A scaled gradient descent method for competition of applications of conjugate gradient with priori estimations of the minimum value / This research proposes a novel method of improving the Gradient Descent method in an effort to be competitive with applications of the conjugate gradient method while reducing computation per iteration. Iterative methods for unconstrained optimization have found widespread application in digital signal processing applications for large inverse problems, such as the use of conjugate gradient for parallel image reconstruction in MR Imaging. In these problems, very good estimates of the minimum value at the objective function can be obtained by estimating the noise variance in the signal, or using additional measurements. The method proposed uses an estimation of the minimum to develop a scaling for Gradient Descent at each iteration, thus avoiding the necessity of a computationally extensive line search. A sufficient condition for convergence and proof are provided for the method, as well as an analysis of convergence rates for varying conditioned problems. The method is compared against the gradient descent and conjugate gradient methods. A method with a computationally inexpensive scaling factor is achieved that converges linearly for well-conditioned problems. The method is tested with tricky non-linear problems against gradient descent, but proves unsuccessful without augmenting with a line search. However with line search augmentation the method still outperforms gradient descent in iterations. The method is also benchmarked against conjugate gradient for linear problems, where it achieves similar convergence for well-conditioned problems even without augmenting with a line search. / Thesis / Master of Science (MSc) / This research proposes a novel method of improving the Gradient Descent method in an effort to be competitive with applications of the conjugate gradient method while reducing computation per iteration. Iterative methods for unconstrained optimization have found widespread application in digital signal processing applications for large inverse problems, such as the use of conjugate gradient for parallel image reconstruction in MR Imaging. In these problems, very good estimates of the minimum value at the objective function can be obtained by estimating the noise variance in the signal, or using additional measurements. The method proposed uses an estimation of the minimum to develop a scaling for Gradient Descent at each iteration, thus avoiding the necessity of a computationally extensive line search. A sufficient condition for convergence and proof are provided for the method, as well as an analysis of convergence rates for varying conditioned problems. The method is compared against the gradient descent and conjugate gradient methods. A method with a computationally inexpensive scaling factor is achieved that converges linearly for well-conditioned problems. The method is tested with tricky non-linear problems against gradient descent, but proves unsuccessful without augmenting with a line search. However with line search augmentation the method still outperforms gradient descent in iterations. The method is also benchmarked against conjugate gradient for linear problems, where it achieves similar convergence for well-conditioned problems even without augmenting with a line search.

A precise prediction of the heat loads in metal materials in contact with the hot gas is an increasingly demanding problem in the design phase of the complex cooling schemes in the modern turbine engines. The coupled calculation of the fluid flow and the heat transfer is a promising approach as heat transfer coefficients are not necessary in the calculation and the heat transfer itself is part of the calculation and can be derived from local heat fluxes. Therefore, it is useful to incorporate an appropriate scheme for directly coupled heat transfer computations (conjugate heat transfer), capable of handling complex geometries into the existing Computational fluid dynamics (CFD) codes. The intent of the present work is to add the conjugate heat transfer solving capability to an existing flow solver. The coupled approach is achieved by maintaining a continuous local heat flux and a common temperature at the points along the fluid-solid interface. At every iteration, the temperature which is directly calculated via the equality of the local heat fluxes passing the fluid-solid contacting cell faces serves as the thermal boundary condition on the interfaces, instead of traditional isothermal/adiabatic thermal boundary conditions. In the solid domain, simplified energy equation is solved using the discretization and computational methods which have been used in the flow by introducing an effective equation of state. The connectivity is built for the points at the fluid-solid interfaces in order to communicate the thermal conditions with each other. Validation of the developed conjugate capability has been investigated. Computed results have been compared with theoretical or experimental results for laminar flat plate, high pressure guide vane, cooled plate, and effusion-cooled plate. All results obtained thus far compare rather favorably with theoretical or experimental results.

No description available.

The versatility of organoboron compounds has been demonstrated by their use as synthetic intermediates and more recently in therapeutic applications since the FDA approval of Velcade©. As a result, transition metal-catalyzed protocols to incorporate boron reagents into unsaturated compounds have been extensively researched. While an abundance of literature protocols have been reported, the majority utilize harsh reaction conditions in combination with expensive reagents. This dissertation discloses the author’s contributions to the development of efficient, cost-effective, and operationally simple transition metal-catalyzed borylation protocols with alkynes and diboron reagents. An open-to-air copper(II)-catalyzed aqueous borylation protocol of alkynoates and a symmetrical diboron reagent is reported. Conjugate addition of the boryl-copper species to the electrophilic β-carbon provided β-boryl-α,β-unsaturated esters in moderate to excellent yields. Exclusive (Z)-stereochemistry was confirmed by nOe experiments. The resulting vinyl boronate esters are useful cross-coupling partners. The scope of the aqueous β-borylation protocol was extended to the unsymmetrical diboron reagent, pinB-Bdan. This alternative protecting group has emerged as an orthogonal protecting group and alters the reactivity of the boron moiety. Activation of the pinacol moiety to form the Lewis acid-base adduct allowed for the chemoselective transfer of the 1,8- diaminonapthalene moiety to the β-carbon. An alternative novel synthesis of vinyl, allyl diboronate esters from propargylic alcohols has also been described. Formation of a leaving group in-situ with a palladium- and coppercatalyzed protocol can lead to several competing reaction pathways and the formation of multiple products. Fortunately, the resulting vinyl, allyl diboronate esters were stereoselectively synthesized in moderate GC yields despite significate decomposition during purification, as confirmed by stability studies. The terminal diboration of allenes was previously the only reported method for the synthesis of vinyl, allyl diboronate esters. / Ph. D.

Organoboron compounds have shown a wide variety of applications in both organic synthesis and the pharmaceutical field in the past decades. Transition metal-catalyzed boration of unsaturated compounds has been studied extensively as an efficient method to install C-B bonds. Most of the previous examples employed symmetrical diboron reagents such as B₂(pin)₂ (pin = pinacolate) and B₂(cat)₂ (cat = catecholate). There are, however, limited examples of boration using unsymmetrical diboron reagents. This dissertation discloses two transition metal-catalyzed borations of unsaturated compounds with unsymmetrical diboron compounds. A Cu-catalyzed β-boration of electrophilic allenoates with a novel sp²-sp³ hybridized diboron reagent (PDIPA) is described. This unsymmetrical diboron reagent is preactivated and allows the boration to go smoothly under mild reaction conditions. The reaction provides β-borylated β,γ- unsaturated esters with exclusive (Z)-double bond geometry. These borylated products are useful intermediates for subsequent Suzuki-Miyaura cross-coupling reaction. In order to install two C-B bonds in one reaction, a Pt-catalyzed diboration of allenes with a differentially protected diboron reagent (PDAN) is presented. This unsymmetrical diboron reagent is prepared from the sp²-sp³ hybridized diboron compound, and it reacts with a series of 1,1- disubstituted allenes chemo- and regioselectively. Steric control ensures that both boryl moieties add to the terminal double bond, and the pinacol boronate preferentially attaches to the sp-hybridized carbon. The bis-boronyl products can be further converted to other functional groups as well as cross-coupling reactions. A collaborative project with Department of Physics and Department of Chemical Engineering is also discussed. In this project, a series of 𝑜-nitrobenzyl ligands containing a disulfide group as the anchor to gold surfaces are synthesized. The 𝑜-nitrobenzyl group uncages an amine upon photoexcitation. Attempts to make a water soluble analog failed, however, the mixture of methanol and water as the solvent was sufficient to attach them on gold surfaces. / Ph. D.

Our research seeks new methods for functionalizing organic small molecules using organoboronic derivatives as a versatile handle for late-stage manipulations. Metal-catalyzed formation of new carbon-boron bonds and their subsequent transformations are highlighted. Among the myriad of unsaturated substrates for conducting borylation reactions, allenes have received minimal attention. These substrates are uniquely advantageous given that diboration results in the formation of both allylic and vinylic boronates. Orthogonal reactivity of the sp2 and the sp3 C-B bonds can allow for chemoselective transformations. However, oxidation of the carbon-boron bond is one example in which the conditions are unselective. To address this shortcoming, a platinum catalyst was developed for the diboration of 1,1-diaryl allenes with a differentially protected diboron reagent, pinB-Bdan. The reaction proceeds regioselectively in high yields to furnish olefins bearing a vinylic Bpin and an allylic Bdan moiety. The subsequent chemoselective transformation of each boron center was demonstrated. Methods for preparing 1,8-diaminonaphthalene protected vinylboronates conjugated to carbonyl groups are severely limited. A simple and efficient protocol was developed for carrying out an environmentally friendly copper(II)-catalyzed beta-borylation of alkynoates and alkynamides in water and open-to-air. Following the discriminative activation of the more Lewis acidic pinacol protected boron center in pinB-Bdan, a regio-, stereo- and chemoselective beta-borylation of acetylenic substrates delivers (Z)-beta-boryl enoates and primary, secondary, and tertiary enamides under very mild conditions. As an inexpensive and earth abundant metal, catalysts based on copper are highly desirable. An international collaborative project to develop a copper-catalyzed cross-coupling reaction of beta-boryl carbonyl compounds was explored. Preliminary results found these substrates to be either unstable towards or unreactive under the reactions conditions screened. / Ph. D.

Elastin like peptides (ELPs)—derived from the protein elastin—are widely used as thermoresponsive components in biomaterials due to their LCST (lower critical solution temperature) behavior at a characteristic transition temperature (Tt). While linear ELPs have been well investigated, few reports focused on branched ELPs. Using lysine (Lys, with an additional side-chain amine) as branching units, ELP dendrimers were synthesized by solid-phase peptide synthesis (SPPS) with up to 155 amino acid residues. A secondary structure change with decreasing ratio of random coil and increasing ratio of β-turn upon heating, which is typical of linear ELPs, was confirmed by circular dichroism spectroscopy for all peptides. Conformational change did not show evident dependence on topology, while a higher Tt was observed for dendritic peptides than for their linear control peptides with the same number of GLPGL repeats. Variable-temperature small-angle X-ray scattering (SAXS) measurements showed a size increase and fractal dimension upon heating, even below the Tt. These results were further confirmed by cryogenic transmission electron microscopy (cryo-TEM), and micro differential scanning calorimetry (micro-DSC), revealing the presence of aggregates below the Tt. These results indicated the presence of a pre-coacervation step in the LCST phase transition of the ELP dendrimers. We further prepared hydrogels by crosslinking hyaluronic acid (HA) with ELP dendrimers. We invesigated their physical properties with scanning electron microscopy (SEM), swelling tests, SAXS, and model drug loading/release experiments. Most of the HA_denELP hydrogels retained transparent upon gelation, but after lyophilization and reswelling remained opaque for days. This reswelling process was carefully investigated with time-course SAXS studies, and was attributed to forming pre-coacervates in the gelation step, which slowly reswelled during rehydration. We then prepared hydrogels with H2S-releasing aroylthiooxime (SATO) groups and showed human neutrophil elastase-responsive H2S-releasing properties with potential applications in treating chronic diseases with recurring inflammation. Furthermore, we prepared a series of wedge-shaped triblock polyethylene glycol (PEG)-ELP dendrimer-C16 (palmitic acid) conjugate amphiphiles with adjustable Tts. Various techniques were used to investigate their hierarchical structures. The triblock PEG-peptide-C16 conjugate amphiphiles were thermoresponsive and showed a morphology change from small micelles to large aggregates. However, the hydrophilic shell and strong tendency for micelle formation limited the thermoresponsive assembly, leading to slow turbidity change in the LCST transition. The secondary structure was twisted from conventional β-sheet, and the thermoresponsive trend observed in typical ELP systems was not observed, either. Variable temperature NMR showed evidence for coherent dehydration of the PEG and ELP segments, probably due to the relatively short blocks. Utilizing the micelles with hydrophobic cavity, we were able to encapsulate hydrophobic drugs, with promising applications for localized drug release in hyperthermia. / Doctor of Philosophy / Elastin like peptides (ELPs) are similar to the protein elastin in terms of amino acid sequence. They are used widely as thermoresponsive (change in properties at different temperatures) components in biomaterials due to their abnormally lower solubility at higher temperatures. While linear ELPs have been thoroughly investigated, few investigations in ELP dendrimers have been studied. Dendrimers are molecules that branch in a controlled way to achieve sphere-like structures with rich surface functionalities. We synthesized the ELP dendrimers by using lysine amino acids as branching units. A protein secondary structure change, typical of ELPs, was observed for all peptide dendrimers. Secondary structure transitions showed no dependence on the molecular branching/linear structures, but a higher transition temperature (T_t) was observed for dendritic peptides than for their linear control peptides with the same number of amino acids. Various techniques confirmed the existence of aggregates below the T_ts, which was never reported before. We further fabricated hydrogels that mimic the native extracellular matrix, by connecting hyaluronic acid (HA) with ELP dendrimers. Interestingly, most of the hydrogels studied retained transparent upon gelation, but after freeze-drying and addition of water remained opaque for days. This phenomenon was attributed to forming of small aggregates in the gelation step, which resulted in slow reswelling. We then prepared hydrogels with H₂S-releasing groups, which showed human neutrophil elastase-responsive H₂S-releasing properties with potential applications in treating chronic diseases with recurring inflammation. We then prepared a series of wedge-shaped triblock poly (ethylene glycol) (PEG)- ELP dendrimer-alkyl chain molecules. The triblock molecules were thermoresponsive and showed a change from small spheres to large aggregates. However, the hydrophilic shell limited the thermoresponsive assembly, leading to slow turbidity change in the LCST transition. We found evidence of coherent assembly of the PEG and ELP parts, probably due to the relatively short polymer chains. Utilizing the micelles with hydrophobic cavity, we were able to encapsulate hydrophobic drugs, with promising applications for localized drug release for cancer treatment.

The first successful synthesis and isolation of a boronic acid was reported in 1860 by Frankland in the pursuit of novel organometallic compounds. For more than a century, further studies of boronic acids were sparsely published. Suzuki and Miyaura jumpstarted the field in 1979 with an innovative carbon-carbon bond forming reaction employing an organoboronic acid and a carbon halide under palladium catalysis. Indeed, the Nobel Prize in Chemistry was awarded to Professor Akira Suzuki, along with Professors Richard Heck and Ei-ichi Negishi, in 2010 for their important contributions in palladium-catalyzed cross-coupling chemistry. Over the last 30 years, reports on organoboron compounds have increased exponentially. This dissertation describes the author's contributions to the development of preparative methods for organoboronic acid derivatives using transition metal-catalyzed reactions of diboron reagents. A unique "mixed" diboron reagent was developed (PDIPA diboron) that contains sp2- and sp3-hybridized boron atoms, unambiguously confirmed by X-ray crystallography. PDIPA diboron is sufficiently activated internally through a dative-bonding amine to selectively transfer the sp2-hybridized boron regioselectively, in the presence of copper, to electron deficient alkenes including α,β-unsaturated ketones, esters, amides, aldehydes, and nitriles to provide the corresponding boratohomoenolates. A unique β,β-diboration of an α,β-acetylenic ketone was also discovered. The scope of PDIPA diboron reactions was then expanded to a set of substrates with a more complex structural backbone. Allenoates are α,β,γ-unsaturated esters with orthogonal pi systems, which pose several possible difficulties with the regioselectivity of addition, not to mention known isomerizations catalyzed by copper. However, we successfully installed the boron moiety regioselectively on the β-carbon of a variety of allenoates, providing a vinyl boronic ester, and also observed exclusive formation of the (Z)-isomer from racemic starting materials. The resulting vinyl boronic ester was then shown to be an excellent Suzuki-Miyaura cross-coupling partner, affording a diastereopure, trisubstituted alkene in quantitative yield. Commercially available bis(pinacolato)diboron has shown remarkable stability towards hydrolysis and autoxidation. Using this reagent, we developed a copper- and amine-catalyzed boration protocol performed entirely in water and open to air. Using only 1 mol% copper, extraordinary activity was observed. UV-Vis, 11B NMR, and solvent kinetic isotope experiments were employed to gain insight into the mechanism, which showed the possibility of autocatalysis. Attempts to control stereoselectivity were not successful, although these results were rationalized by a dynamic catalyst structure. / Ph. D.

A generalized Conjugate Gradient like method is used to solve the linear systems of equations formed at each time-integration step of the unsteady, two-dimensional, compressible Navier-Stokes equations of fluid flow. The Navier-Stokes equations are cast in an implicit, upwind finite-volume, flux split formulation. Preconditioning techniques are employed with the Conjugate Gradient like method to enhance the stability and convergence rate of the overall iterative method. The superiority of the new solver is established by comparisons with a conventional Line GaussSeidel Relaxation (LGSR) solver. Comparisons are based on 'number of iterations required to converge to a steady-state solution' and 'total CPU time required for convergence'. Three test cases representing widely varying flow physics are chosen to investigate the performance of the solvers. Computational test results for very low speed (incompressible flow over a backward facing step at Mach 0.1), transonic flow (trailing edge flow in a transonic turbine cascade) and hypersonic flow (shockon- shock interactions on a cylindrical leading edge at Mach 6.0) are presented. For the 1vfach 0.1 case, speed-up factors of 30 (in terms of iterations) and 20 (in terms of CPU time) are found in favor of the new solver when compared with the LGSR solver. The corresponding speed-up factors for the transonic flow case are 20 and 18, respectively. The hypersonic case shows relatively lower speed-up factors of 5 and 4, respectively. This study reveals that preconditioning can greatly enhance the range of applicability and improve the performance of Conjugate Gradient like methods. / Ph. D.

No description available.