, we propose modifications to the models to better model the realities of the cellular environment, and to enable more efficient computational implementations. We use the models to make predictions about how and why cells behave the way they do, from mechanisms of self-organisation to noise reduction. We conclude that both models are extremely powerful tools for clarifying the details of the mysterious relationship between chemistry and biology.

Kwan, Lok Yin. / Thesis (M.Phil.)--Chinese University of Hong Kong, 2007. / Includes bibliographical references (leaves 80-83). / Abstracts in English and Chinese. / Chapter CHAPTER ONE: --- INTRODUCTION --- p.1 / The basic mediation model --- p.1 / General approaches in mediation analysis --- p.2 / Resampling methods --- p.8 / Comparing indirect effects --- p.9 / A sequential model fitting method --- p.10 / Current interest of study --- p.13 / Chapter CHAPTER TWO: --- STANDARDIZATION OF PATH COEFFICIENTS --- p.15 / Chapter CHAPTER THREE: --- COMPARING STANDARDIZED INDIRECT EFFECTS --- p.19 / Chapter CHAPTER FOUR: --- REAL EXAMPLES --- p.28 / Chapter CHAPTER FIVE: --- DISCUSSION --- p.55 / Chapter CHAPTER SIX: --- CONCLUSION --- p.57 / APPENDICES --- p.58 / REFERENCES --- p.80

The present study evaluated direct and indirect associations between aerobic fitness, executive control, and emotion regulation among a sample of children aged 8-12 years. To evaluate these associations, the study employed a cross-sectional design and full-information maximum likelihood (FIML) structural equation modeling. Although the hypothesized factor analytic model failed to converge, an alternative exploratory model allowed for the evaluation of associations between primary study variables. Results supported a moderate direct association between childhood aerobic fitness and executive control, a strong direct negative association between executive control and emotion regulation, and a moderate indirect association between aerobic fitness and emotion regulation through executive control. These findings provide preliminary evidence that executive control functions as a mediator between aerobic fitness and emotion regulation and may help explain the means by which aerobic exercise exerts its influence on emotional wellbeing among preadolescent children.

There are many products, including hard drives, which require trace amounts, on the order of several mg, of lubricants for proper operation. The following study investigated the evaporation rates of pump oil and several alkanes, which have a wide range of applications, using a thermogravimetric machine. Both static and dynamic temperature tests were conducted. The rate of evaporation of the test specimen was determined as the percentage of mass loss per unit time. Using the Arrhenius Equation, the activation energy of the evaporation process, Ea, can be calculated as the slope of the best fit line for a plot of the ln(k) vs. 1/T (where k represents the rate of the evaporation). These values were shown to have good agreement with the enthalpy of vaporization calculated from the Clausius Clapeyron Equation and with the activation energy calculated using the Freeman and Carroll Method. The alkanes were compared using the rate of evaporation and the amount of activation energy required for evaporation as model systems. Further investigations were conducted to determine the relationship of surface area of the evaporating liquid and the rate of evaporation. It is suggested that the surface area is a function that depends on the activation, bonding, and interfacial energies of the liquid. However, the wetting angle, which aids in the description of the surface area, depends on the surface energy. Subsequent modeling was conducted in an attempt to predict the evaporation characteristics of other lubricants for the purpose of comparison.

In non-relativistic quantum mechanics, stationary states of molecules and atoms are described by eigenvectors of the Hamiltonian operator. For one-electron systems, such as the hydrogen atom, the solution of the eigenvalue problem (Schro ̈dinger’s equation) is straightforward, and the results show excellent agreement with experiment. Despite this success, the multi electron problem corresponding to virtually every system of interest in chemistry has resisted attempts at exact solution. Perhaps the most popular method for obtaining approximate, yet very accurate results for the ground states of molecules is the coupled cluster approximation. Coupled cluster methods move beyond the simple, average field Hartree-Fock approximation by including the effects of excited configurations generated in a size consistent manner. In this paper, the coupled cluster approximation is developed from first principles. Diagrammatic methods are introduced which permit the rapid calculation of matrix elements appearing in the coupled cluster equations, along with a systematic approach for unambiguously determining all necessary diagrams. A simple error bound is obtained for the ground state energy by considering the coupled cluster equations as entries in the first column of a matrix whose eigenvalues are the exact eigenvalues of the Hamiltonian. In addition, a strategy is considered for treating the error in the ground state energy perturbatively.

In the classical case we make use of Pells equation to compute units in the ring OF. Consider the parallel to the classical case and the quadratic field extension that creates the ring OK. We use the generalized Pell's equation to find the units in this ring since they are solutions. Through the use of continued fractions we may further characterize this ring and compute its units.

Cette thèse porte sur le développement, l'analyse et la mise en oeuvre de nouvelles méthodes bi-grilles en éléments finis pour des équations de réaction-diffusion de type champs de phase (Allen-Cahn, Cahn-Hilliard) ainsi que leur couplage avec les équations de Navier-Stokes 2D incompressible. La présence d'un petit paramètre (largeur de l'interface) dans les modèles à interface diffuse demande à utiliser des schémas temporels implicites et coûteux tandis que ceux semi implicites sont rapides mais limités en stabilité. Les nouveaux schémas introduits ici reposent sur l'utilisation conjointe de deux espaces d'éléments finis, un grossier VH et un fin Vh, de plus grande dimension, permettant de décomposer la solution en partie principale portant les composantes bas modeset en une partie fluctuante portant les modes élevés. L'approche bi-grilles proposée consiste à appliquer les schémas stables (coûteux) sur VH (prédiction) et à effectuer une correction sur Vh à l'aide d'un schéma linéaire dont les composantes modes élevés sont stabilisées. Un gain important en temps CPU est obtenu au prix d'une faible perte de consistance. Dans ce contexte, de nouvelles méthodes numériques sont proposées pour les modèles de champs de phase et leur couplage fluide. Nous donnons des résultats de stabilité et validons l'approche sur des bancs d'essais / This thesis deals with the development, the analysis and the implementation of new bi-grid schemes in finite elements, when applied to phase-field models such as Allen-Cahn (AC) and Cahn-Hilliard (CH) equations but also their coupling with 2D incompressible Navier-Stokes equations. Due to the presence of a small parameter, namely the length of the diffuse interface, and in order to recover the intrinsic properties of the solution, (costly) implicit time schemes must be used; semi-implicit time schemes are fast but suffer from a hard time step limitation. The new schemes introduced in the present work are based on the use of two FEM spaces, one coarse VH and one fine Vh, of larger dimension. This allows to decompose the solution into a main part (containing only low mode components) and a fluctuant part capturing the high mode ones. The bi-grid approach consists then in applying as a prediction an unconditional stable scheme (costly) to VH and to update the solution in Vh by using a high mode stabilized linear scheme. A gain in CPU time is obtained while the consistency is not deteriorated. This approach is extended to NSE and to coupled models (AC/NSE) and (CH/NSE). Stability results are given, the numerical simulations are validated on reference benchmarks

This thesis investigates the use of Daubechies wavelets to separate scales in local quantum field theory. Field theories have an infinite number of degrees of freedom on all distance scales. Quantum field theories are believed to describe the physics of subatomic particles. These theories have no known mathematically convergent approximation methods. Daubechies wavelet bases can be used separate degrees of freedom on different distance scales. Volume and resolution truncations lead to mathematically well-defined truncated theories that can be treated using established methods. This work demonstrates that flow equation methods can be used to block diagonalize truncated field theoretic Hamiltonians by scale. This eliminates the fine scale degrees of freedom. This may lead to approximation methods and provide an understanding of how to formulate well-defined fine resolution limits.

The movement of water in soil presents many interesting problems to the research worker. It is also a subject which finds wide and important application in agriculture and several branches of engineering. The object of this work was to examine the usefulness of a new equation of flow of water in unsaturated soil. If valid, this new approach may be able to eliminate some of the gaps in our present knowledge of the subject. All soil lying above the capillary fringe of a water table is in the unsaturated state with respect to water. This means that in any macroscopic volume element of soil three phases are present-- solid, liquid and gas. The volume fraction of each of these phases show wide variation in both space and time in field soils. The variation in both space and time in field soils. The variation in the volume fraction of the liquid or water phase is accompanied by a considerable change in the physical properties of the water. In the strictest sense the unsaturated state covers all intermediate conditions between saturation and an incomplete monomolecular layer of absorbed water. It is important to recognize that the solid phase is also dynamic. It consists of unconsolidated particles with great variation of size and shape. Many solid phase properties show a complex dependence upon the amount of water present. Swelling and shrinking are well known in soils and these changes affect water movement.