Global regularity of three-dimensional Ricci limit spaces

In their recent work [ST17], Miles Simon and the second author established a local bi-Hölder correspondence between weakly noncollapsed Ricci limit spaces in three dimensions and smooth manifolds. In particular, any open ball of finite radius in such a limit space must be bi-Hölder homeomorphic to some open subset of a complete smooth Riemannian three-manifold. In this work we build on the technology from [ST16, ST17] to improve this local correspondence to a global-local correspondence. That is, we construct a smooth three-manifold M, and prove that the entire (weakly) noncollapsed three-dimensional Ricci limit space is homeomorphic to M via a globally-defined homeomorphism that is bi-Hölder once restricted to any compact subset. Here the bi-Hölder regularity is with respect to the distance dg on M, where g is any smooth complete metric on M. A key step in our proof is the construction of local pyramid Ricci flows, existing on uniform regions of spacetime, that are inspired by Hochard’s partial Ricci flows [Hoc16]. Suppose (M, g0, x0) is a complete smooth pointed Riemannian three-manifold that is (weakly) noncollapsed and satisfies a lower Ricci bound. Then, given any k ∈ N, we construct a smooth Ricci flow g(t) living on a subset of spacetime that contains, for each j ∈ {1, . . . , k}, a cylinder Bg0 (x0, j) × [0, Tj ], where Tj is dependent only on the Ricci lower bound, the (weakly) noncollapsed volume lower bound and the radius j (in particular independent of k) and with the property that g(0) = g0 throughout Bg0 (x0, k).</p

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

Herd-level risk factors associated with the presence of Phage type 21/28 E. coli O157 on Scottish cattle farms

&lt;p&gt;Background: E. coli O157 is a bacterial pathogen that is shed by cattle and can cause severe disease in humans. Phage type (PT) 21/28 is a subtype of E. coli O157 that is found across Scotland and is associated with particularly severe human morbidity.&lt;/p&gt; &lt;p&gt;Methods: A cross-sectional survey of Scottish cattle farms was conducted in the period Feb 2002-Feb 2004 to determine the prevalence of E. coli O157 in cattle herds. Data from 88 farms on which E. coli O157 was present were analysed using generalised linear mixed models to identify risk factors for the presence of PT 21/28 specifically.&lt;/p&gt; &lt;p&gt;Results: The analysis identified private water supply, and northerly farm location as risk factors for PT 21/28 presence. There was a significant association between the presence of PT 21/28 and an increased number of E. coli O157 positive pat samples from a farm, and PT 21/28 was significantly associated with larger E. coli O157 counts than non-PT 21/28 E. coli O157.&lt;/p&gt; &lt;p&gt;Conclusion: PT 21/28 has significant risk factors that distinguish it from other phage types of E. coli O157. This finding has implications for the control of E. coli O157 as a whole and suggests that control could be tailored to target the locally dominant PT.&lt;/p&gt

New and extended parameterization of the thermodynamic model AIOMFAC: calculation of activity coefficients for organic-inorganic mixtures containing carboxyl, hydroxyl, carbonyl, ether, ester, alkenyl, alkyl, and aromatic functional groups

We present a new and considerably extended parameterization of the thermodynamic activity coefficient model AIOMFAC (Aerosol Inorganic-Organic Mixtures Functional groups Activity Coefficients) at room temperature. AIOMFAC combines a Pitzer-like electrolyte solution model with a UNIFAC-based group-contribution approach and explicitly accounts for interactions between organic functional groups and inorganic ions. Such interactions constitute the salt-effect, may cause liquid-liquid phase separation, and affect the gas-particle partitioning of aerosols. The previous AIOMFAC version was parameterized for alkyl and hydroxyl functional groups of alcohols and polyols. With the goal to describe a wide variety of organic compounds found in atmospheric aerosols, we extend here the parameterization of AIOMFAC to include the functional groups carboxyl, hydroxyl, ketone, aldehyde, ether, ester, alkenyl, alkyl, aromatic carbon-alcohol, and aromatic hydrocarbon. Thermodynamic equilibrium data of organic-inorganic systems from the literature are critically assessed and complemented with new measurements to establish a comprehensive database. The database is used to determine simultaneously the AIOMFAC parameters describing interactions of organic functional groups with the ions H^+, Li^+, Na^+, K^+, NH_(4)^+, Mg^(2+), Ca^(2+), Cl^−, Br^−, NO_(3)^−, HSO_(4)^−, and SO_(4)^(2−). Detailed descriptions of different types of thermodynamic data, such as vapor-liquid, solid-liquid, and liquid-liquid equilibria, and their use for the model parameterization are provided. Issues regarding deficiencies of the database, types and uncertainties of experimental data, and limitations of the model, are discussed. The challenging parameter optimization problem is solved with a novel combination of powerful global minimization algorithms. A number of exemplary calculations for systems containing atmospherically relevant aerosol components are shown. Amongst others, we discuss aqueous mixtures of ammonium sulfate with dicarboxylic acids and with levoglucosan. Overall, the new parameterization of AIOMFAC agrees well with a large number of experimental datasets. However, due to various reasons, for certain mixtures important deviations can occur. The new parameterization makes AIOMFAC a versatile thermodynamic tool. It enables the calculation of activity coefficients of thousands of different organic compounds in organic-inorganic mixtures of numerous components. Models based on AIOMFAC can be used to compute deliquescence relative humidities, liquid-liquid phase separations, and gas-particle partitioning of multicomponent mixtures of relevance for atmospheric chemistry or in other scientific fields

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

Existence of Ricci flows of incomplete surfaces

We prove a general existence result for instantaneously complete Ricci flows starting at an arbitrary Riemannian surface which may be incomplete and may have unbounded curvature. We give an explicit formula for the maximal existence time, and describe the asymptotic behaviour in most cases.Comment: 20 pages; updated to reflect galley proof correction

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 &ndash; 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, &lt;i&gt;p&lt;/i&gt;&lt;sup&gt;0&lt;/sup&gt;, and activity coefficients, &lt;i&gt;γ&lt;/i&gt;&lt;sub&gt;&lt;i&gt;i&lt;/i&gt;&lt;/sub&gt;, 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 &lt;i&gt;p&lt;/i&gt;&lt;sup&gt;0&lt;/sup&gt; and &lt;i&gt;γ&lt;/i&gt;&lt;sub&gt;&lt;i&gt;i&lt;/i&gt;&lt;/sub&gt; 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 &lt;i&gt;p&lt;/i&gt;&lt;sup&gt;0&lt;/sup&gt; and &lt;i&gt;γ&lt;/i&gt;&lt;sub&gt;&lt;i&gt;i&lt;/i&gt;&lt;/sub&gt; 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