Ricci flows with unbounded curvature

We show that any noncompact Riemann surface admits a complete Ricci flow g(t), t\in[0,\infty), which has unbounded curvature for all t\in[0,\infty).Comment: 12 pages, 1 figure; updated reference

Vapor deposited europium doped lutetium oxide for X-ray imaging applications

Thesis (Ph.D.)--Boston UniversityLutetium oxide doped with europium oxide (Lu20 3:Eu3+) has been established to be a bright, dense scintillator materi al with vast potential in both medical and high resolution X-ray imaging applications. Unfortunately its commercial viability has been restricted due to the manufacturing and post treatment costs associated with device fabrication. This research was aimed at the development of two vapor deposition techniques; chemical and physical vapor deposition (CVD and PVD), to produce coatings of Lu203:Eu3+ for various X-ray imaging applications. A customized CVD process to codeposit Lu20 3 and Eu20 3 was developed using lutetium and europium chloride (LuCb and EuCI3) precursors and reacting with carbon dioxide (C02) and hydrogen (H2) . An in depth study was performed by systematically varying the process parameters to explore the deposition kinetics and identify the rate limiting steps and their effects on the growth morphology using both cold and hot wall CVD reactors. The activation energy for the kinetically limited deposition of Lu20 3 from the LuCI3 - Ar - C02 - H2 system was identified to be approximately 170 kJ/mol , which is significantly lower than expected. The predominant growth orientations were identified to be { 111} and { 100} , depending on the deposition conditions. As the temperature is increased, the growth orientation preference decreases to produce a randomly oriented growth at 1150°C. The scintillation and X-ray imaging characteristics of a co-deposited Lu203:Eu3+ thin film with a {100} orientation were measured, confirming the feasibility and applicability of the CVD system to produce thick scintillator x-ray imaging devices. A fundamental study of the PVD process was performed by sputtering of Lu203:Eu3+ using a single target magnetron sputtering gun. Systematic vatiations of the deposition parameters were used to understand the effect of the ejected flux kinetic energies and deposition rate on the deposit density, stress, optical and scintillation properties. The deposition system was subsequently optimized for rapid, dense growth of a 10 um thick Lu203:Eu3+ coating at elevated temperatures. The X-ray imaging properties were measured and the results yielded an X-ray imaging resolution slightly better than 1 um with the potential for 0.5 um with further optimization, a level never before attained

Modelling multi-phase halogen chemistry in the remote marine boundary layer: Investigation of the influence of aerosol size resolution on predicted gas-and condensed-phase chemistry

A coupled box model of photochemistry and aerosol microphysics which explicitly accounts for size-dependent chemical properties of the condensed-phase has been developed to simulate the multi-phase chemistry of chlorine, bromine and iodine in the marine boundary layer (MBL). The model contains separate seasalt and non-seasalt modes, each of which may be composed of 1–16 size-bins. By comparison of gaseous and aerosol compositions predicted using different size-resolutions with both fixed and size-dependent aerosol turnover rates, it was found that, for halogen-activation processes, the physical property initialisation of the aerosol-mode has a significant influence on gas-phase chemistry. Failure to adequately represent the appropriate physical properties can lead to substantial errors in gas-phase chemistry. The size-resolution of condensed-phase composition has a less significant influence on gas-phase chemistry

Ricci flows with bursts of unbounded curvature

Given a completely arbitrary surface, whether or not it has bounded curvature, or even whether or not it is complete, there exists an instantaneously complete Ricci flow evolution of that surface that exists for a specific amount of time [GT11]. In the case that the underlying Riemann surface supports a hyperbolic metric, this Ricci flow always exists for all time and converges (after scaling by a factor 1/2t ) to this hyperbolic metric [GT11], i.e. our Ricci flow geometrises the surface. In this paper we show that there exist complete, bounded curvature initial metrics, including those conformal to a hyperbolic metric, which have subsequent Ricci flows developing unbounded curvature at certain intermediate times. In particular, when coupled with the uniqueness from [Top13], we find that any complete Ricci flow starting with such initial metrics must develop unbounded curvature over some intermediate time interval, but that nevertheless, the curvature must later become bounded and the flow must achieve geometrisation as t → ∞, even though there are other conformal deformations to hyperbolic metrics that do not involve unbounded curvature. Another consequence of our constructions is that while our Ricci flow from [GT11] must agree initially with the classical flow of Hamilton and Shi in the special case that the initial surface is complete and of bounded curvature, by uniqueness, it is now clear that our flow lasts for a longer time interval in general, with Shi’s flow stopping when the curvature blows up, but our flow continuing strictly beyond in these situations. All our constructions of unbounded curvature developing and then disappearing are in two dimensions. Generalisations to higher dimensions are then immediate

Partial Derivative Fitted Taylor Expansion: An efficient method for calculating gas/liquid equilibria in atmospheric aerosol particles - Part 2: Organic compounds

A flexible mixing rule is presented which allows the calculation of activity coefficients of organic compounds in a multi-component aqueous solution. Based on the same fitting methodology as a previously published inorganic model (Partial Differential Fitted Taylor series Expansion; PD-FiTE), organic PD-FiTE treats interactions between binary pairs of solutes with polynomials of varying order. The numerical framework of organic PD-FiTE is not based on empirical observations of activity coefficient variation, rather a simple application of a Taylor Series expansion. Using 13 example compounds extracted from a recent sensitivity study, the framework is benchmarked against the UNIFAC model. For 1000 randomly derived concentration ranges and 10 relative humidities between 10 and 99%, the average deviation in predicted activity coefficients was calculated to be 3.8%. Whilst compound specific deviations are present, the median and inter-quartile values across all relative humidity range always fell within ±20% of the UNIFAC value. Comparisons were made with the UNIFAC model by assuming interactions between solutes can be set to zero within PD-FiTE. In this case, deviations in activity coefficients as low as −40% and as high as +70% were found. Both the fully coupled and uncoupled organic PD-FiTE are up to a factor of ≈12 and ≈66 times more efficient than calling the UNIFAC model using the same water content, and ≈310 and ≈1800 times more efficient than an iterative model using UNIFAC. The use of PD-FiTE within a dynamical framework is presented, demonstrating the potential inaccuracy of prescribing fixed negative or positive deviations from ideality when modelling the evolving chemical composition of aerosol particles

A curved multi-component aerosol hygroscopicity model framework: Part 1 – Inorganic compounds

A thermodynamic modelling framework to predict the equilibrium behaviour of mixed inorganic salt aerosols is developed, and then coupled with a technique for finding a solution to the Kohler equation in order to create a diameter dependent hygroscopic aerosol model (Aerosol Diameter Dependent Equilibrium Model – ADDEM). The model described here provides a robust and accurate inorganic basis using a mole fraction based activity coefficient model and adjusted energies of formation for treating solid precipitation. The model framework can accommodate organic components, though this added complexity is considered in a companion paper, this paper describes the development of the modelling architecture to be used and predictions of an inorganic model alone. The modelling framework has been developed to flexibly use a combination of mixing rules and other potentially more accurate techniques where available to calculate the water content. Comparisons with other state-of-the-art general equilibrium models and experimental data are presented and show excellent agreement. The Kelvin effect can be considered in this scheme using a variety of surface tension models. Comparison of predicted diameter dependent phenomena, such as the increased relative humidity for onset of deliquescence with decreasing diameter, with another diameter dependent model is very good despite the different approach used. The model is subject to various sensitivities. For the inorganic systems studied here, the model is sensitive to choice of surface tension scheme used, which decreases for larger aerosol. Large sensitivities are found for the value of dry density used. It is thus likely that the history of the aerosol studied in a hygroscopic tandem differential mobility analyser (HTDMA), specifically the nature of the drying process that will influence the final crystalline form, will create systematic uncertainties upon comparisons with theoretical predictions. However, the magnitudes of all of the above sensitivities are potentially less than those introduced when using a semi ideal growth factor analogue for certain conditions

The sensitivity of secondary organic aerosol component partitioning to the predictions of component properties – Part 1: A systematic evaluation of some available estimation techniques

A large number of calculations of the absorptive partitioning of organic compounds have been made using a number of methods to predict the component vapour pressures, <i>p</i><sup>0</sup>, and activity coefficients, <i>γ</i><sub><i>i</i></sub>, required in the calculations. The sensitivities of the predictions in terms of the condensed component masses, volatility, O:C ratio, molar mass and functionality distributions to the choice of <i>p</i><sup>0</sup> and <i>γ</i><sub><i>i</i></sub> models and to the number of components to represent the organic mixture have been systematically compared. The condensed component mass was found to be highly sensitive to the vapour pressure model, and less sensitive to both the activity coefficient model and the number of components used to represent the mixture although the sensitivity to the change in property estimation method increased substantially with increased simplification in the treatment of the organic mixture. This was a general finding and was also clearly evident in terms of the predicted component functionality, O:C ratio, molar mass and volatility distributions of the condensed organic components. Within the limitations of the study, this clearly demonstrates the requirement for more accurate representation of the <i>p</i><sup>0</sup> and <i>γ</i><sub><i>i</i></sub> of the semi-volatile organic proxy components used in simplified models as the degree of simplification increases. This presents an interesting paradox, since such reduction in complexity necessarily leads to divergence from the complex behaviour of real multicomponent atmospheric aerosol

A curved multi-component aerosol hygroscopicity model framework: Part 2 - Including organic compounds

International audienceThis paper describes the inclusion of organic particulate material within the Aerosol Diameter Dependent Equilibrium Model (ADDEM) framework described in the companion paper applied to inorganic aerosol components. The performance of ADDEM is analysed in terms of its capability to reproduce the behaviour of various organic and mixed inorganic/organic systems using recently published bulk data. Within the modelling architecture already described two separate thermodynamic models are coupled in an additive approach and combined with a method for solving the Kohler equation in order to develop a tool for predicting the water content associated with an aerosol of known inorganic/organic composition and dry size. For development of the organic module, the widely used group contribution method UNIFAC is employed to explicitly deal with the non-ideality in solution. The UNIFAC predictions for components of atmospheric importance were improved considerably by using revised interaction parameters derived from electro-dynamic balance studies. Using such parameters, the model was found to adequately describe mixed systems including 5?6 dicarboxylic acids, down to low relative humidity conditions. By comparison with electrodynamic balance data, it was also found that the model was capable of capturing the behaviour of aqueous aerosols containing Suwannee River Fulvic acid, a structure previously used to represent the functionality of complex oxidised macromolecules often found in atmospheric aerosols. The additive approach for modelling mixed inorganic/organic systems worked well for a variety of mixtures. As expected, deviations between model predictions and measurements increase with increasing concentration. Available surface tension models, used in evaluating the Kelvin term, were found to reproduce measured data with varying success. Deviations from experimental data increased with increased organic compound complexity. For components only slightly soluble in water, significant deviations from measured surface tension depression behaviour were predicted with both model formalisms tested. A Sensitivity analysis showed that such variation is likely to lead to predicted growth factors within the measurement uncertainty for growth factor taken in the sub-saturated regime. Greater sensitivity was found for the value of dry density used in the assumed form of the dried out aerosol. Comparison with a coupled thermodynamic approach showed that assumed values for interactions parameters may lead to erroneous results where a simple additive approach may provide more accurate results. However, where available, the use of coupled thermodynamics can better reproduce measured behaviour. Further work (and laboratory data) is required to assess whether this difference lies within the experimental uncertainty of observed hygroscopic behaviour for a variety of systems

Cloud condensation nucleus (CCN) behavior of organic aerosol particles generated by atomization of water and methanol solutions

Cloud condensation nucleus (CCN) experiments were carried out for malonic acid, succinic acid, oxalacetic acid, DL-malic acid, glutaric acid, DL-glutamic acid monohydrate, and adipic acid, using both water and methanol as atomization solvents, at three operating supersaturations (0.11%, 0.21%, and 0.32%) in the Caltech three-column CCN instrument (CCNC3). Predictions of CCN behavior for five of these compounds were made using the Aerosol Diameter Dependent Equilibrium Model (ADDEM). The experiments presented here expose important considerations associated with the laboratory measurement of the CCN behavior of organic compounds. Choice of atomization solvent results in significant differences in CCN activation for some of the compounds studied, which could result from residual solvent, particle morphology differences, and chemical reactions between the particle and gas phases. Also, significant changes in aerosol size distribution occurred after classification in a differential mobility analyzer (DMA) for malonic acid and glutaric acid. Filter analysis of adipic acid atomized from methanol solution indicates that gas-particle phase reactions may have taken place after atomization and before the methanol was removed from the sample gas stream. Careful consideration of these experimental issues is necessary for successful design and interpretation of laboratory CCN measurements

Sensitivities of the absorptive partitioning model of secondary organic aerosol formation to the inclusion of water

The predicted distribution of semi-volatile organic components between the gaseous and condensed phase as a function of ambient relative humidity and the specific form of the partitioning model used has been investigated. A mole fraction based model, modified so as not to use molar mass in the calculation, was found to predict identical RH dependence of component partitioning to that predicted by the conventional mass-based partitioning model which uses a molar mass averaged according to the number of moles in the condensed phase. A recently reported third version of the partitioning model using individual component molar masses was shown to give significantly different results to the other two models. Further sensitivities to an assumed pre-existing particulate loading and to parameterised organic component non-ideality are explored and shown to contribute significantly to the variation in predicted secondary organic particulate loading