This research focuses on diterpenoids from Taiwanese soft corals Xenia umbellata Lamarck, Junceella juncea Pallas and Junceella fragilis Ridley. Twelve diterpenoids in addition to one sesequiterpenoid were isolated. Our investigation of the soft coral X. umbellata Lamarck afforded five natural products, including two new xenicane diterpenes, xenibelatols A-B (1-2), together with two known xenicane diterpenes, 7,8-oxido- isoxeniolide (3), 9-hydroxyxeniolide-F (4), and a cadinene sesequiterpene, xenitorin A (5). Chemical investigation of the gorgonian J. juncea Pallas, has resulted in isolation of a new briarane diterpene, juncenolide H (6). Continuing our investigation of the gorgonian J. fragilis Ridley, we isolated seven briarane diterpenes, including four new briaranes, flajunolides A-D (7-10), along with three known briaranes, junceellolide E (11), umbraculolide A (12), 11This research focuses on diterpenoids from Taiwanese soft corals Xenia umbellata Lamarck, Junceella juncea Pallas and Junceella fragilis Ridley. Twelve diterpenoids in addition to one sesequiterpenoid were isolated. Our investigation of the soft coral X. umbellata Lamarck afforded five natural products, including two new xenicane diterpenes, xenibelatols A-B (1-2), together with two known xenicane diterpenes, 7,8-oxido- isoxeniolide (3), 9-hydroxyxeniolide-F (4), and a cadinene sesequiterpene, xenitorin A (5). Chemical investigation of the gorgonian J. juncea Pallas, has resulted in isolation of a new briarane diterpene, juncenolide H (6). Continuing our investigation of the gorgonian J. fragilis Ridley, we isolated seven briarane diterpenes, including four new briaranes, flajunolides A-D (7-10), along with three known briaranes, junceellolide E (11), umbraculolide A (12),11£\, 20£\-epoxy-4-deacetoxy junceellolide D (13). The new compounds 1,2 and 6-10 possess xenicane-type and briarane-type skeletons respectively. The structures of new compounds were determined by 1D-, 2D-NMR spectroscopic analysis and physical methods such as optical rotation, UV, IR, mass spectrum, as well as comparison with the spectroscopic data reported for related compounds. Compounds 1 and 2 are geometric isomers of compounds 3 and 4. The only difference between them resides in the side chain. The geometry of the side chain influenced the relative spatial proximity of H-12, H-13, H-14 to the carbonyl at C-3, and consequently the extent to which these protons are subjected to the anisotropic effects of the carbonyl. Compounds 6-10 have acetyl groups at C-2, C-9, C-12, C-14 positions. Because of structural difference appears in briarane skeleton, they showed different chemical shifts in specific positions. Biological activity test¡Arevealed that compound 5 exhibited moderate cytotoxic activity against KB and WiDr cancer cell lines with ED50 values at 5.9 and 9.9 £gg/ml respectively.

This thesis presents the development of electrochemical etch-stop techniques (ECES) to achieve high precision 3-dimensional integrated MEMS sensors with wet anisotropic etching by applying proper voltages to various regions in silicon. The anisotropic etchant is selected as tetra methyl ammonium hydroxide, TMAH, considering its high silicon etch rate, selectivity towards SiO2, and CMOS compatibility, especially during front-side etching of the chip/wafer. A number of parameters affecting the etching are investigated, including the effect of temperature, illumination, and concentration of the etchant over the etch rate of silicon, surface roughness, and biasing voltages. The biasing voltages for passivating the n-well and enhancing the etching reactions on p-substrate are determined as -0.5V and -1.6V, respectively, after a series of current-voltage characteristic experiments. The surface roughness due to TMAH etching is prevented with the addition of ammonium peroxodisulfate, AP. A proper etching process is achieved using a 10wt.% TMAH at 85&deg / C with 10gr/lt. AP. Different silicon etch samples are produced in METU-MET facilities to understand and optimize ECES parameters that can be used for CMOS microbolometers. The etch samples are fabricated using various processes, including thermal oxidation, boron and phosphorus diffusions, aluminum and silicon nitride layer deposition processes. Etching with the prepared samples shows the dependency of the depletion layer between p-substrate and n&amp / #8209 / well, explaining the reason of the previous failures during post-CMOS etching of CMOS microbolometers from the front side. Succesfully etched CMOS microbolometers are achieved with back side etching in 6M KOH at 90 &deg / C, where &amp / #8209 / 3.5V and 1.5V are applied to the p-substrate and n-well. In summary, this study provides an extensive understanding of the ECES process for successful implementations of integrated MEMS sensors.

In this thesis, mechanical and elastic behaviour of anisotropic materials are inves- tigated in order to understand the optimum mechanical behaviour of them in selected directions. For an anisotropic material with known elastic constants, it is possible to choose the best set of e&curren / ective elastic constants and e&curren / ective eigen- values which determine the optimum mechanical and elastic properties of it and also represent the material in a speci.ed greater material symmetry. For this reason, bounds on the e&curren / ective elastic constants which are the best set of elastic constants and e&curren / ective eigenvalues of materials have been constructed symbollicaly for all anisotropic elastic symmetries by using Hill [4,13] approach. Anisotropic Hooke.s law and its Kelvin inspired formulation are described and generalized Hill inequalities are explained in detail. For di&curren / erent types of sym- metries, materials were selected randomly and data of elastic constants for them were collected. These data have been used to calculate bounds on the e&curren / ective elastic constants and e&curren / ective eigenvalues. Finally, by examining numerical results of bounds given in tables, it is seen that the materials selected from the same symmetry type which have larger interval between the bounds, are more anisotropic, whereas some materials which have smaller interval between the bounds, are closer to isotropy.

Electrical conductivity of biological tissues is a distinctive property which differs among tissues. It also varies according to the physiological and pathological state of tissues. Furthermore, in order to solve the bioelectric field problems accurately, electrical conductivity information is essential. Magnetic Resonance Electrical Impedance Tomography (MREIT) technique is proposed to image this information with high spatial resolution. However, almost all MREIT algorithms proposed to date assumes isotropic conductivity in order to simplify the underlying mathematics. But it is known that most of the tissues in human body have anisotropic conductivity values. The aim of this study is to reconstruct anisotropic conductivity images with MREIT. In the study, five novel anisotropic conductivity reconstruction algorithms are developed and implemented. Proposed algorithms are grouped into two: current density based reconstruction algorithms (Type-I) and magnetic flux density based algorithms (Type-II). Performances of the algorithms are evaluated in several aspects and compared with each other. The technique is experimentally realized using 0.15T METU &ndash / EE MRI System and anisotropic conductivity images of test phantoms are reconstructed using all proposed algorithms.

Poly(p-phenylenebenzobisimidazole), PBI, is a rigid-rod polymer with a fully conjugated backbone having superior mechanical properties, thermo-oxi- dative and solvent stabilities. The stabilities cause processing difficulties and in terms limit its applications in critical technologies, such as conducting polymers, nonlinear optics, and solid polyelectrolytes. In this study, a chemical derivative of PBI, poly[1,7-dihydrobenzo[1,2- d:4,5-d¡¦]diimidazo-2,6-diyl[2-(2-sulfo)-p-phenylene]], sPBI, was synthesized by polycondensation reaction of 1,2,4,5-tetraaminobenzene tetrahydrochloride with 2-sulfoterephthalic acid in poly(phosphoric acid). Isolated sPBI was measured in 30oC methanesulfonic acid for an intrinsic viscosity as high as 10.5 dL/g. sPBI polymer was then reacted with 1,3-propanesultone in dimethylsulfoxide containing sodium hydride for water-soluble rigid-rod polyelectrolyte, poly[1,7- dipropylsulfobenzo-[1,2-d:4,5-d¡¦]diimidazo-2,6-diyl-[2,(2-sulfo)-p-phenylene]], sPBI-PS(Na+). sPBI-PS(Na+) was further converted to sPBI-PS(Li+) with hydrochloride and followed with lithium hydroxide. Various analyses were applied to ascertain chemical structure, purities and thermal properties of synthesized monomers and polymers. sPBI-PS(Li+) aqueous solutions were doped individually with lithium salts of LiI, LiBF4, and LiCF3SO3 at concentrations up to 1.7¡Ñ10-5 wt./wt., which were cast into freestanding films of 10-25 £gm in thickness. Direct-current conductivity measured at room- temperature parallel to the film surface was as large as 9.74¡Ñ10-5 S/cm. The ionic nature of the conductivity was revealed by constant-voltage depletion measurements. X-ray scattering results suggested that the cast film was in-plane isotropic but out-of-the plane anisotropic with the rigid-rod backbone lying in the plane of the film.

Many technologically important alloys such as Ni base superalloys and Ti-Al base alloys benefit from the precipitation of an ordered β phase from a disordered α matrix. When the crystallographic symmetry of the β phase is a subgroup of that of the disordered α phase, the microstructure may contain multiple orientational variants of the β phase, each with its own (anisotropic, crystallographically equivalent) misfit (lattice parameter mismatch) with the matrix phase. Examples include orthorhombic precipitates in a hexagonal matrix in Ti-Al-Nb alloys, and tetragonal precipitates in a cubic matrix in ZrO2-Y2O3. We have studied two-phase microstructures containing multiple variants of the precipitate phase. In particular, we have used phase field simulations to study the effect of elastic stresses in a two dimensional system containing a disordered matrix and three different orientational variants of the precipitate phase, with a view to elucidate the effect of different levels of anisotropy in misfit. We consider a two dimensional, elastically homogeneous and isotropic model system in which the matrix (α) and precipitate (β) phases have hexagonal and rectangular symmetries, respectively, giving rise to three orientational variants of the β phase. Therefore, our phase field model has composition (c) and three order parameters (η1, η2, η3) as the field variables.Due to the difference in crystallographic symmetry, the precipitate-matrix misfit strain tensor, ε*, can be anisotropic. ε*maybe represented in its principal form as ε *= (ε xx 0 ) 0 εyy where ε xx and ε yy are the principal components of the misfit tensor. We define t= εyy/εxx as the parameter representing anisotropy in the misfit. In this thesis, we report the results of our systematic study of microstructural evolution in systems with different values of t, representing different levels of anisotropy in misfit: •Case A: t=1 (dilatational or isotropic misfit) • Case B: 0 <t<1 (principal misfit components are unequal but have the same sign) • Case C: t=0 (the principal misfit along the y direction is zero) • Case D: -1 <t<0 (principal misfit components have opposite signs and unequal magnitudes) • Case E: t= -1 (principal misfit components are equal, but with opposite signs; pure shear) In Cases D and E, there is an invariant line along which the normal misfit is zero. In Case D, this invariant line is at ±54.72◦, and in Case E, it is at ±45◦, with respect to the x-axis. Our simulations of microstructural evolution in this system are based on numerical integration of the Cahn-Hilliard and Cahn-Allen equations which govern the evolution of composition and order parameter fields, respectively. In each case, we have studied two different situations: isolated particle (single variant) and many interacting particles (multivariant). Dynamical growth shape of an isolated precipitate In systems with an isotropic misfit (Case A), the precipitate shape remains circular at all sizes. In Cases B and C, the precipitate shape is elongated along the y-axis, which is also the direction in which the magnitude of the misfit strain is lower. In all these cases, the symmetry of the particle shape remains unaltered at all sizes. In contrast, in Cases D and E, the particle shape exhibits a symmetry-breaking transition. In Case D, the precipitate elongates initially along the y direction (i.e. the direction of lower absolute misfit), before undergoing a transition in which the mirror symmetry normal to x and yaxes is lost. In Case E, the particle has an initial square-like shape (with its sides normal to the 11directions) before losing its four-fold rotation axis to become rectangle-like with its long axis along one of the the 11directions. The critical precipitate size at which the symmetry-breaking shape transition occurs is obtained using bifurcation diagrams. In both Cases D and E, the critical size for the dynamical growth shapes is larger than those for equilibrium shapes[1].This critical size is larger when the matrix supersaturation is higher or shear modulus is lower. Microstructural Evolution In all the five cases, the elastic stresses have a common effect: they lead to microstructures in which the precipitate volume fraction is lower than that in a system with no misfit. This observation is consistent with the results from the thermodynamics of stressed solids that show that a precipitate-matrix misfit increases the interfacial composition in both the matrix and the precipitate phase. In systems with isotropic misfit (Case A), the microstructure consists of isolated circular domains of the precipitate phase that retain their circular shape during growth and subsequent coarsening. In Cases B and C with anisotropic misfit with t≥0, the three orientational variants of the precipitate phase are elongated along the directions of lower misfit (y-axis and ±120◦to y-axis). At a given size, particles in Case C (in which one of the principal misfits is zero) are more elongated than those in Case B. Systems with a higher shear modulus enhance the effect of misfit stresses, and therefore, lead to thinner and longer precipitates. When the precipitate volume fraction is increased, these elongated precipitates interact with (and impinge against) one another to a greater extent, and acquire a more jagged appearance. For Cases D and E, each orientation domain is associated with an invariant line along which the normal misfit is zero. Thus, in Case D, early stage microstructures show particles elongated along directions of lower absolute misfit (y-axis and ±120°to y-axis). At the later stages, the domains of the precipitate phase tend to orient along the invariant lines; this leads some of the particles to acquire a ‘Z’ shape before they completely re-orient themselves along the invariant line. In Case E, each variant grows as a thin plate elongating along the invariant line. The growth and impingement of these thin plates leads to a microstructure exhibiting complex multi-domain patterns such as stars, wedges, triangles, and checkerboard. These patterns have been compared (and are in good agreement) with experimental observations in Ti-Al-Nb alloys containing the precipitate (O) and matrix (α2)phases[2]. Since in Case E the sum of misfit strains of the three variants is zero, elastic energy considerations point to the possibility of compact, self-accommodating clusters of the three variants, sharing antiphase boundaries (APBs). Thus, if the APB energy is sufficiently low, the microstructure may consist of such compact clusters. Our simulations with such low APB energy do show triangle shaped clusters with six separate particles (two of each variant)in a self-accommodating pattern. (Refer PDF file)

Some boundary value problems yield anisotropic solutions, e.g. solutions with boundary layers. If such problems are to be solved with the finite element method (FEM), anisotropically refined meshes can be advantageous. In order to construct these meshes or to control the error one aims at reliable error estimators. For \emph{isotropic} meshes many estimators are known, but they either fail when used on \emph{anisotropic} meshes, or they were not applied yet. For rectangular (or cuboidal) anisotropic meshes a modified error estimator had already been found. We are investigating error estimators on anisotropic tetrahedral or triangular meshes because such grids offer greater geometrical flexibility. For the Poisson equation a residual error estimator, a local Dirichlet problem error estimator, and an $L_2$ error estimator are derived, respectively. Additionally a residual error estimator is presented for a singularly perturbed reaction diffusion equation. It is important that the anisotropic mesh corresponds to the anisotropic solution. Provided that a certain condition is satisfied, we have proven that all estimators bound the error reliably.

We consider a singularly perturbed reaction-diffusion problem and derive and rigorously analyse an a posteriori residual error estimator that can be applied to anisotropic finite element meshes. The quotient of the upper and lower error bounds is the so-called matching function which depends on the anisotropy (of the mesh and the solution) but not on the small perturbation parameter. This matching function measures how well the anisotropic finite element mesh corresponds to the anisotropic problem. Provided this correspondence is sufficiently good, the matching function is O(1). Hence one obtains tight error bounds, i.e. the error estimator is reliable and efficient as well as robust with respect to the small perturbation parameter. A numerical example supports the anisotropic error analysis.

Singularly perturbed problems often yield solutions ith strong directional features, e.g. with boundary layers. Such anisotropic solutions lend themselves to adapted, anisotropic discretizations. The quality of the corresponding numerical solution is a key issue in any computational simulation. To this end we present a new robust error estimator for a singularly perturbed reaction-diffusion problem. In contrast to conventional estimators, our proposal is suitable for anisotropic finite element meshes. The estimator is based on the solution of a local problem, and yields error bounds uniformly in the small perturbation parameter. The error estimation is efficient, i.e. a lower error bound holds. The error estimator is also reliable, i.e. an upper error bound holds, provided that the anisotropic mesh discretizes the problem sufficiently well. A numerical example supports the analysis of our anisotropic error estimator.

We consider a posteriori error estimators that can be applied to anisotropic tetrahedral finite element meshes, i.e. meshes where the aspect ratio of the elements can be arbitrarily large. Two kinds of Zienkiewicz-Zhu (ZZ) type error estimators are derived which are both based on some recovered gradient. Two different, rigorous analytical approaches yield the equivalence of both ZZ error estimators to a known residual error estimator. Thus reliability and efficiency of the ZZ error estimation is obtained. Particular attention is paid to the requirements on the anisotropic mesh. The analysis is complemented and confirmed by several numerical examples.