The old question concerning the mathematical formulation of the fluid dynamic limits of kinetic theory is examined by studying the solution of the Cauchy problem for two differently scaled linearized Boltzmann equations on periodic domain as the mean free path of the particles becomes small. Under minimal assumptions on the initial data, by using an a priori estimate, it is possible, in a Hilbert space functional frame, to prove the weak convergence of solutions toward a function that has the form of an infinitesimal maxwellian in the velocity variable. The velocity moments of this function are then proved to satisfy either the linearized Euler or the Stokes system of equations (depending on the chosen scaling), by passing to the limit in the conservation relations derived from the Boltzmann equation. A theorem injecting continuously the intersection of certain weak spaces into a normed one is proved. Together with properties of the Euler semigroup, this allows to show strong convergence of the first three moments of the distribution function toward the macroscopic quantities density, bulk velocity and temperature, solutions of the linearized Euler system. The Stokes case is treated somewhat differently, through the introduction of a result, proved by using the adjoint formulation for linear kinetic equations, that extends the averaging theory of Golse-Lions-Perthame-Sentis. The desired convergence for the divergence-free component of the second moment toward the macroscopic velocity is then shown.

Electrophoresis of solutes was studied in aqueous two-phase systems, concentrating on the special behavior in the interfacial region. Moving boundary electrophoresis was examined in a free fluid U-tube apparatus. Zone electrophoresis was investigated in two-phase systems which were gelled by the addition of acrylamide, which was subsequently polymerized. The size and nature (concentration or dilution) of polarizations which were found to occur was found to depend on the magnitude of the equilibrium partition coefficient of the solute in the two-phase system, as well as the direction of migration across the interface. These polarizations are in addition to those commonly known to occur near regions where electrophoretic flux changes radically, such as near interfaces. They can be a direct result of the requirement for equilibrium across the interface, as demonstrated by our experiments. Models were constructed to numerically simulate this behavior, which accounted for unsteady state electrophoresis and diffusion of multiple proteins or other amphoteric solutes. Two cases were explored, one requiring instantaneous solute equilibration across the interface, the other allowing for a resistance to mass transfer here. All models demonstrated a characteristic noted in experimental studies, concentration at interfaces when electrophoresis is from equilibrium preferred phase towards non-preferred phase. Furthermore, the equilibrium model correctly predicted the complex relationship between partition coefficient, direction of migration, and moving boundary or zone electrophoresis, which causes differences in the polarizations observed in these various systems. The simulation could also quantitatively estimate the width of the polarized region to within an order of magnitude, in comparison with experimental results, while hampered by a lack of mobility data for solutes in solutions containing polymers.

A new discrete ordinates method designed for use on modern, large memory, vector and/or parallel processing super computers has been developed. The method is similar to conventional SN techniques in that the medium is divided into spatial mesh cells and that discrete directions are used. However, in place of an approximate differencing scheme, a nearly exact matrix representation of the streaming operator is determined. Although extremely large, this matrix can be stored on today's computers for repeated use in the source iteration. Since the source iteration is cast in matrix form it benefits enormously from vector and/or parallel processing, if available. Several test results are presented demonstrating the reduction in numerical diffusion and elimination of ray effects.

M.Phil. (Energy Studies) / SAFARI-1 is a 20 MW research reactor, which is over 45 years old, and is expected to reach the end of its operating life between 2020 and 2030. The aim of this work is to investigate various alternative conceptual core layouts of the SAFARI-1 reactor in order to facilitate more e ective utilization of the reactor, while potentially expanding its operating lifetime. The spatial and energy neutron distribution is one of the most signi cant parameters in the characterization of such an alternative core layout. This neutron distribution is a result of basic physics processes such as particle matter interactions, nuclear reactions, material properties, e ects of temperature and the time evolution of the system. This study focuses on the steady-state neutron distribution within the highly heterogeneous and complex geometry of the reactor core for the various alternative core layouts. This work has searched for and found a di erent inhomogeneous neutron distribution within the core, arising from a di erent core layout, which can nonetheless still achieve e ciency in the operation for various design purposes, but with a lower power output. Via numerical analysis with the OSCAR-4 code system, the safety and utilization requirements for the SAFARI-1 reactor are evaluated and quantied in terms of its steady-state neutron ux distribution. A SAFARI-1 reference core, obtained via an equilibrium cycle calculation, was used to generate a set of safety and utilization targets against which alternative designs may be measured. Alternative core layouts were developed by using a parametric study to scope the size and power level of potential candidate conceptual cores with the aim of minimizing the power level while adhering to the safety requirements. Utilization parameters of interest include isotope production capability, thermal ux levels in beam tubes and production levels in the silicon doping facility...

Lee Wai Ming. / Thesis (M.Phil.)--Chinese University of Hong Kong, 1994. / Includes bibliographical references (leaves 177-181). / List of Figures and Tables --- p.iii / Chapter 1 --- Introduction --- p.1 / Chapter 1.1 --- Photonic Band Gap materials --- p.1 / Chapter 1.2 --- Theoretical Calculation on PBG materials --- p.5 / Chapter 2 --- Plane Wave Expansion --- p.13 / Chapter 2.1 --- Plane Wave Expansion within Scalar Wave Approximation --- p.14 / Chapter 2.2 --- Plane Wave Expansion to Scalar I and II Equations --- p.21 / Chapter 3 --- Formalism of Photonic k.p Theory --- p.33 / Chapter 3.1 --- Vectorial k.p formulation --- p.33 / Chapter 3.2 --- Scalar k. p formulations --- p.36 / Chapter 4 --- Implementation and k.p Band Structures --- p.38 / Chapter 4.1 --- Evaluation of Integrals plj and qlj --- p.38 / Chapter 4.2 --- k.p Band Models --- p.47 / Chapter 5 --- Dependence of k .p Parameters on Dielectric Contrast and Fill- ing Ratio --- p.57 / Chapter 5.1 --- Accuracy of Integrals plj and qlj --- p.57 / Chapter 5.2 --- Sensitivity of k.p Parameters to System Parameters --- p.71 / Chapter 6 --- Empirical Tight-binding Scheme --- p.99 / Chapter 6.1 --- Electronic Tight Binding Approximation --- p.99 / Chapter 6.2 --- Empirical Tight-binding Scheme --- p.101 / Chapter 7 --- Summary --- p.137 / Chapter A --- Preprint of Ref. [36] --- p.144 / Chapter B --- The Coefficients in Eq. (2.22) --- p.161 / Chapter C --- Formalism of Photonic k.p Theory --- p.163 / Chapter D --- The Coefficients in Eq. (5.2) --- p.166 / Chapter E --- The Coefficients in Eq. (5.3) --- p.168 / Chapter F --- The Coefficients in Eq. (6.15) --- p.170

One of the daunting challenges in wave physics is to accurately control the flow of light at the subwavelength scale. By patterning the optical medium one can design anisotropic artificial medium, this engineering method is commonly known as photonic crystals or metamaterials. Negative or zero index of refraction, slow-light propagation, cloaking with transformation optics material, and beam collimation are only a few such unique functionalities that can be achieved in engineered media at the subwavelength scale. Another interesting phenomenon in wave physics, Anderson localization, which suggests electron localization inside a semiconductor, has been intensely investigated over the past years, including transverse localization in bulk and waveguide arrays periodic in one and two dimensions. Here we report the photon transport and collimation enhanced by transverse Anderson localization in chip-scale anisotropic artificial medium, a similar physical model to doping the impurity in insulator and turning it into a semiconductor. First, by engineering the photonic crystal, we demonstrate a new type of anisotropic artificial medium for diffraction-free transport through cascaded tunneling of guided resonances. High-resolution near-field measurements demonstrate the coupling of transverse guided resonances, supported by large-scale numerical modeling. Second, with the disordered scattering sites in this superlattices, we uncover the mechanism of disorder-induced transverse localization in chip-scale. Arrested spatial divergence is captured in the power-law scaling, along with the exponential asymmetric mode profiles and enhanced collimation bandwidth for increasing disorder, over 4,000 scattering sites. With increasing disorder, we observe the crossover from cascaded guided resonances into transverse localization regimes, beyond the ballistic and diffusive transport of photons. As disorder is ubiquitous in natural and artificial materials, the transport through random media is of great importance. It also leads to various interesting optical phenomena, of which the most surprising one is Anderson localization of light. However, not all the states in disordered system are localized. Nonlocalized modes that extend over the whole sample via coupling between multiple local cavities with similar resonance frequencies are also present in disordered systems. These extended modes are called necklace states. Here, we also show that long-distance beam collimation can be witnessed in millimeter-scale photonic crystals that were fabricated lithographically with ultrahigh resolutions. By precisely controlling the disorder level of three million scattering sites in photonic crystals, we uncovered the transformation of light flows from the propagation of regular Bloch modes to necklace states.

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This work focuses on solute mass transport in a highly heterogeneous two-region porous medium consisting of spherical low-hydraulic conductivity inclusions, embedded in a high-hydraulic conductivity matrix. The transport processes occuring in the system are described by three distinct time scales. The first time scale reflects the characteristic time for convective transport in the high-conductivity matrix. The second time scale reflects the characteristic time for diffusive transport in the low-conductivity inclusions. The third time scale reflects the characteristic time for convection within the inclusions. Two Péclet numbers can be defined that compare the time scales and provide qualitative insight into the net transport behavior in two-region media. To model this system, four different representations were developed: (1) a Darcy-scale model that involved direct microscale computation over the entire domain of the experimental system, (2) a direct microscale simulation computed on a simplified domain that had similar geometric parameters (e.g. volume fraction of inclusions) as the complete domain for the experimental system, (3) a volume averaged model (after Chastanet and Wood [2008]) which uses a constant mass transfer coefficient and (4) a volume averaged model which employs a time-dependent mass transfer coefficient. Two different experimental conditions were investigated: a high flow rate, and a low flow rate. Detailed understanding of the experimental system was developed, which led to accurate prediction of the system's behavior for the higher flow rate. Accurate early time fit of the data was achieved for the experiment with the lower flow rate, while late time behavior between the models and experimental data diverged. Further investigations of the experimental system were conducted to examine possible sources of errors that could lead to an inaccurate description of the system's properties. Additional mixing within the system, inhomogeneous distribution of the effective diffusion coefficient and imprecise initial estimates of the hydraulic parameters are all possible explanations for the inaccurate model representation of the system's behavior for the lower flow rate case. / Graduation date: 2012

E.H. Sondheimer. / "March 15, 1950." / Bibliography: p. 31. / Army Signal Corps Contract No. W36-039-sc-32037 Project No. 102B Dept. of the Army Project No. 3-99-10-022

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