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

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

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 &amp;approx;12 and &amp;approx;66 times more efficient than calling the UNIFAC model using the same water content, and &amp;approx;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

Composition of Templates for Transitional Legged Behaviors

Compositional methods for developing, analyzing and synthesizing robot behaviors construed as controlled hybrid dynamical systems with regular properties [1] has proven an effective framework for achieving steady state gaits [2,3]. Exploiting their potential for programming transitional behaviors, requiring more complicated interactions with the environment [4,5] has been limited by our inability to find appropriate constituent models (“templates” [6]) from which to construct these complex behaviors

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

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