Generalizing Optical Geometry

We show that by employing the standard projected curvature as a measure of spatial curvature, we can make a certain generalization of optical geometry (Abramowicz and Lasota 1997, Class. Quantum Grav. 14 (1997) A23). This generalization applies to any spacetime that admits a hypersurface orthogonal shearfree congruence of worldlines. This is a somewhat larger class of spacetimes than the conformally static spacetimes assumed in standard optical geometry. In the generalized optical geometry, which in the generic case is time dependent, photons move with unit speed along spatial geodesics and the sideways force experienced by a particle following a spatially straight line is independent of the velocity. Also gyroscopes moving along spatial geodesics do not precess (relative to the forward direction). Gyroscopes that follow a curved spatial trajectory precess according to a very simple law of three-rotation. We also present an inertial force formalism in coordinate representation for this generalization. Furthermore, we show that by employing a new sense of spatial curvature (Jonsson, Class. Quantum Grav. 23 (2006) 1) closely connected to Fermat's principle, we can make a more extensive generalization of optical geometry that applies to arbitrary spacetimes. In general this optical geometry will be time dependent, but still geodesic photons move with unit speed and follow lines that are spatially straight in the new sense. Also, the sideways experienced (comoving) force on a test particle following a line that is straight in the new sense will be independent of the velocity.Comment: 19 pages, 1 figure. A more general analysis is presented than in the former version. See also the companion papers arXiv:0708.2493, arXiv:0708.2533 and arXiv:0708.253

Ozonolysis of a-phellandrene - Part 2 : Compositional analysis of secondary organic aerosol highlights the role of stabilized Criegee intermediates

The molecular composition of secondary organic aerosol (SOA) generated from the ozonolysis of α-phellandrene is investigated for the first time using high pressure liquid chromatography coupled to high-resolution Quadrupole-Orbitrap tandem mass spectrometry. In total, 21 prominent products or isomeric product groups were identified using both positive and negative ionisation modes, with potential formation mechanisms discussed. The aerosol was found to be composed primarily of polyfunctional first- and second-generation species containing one or more carbonyl, acid, alcohol and hydroperoxide functionalities, with the products significantly more complex than those proposed from basic gas-phase chemistry in the companion paper (Mackenzie-Rae et al., 2017a). Mass spectra show a large number of dimeric products are also formed. Both direct scavenging evidence using formic acid, and indirect evidence from double bond equivalency factors, suggests the dominant oligomerisation mechanism is the bimolecular reaction of stabilised Criegee intermediates (SCIs) with non-radical ozonolysis products. Saturation vapour concentration estimates suggest monomeric species cannot explain the rapid nucleation burst of fresh aerosol observed in chamber experiments, hence dimeric species are believed to be responsible for new particle formation, with detected first- and second-generation products driving further particle growth in the system. Ultimately, identification of the major constituents and formation pathways of α-phellandrene SOA leads to a greater understanding of the atmospheric processes and implications of monoterpene emissions and SCIs, especially around Eucalypt forests regions where α-phellandrene is primarily emitted

Seasonal dependence of peroxy radical concentrations at a Northern hemisphere marine boundary layer site during summer and winter: evidence for radical activity in winter

Peroxy radicals (HO2+Σ RO2) were measured at the Weybourne Atmospheric Observatory (52° N, 1° E), Norfolk using a PEroxy Radical Chemical Amplifier (PERCA) during the winter and summer of 2002. The peroxy radical diurnal cycles showed a marked difference between the winter and summer campaigns with maximum concentrations of 12 pptv at midday in the summer and maximum concentrations as high as 30 pptv (10 min averages) in winter at night. The corresponding nighttime peroxy radical concentrations were not as high in summer (3 pptv). The peroxy radical concentration shows a distinct anti-correlation with increasing NOx during the daylight hours. At night, peroxy radicals increase with increasing NOx indicative of the role of NO3 chemistry. The average diurnal cycles for net ozone production, N(O3) show a large variability in ozone production, P(O3), and a large ozone loss, L(O3) in summer relative to winter. For a daylight average, net ozone production in summer was higher than winter (1.51±0.5 ppbv h−1 and 1.11±0.47 ppbv h−1, respectively). The variability in NO concentration has a much larger effect on N(O3) than the peroxy radical concentrations. Photostationary state (PSS) calculations show an NO2 lifetime of 5 min in summer and 21 minutes in the winter, implying that steady-state NO-NO2 ratios are not always attained during the winter months. The results show an active peroxy radical chemistry at night and that significant oxidant levels are sustained in winter. The net effect of this with respect to production of ozone in winter is unclear owing to the breakdown in the photostationary state

The homotopy theory of dg-categories and derived Morita theory

The main purpose of this work is the study of the homotopy theory of dg-categories up to quasi-equivalences. Our main result provides a natural description of the mapping spaces between two dg-categories $C$ and $D$ in terms of the nerve of a certain category of $(C,D)$-bimodules. We also prove that the homotopy category $Ho(dg-Cat)$ is cartesian closed (i.e. possesses internal Hom's relative to the tensor product). We use these two results in order to prove a derived version of Morita theory, describing the morphisms between dg-categories of modules over two dg-categories $C$ and $D$ as the dg-category of $(C,D)$-bi-modules. Finally, we give three applications of our results. The first one expresses Hochschild cohomology as endomorphisms of the identity functor, as well as higher homotopy groups of the \emph{classifying space of dg-categories} (i.e. the nerve of the category of dg-categories and quasi-equivalences between them). The second application is the existence of a good theory of localization for dg-categories, defined in terms of a natural universal property. Our last application states that the dg-category of (continuous) morphisms between the dg-categories of quasi-coherent (resp. perfect) complexes on two schemes (resp. smooth and proper schemes) is quasi-equivalent to the dg-category of quasi-coherent complexes (resp. perfect) on their product.Comment: 50 pages. Few mistakes corrected, and some references added. Thm. 8.15 is new. Minor corrections. Final version, to appear in Inventione

Inertial forces and the foundations of optical geometry

Assuming a general timelike congruence of worldlines as a reference frame, we derive a covariant general formalism of inertial forces in General Relativity. Inspired by the works of Abramowicz et. al. (see e.g. Abramowicz and Lasota, Class. Quantum Grav. 14 (1997) A23), we also study conformal rescalings of spacetime and investigate how these affect the inertial force formalism. While many ways of describing spatial curvature of a trajectory has been discussed in papers prior to this, one particular prescription (which differs from the standard projected curvature when the reference is shearing) appears novel. For the particular case of a hypersurface-forming congruence, using a suitable rescaling of spacetime, we show that a geodesic photon is always following a line that is spatially straight with respect to the new curvature measure. This fact is intimately connected to Fermat's principle, and allows for a certain generalization of the optical geometry as will be further pursued in a companion paper (Jonsson and Westman, Class. Quantum Grav. 23 (2006) 61). For the particular case when the shear-tensor vanishes, we present the inertial force equation in three-dimensional form (using the bold face vector notation), and note how similar it is to its Newtonian counterpart. From the spatial curvature measures that we introduce, we derive corresponding covariant differentiations of a vector defined along a spacetime trajectory. This allows us to connect the formalism of this paper to that of Jantzen et. al. (see e.g. Bini et. al., Int. J. Mod. Phys. D 6 (1997) 143).Comment: 42 pages, 7 figure

The atmospheric impacts of monoterpene ozonolysis on global stabilised Criegee intermediate budgets and SO2 oxidation : experiment, theory and modelling

The gas-phase reaction of alkenes with ozone is known to produce stabilised Criegee intermediates (SCIs). These biradical/zwitterionic species have the potential to act as atmospheric oxidants for trace pollutants such as SO₂, enhancing the formation of sulfate aerosol with impacts on air quality and health, radiative transfer and climate. However, the importance of this chemistry is uncertain as a consequence of limited understanding of the abundance and atmospheric fate of SCIs. In this work we apply experimental, theoretical and numerical modelling methods to quantify the atmospheric impacts, abundance and fate of the structurally diverse SCIs derived from the ozonolysis of monoterpenes, the second most abundant group of unsaturated hydrocarbons in the atmosphere. We have investigated the removal of SO₂ by SCIs formed from the ozonolysis of three atmospherically important monoterpenes (<i>α</i>-pinene, <i>β</i>-pinene and limonene) in the presence of varying amounts of water vapour in large-scale simulation chamber experiments that are representative of boundary layer conditions. The SO₂ removal displays a clear dependence on water vapour concentration, but this dependence is not linear across the range of [H₂O] explored. At low [H₂O] a strong dependence of SO₂ removal on [H₂O] is observed, while at higher [H₂O] this dependence becomes much weaker. This is interpreted as being caused by the production of a variety of structurally (and hence chemically) different SCIs in each of the systems studied, which displayed different rates of reaction with water and of unimolecular rearrangement or decomposition. The determined rate constants, <i>k</i>(SCI+H₂O), for those SCIs that react primarily with H₂O range from 4 to 310  ×  10⁻¹⁵ cm³ s⁻¹. For those SCIs that predominantly react unimolecularly, determined rates range from 130 to 240 s⁻¹. These values are in line with previous results for the (analogous) stereo-specific SCI system of <i>syn</i>-/<i>anti</i>-CH₃CHOO. The experimental results are interpreted through theoretical studies of the SCI unimolecular reactions and bimolecular reactions with H₂O, characterised for <i>α</i>-pinene and <i>β</i>-pinene at the M06-2X/aug-cc-pVTZ level of theory. The theoretically derived rates agree with the experimental results within the uncertainties. A global modelling study, applying the experimental results within the GEOS-Chem chemical transport model, suggests that &gt; 97 % of the total monoterpene-derived global SCI burden is comprised of SCIs with a structure that determines that they react slowly with water and that their atmospheric fate is dominated by unimolecular reactions. Seasonally averaged boundary layer concentrations of monoterpene-derived SCIs reach up to 1.4  ×  10⁴ cm⁻³ in regions of elevated monoterpene emissions in the tropics. Reactions of monoterpene-derived SCIs with SO₂ account for &lt; 1 % globally but may account for up to 60 % of the gas-phase SO₂ removal over areas of tropical forests, with significant localised impacts on the formation of sulfate aerosol and hence the lifetime and distribution of SO₂

On Morita and derived equivalences for cohomological Mackey algebras

By results of the second author, a source algebra equivalence between two p-blocks of finite groups induces an equivalence between the categories of cohomological Mackey functors associated with these blocks, and a splendid derived equivalence between two blocks induces a derived equivalence between the corresponding categories ofcohomological Mackey functors. The main result of this paper proves a partial converse: an equivalence (resp. Rickard equivalence) between the categories of cohomological Mackey functors of two blocks of finite groups induces a permeable Morita (resp. derived) equivalence between the two block algebras

Atmospheric isoprene ozonolysis: impacts of stabilised Criegee intermediate reactions with SO₂, H₂O and dimethyl sulfide

Isoprene is the dominant global biogenic volatile organic compound (VOC) emission. Reactions of isoprene with ozone are known to form stabilised Criegee intermediates (SCIs), which have recently been shown to be potentially important oxidants for SO2 and NO2 in the atmosphere; however the significance of this chemistry for SO2 processing (affecting sulfate aerosol) and NO2 processing (affecting NOx levels) depends critically upon the fate of the SCIs with respect to reaction with water and decomposition. Here, we have investigated the removal of SO2 in the presence of isoprene and ozone, as a function of humidity, under atmospheric boundary layer conditions. The SO2 removal displays a clear dependence on relative humidity, confirming a significant reaction for isoprene-derived SCIs with H2O. Under excess SO2 conditions, the total isoprene ozonolysis SCI yield was calculated to be 0.56 (+/-0.03). The observed SO2 removal kinetics are consistent with a relative rate constant, k (SCI + H2O) = k (SCI + SO2), of 3.1 (+/-0.5) x 10(-5) for isoprene-derived SCIs. The relative rate constant for k (SCI decomposition) = k (SCI + SO2) is 3.0 (+/-3.2) x 10(11) cm(-3). Uncertainties are +/-2 sigma and represent combined systematic and precision components. These kinetic parameters are based on the simplification that a single SCI species is formed in isoprene ozonolysis, an approximation which describes the results well across the full range of experimental conditions. Our data indicate that isoprenederived SCIs are unlikely to make a substantial contribution to gas-phase SO2 oxidation in the troposphere. We also present results from an analogous set of experiments, which show a clear dependence of SO2 removal in the isopreneozone system as a function of dimethyl sulfide concentration. We propose that this behaviour arises from a rapid reaction between isoprene-derived SCIs and dimethyl sulfide (DMS); the observed SO2 removal kinetics are consistent with a relative rate constant, k (SCI + DMS) = k (SCI + SO2), of 3.5 (+/-1.8). This result suggests that SCIs may contribute to the oxidation of DMS in the atmosphere and that this process could therefore influence new particle formation in regions impacted by emissions of unsaturated hydrocarbons and DMS

Estimation of rate coefficients and branching ratios for gas-phase reactions of OH with aromatic organic compounds for use in automated mechanism construction

Reaction with the hydroxyl (OH) radical is the dominant removal process for volatile organic compounds (VOCs) in the atmosphere. Rate coefficients for the reactions of OH with VOCs are therefore essential parameters for chemical mechanisms used in chemistry transport models, and are required more generally for impact assessments involving estimation of atmospheric lifetimes or oxidation rates for VOCs. A structure–activity relationship (SAR) method is presented for the reactions of OH with aromatic organic compounds, with the reactions of aliphatic organic compounds considered in the preceding companion paper. The SAR is optimized using a preferred set of data including reactions of OH with 67 monocyclic aromatic hydrocarbons and oxygenated organic compounds. In each case, the rate coefficient is defined in terms of a summation of partial rate coefficients for H abstraction or OH addition at each relevant site in the given organic compound, so that the attack distribution is defined. The SAR can therefore guide the representation of the OH reactions in the next generation of explicit detailed chemical mechanisms. Rules governing the representation of the reactions of the product radicals under tropospheric conditions are also summarized, specifically the rapid reaction sequences initiated by their reactions with O2

Torsion pairs and simple-minded systems in triangulated categories

Let T be a Hom-finite triangulated Krull-Schmidt category over a field k. Inspired by a definition of Koenig and Liu, we say that a family S of pairwise orthogonal objects in T with trivial endomorphism rings is a simple-minded system if its closure under extensions is all of T. We construct torsion pairs in T associated to any subset X of a simple-minded system S, and use these to define left and right mutations of S relative to X. When T has a Serre functor \nu, and S and X are invariant under \nu[1], we show that these mutations are again simple-minded systems. We are particularly interested in the case where T is the stable module category of a self-injective algebra \Lambda. In this case, our mutation procedure parallels that introduced by Koenig and Yang for simple-minded collections in the derived category of \Lambda. It follows that the mutation of the set of simple \Lambda-modules relative to X yields the images of the simple \Gamma-modules under a stable equivalence between \Gamma\ and \Lambda, where \Gamma\ is the tilting mutation of \Lambda\ relative to X.Comment: Minor corrections. To appear in Applied Categorical Structures. The final publication is available at springerlink.com: http://link.springer.com/article/10.1007%2Fs10485-014-9365-