Solid-state production of complex organic molecules: H-atom addition versus UV irradiation

Complex organic molecules (COMs) have been observed in comets, hot cores and cold dense regions of the interstellar medium. It is generally accepted that these COMs form on icy dust grain through the recombination reaction of radicals triggered by either energetic UV- photon or non-energetic H-atom addition processing. In this work, we present for the first time laboratory studies that allow for quantitative comparison of hydrogenation and UV-induced reactions as well as their cumulative effect in astronomically relevant CO:CH3OH=4:1 ice analogues. The formation of glycolaldehyde (GA) and ethylene glycol (EG) is confirmed in pure hydrogenation experiments at 14 K, except methyl formate (MF), which is only clearly observed in photolysis. The fractions for MF:GA:EG are 0 : (0.2-0.4) : (0.8-0.6) for pure hydrogenation, and 0.2 : 0.3 : 0.5 for UV involving experiments and can offer a diagnostic tool to derive the chemical origin of these species. The GA/EG ratios in the laboratory (0.3-1.5) compare well with observations toward different objects.Comment: Astrochemistry VII Through the Cosmos from Galaxies to Planets Proceedings IAU Symposium No. 332, 2017. arXiv admin note: This version has been removed because it is in violation of arXiv's copyright polic

Symmetric groups, wreath products, Morita equivalences, and Broue's abelian defect group conjecture

It is shown that for any prime p, and any non-negative integer w less than p, there exist p-blocks of symmetric groups of defect w, which are Morita equivalent to the principal p-block of the group Sp [rmoust ] Sw. Combined with work of J. Rickard, this proves that Broué's abelian defect group conjecture holds for p-blocks of symmetric groups of defect at most 5

Derived equivalences for symmetric groups and sl2- categorification

We define and study sl2-categorifications on abelian categories. We show in particular that there is a self-derived (even homotopy) equivalence categorifying the adjoint action of the simple reflection. We construct categorifications for blocks of symmetric groups and deduce that two blocks are splendidly Rickard equivalent whenever they have isomorphic defect groups and we show that this implies Brou´e’s abelian defect group conjecture for symmetric groups. We give similar results for general linear groups over finite fields. The constructions extend to cyclotomic Hecke algebras. We also construct categorifications for category O of gln(C) and for rational representations of general linear groups over ¯Fp, where we deduce that two blocks corresponding to weights with the same stabilizer under the dot action of the affine Weyl group have equivalent derived (and homotopy) categories, as conjectured by Rickard

Abstract Hodge decomposition and minimal models for cyclic algebras

We show that an algebra over a cyclic operad supplied with an additional linear algebra datum called Hodge decomposition admits a minimal model whose structure maps are given in terms of summation over trees. This minimal model is unique up to homotopy

Feynman diagrams and minimal models for operadic algebras

We construct an explicit minimal model for an algebra over the cobar-construction of a differential graded operad. The structure maps of this minimal model are expressed in terms of sums over decorated trees. We introduce the appropriate notion of a homotopy equivalence of operadic algebras and show that our minimal model is homotopy equivalent to the original algebra. All this generalizes and gives a conceptual explanation of well-known results for A∞-algebras. Furthermore, we show that these results carry over to the case of algebras over modular operads; the sums over trees get replaced by sums over general Feynman graphs. As a by-product of our work we prove gauge-independence of Kontsevich's ‘dual construction’ producing graph cohomology classes from contractible differential graded Frobenius algebras

Representations of wreath products of algebras

Filtrations of modules over wreath products of algebras are studied and corresponding multiplicity formulas are given in terms of Littlewood–Richardson coefficients. An example relevant to Jantzen filtrations in Schur algebras is presented

Free resolutions of algebras

Given an algebra A, presented by generators and relations, i.e. as a quotient of a tensor algebra by an ideal, we construct a free algebra resolution of A, i.e. a differential graded algebra which is quasi-isomorphic to A and which is itself a tensor algebra. The construction rests combinatorially on the set of bracketings that arise naturally in the description of a free contractible differential graded algebra with given generators

Prediction of the number of cloud droplets in the ECHAM GCM

In this paper a prognostic equation for the number of cloud droplets (CDNC) is introduced into the ECHAM general circulation model. The initial CDNC is based on the mechanistic model of Chuang and Penner [1995], providing a more realistical prediction of CDNC than the empirical method previously used. Cloud droplet nucleation is parameterized as a function of total aerosol number concentration, updraft velocity, and a shape parameter, which takes the aerosol composition and size distribution into account. The total number of aerosol particles is obtained as the sum of marine sulfate aerosols produced from dimethyl sulfide, hydrophylic organic and black carbon, submicron dust, and sea-salt aerosols. Anthropogenic sulfate aerosols only add mass to the preexisting aerosols but do not form new particles. The simulated annual mean liquid water path, column CDNC, and effective radius agree well with observations, as does the frequency distributions of column CDNC for clouds over oceans and the variations of cloud optical depth with effective radius

Combinatorics and formal geometry of the master equation

We give a general treatment of the master equation in homotopy algebras and describe the operads and formal differential geometric objects governing the corresponding algebraic structures. We show that the notion of Maurer-Cartan twisting is encoded in certain automorphisms of these universal objects