Non-linear dispersive waves with a small dissipation

The general theory of Whitham for slowly-varying non-linear wavetrains is extended to the case where some of the defining partial differential equations cannot be put into conservation form. Typical examples are considered in plasma dynamics and water waves in which the lack of a conservation form is due to dissipation; an additional non-conservative element, the presence of an external force, is treated for the plasma dynamics example. Certain numerical solutions of the water waves problem (the Korteweg-de Vries equation with dissipation) are considered and compared with perturbation expansions about the linearized solution; it is found that the first correction term in the perturbation expansion is an excellent qualitative indicator of the deviation of the dissipative decay rate from linearity.

A method for deriving necessary and sufficient conditions for the existence of a general uniform wavetrain solution is presented and illustrated in the plasma dynamics problem. Peaking of the plasma wave is demonstrated, and it is shown that the necessary and sufficient existence conditions are essentially equivalent to the statement that no wave may have an amplitude larger than the peaked wave.

A new type of fully non-linear stability criterion is developed for the plasma uniform wavetrain. It is shown explicitly that this wavetrain is stable in the near-linear limit. The nature of this new type of stability is discussed.

Steady shock solutions are also considered. By a quite general method, it is demonstrated that the plasma equations studied here have no steady shock solutions whatsoever. A special type of steady shock is proposed, in which a uniform wavetrain joins across a jump discontinuity to a constant state. Such shocks may indeed exist for the Korteweg-de Vries equation, but are barred from the plasma problem because entropy would decrease across the shock front.

Finally, a way of including the Landau damping mechanism in the plasma equations is given. It involves putting in a dissipation term of convolution integral form, and parallels a similar approach of Whitham in water wave theory. An important application of this would be towards resolving long-standing difficulties about the "collisionless" shock.

Movement of a Spherical Brownian Particle Between Infinite Parallel Plates: Hindered Dispersion and Sedimentation

The dispersion of an isolated, spherical, Brownian particle immersed in a Newtonian fluid between infinite parallel plates is investigated. Expressions are developed for both a 'molecular' contribution to dispersion, which arises from random thermal fluctuations, and a 'convective' contribution, arising when a shear flow is applied between the plates. These expressions are evaluated numerically for all sizes of the particle relative to the bounding plates, and the method of matched asymptotic expansions is used to develop analytical expressions for the dispersion coefficients as a function of particle size to plate spacing ratio for small values of this parameter.

It is shown that both the molecular and convective dispersion coefficients decrease as the size of the particle relative to the bounding plates increase. When the particle is small compared to the plate spacing, the coefficients decrease roughly proportional to the particle size to plate spacing ratio. When the particle closely fills the space between the plates, the molecular dispersion coefficient approaches zero slowly as an inverse logarithmic function of the particle size to plate spacing ratio, and the convective dispersion coefficent approaches zero approximately proportional to the width of the gap between the edges of the sphere and the bounding plates.

Asymptotic analysis of thin plates under normal load and horizontal edge thrust

We consider the radially symmetric nonlinear von Kármán plate equations for circular or annular plates in the limit of small thickness. The loads on the plate consist of a radially symmetric pressure load and a uniform edge load. The dependence of the steady states on the edge load and thickness is studied using asymptotics as well as numerical calculations. The von Kármán plate equations are a singular perturbation of the Fӧppl membrane equation in the asymptotic limit of small thickness. We study the role of compressive membrane solutions in the small thickness asymptotic behavior of the plate solutions.

We give evidence for the existence of a singular compressive solution for the circular membrane and show by a singular perturbation expansion that the nonsingular compressive solution approach this singular solution as the radial stress at the center of the plate vanishes. In this limit, an infinite number of folds occur with respect to the edge load. Similar behavior is observed for the annular membrane with zero edge load at the inner radius in the limit as the circumferential stress vanishes.

We develop multiscale expansions, which are asymptotic to members of this family for plates with edges that are elastically supported against rotation. At some thicknesses this approximation breaks down and a boundary layer appears at the center of the plate. In the limit of small normal load, the points of breakdown approach the bifurcation points corresponding to buckling of the nondeflected state. A uniform asymptotic expansion for small thickness combining the boundary layer with a multiscale approximation of the outer solution is developed for this case. These approximations complement the well known boundary layer expansions based on tensile membrane solutions in describing the bending and stretching of thin plates. The approximation becomes inconsistent as the clamped state is approached by increasing the resistance against rotation at the edge. We prove that such an expansion for the clamped circular plate cannot exist unless the pressure load is self-equilibrating.

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.

Physical investigations of small particles : (I) aerosol particle charging and flux enhancement and (II) whispering gallery mode sensing

Part I

Particles are a key feature of planetary atmospheres. On Earth they represent the greatest source of uncertainty in the global energy budget. This uncertainty can be addressed by making more measurement, by improving the theoretical analysis of measurements, and by better modeling basic particle nucleation and initial particle growth within an atmosphere. This work will focus on the latter two methods of improvement.

Uncertainty in measurements is largely due to particle charging. Accurate descriptions of particle charging are challenging because one deals with particles in a gas as opposed to a vacuum, so different length scales come into play. Previous studies have considered the effects of transition between the continuum and kinetic regime and the effects of two and three body interactions within the kinetic regime. These studies, however, use questionable assumptions about the charging process which resulted in skewed observations, and bias in the proposed dynamics of aerosol particles. These assumptions affect both the ions and particles in the system. Ions are assumed to be point monopoles that have a single characteristic speed rather than follow a distribution. Particles are assumed to be perfect conductors that have up to five elementary charges on them. The effects of three body interaction, ion-molecule-particle, are also overestimated. By revising this theory so that the basic physical attributes of both ions and particles and their interactions are better represented, we are able to make more accurate predictions of particle charging in both the kinetic and continuum regimes.

The same revised theory that was used above to model ion charging can also be applied to the flux of neutral vapor phase molecules to a particle or initial cluster. Using these results we can model the vapor flux to a neutral or charged particle due to diffusion and electromagnetic interactions. In many classical theories currently applied to these models, the finite size of the molecule and the electromagnetic interaction between the molecule and particle, especially for the neutral particle case, are completely ignored, or, as is often the case for a permanent dipole vapor species, strongly underestimated. Comparing our model to these classical models we determine an “enhancement factor” to characterize how important the addition of these physical parameters and processes is to the understanding of particle nucleation and growth.

Part II

Whispering gallery mode (WGM) optical biosensors are capable of extraordinarily sensitive specific and non-specific detection of species suspended in a gas or fluid. Recent experimental results suggest that these devices may attain single-molecule sensitivity to protein solutions in the form of stepwise shifts in their resonance wavelength, \lambda_{R}, but present sensor models predict much smaller steps than were reported. This study examines the physical interaction between a WGM sensor and a molecule adsorbed to its surface, exploring assumptions made in previous efforts to model WGM sensor behavior, and describing computational schemes that model the experiments for which single protein sensitivity was reported. The resulting model is used to simulate sensor performance, within constraints imposed by the limited material property data. On this basis, we conclude that nonlinear optical effects would be needed to attain the reported sensitivity, and that, in the experiments for which extreme sensitivity was reported, a bound protein experiences optical energy fluxes too high for such effects to be ignored.

Lattice quantum codes and exotic topological phases of matter

This thesis addresses whether it is possible to build a robust memory device for quantum information. Many schemes for fault-tolerant quantum information processing have been developed so far, one of which, called topological quantum computation, makes use of degrees of freedom that are inherently insensitive to local errors. However, this scheme is not so reliable against thermal errors. Other fault-tolerant schemes achieve better reliability through active error correction, but incur a substantial overhead cost. Thus, it is of practical importance and theoretical interest to design and assess fault-tolerant schemes that work well at finite temperature without active error correction.

In this thesis, a three-dimensional gapped lattice spin model is found which demonstrates for the first time that a reliable quantum memory at finite temperature is possible, at least to some extent. When quantum information is encoded into a highly entangled ground state of this model and subjected to thermal errors, the errors remain easily correctable for a long time without any active intervention, because a macroscopic energy barrier keeps the errors well localized. As a result, stored quantum information can be retrieved faithfully for a memory time which grows exponentially with the square of the inverse temperature. In contrast, for previously known types of topological quantum storage in three or fewer spatial dimensions the memory time scales exponentially with the inverse temperature, rather than its square.

This spin model exhibits a previously unexpected topological quantum order, in which ground states are locally indistinguishable, pointlike excitations are immobile, and the immobility is not affected by small perturbations of the Hamiltonian. The degeneracy of the ground state, though also insensitive to perturbations, is a complicated number-theoretic function of the system size, and the system bifurcates into multiple noninteracting copies of itself under real-space renormalization group transformations. The degeneracy, the excitations, and the renormalization group flow can be analyzed using a framework that exploits the spin model's symmetry and some associated free resolutions of modules over polynomial algebras.

Reactions of small molecules facilitated by metal-acceptor interactions

The role of metal-acceptor interactions arising from M–BR3 and M–PR3 bonding is discussed with respect to reactions between first-row transition metals and N2, H2, and CO. Thermally robust, S = 1/2 (TPB)Co(H2) and (TPB)Co(N2) complexes (TPB = tris(2- (diisopropylphosphino)phenyl)borane) are described and the energetics of N2 and H2 binding are measured. The H2 and N2 ligands are bound more weakly in the (TPB)Co complexes than in related (SiP3)M(L) complexes (SiP3 = tris(2- (diisopropylphosphino)phenyl)silyl). Comparisons within and between these two ligand platforms allow for the factors that affect N2 (and H2) binding and activation to be delineated. The characterization and reactivity of (DPB)Fe complexes (DPB = bis(2- (diisopropylphosphino)phenyl)phenylborane) in the context of N2 functionalization and E–H bond addition (E = H, C, N, Si) are described. This platform allows for the one-pot transformation of free N2 to an Fe hydrazido(-) complex via an Fe aminoimide intermediate. The principles learned from the N2 chemistry using (DPB)Fe are applied to CO reduction on the same system. The preparation of (DPB)Fe(CO)2 is described as well as its reductive functionalization to generate an unprecedented Fe dicarbyne. The bonding in this highly covalent complex is discussed in detail. Initial studies of the reactivity of the Fe dicarbyne reveal that a CO-derived olefin is released upon hydrogenation. Alternative approaches to uncovering unusual reactivity using metal- acceptor interactions are described in Chapters 5 and 6, including initial studies on a new π-accepting tridentate diphosphinosulfinyl ligand and strategies for designing ligands that undergo site-selective metallation to generate heterobimetallic complexes.

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.

Selective hydroxylation of small alkanes by the particulate methane monooxygenase

The particulate methane monooxygenase (pMMO) catalyzes the oxidation of methane to methanol under ambient temperatures and pressures. Other small alkanes and alkenes are also substrates of this enzyme. We measured and compared the initial rate constants of oxidation of small alkanes (C1 to C5) catalyzed by pMMO. Both primary and secondary alcohols were formed from oxidation of n-butane and n-pentane. The alcohols produced from alkane oxidation can be further oxidized, probably by pMMO, to aldehydes and ketones. The apparent regioselectivity for n-butane and n-pentane is 100% 2-alcohols because the formation of primary alcohols is slower than further oxidation of these alcohols. The hydroxylation at the secondary carbons is highly stereoselective: (R)-alcohols are preferentially formed. The enantiomeric excess increases slightly with decreasing reaction temperature. The steric course of hydroxylation on primary carbons was also studied by using isotopically substituted ethane: (S)- or (R)-CH_3-CHDT, and (S)- or (R)-CD_3- CHDT and the reactions were found to proceed with 100% retention of configuration. A primary isotopic effect of k_H/k_D=5.0 was observed in these experiments.

Crystal Coulomb energies: I. Organic donor-acceptor complexes--a review. II. Classical Ewald calculations of the Coulomb binding energy of four donor-acceptor crystals and Wurster's blue perchlorate. III. A rapid-convergence quantum-mechanical formalism for crystal electronic energies

Chapter I

Theories for organic donor-acceptor (DA) complexes in solution and in the solid state are reviewed, and compared with the available experimental data. As shown by McConnell et al. (Proc. Natl. Acad. Sci. U.S., 53, 46-50 (1965)), the DA crystals fall into two classes, the holoionic class with a fully or almost fully ionic ground state, and the nonionic class with little or no ionic character. If the total lattice binding energy 2ε₁ (per DA pair) gained in ionizing a DA lattice exceeds the cost 2ε_o of ionizing each DA pair, ε₁ + ε_o less than 0, then the lattice is holoionic. The charge-transfer (CT) band in crystals and in solution can be explained, following Mulliken, by a second-order mixing of states, or by any theory that makes the CT transition strongly allowed, and yet due to a small change in the ground state of the non-interacting components D and A (or D⁺ and A^-). The magnetic properties of the DA crystals are discussed.

Chapter II

A computer program, EWALD, was written to calculate by the Ewald fast-convergence method the crystal Coulomb binding energy E_C due to classical monopole-monopole interactions for crystals of any symmetry. The precision of E_C values obtained is high: the uncertainties, estimated by the effect on E_C of changing the Ewald convergence parameter η, ranged from ± 0.00002 eV to ± 0.01 eV in the worst case. The charge distribution for organic ions was idealized as fractional point charges localized at the crystallographic atomic positions: these charges were chosen from available theoretical and experimental estimates. The uncertainty in E_C due to different charge distribution models is typically ± 0.1 eV (± 3%): thus, even the simple Hückel model can give decent results.

E_C for Wurster's Blue Perchl orate is -4.1 eV/molecule: the crystal is stable under the binding provided by direct Coulomb interactions. E_C for N-Methylphenazinium Tetracyanoquino- dimethanide is 0.1 eV: exchange Coulomb interactions, which cannot be estimated classically, must provide the necessary binding.

EWALD was also used to test the McConnell classification of DA crystals. For the holoionic (1:1)-(N,N,N',N'-Tetramethyl-para- phenylenediamine: 7,7,8,8-Tetracyanoquinodimethan) E_C = -4.0 eV while 2ε_o = 4.6₅ eV: clearly, exchange forces must provide the balance. For the holoionic (1:1)-(N,N,N',N'-Tetramethyl-para- phenylenediamine:para-Chloranil) E_C = -4.4 eV, while 2ε_o = 5.0 eV: again EC falls short of 2ε₁. As a Gedankenexperiment, two nonionic crystals were assumed to be ionized: for (1:1)-(Hexamethyl- benzene:para-Chloranil) E_C = -4.5 eV, 2ε_o = 6.6 eV; for (1:1)- (Napthalene:Tetracyanoethylene) E_C = -4.3 eV, 2ε_o = 6.5 eV. Thus, exchange energies in these nonionic crystals must not exceed 1 eV.

Chapter III

A rapid-convergence quantum-mechanical formalism is derived to calculate the electronic energy of an arbitrary molecular (or molecular-ion) crystal: this provides estimates of crystal binding energies which include the exchange Coulomb inter- actions. Previously obtained LCAO-MO wavefunctions for the isolated molecule(s) ("unit cell spin-orbitals") provide the starting-point. Bloch's theorem is used to construct "crystal spin-orbitals". Overlap between the unit cell orbitals localized in different unit cells is neglected, or is eliminated by Löwdin orthogonalization. Then simple formulas for the total kinetic energy Q^(XT)_λ, nuclear attraction [λ/λ]^XT, direct Coulomb [λλ/λ'λ']^XT and exchange Coulomb [λλ'/λ'λ]^XT integrals are obtained, and direct-space brute-force expansions in atomic wavefunctions are given. Fourier series are obtained for [λ/λ]^XT, [λλ/λ'λ']^XT, and [λλ/λ'λ]^XT with the help of the convolution theorem; the Fourier coefficients require the evaluation of Silverstone's two-center Fourier transform integrals. If the short-range interactions are calculated by brute-force integrations in direct space, and the long-range effects are summed in Fourier space, then rapid convergence is possible for [λ/λ]^XT, [λλ/λ'λ']^XT and [λλ'/λ'λ]^XT. This is achieved, as in the Ewald method, by modifying each atomic wavefunction by a "Gaussian convergence acceleration factor", and evaluating separately in direct and in Fourier space appropriate portions of [λ/λ]^XT, etc., where some of the portions contain the Gaussian factor.

Origin of Th/U variations in chondritic meteorites

Isotope dilution thorium and uranium analyses of the Harleton chondrite show a larger scatter than previously observed in equilibrated ordinary chondrites (EOC). The linear correlation of Th/U with 1/U in Harleton (and all EOC data) is produced by variation in the chlorapatite to merrillite mixing ratio. Apatite variations control the U concentrations. Phosphorus variations are compensated by inverse variations in U to preserve the Th/U vs. 1/U correlation. Because the Th/U variations reflect phosphate ampling, a weighted Th/U average should converge to an improved solar system Th/U. We obtain Th/U=3.53 (1_-mean=0.10), significantly lower and more precise than previous estimates.

To test whether apatite also produces Th/U variation in CI and CM chondrites, we performed P analyses on the solutions from leaching experiments of Orgueil and Murchison meteorites.

A linear Th/U vs. 1/U correlation in CI can be explained by redistribution of hexavalent U by aqueous fluids into carbonates and sulfates.

Unlike CI and EOC, whole rock Th/U variations in CMs are mostly due to Th variations. A Th/U vs. 1/U linear correlation suggested by previous data for CMs is not real. We distinguish 4 components responsible for the whole rock Th/U variations: (1) P and actinide-depleted matrix containing small amounts of U-rich carbonate/sulfate phases (similar to CIs); (2) CAIs and (3) chondrules are major reservoirs for actinides, (4) an easily leachable phase of high Th/U. likely carbonate produced by CAI alteration. Phosphates play a minor role as actinide and P carrier phases in CM chondrites.

Using our Th/U and minimum galactic ages from halo globular clusters, we calculate relative supernovae production rates for ²³²Th/²³⁸U and ²³⁵U/²³⁸U for different models of r-process nucleosynthesis. For uniform galactic production, the beginning of the r-process nucleosynthesis must be less than 13 Gyr. Exponentially decreasing production is also consistent with a 13 Gyr age, but very slow decay times are required (less than 35 Gyr), approaching the uniform production. The 15 Gyr Galaxy requires either a fast initial production growth (infall time constant less than 0.5 Gyr) followed by very low decrease (decay time constant greater than 100 Gyr), or the fastest possible decrease (≈8 Gyr) preceded by slow in fall (≈7.5 Gyr).

Theory of viscous and thermal attenuation of sound by small spheres

The problem is to calculate the attenuation of plane sound waves passing through a viscous, heat-conducting fluid containing small spherical inhomogeneities. The attenuation is calculated by evaluating the rate of increase of entropy caused by two irreversible processes: (1) the mechanical work done by the viscous stresses in the presence of velocity gradients, and (2) the flow of heat down the thermal gradients. The method is first applied to a homogeneous fluid with no spheres and shown to give the classical Stokes-Kirchhoff expressions. The method is then used to calculate the additional viscous and thermal attenuation when small spheres are present. The viscous attenuation agrees with Epstein's result obtained in 1941 for a non-heat-conducting fluid. The thermal attenuation is found to be similar in form to the viscous attenuation and, for gases, of comparable magnitude. The general results are applied to the case of water drops in air and air bubbles in water.

For water drops in air the viscous and thermal attenuations are camparable; the thermal losses occur almost entirely in the air, the thermal dissipation in the water being negligible. The theoretical values are compared with Knudsen's experimental data for fogs and found to agree in order of magnitude and dependence on frequency. For air bubbles in water the viscous losses are negligible and the calculated attenuation is almost completely due to thermal losses occurring in the air inside the bubbles, the thermal dissipation in the water being relatively small. (These results apply only to non-resonant bubbles whose radius changes but slightly during the acoustic cycle.)

A small perturbation theory for cycloidal propellers

A hydromechanical theory is developed for cycloidal propellers for two limiting modes of operation wherein U » ΩR and U « ΩR, with U the rectilinear propeller speed (speed of advance) and ΩR the rotational blade speed. A first order theory is developed from the basic principles of the kinematics and dynamics of fluid motion and proceeds from the point of view of unsteady hydrofoil theory.

Explicit expressions for the instantaneous forces and moments produced by blade motions are presented. On the basis of these results an optimization procedure is carried out which minimizes the energy loss under the constraint of specified mean thrust. Under optimal conditions the propeller is found to possess high Froude efficiencies in both the high and low speed modes of propulsion. This efficiency is defined as the ratio of the average useful work obtained during one cycle of propeller operation to the average power input required to sustain the motion of the propeller during the cycle.

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.

Solar System Small-Body Demographics with the Palomar Transient Factory Survey

Observational studies of our solar system's small-body populations (asteroids and comets) offer insight into the history of our planetary system, as these minor planets represent the left-over building blocks from its formation. The Palomar Transient Factory (PTF) survey began in 2009 as the latest wide-field sky-survey program to be conducted on the 1.2-meter Samuel Oschin telescope at Palomar Observatory. Though its main science program has been the discovery of high-energy extragalactic sources (such as supernovae), during its first five years PTF has collected nearly five million observations of over half a million unique solar system small bodies. This thesis begins to analyze this vast data set to address key population-level science topics, including: the detection rates of rare main-belt comets and small near-Earth asteroids, the spin and shape properties of asteroids as inferred from their lightcurves, the applicability of this visible light data to the interpretation of ultraviolet asteroid observations, and a comparison of the physical properties of main-belt and Jovian Trojan asteroids. Future sky-surveys would benefit from application of the analytical techniques presented herein, which include novel modeling methods and unique applications of machine-learning classification. The PTF asteroid small-body data produced in the course of this thesis work should remain a fertile source of solar system science and discovery for years to come.