Fermionic quantum systems. Part I: Phase transitions in quantum dots. Part II: Nuclear matter on a lattice

In the first part I perform Hartree-Fock calculations to show that quantum dots (i.e., two-dimensional systems of up to twenty interacting electrons in an external parabolic potential) undergo a gradual transition to a spin-polarized Wigner crystal with increasing magnetic field strength. The phase diagram and ground state energies have been determined. I tried to improve the ground state of the Wigner crystal by introducing a Jastrow ansatz for the wave function and performing a variational Monte Carlo calculation. The existence of so called magic numbers was also investigated. Finally, I also calculated the heat capacity associated with the rotational degree of freedom of deformed many-body states and suggest an experimental method to detect Wigner crystals.

The second part of the thesis investigates infinite nuclear matter on a cubic lattice. The exact thermal formalism describes nucleons with a Hamiltonian that accommodates on-site and next-neighbor parts of the central, spin-exchange and isospin-exchange interaction. Using auxiliary field Monte Carlo methods, I show that energy and basic saturation properties of nuclear matter can be reproduced. A first order phase transition from an uncorrelated Fermi gas to a clustered system is observed by computing mechanical and thermodynamical quantities such as compressibility, heat capacity, entropy and grand potential. The structure of the clusters is investigated with the help two-body correlations. I compare symmetry energy and first sound velocities with literature and find reasonable agreement. I also calculate the energy of pure neutron matter and search for a similar phase transition, but the survey is restricted by the infamous Monte Carlo sign problem. Also, a regularization scheme to extract potential parameters from scattering lengths and effective ranges is investigated.

Cooperative properties of lipid bilayers : collective director fluctuations and the effects of hydrophobic mismatch in protein/lipid membrane systems

Cooperative director fluctuations in lipid bilayers have been postulated for many years. ^2H-NMR T_1^(-1), T_(1P)^(-1) , and T_2^(-1); measurements have been used identify these motions and to determine the origin of increased slow bilayer motion upon addition of unlike lipids or proteins to a pure lipid bilayer.

The contribution of cooperative director fluctuations to NMR relaxation in lipid bilayers has been expressed mathematically using the approach of Doane et al.^1 and Pace and Chan.^2 The T_2^(-1)’s of pure dimyristoyllecithin (DML) bilayers deuterated at the 2, 9 and 10, and all positions on both lipid hydrocarbon chains have been measured. Several characteristics of these measurements indicate the presence of cooperative director fluctuations. First of all, T_2^(-1) exhibits a linear dependence on S2/CD. Secondly, T_2^(-1) varies across the ^2H-NMR powder pattern as sin^2 (2, β), where , β is the angle between the average bilayer director and the external magnetic field. Furthermore, these fluctuations are restricted near the lecithin head group suggesting that the head group does not participate in these motions but, rather, anchors the hydrocarbon chains in the bilayer.

T_2^(-1)has been measured for selectively deuterated liquid crystalline DML hilayers to which a host of other lipids and proteins have been added. The T_2^(-1) of the DML bilayer is found to increase drastically when chlorophyll a (chl a) and Gramicidin A' (GA') are added to the bilayer. Both these molecules interfere with the lecithin head group spacing in the bilayer. Molecules such as myristic acid, distearoyllecithin (DSL), phytol, and cholesterol, whose hydrocarbon regions are quite different from DML but which have small,neutral polar head groups, leave cooperative fluctuations in the DML bilayer unchanged.

The effect of chl a on cooperative fluctuations in the DML bilayer has been examined in detail using ^2H-NMR T_1^(-1), T_(1P)^(-1) , and T_2^(-1); measurements. Cooperative fluctuations have been modelled using the continuum theory of the nematic state of liquid crystals. Chl a is found to decrease both the correlation length and the elastic constants in the DML bilayer.

A mismatch between the hydrophobic length of a lipid bilayer and that of an added protein has also been found to change the cooperative properties of the lecithin bilayer. Hydrophobic mismatch has been studied in a series GA' / lecithin bilayers. The dependence of 2H-NMR order parameters and relaxation rates on GA' concentration has been measured in selectively deuterated DML, dipalmitoyllecithin (DPL), and DSL systems. Order parameters, cooperative lengths, and elastic constants of the DML bilayer are most disrupted by GA', while the DSL bilayer is the least perturbed by GA'. Thus, it is concluded that the hydrophobic length of GA' best matches that of the DSL bilayer. Preliminary Raman spectroscopy and Differential Scanning Calorimetry experiments of GA' /lecithin systems support this conclusion. Accommodation of hydrophobic mismatch is used to rationalize the absence of H_(II) phase formation in GA' /DML systems and the observation of H_(II) phase in GA' /DPL and GA' /DSL systems.

1. J. W. Doane and D. L. Johnson, Chem. Phy3. Lett., 6, 291-295 (1970). 2. R. J. Pace and S. I. Chan, J. Chem. Phy3., 16, 4217-4227 (1982).

Nonlinear dynamic transfer functions for certain retinal neuronal systems

The applicability of the white-noise method to the identification of a nonlinear system is investigated. Subsequently, the method is applied to certain vertebrate retinal neuronal systems and nonlinear, dynamic transfer functions are derived which describe quantitatively the information transformations starting with the light-pattern stimulus and culminating in the ganglion response which constitutes the visually-derived input to the brain. The retina of the catfish, Ictalurus punctatus, is used for the experiments.

The Wiener formulation of the white-noise theory is shown to be impractical and difficult to apply to a physical system. A different formulation based on crosscorrelation techniques is shown to be applicable to a wide range of physical systems provided certain considerations are taken into account. These considerations include the time-invariancy of the system, an optimum choice of the white-noise input bandwidth, nonlinearities that allow a representation in terms of a small number of characterizing kernels, the memory of the system and the temporal length of the characterizing experiment. Error analysis of the kernel estimates is made taking into account various sources of error such as noise at the input and output, bandwidth of white-noise input and the truncation of the gaussian by the apparatus.

Nonlinear transfer functions are obtained, as sets of kernels, for several neuronal systems: Light → Receptors, Light → Horizontal, Horizontal → Ganglion, Light → Ganglion and Light → ERG. The derived models can predict, with reasonable accuracy, the system response to any input. Comparison of model and physical system performance showed close agreement for a great number of tests, the most stringent of which is comparison of their responses to a white-noise input. Other tests include step and sine responses and power spectra.

Many functional traits are revealed by these models. Some are: (a) the receptor and horizontal cell systems are nearly linear (small signal) with certain "small" nonlinearities, and become faster (latency-wise and frequency-response-wise) at higher intensity levels, (b) all ganglion systems are nonlinear (half-wave rectification), (c) the receptive field center to ganglion system is slower (latency-wise and frequency-response-wise) than the periphery to ganglion system, (d) the lateral (eccentric) ganglion systems are just as fast (latency and frequency response) as the concentric ones, (e) (bipolar response) = (input from receptors) - (input from horizontal cell), (f) receptive field center and periphery exert an antagonistic influence on the ganglion response, (g) implications about the origin of ERG, and many others.

An analytical solution is obtained for the spatial distribution of potential in the S-space, which fits very well experimental data. Different synaptic mechanisms of excitation for the external and internal horizontal cells are implied.

Theory of ozone isotopic effects and various electron transfer reactions

Three separate topics, each stimulated by experiments, are treated theoretically in this dessertation: isotopic effects of ozone, electron transfer at interfaces, and intramolecular directional electron transfer in a supramolecular system.

The strange mass-independent isotope effect for the enrichment of ozone, which has been a puzzle in the literature for some 20 years, and the equally puzzling unconventional strong mass-dependent effect of individual reaction rate constants are studied as different aspects of a symmetry-driven behavior. A statistical (RRKM-based) theory with a hindered-rotor transition state is used. The individual rate constant ratios of recombination reactions at low pressures are calculated using the theory involving (1) small deviation from the statistical density of states for symmetric isotopomers, and (2) weak collisions for deactivation of the vibrationally excited ozone molecules. The weak collision and partitioning among exit channels play major roles in producing the large unconventional isotope effect in "unscrambled" systems. The enrichment studies reflect instead the non-statistical effect in "scrambled" systems. The theoretical results of low-pressure ozone enrichments and individual rate constant ratios obtained from these calculations are consistent with the corresponding experimental results. The isotopic exchange rate constant for the reaction ^(16)O + ^(18)O ^(18)O→+ ^(16)O ^(18)O + ^(18)O provides information on the nature of a variationally determined hindered-rotor transition state using experimental data at 130 K and 300 K. Pressure effects on the recombination rate constant, on the individual rate constant ratios and on the enrichments are also investigated. The theoretical results are consistent with the experimental data. The temperature dependence of the enrichment and rate constant ratios is also discussed, and experimental tests are suggested. The desirability of a more accurate potential energy surface for ozone in the transition state region is also noted.

Electron transfer reactions at semiconductor /liquid interfaces are studied using a tight-binding model for the semiconductors. The slab method and a z-transform method are employed in obtaining the tight-binding electronic structures of semiconductors having surfaces. The maximum electron transfer rate constants at Si/viologen^(2-/+) and InP /Me_(2)Fc^(+/O) interfaces are computed using the tight-binding type calculations for the solid and the extended-Huckel for the coupling to the redox agent at the interface. These electron transfer reactions are also studied using a free electron model for the semiconductor and the redox molecule, where Bardeen's method is adapted to calculate the coupling matrix element between the molecular and semiconductor electronic states. The calculated results for maximum rate constant of the electron transfer from the semiconductor bulk states are compared with the experimentally measured values of Lewis and coworkers, and are in reasonable agreement, without adjusting parameters. In the case of InP /liquid interface, the unusual current vs applied potential behavior is additionally interpreted, in part, by the presence of surface states.

Photoinduced electron transfer reactions in small supramolecular systems, such as 4-aminonaphthalimide compounds, are interesting in that there are, in principle, two alternative pathways (directions) for the electron transfer. The electron transfer, however, is unidirectional, as deduced from pH-dependent fluorescence quenching studies on different compounds. The role of electronic coupling matrix element and the charges in protonation are considered to explain the directionality of the electron transfer and other various results. A related mechanism is proposed to interpret the fluorescence behavior of similar molecules as fluorescent sensors of metal ions.

Neutron slowing down with inelastic scattering

The emphasis in reactor physics research has shifted toward investigations of fast reactors. The effects of high energy neutron processes have thus become fundamental to our understanding, and one of the most important of these processes is nuclear inelastic scattering. In this research we include inelastic scattering as a primary energy transfer mechanism, and study the resultant neutron energy spectrum in an infinite medium. We assume that the moderator material has a high mass number, so that in a laboratory coordinate system the energy loss of an inelastically scattered neutron may be taken as discrete. It is then consistent to treat elastic scattering with an age theory expansion. Mathematically these assumptions lead to balance equations of the differential-difference type.

The steady state problem is explored first by way of Laplace transformation of the energy variable. We then develop another steady state technique, valid for multiple inelastic level excitations, which depends on the level structure satisfying a physically reasonable constraint. In all cases the solutions we generate are compared with results obtained by modeling inelastic scattering with a separable, evaporative kernel.

The time dependent problem presents some new difficulties. By modeling the elastic scattering cross section in a particular way, we generate solutions to this more interesting problem. We conjecture the method of characteristics may be useful in analyzing time dependent problems with general cross sections. These ideas are briefly explored.

Optical properties of excited silicon and germanium at low temperatures

Part I of this thesis deals with 3 topics concerning the luminescence from bound multi-exciton complexes in Si. Part II presents a model for the decay of electron-hole droplets in pure and doped Ge.

Part I.

We present high resolution photoluminescence data for Si doped With Al, Ga, and In. We observe emission lines due to recombination of electron-hole pairs in bound excitons and satellite lines which have been interpreted in terms of complexes of several excitons bound to an impurity. The bound exciton luminescence in Si:Ga and Si:Al consists of three emission lines due to transitions from the ground state and two low lying excited states. In Si:Ga, we observe a second triplet of emission lines which precisely mirror the triplet due to the bound exciton. This second triplet is interpreted as due to decay of a two exciton complex into the bound exciton. The observation of the second complete triplet in Si:Ga conclusively demonstrates that more than one exciton will bind to an impurity. Similar results are found for Si:Al. The energy of the lines show that the second exciton is less tightly bound than the first in Si:Ga. Other lines are observed at lower energies. The assumption of ground state to ground-state transitions for the lower energy lines is shown to produce a complicated dependence of binding energy of the last exciton on the number of excitons in a complex. No line attributable to the decay of a two exciton complex is observed in Si:In.

We present measurements of the bound exciton lifetimes for the four common acceptors in Si and for the first two bound multi-exciton complexes in Si:Ga and Si:Al. These results are shown to be in agreement with a calculation by Osbourn and Smith of Auger transition rates for acceptor bound excitons in Si. Kinetics determine the relative populations of complexes of various sizes and work functions, at temperatures which do not allow them to thermalize with respect to one another. It is shown that kinetic limitations may make it impossible to form two-exciton complexes in Si:In from a gas of free excitons.

We present direct thermodynamic measurements of the work functions of bound multi-exciton complexes in Al, B, P and Li doped Si. We find that in general the work functions are smaller than previously believed. These data remove one obstacle to the bound multi-exciton complex picture which has been the need to explain the very large apparent work functions for the larger complexes obtained by assuming that some of the observed lines are ground-state to ground-state transitions. None of the measured work functions exceed that of the electron-hole liquid.

Part II.

A new model for the decay of electron-hole-droplets in Ge is presented. The model is based on the existence of a cloud of droplets within the crystal and incorporates exciton flow among the drops in the cloud and the diffusion of excitons away from the cloud. It is able to fit the experimental luminescence decays for pure Ge at different temperatures and pump powers while retaining physically reasonable parameters for the drops. It predicts the shrinkage of the cloud at higher temperatures which has been verified by spatially and temporally resolved infrared absorption experiments. The model also accounts for the nearly exponential decay of electron-hole-droplets in lightly doped Ge at higher temperatures.

Cyclotron harmonic emission in a Penning discharge

Microwave noise emission at the harmonics of the electron cyclotron frequency from the magnetized plasma column of a Penning discharge is investigated experimentally. The harmonic emission spectrum is observed using oxygen gas in a variety of discharge configurations. It is found that grid stabilization of the plasma column has very little effect on the emission spectrum. Measurements of the shape and location of the harmonic emission lines are described in detail. On the basis of a microwave interferometer measurement of the electron density, it is concluded that the existence of a hybrid layer somewhere on the plasma column is a necessary condition for the observation of harmonic emission. The relaxation time and the cathode voltage dependence of the harmonic emission are investigated using a pulse modulation technique. It is found that the emission intensity increases rapidly with the magnitude of the cathode voltage and that the relaxation time decreases with increasing neutral gas pressure. High intensity nonharmonic radiation is observed and identified as resulting from a beam-plasma wave instability thereby eliminating the same instability as a possible source of the harmonic emission. It is found that the collective experimental results are in reasonable agreement with the single particle electrostatic radiation theory of Canobbio and Croci.

Monitoring fish populations in Lower Lough Erne, Northern Ireland: applicability of current methods and implications for future monitoring under the EC Water Framework Directive

The proposed EC Water Framework Directive (WFD) will require member states to monitor both biotic and abiotic components of lake environments. With adoption of the WFD some measurement of fish populations will also be required. This paper describes work carried out since 1971, and particularly since 1991, on the status of fish populations in Lower Lough Erne, Northern Ireland, with an emphasis on defining change over time due to human impacts on the lake. This offers a reasonable starting point from which to develop a monitoring programme suitable for the needs of the WFD in this lake. The implications for as yet unmonitored fish populations in lakes are also determined.

Did galaxies reionize the universe?

The epoch of reionization remains one of the last uncharted eras of cosmic history, yet this time is of crucial importance, encompassing the formation of both the first galaxies and the first metals in the universe. In this thesis, I present four related projects that both characterize the abundance and properties of these first galaxies and uses follow-up observations of these galaxies to achieve one of the first observations of the neutral fraction of the intergalactic medium during the heart of the reionization era.

First, we present the results of a spectroscopic survey using the Keck telescopes targeting 6.3 < z < 8.8 star-forming galaxies. We secured observations of 19 candidates, initially selected by applying the Lyman break technique to infrared imaging data from the Wide Field Camera 3 (WFC3) onboard the Hubble Space Telescope (HST). This survey builds upon earlier work from Stark et al. (2010, 2011), which showed that star-forming galaxies at 3 < z < 6, when the universe was highly ionized, displayed a significant increase in strong Lyman alpha emission with redshift. Our work uses the LRIS and NIRSPEC instruments to search for Lyman alpha emission in candidates at a greater redshift in the observed near-infrared, in order to discern if this evolution continues, or is quenched by an increase in the neutral fraction of the intergalactic medium. Our spectroscopic observations typically reach a 5-sigma limiting sensitivity of < 50 AA. Despite expecting to detect Lyman alpha at 5-sigma in 7-8 galaxies based on our Monte Carlo simulations, we only achieve secure detections in two of 19 sources. Combining these results with a similar sample of 7 galaxies from Fontana et al. (2010), we determine that these few detections would only occur in < 1% of simulations if the intrinsic distribution was the same as that at z ~ 6. We consider other explanations for this decline, but find the most convincing explanation to be an increase in the neutral fraction of the intergalactic medium. Using theoretical models, we infer a neutral fraction of X_HI ~ 0.44 at z = 7.

Second, we characterize the abundance of star-forming galaxies at z > 6.5 again using WFC3 onboard the HST. This project conducted a detailed search for candidates both in the Hubble Ultra Deep Field as well as a number of additional wider Hubble Space Telescope surveys to construct luminosity functions at both z ~ 7 and 8, reaching 0.65 and 0.25 mag fainter than any previous surveys, respectively. With this increased depth, we achieve some of the most robust constraints on the Schechter function faint end slopes at these redshifts, finding very steep values of alpha_{z~7} = -1.87 +/- 0.18 and alpha_{z~8} = -1.94 +/- 0.23. We discuss these results in the context of cosmic reionization, and show that given reasonable assumptions about the ionizing spectra and escape fraction of ionizing photons, only half the photons needed to maintain reionization are provided by currently observable galaxies at z ~ 7-8. We show that an extension of the luminosity function down to M_{UV} = -13.0, coupled with a low level of star-formation out to higher redshift, can fit all available constraints on the ionization history of the universe.

Third, we investigate the strength of nebular emission in 3 < z < 5 star-forming galaxies. We begin by using the Infrared Array Camera (IRAC) onboard the Spitzer Space Telescope to investigate the strength of H alpha emission in a sample of 3.8 < z < 5.0 spectroscopically confirmed galaxies. We then conduct near-infrared observations of star-forming galaxies at 3 < z < 3.8 to investigate the strength of the [OIII] 4959/5007 and H beta emission lines from the ground using MOSFIRE. In both cases, we uncover near-ubiquitous strong nebular emission, and find excellent agreement between the fluxes derived using the separate methods. For a subset of 9 objects in our MOSFIRE sample that have secure Spitzer IRAC detections, we compare the emission line flux derived from the excess in the K_s band photometry to that derived from direct spectroscopy and find 7 to agree within a factor of 1.6, with only one catastrophic outlier. Finally, for a different subset for which we also have DEIMOS rest-UV spectroscopy, we compare the relative velocities of Lyman alpha and the rest-optical nebular lines which should trace the cites of star-formation. We find a median velocity offset of only v_{Ly alpha} = 149 km/s, significantly less than the 400 km/s observed for star-forming galaxies with weaker Lyman alpha emission at z = 2-3 (Steidel et al. 2010), and show that this decrease can be explained by a decrease in the neutral hydrogen column density covering the galaxy. We discuss how this will imply a lower neutral fraction for a given observed extinction of Lyman alpha when its visibility is used to probe the ionization state of the intergalactic medium.

Finally, we utilize the recent CANDELS wide-field, infra-red photometry over the GOODS-N and S fields to re-analyze the use of Lyman alpha emission to evaluate the neutrality of the intergalactic medium. With this new data, we derive accurate ultraviolet spectral slopes for a sample of 468 3 < z < 6 star-forming galaxies, already observed in the rest-UV with the Keck spectroscopic survey (Stark et al. 2010). We use a Bayesian fitting method which accurately accounts for contamination and obscuration by skylines to derive a relationship between the UV-slope of a galaxy and its intrinsic Lyman alpha equivalent width probability distribution. We then apply this data to spectroscopic surveys during the reionization era, including our own, to accurately interpret the drop in observed Lyman alpha emission. From our most recent such MOSFIRE survey, we also present evidence for the most distant galaxy confirmed through emission line spectroscopy at z = 7.62, as well as a first detection of the CIII]1907/1909 doublet at z > 7.

We conclude the thesis by exploring future prospects and summarizing the results of Robertson et al. (2013). This work synthesizes many of the measurements in this thesis, along with external constraints, to create a model of reionization that fits nearly all available constraints.

Convex Relaxation for Low-Dimensional Representation: Phase Transitions and Limitations

There is a growing interest in taking advantage of possible patterns and structures in data so as to extract the desired information and overcome the curse of dimensionality. In a wide range of applications, including computer vision, machine learning, medical imaging, and social networks, the signal that gives rise to the observations can be modeled to be approximately sparse and exploiting this fact can be very beneficial. This has led to an immense interest in the problem of efficiently reconstructing a sparse signal from limited linear observations. More recently, low-rank approximation techniques have become prominent tools to approach problems arising in machine learning, system identification and quantum tomography.

In sparse and low-rank estimation problems, the challenge is the inherent intractability of the objective function, and one needs efficient methods to capture the low-dimensionality of these models. Convex optimization is often a promising tool to attack such problems. An intractable problem with a combinatorial objective can often be "relaxed" to obtain a tractable but almost as powerful convex optimization problem. This dissertation studies convex optimization techniques that can take advantage of low-dimensional representations of the underlying high-dimensional data. We provide provable guarantees that ensure that the proposed algorithms will succeed under reasonable conditions, and answer questions of the following flavor:

More specifically, i) Focusing on linear inverse problems, we generalize the classical error bounds known for the least-squares technique to the lasso formulation, which incorporates the signal model. ii) We show that intuitive convex approaches do not perform as well as expected when it comes to signals that have multiple low-dimensional structures simultaneously. iii) Finally, we propose convex relaxations for the graph clustering problem and give sharp performance guarantees for a family of graphs arising from the so-called stochastic block model. We pay particular attention to the following aspects. For i) and ii), we aim to provide a general geometric framework, in which the results on sparse and low-rank estimation can be obtained as special cases. For i) and iii), we investigate the precise performance characterization, which yields the right constants in our bounds and the true dependence between the problem parameters.

Development of Metalloenzyme Dioxygen Reduction Cathodes

The prime thrust of this dissertation is to advance the development of fuel cell dioxygen reduction cathodes that employ some variant of multicopper oxidase enzymes as the catalyst. The low earth-abundance of platinum metal and its correspondingly high market cost has prompted a general search amongst chemists and materials scientists for reasonable alternatives to this metal for facilitating catalytic dioxygen reduction chemistry. The multicopper oxidases (MCOs), which constitute a class of enzyme that naturally catalyze the reaction O₂ + 4H⁺ + 4e^- → 2H₂O, provide a promising set of biochemical contenders for fuel cell cathode catalysts. In MCOs, a substrate reduces a copper atom at the type 1 site, where charge is then transferred to a trinuclear copper cluster consisting of a mononuclear type 2 or “normal copper” site and a binuclear type 3 copper site. Following the reduction of all four copper atoms in the enzyme, dioxygen is then reduced to water in two two-electron steps, upon binding to the trinuclear copper cluster. We identified an MCO, a laccase from the hyperthermophilic bacterium Thermus thermophilus strain HB27, as a promising candidate for cathodic fuel cell catalysis. This protein demonstrates resilience at high temperatures, exhibiting no denaturing transition at temperatures high as 95°C, conditions relevant to typical polymer electrolyte fuel cell operation.

In Chapter I of this thesis, we discuss initial efforts to physically characterize the enzyme when operating as a heterogeneous cathode catalyst. Following this, in Chapter II we then outline the development of a model capable of describing the observed electrochemical behavior of this enzyme when operating on porous carbon electrodes. Developing a rigorous mathematical framework with which to describe this system had the potential to improve our understanding of MCO electrokinetics, while also providing a level of predictive power that might guide any future efforts to fabricate MCO cathodes with optimized electrochemical performance. In Chapter III we detail efforts to reduce electrode overpotentials through site-directed mutagenesis of the inner and outer-sphere ligands of the Cu sites in laccase, using electrochemical methods and electronic spectroscopy to try and understand the resultant behavior of our mutant constructs. Finally, in Chapter IV, we examine future work concerning the fabrication of enhanced MCO cathodes, exploring the possibility of new cathode materials and advanced enzyme deposition techniques.

A quantitative investigation of the solar modulation of cosmic-ray protons and helium nuclei

The differential energy spectra of cosmic-ray protons and He nuclei have been measured at energies up to 315 MeV/nucleon using balloon- and satellite-borne instruments. These spectra are presented for solar quiet times for the years 1966 through 1970. The data analysis is verified by extensive accelerator calibrations of the detector systems and by calculations and measurements of the production of secondary protons in the atmosphere.

The spectra of protons and He nuclei in this energy range are dominated by the solar modulation of the local interstellar spectra. The transport equation governing this process includes as parameters the solar-wind velocity, V, and a diffusion coefficient, K(r,R), which is assumed to be a scalar function of heliocentric radius, r, and magnetic rigidity, R. The interstellar spectra, j_D, enter as boundary conditions on the solutions to the transport equation. Solutions to the transport equation have been calculated for a broad range of assumed values for K(r,R) and j_D and have been compared with the measured spectra.

It is found that the solutions may be characterized in terms of a dimensionless parameter, ψ(r,R) = ^∞∫_r V dr'/(K(r',R). The amount of modulation is roughly proportional to ψ. At high energies or far from the Sun, where the modulation is weak, the solution is determined primarily by the value of ψ (and the interstellar spectrum) and is not sensitive to the radial dependence of the diffusion coefficient. At low energies and for small r, where the effects of adiabatic deceleration are found to be large, the spectra are largely determined by the radial dependence of the diffusion coefficient and are not very sensitive to the magnitude of ψ or to the interstellar spectra. This lack of sensitivity to j_D implies that the shape of the spectra at Earth cannot be used to determine the interstellar intensities at low energies.

Values of ψ determined from electron data were used to calculate the spectra of protons and He nuclei near Earth. Interstellar spectra of the form j_D α (W - 0.25m)^-2.65 for both protons and He nuclei were found to yield the best fits to the measured spectra for these values of ψ, where W is the total energy and m is the rest energy. A simple model for the diffusion coefficient was used in which the radial and rigidity dependence are separable and K is independent of radius inside a modulation region which has a boundary at a distance D. Good agreement was found between the measured and calculated spectra for the years 1965 through 1968, using typical boundary distances of 2.7 and 6.1 A.U. The proton spectra observed in 1969 and 1970 were flatter than in previous years. This flattening could be explained in part by an increase in D, but also seemed to require that a noticeable fraction of the observed protons at energies as high at 50 to 100 MeV be attributed to quiet-time solar emission. The turnup in the spectra at low energies observed in all years was also attributed to solar emission. The diffusion coefficient used to fit the 1965 spectra is in reasonable agreement with that determined from the power spectra of the interplanetary magnetic field (Jokipii and Coleman, 1968). We find a factor of roughly 3 increase in ψ from 1965 to 1970, corresponding to the roughly order of magnitude decrease in the proton intensity at 250 MeV. The change in ψ might be attributed to a decrease in the diffusion coefficient, or, if the diffusion coefficient is essentially unchanged over that period (Mathews et al., 1971), might be attributed to an increase in the boundary distance, D.

A photographic record of a pre- and post-lake creation event from World War II at Valley, Isle of Anglesey, UK

The article compares a recent aerial photograph of the lowlands of the Isle of Anglesey area with a German surveillance photograph from 1941. The authors aim to infer the environmental changes made to this sand dune and lake system as a direct consequence of constructing the airfield. Part of Tywyn Trewan, the extensive sand dune system, was completely destroyed in order to create runways and the technical and domestic accommodation to house a strategic airfield. As part of the dredging, six new water bodies with a combined surface area of approximately 6 ha were created.

Nanofabrication for On-Chip Optical Levitation, Atom-Trapping, and Superconducting Quantum Circuits

Researchers have spent decades refining and improving their methods for fabricating smaller, finer-tuned, higher-quality nanoscale optical elements with the goal of making more sensitive and accurate measurements of the world around them using optics. Quantum optics has been a well-established tool of choice in making these increasingly sensitive measurements which have repeatedly pushed the limits on the accuracy of measurement set forth by quantum mechanics. A recent development in quantum optics has been a creative integration of robust, high-quality, and well-established macroscopic experimental systems with highly-engineerable on-chip nanoscale oscillators fabricated in cleanrooms. However, merging large systems with nanoscale oscillators often require them to have extremely high aspect-ratios, which make them extremely delicate and difficult to fabricate with an "experimentally reasonable" repeatability, yield and high quality. In this work we give an overview of our research, which focused on microscopic oscillators which are coupled with macroscopic optical cavities towards the goal of cooling them to their motional ground state in room temperature environments. The quality factor of a mechanical resonator is an important figure of merit for various sensing applications and observing quantum behavior. We demonstrated a technique for pushing the quality factor of a micromechanical resonator beyond conventional material and fabrication limits by using an optical field to stiffen and trap a particular motional mode of a nanoscale oscillator. Optical forces increase the oscillation frequency by storing most of the mechanical energy in a nearly loss-less optical potential, thereby strongly diluting the effects of material dissipation. By placing a 130 nm thick SiO₂ pendulum in an optical standing wave, we achieve an increase in the pendulum center-of-mass frequency from 6.2 to 145 kHz. The corresponding quality factor increases 50-fold from its intrinsic value to a final value of Q_m = 5.8(1.1) x 10⁵, representing more than an order of magnitude improvement over the conventional limits of SiO₂ for a pendulum geometry. Our technique may enable new opportunities for mechanical sensing and facilitate observations of quantum behavior in this class of mechanical systems. We then give a detailed overview of the techniques used to produce high-aspect-ratio nanostructures with applications in a wide range of quantum optics experiments. The ability to fabricate such nanodevices with high precision opens the door to a vast array of experiments which integrate macroscopic optical setups with lithographically engineered nanodevices. Coupled with atom-trapping experiments in the Kimble Lab, we use these techniques to realize a new waveguide chip designed to address ultra-cold atoms along lithographically patterned nanobeams which have large atom-photon coupling and near 4π Steradian optical access for cooling and trapping atoms. We describe a fully integrated and scalable design where cold atoms are spatially overlapped with the nanostring cavities in order to observe a resonant optical depth of d₀ ≈ 0.15. The nanodevice illuminates new possibilities for integrating atoms into photonic circuits and engineering quantum states of atoms and light on a microscopic scale. We then describe our work with superconducting microwave resonators coupled to a phononic cavity towards the goal of building an integrated device for quantum-limited microwave-to-optical wavelength conversion. We give an overview of our characterizations of several types of substrates for fabricating a low-loss high-frequency electromechanical system. We describe our electromechanical system fabricated on a Si₃N₄ membrane which consists of a 12 GHz superconducting LC resonator coupled capacitively to the high frequency localized modes of a phononic nanobeam. Using our suspended membrane geometry we isolate our system from substrates with significant loss tangents, drastically reducing the parasitic capacitance of our superconducting circuit to ≈ 2.5$ fF. This opens up a number of possibilities in making a new class of low-loss high-frequency electromechanics with relatively large electromechanical coupling. We present our substrate studies, fabrication methods, and device characterization.

Investigation of Fundamental Processes Governing Secondary Organic Aerosol Formation in Laboratory Chambers

Our understanding of the processes and mechanisms by which secondary organic aerosol (SOA) is formed is derived from laboratory chamber studies. In the atmosphere, SOA formation is primarily driven by progressive photooxidation of SOA precursors, coupled with their gas-particle partitioning. In the chamber environment, SOA-forming vapors undergo multiple chemical and physical processes that involve production and removal via gas-phase reactions; partitioning onto suspended particles vs. particles deposited on the chamber wall; and direct deposition on the chamber wall. The main focus of this dissertation is to characterize the interactions of organic vapors with suspended particles and the chamber wall and explore how these intertwined processes in laboratory chambers govern SOA formation and evolution.

A Functional Group Oxidation Model (FGOM) that represents SOA formation and evolution in terms of the competition between functionalization and fragmentation, the extent of oxygen atom addition, and the change of volatility, is developed. The FGOM contains a set of parameters that are to be determined by fitting of the model to laboratory chamber data. The sensitivity of the model prediction to variation of the adjustable parameters allows one to assess the relative importance of various pathways involved in SOA formation.

A critical aspect of the environmental chamber is the presence of the wall, which can induce deposition of SOA-forming vapors and promote heterogeneous reactions. An experimental protocol and model framework are first developed to constrain the vapor-wall interactions. By optimal fitting the model predictions to the observed wall-induced decay profiles of 25 oxidized organic compounds, the dominant parameter governing the extent of wall deposition of a compound is identified, i.e., wall accommodation coefficient. By correlating this parameter with the molecular properties of a compound via its volatility, the wall-induced deposition rate of an organic compound can be predicted based on its carbon and oxygen numbers in the molecule.

Heterogeneous transformation of δ-hydroxycarbonyl, a major first-generation product from long-chain alkane photochemistry, is observed on the surface of particles and walls. The uniqueness of this reaction scheme is the production of substituted dihydrofuran, which is highly reactive towards ozone, OH, and NO3, thereby opening a reaction pathway that is not usually accessible to alkanes. A spectrum of highly-oxygenated products with carboxylic acid, ester, and ether functional groups is produced from the substituted dihydrofuran chemistry, thereby affecting the average oxidation state of the alkane-derived SOA.

The vapor wall loss correction is applied to several chamber-derived SOA systems generated from both anthropogenic and biogenic sources. Experimental and modeling approaches are employed to constrain the partitioning behavior of SOA-forming vapors onto suspended particles vs. chamber walls. It is demonstrated that deposition of SOA-forming vapors to the chamber wall during photooxidation experiments can lead to substantial and systematic underestimation of SOA. Therefore, it is likely that a lack of proper accounting for vapor wall losses that suppress chamber-derived SOA yields contribute substantially to the underprediction of ambient SOA concentrations in atmospheric models.