Compressible flows at small Reynolds numbers

The problem of the slow viscous flow of a gas past a sphere is considered. The fluid cannot be treated incompressible in the limit when the Reynolds number Re, and the Mach number M, tend to zero in such a way that Re ~ o(M^2 ). In this case, the lowest order approximation to the steady Navier-Stokes equations of motion leads to a paradox discovered by Lagerstrom and Chester. This paradox is resolved within the framework of continuum mechanics using the classical slip condition and an iteration scheme that takes into account certain terms in the full Navier-Stokes equations that drop out in the approximation used by the above authors. It is found however that the drag predicted by the theory does not agree with R. A. Millikan's classic experiments on sphere drag.

The whole question of the applicability of the Navier-Stokes theory when the Knudsen number M/Re is not small is examined. A new slip condition is proposed. The idea that the Navier-Stokes equations coupled with this condition may adequately describe small Reynolds number flows when the Knudsen number is not too large is looked at in some detail. First, a general discussion of asymptotic solutions of the equations for all such flows is given. The theory is then applied to several concrete problems of fluid motion. The deductions from this theory appear to interpret and summarize the results of Millikan over a much wider range of Knudsen numbers (almost up to the free molecular or kinetic limit) than hitherto Believed possible by a purely continuum theory. Further experimental tests are suggested and certain interesting applications to the theory of dilute suspensions in gases are noted. Some of the questions raised in the main body of the work are explored further in the appendices.

Towards conditional RNAi : shape and sequence transduction with small conditional RNAs

RNA interference (RNAi) is a powerful biological pathway allowing for sequence-specific knockdown of any gene of interest. While RNAi is a proven tool for probing gene function in biological circuits, it is limited by being constitutively ON and executes the logical operation: silence gene Y. To provide greater control over post-transcriptional gene silencing, we propose engineering a biological logic gate to implement “conditional RNAi.” Such a logic gate would silence gene Y only upon the expression of gene X, a completely unrelated gene, executing the logic: if gene X is transcribed, silence independent gene Y. Silencing of gene Y could be confined to a specific time and/or tissue by appropriately selecting gene X.

To implement the logic of conditional RNAi, we present the design and experimental validation of three nucleic acid self-assembly mechanisms which detect a sub-sequence of mRNA X and produce a Dicer substrate specific to gene Y. We introduce small conditional RNAs (scRNAs) to execute the signal transduction under isothermal conditions. scRNAs are small RNAs which change conformation, leading to both shape and sequence signal transduction, in response to hybridization to an input nucleic acid target. While all three conditional RNAi mechanisms execute the same logical operation, they explore various design alternatives for nucleic acid self-assembly pathways, including the use of duplex and monomer scRNAs, stable versus metastable reactants, multiple methods of nucleation, and 3-way and 4-way branch migration.

We demonstrate the isothermal execution of the conditional RNAi mechanisms in a test tube with recombinant Dicer. These mechanisms execute the logic: if mRNA X is detected, produce a Dicer substrate targeting independent mRNA Y. Only the final Dicer substrate, not the scRNA reactants or intermediates, is efficiently processed by Dicer. Additional work in human whole-cell extracts and a model tissue-culture system delves into both the promise and challenge of implementing conditional RNAi in vivo.

Optimal procurement and contracting with research and development

Government procurement of a new good or service is a process that usually includes basic research, development, and production. Empirical evidences indicate that investments in research and development (R and D) before production are significant in many defense procurements. Thus, optimal procurement policy should not be only to select the most efficient producer, but also to induce the contractors to design the best product and to develop the best technology. It is difficult to apply the current economic theory of optimal procurement and contracting, which has emphasized production, but ignored R and D, to many cases of procurement.

In this thesis, I provide basic models of both R and D and production in the procurement process where a number of firms invest in private R and D and compete for a government contract. R and D is modeled as a stochastic cost-reduction process. The government is considered both as a profit-maximizer and a procurement cost minimizer. In comparison to the literature, the following results derived from my models are significant. First, R and D matters in procurement contracting. When offering the optimal contract the government will be better off if it correctly takes into account costly private R and D investment. Second, competition matters. The optimal contract and the total equilibrium R and D expenditures vary with the number of firms. The government usually does not prefer infinite competition among firms. Instead, it prefers free entry of firms. Third, under a R and D technology with the constant marginal returns-to-scale, it is socially optimal to have only one firm to conduct all of the R and D and production. Fourth, in an independent private values environment with risk-neutral firms, an informed government should select one of four standard auction procedures with an appropriate announced reserve price, acting as if it does not have any private information.

Site-Specific Isotopes in Small Organic Molecules

Stable isotope geochemistry is a valuable toolkit for addressing a broad range of problems in the geosciences. Recent technical advances provide information that was previously unattainable or provide unprecedented precision and accuracy. Two such techniques are site-specific stable isotope mass spectrometry and clumped isotope thermometry. In this thesis, I use site-specific isotope and clumped isotope data to explore natural gas development and carbonate reaction kinetics. In the first chapter, I develop an equilibrium thermodynamics model to calculate equilibrium constants for isotope exchange reactions in small organic molecules. This equilibrium data provides a framework for interpreting the more complex data in the later chapters. In the second chapter, I demonstrate a method for measuring site-specific carbon isotopes in propane using high-resolution gas source mass spectrometry. This method relies on the characteristic fragments created during electron ionization, in which I measure the relative isotopic enrichment of separate parts of the molecule. My technique will be applied to a range of organic compounds in the future. For the third chapter, I use this technique to explore diffusion, mixing, and other natural processes in natural gas basins. As time progresses and the mixture matures, different components like kerogen and oil contribute to the propane in a natural gas sample. Each component imparts a distinct fingerprint on the site-specific isotope distribution within propane that I can observe to understand the source composition and maturation of the basin. Finally, in Chapter Four, I study the reaction kinetics of clumped isotopes in aragonite. Despite its frequent use as a clumped isotope thermometer, the aragonite blocking temperature is not known. Using laboratory heating experiments, I determine that the aragonite clumped isotope thermometer has a blocking temperature of 50-100°C. I compare this result to natural samples from the San Juan Islands that exhibit a maximum clumped isotope temperature that matches this blocking temperature. This thesis presents a framework for measuring site-specific carbon isotopes in organic molecules and new constraints on aragonite reaction kinetics. This study represents the foundation of a future generation of geochemical tools for the study of complex geologic systems.

I. Thermochemistry and reaction kinetics of disolvated protons by ion cyclotron resonance spectroscopy. II. Thermochemical studies of small fluorocarbons by photoionization mass spectrometry

The disolvated proton, H(OH₂)₂⁺ is employed as a chemical reagent in low pressure (˂ 10^-5 torr) investigations by ion cyclotron resonance spectroscopy. Since termolecular reactions are absent at low pressure, disolvated protons are not generally observed. However H(OH₂)₂⁺ is produced in a sequence of bimolecular reactions in mixtures containing H₂O and one of a small number of organohalide precursors. Then a series of hydrated Lewis bases is produced by H₃O⁺ transfer from H(OH₂)₂⁺. In Chapter II, the relative stability of hydrated bases containing heteroatoms of both first and second row elements is determined from the preferred direction of H₃O⁺ transfer between BH(OH₂)⁺ complexes. S and P containing bases are shown to bind H₃O⁺ more weakly than O and N bases with comparable proton affinities. A simple model of hydrogen bonding is proposed to account for these observations.

H⁺ transfer from H(OH₂)₂⁺ to several Lewis bases also occurs at low pressure. In Chapter III the relative importance of H₃O⁺ transfer and H⁺ transfer from H(OH₂)₂⁺ to a series of bases is observed to be a function of base strength. Beginning with CH₃COOH, the weakest base for which H⁺ transfer is observed, the importance of H⁺ transfer increases with increasing proton affinity of the acceptor base. The nature of neutral products formed from H(OH₂)₂⁺ by loss of H⁺ is also considered.

Chapters IV and V deal with thermochemistry of small fluorocarbons determined by photoionization mass spectrometry. The enthalpy of formation of CF₂ is considered in Chapter IV. Photoionization of perfluoropropylene, perfluorocyclopropane, and trifluoromethyl benzene yield onsets for ions formed by loss of a CF₂ neutral fragment. Earlier determinations of ΔH^°_f298 (CF₂) are reinterpreted using updated thermochemical values and compared with results of this study. The heat of formation of neutral perfluorocyclopropane is also derived. Finally, the energetics of interconversion of perfluoropropylene and perfluorocyclopropane are considered for both the neutrals and their molecular ions.

In Chapter V the heats of formation of CF₃⁺ and CF₃I⁺are derived from photoionization of CF₃I. These are considered with respect to ion-molecule reactions observed in CF₃I monitored by the techniques of ion cyclotron resonance spectroscopy. Results obtained in previous experiments are also compared.