Thesis (Ph. D.)--Massachusetts Institute of Technology, Dept. of Metallurgy and Material Science, 1974. / MICROFICHE COPY AVAILABLE IN ARCHIVES AND SCIENCE. / Vita. Bibliography: leaves 56-59. / by Thomas Maurice Devine, Jr. / Ph.D.

Metamaterials are artificially constructed "materials" which are formed from arrays of engineered elements. By designing individual elements as well as their interactions, the propagation of electromagnetic (EM) waves within the structure can be manipulated, so that new responses can be realised which may not be found in nature. The subject of this research concerns the study of miniaturised elements with strong EM responses so that the constructed metamaterial can better approximate an ordinary low-loss material. The research involves designing miniaturised magnetic resonators operating in the microwave frequency range. A novel resonator prototypes, so-called “helical resonators”, have been successfully designed and fabricated whose physical sizes can fall below 1% of the free space wavelength at resonance. This contributes to a size reduction of 90% compared with previously published work. In addition, an analytical model has been developed, so that the resonance parameters of a helical resonator have explicit expressions. In particular, a constant optimal metallic fill ratio is demonstrated to exist, which can achieve a minimum resonant frequency and a maximum miniaturisation for any given outmost dimension of the element. The accuracy of the model has been verified by both simulation and experiment. The frequency responses of fabricated helical elements were measured using a vector network analyser and a pair of small loop non- resonant dipole probes, and the parameters were extracted using the phase frequency fit method which proves to have the best accuracy and robustness. The properties of a regular square array of helical resonators are subsequently investigated, which can be regarded as a two-dimensional metamaterial. A relevant analytical model has been developed, which characterises the array as an equivalent sheet with surface current distributions, rather than an artificial medium with finite thickness. The relation between the macroscopic EM fields and the small scale properties of individual helical resonators are then established. In particular, the helical resonators are observed to be inherently chiral, thus the assembled interlocking array exhibits dichroism. The transmission coefficients for the circular EM waves with two different polarisation states have been derived, which have been verified by simulation and measurement results as well. In addition, it has been theoretically demonstrated that the resonator elements and their spacings can be engineered, so that the circular EM wave with one particular polarisation state can be totally attenuated around the element resonance, while the other state suffers negligible attenuation. A quadratic relation between the optimal array spacing and the elements’ quality factor has been demonstrated.

The use of metals like titanium (Ti) and vanadium (V) are common in many medical implants for orthopaedic and orthodontic purposes. The most frequent cause of implant failure is aseptic loosening, resulting from an inflammatory reaction and increased osteolysis at the bone-metal interface. Currently, the pathophysiological mechanism of aseptic loosening remains poorly understood. One hypothesis suggests the reactivity of immune cells (metal hypersensitivity) towards metal ions released through the biocorrosion of metal implants. This thesis examines the effects of titanium and vanadium ions on various immune cells like monocytes, dendritic cells (DCs) and T-lymphocytes. Thereby investigating the role and mechanism which titanium and vanadium plays in aseptic loosening. Through energy filtered transmission electron microscopy, the accumulation of titanium ions was visualized in human monocyte-derived DCs and T-lymphocytes after 24 hours exposure. Titanium was seen to co-localise with phosphorous-rich regions, like the cell membrane, organelles and nucleus of these cells. Flow cytometry measured changes in the cell surface marker expression of monocytes, osteoclasts, DCs and T-lymphocytes treated with the metals. Monocytes exposed to titanium (IV) showed an increase of Tartate-Resistant Acid Phosphatase (TRAP), important for osteolysis and indicative of differentiation towards an osteoclast-like phenotype. DCs treated with Ti(IV) and vanadium (III) had reduced antigen presenting MHC class II expression, but not a reduced capacity to proliferate non-adherent peripheral blood monocytic cells (naPBMCs). Under the influence of Ti(IV), T-lymphocytes, DCs and monocytes expressed elevated levels of the chemokine receptor, CCR4. This would allow for the migration of CCR4+ cells towards the bone and skin regions. Functional changes were measured with BrdU incorporation proliferation assays, cytokine assays (CBA Kits) and the successful generation of titanium-specific T-lymphocytes from Ti(IV) treated DCs. Ti(IV) specific T-lymphocytes conceptually shows the possible formation of an antigenic titanium-protein complex, which can be recognized by the immune system. DCs treated with Ti(IV) and V(III) were able to cause the proliferation of naPBMCs, even with a reduced antigen presenting capability. However, there was no additional influence of V(III) on the immune response through DCs. Cytokines released by DCs and T-lymphocytes after Ti(IV) treatments showed a skew towards an inflammatory Th1-type response through the release of TGF-! and IL-12p70. Activated T-lymphocytes exposed to Ti(IV) also released RANK-L, which drives osteoclastogenesis and subsequently increased osteolysis. The research supports and suggests an interaction between immune and bone cells where titanium-induced inflammation drives an osteolytic cycle that prevents the integration of metal implants into the bone. Hence, suggesting a mechanism for implant failure through aseptic loosening in patients with titanium-vanadium implants.

The principle of coordinate invariance states that all physical laws must be formulated in a mathematical form that is independent of the geometrical properties of any particular coordinate system. Embracing this principle is the key to understand how to systematically incorporate curved material interfaces into a numerical solution of Maxwell’s equations. This dissertation describes how to generate a coordinate invariant representation of Maxwell’s equations in differential form, and it demonstrates why employing such representation is crucial to the development of robust finite-difference discretisations with consistent global error properties. As part of this process, two original contributions are presented that address the issue of constructing finite-difference approximations at the locations of material interfaces. The first contribution is a domain-decomposition procedure to enforce the tangential field continuity conditions with a second-order local truncation error that can be applied in 2-D or 3-D. The second contribution is a similar domain-decomposition procedure that enforces the tangential field continuity conditions with a local truncation of order 2L—where L is an integer greater or equal to one—but that can only be applied in 1-D. To conclude, the dissertation also describes the interesting connection that exists between the use of a coordinate invariant representation of Maxwell’s equations to design artificial materials and the use of the same representation to model curved material interfaces in a finite-difference discretisation.

The principle of coordinate invariance states that all physical laws must be formulated in a mathematical form that is independent of the geometrical properties of any particular coordinate system. Embracing this principle is the key to understand how to systematically incorporate curved material interfaces into a numerical solution of Maxwell’s equations. This dissertation describes how to generate a coordinate invariant representation of Maxwell’s equations in differential form, and it demonstrates why employing such representation is crucial to the development of robust finite-difference discretisations with consistent global error properties. As part of this process, two original contributions are presented that address the issue of constructing finite-difference approximations at the locations of material interfaces. The first contribution is a domain-decomposition procedure to enforce the tangential field continuity conditions with a second-order local truncation error that can be applied in 2-D or 3-D. The second contribution is a similar domain-decomposition procedure that enforces the tangential field continuity conditions with a local truncation of order 2L—where L is an integer greater or equal to one—but that can only be applied in 1-D. To conclude, the dissertation also describes the interesting connection that exists between the use of a coordinate invariant representation of Maxwell’s equations to design artificial materials and the use of the same representation to model curved material interfaces in a finite-difference discretisation.