Bayer-Macr\`i decomposition on Bridgeland moduli spaces over surfaces

We find a decomposition formula of the local Bayer-Macr\`i map for the nef line bundle theory on the Bridgeland moduli space over surface. If there is a global Bayer-Macr\`i map, such decomposition gives a precise correspondence from Bridgeland walls to Mori walls. As an application, we compute the nef cone of the Hilbert scheme $S^{[n]}$ of $n$-points over special kinds of fibered surface $S$ of Picard rank two.Comment: 23 page

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How to use the Brookes wiki task list macr

A study of the ozonolysis of isoprene in a cryogenic buffer gas cell by high resolution microwave spectroscopy

We have developed a method to quantify reaction product ratios using high resolution microwave spectroscopy in a cryogenic buffer gas cell. We demonstrate the power of this method with the study of the ozonolysis of isoprene, CH2=C(CH3)-CH=CH2, the most abundant, non-methane hydrocarbon emitted into the atmosphere by vegetation. Isoprene is an asymmetric diene, and reacts with O3 at the 1,2 position to produce methyl vinyl ketone (MVK), formaldehyde, and a pair of carbonyl oxides: [CH3CO-CH=CH2 + CH2=OO] + [CH2=O + CH3COO-CH=CH2]. Alternatively, O3 could attack at the 3,4 position to produce methacrolein (MACR), formaldehyde, and two carbonyl oxides [CH2=C(CH3)-CHO + CH2=OO] + [CH2=O + CH2=C(CH3)-CHOO]. Purified O3 and isoprene were mixed for approximately 10 seconds under dilute (1.5-4% in argon) continuous flow conditions in an alumina tube held at 298 K and 5 Torr. Products exiting the tube were rapidly slowed and cooled within the buffer gas cell by collisions with cryogenic (4-7 K) He. High resolution chirped pulse microwave detection between 12 and 26 GHz was used to achieve highly sensitive (ppb scale), isomer-specific product quantification. We observed a ratio of MACR to MVK of 2.1 +/- 0.4 under 1:1 ozone to isoprene conditions and 2.1 +/- 0.2 under 2:1 ozone to isoprene conditions, a finding which is consistent with previous experimental results. Additionally, we discuss relative quantities of formic acid (HCOOH), an isomer of CH2=OO, and formaldehyde (CH2=O) under varying experimental conditions, and characterize the spectroscopic parameters of the singly-substituted 13C trans-isoprene and 13C anti-periplanar-methacrolein species. This work has the potential to be extended towards a complete branching ratio analysis, as well towards the ability to isolate, identify, and quantify new reactive intermediates in the ozonolysis of alkenes

Yields of oxidized volatile organic compounds during the OH radical initiated oxidation of isoprene, methyl vinyl ketone, and methacrolein under high-NO_x conditions

We present first-generation and total production yields of glyoxal, methylglyoxal, glycolaldehyde, and hydroxyacetone from the oxidation of isoprene, methyl vinyl ketone (MVK), and methacrolein (MACR) with OH under high NO_x conditions. Several of these first-generation yields are not included in commonly used chemical mechanisms, such as the Leeds Master Chemical Mechanism (MCM) v. 3.2. The first-generation yield of glyoxal from isoprene was determined to be 2.1 (±0.6)%. Inclusion of first-generation production of glyoxal, glycolaldehyde and hydroxyacetone from isoprene greatly improves performance of an MCM based model during the initial part of the experiments. In order to further improve performance of the MCM based model, higher generation glyoxal production was reduced by lowering the first-generation yield of glyoxal from C5 hydroxycarbonyls. The results suggest that glyoxal production from reaction of OH with isoprene under high NO_x conditions can be approximated by inclusion of a first-generation production term together with secondary production only via glycolaldehyde. Analogously, methylglyoxal production can be approximated by a first-generation production term from isoprene, and secondary production via MVK, MACR and hydroxyacetone. The first-generation yields reported here correspond to less than 5% of the total oxidized yield from isoprene and thus only have a small effect on the fate of isoprene. However, due to the abundance of isoprene, the combination of first-generation yields and reduced higher generation production of glyoxal from C5 hydroxycarbonyls is important for models that include the production of the small organic molecules from isoprene

Birational Geometry of Singular Moduli Spaces of O'Grady Type

Following Bayer and Macr\`{i}, we study the birational geometry of singular moduli spaces $M$ of sheaves on a K3 surface $X$ which admit symplectic resolutions. More precisely, we use the Bayer-Macr\`{i} map from the space of Bridgeland stability conditions $\mathrm{Stab}(X)$ to the cone of movable divisors on $M$ to relate wall-crossing in $\mathrm{Stab}(X)$ to birational transformations of $M$. We give a complete classification of walls in $\mathrm{Stab}(X)$ and show that every birational model of $M$ obtained by performing a finite sequence of flops from $M$ appears as a moduli space of Bridgeland semistable objects on $X$. An essential ingredient of our proof is an isometry between the orthogonal complement of a Mukai vector inside the algebraic Mukai lattice of $X$ and the N\'{e}ron-Severi lattice of $M$ which generalises results of Yoshioka, as well as Perego and Rapagnetta. Moreover, this allows us to conclude that the symplectic resolution of $M$ is deformation equivalent to the 10-dimensional irreducible holomorphic symplectic manifold found by O'Grady.Comment: Final versio

Reactive intermediates revealed in secondary organic aerosol formation from isoprene

Isoprene is a significant source of atmospheric organic aerosol; however, the oxidation pathways that lead to secondary organic aerosol (SOA) have remained elusive. Here, we identify the role of two key reactive intermediates, epoxydiols of isoprene (IEPOX = β-IEPOX + δ-IEPOX) and methacryloylperoxynitrate (MPAN), which are formed during isoprene oxidation under low- and high-NO_x conditions, respectively. Isoprene low-NO_x SOA is enhanced in the presence of acidified sulfate seed aerosol (mass yield 28.6%) over that in the presence of neutral aerosol (mass yield 1.3%). Increased uptake of IEPOX by acid-catalyzed particle-phase reactions is shown to explain this enhancement. Under high-NO_x conditions, isoprene SOA formation occurs through oxidation of its second-generation product, MPAN. The similarity of the composition of SOA formed from the photooxidation of MPAN to that formed from isoprene and methacrolein demonstrates the role of MPAN in the formation of isoprene high-NO_x SOA. Reactions of IEPOX and MPAN in the presence of anthropogenic pollutants (i.e., acidic aerosol produced from the oxidation of SO_2 and NO_2, respectively) could be a substantial source of “missing urban SOA” not included in current atmospheric models

The space of stability conditions on the local projective plane

We study the space of stability conditions on the total space of the canonical bundle over the projective plane. We explicitly describe a chamber of geometric stability conditions, and show that its translates via autoequivalences cover a whole connected component. We prove that this connected component is simply-connected. We determine the group of autoequivalences preserving this connected component, which turns out to be closely related to Gamma1(3). Finally, we show that there is a submanifold isomorphic to the universal covering of a moduli space of elliptic curves with Gamma1(3)-level structure. The morphism is Gamma1(3)-equivariant, and is given by solutions of Picard-Fuchs equations. This result is motivated by the notion of Pi-stability and by mirror symmetry.Comment: 56 pages, 3 figures. v2: various improvements based on referees' feedback (e.g. in Prop. 3.3); appendix C removed; new Prop. B.4 clarifies relation between support property and "full" stability condition

Surface and boundary layer exchanges of volatile organic compounds, nitrogen oxides and ozone during the GABRIEL campaign

We present an evaluation of sources, sinks and turbulent transport of nitrogen oxides, ozone and volatile organic compounds (VOC) in the boundary layer over French Guyana and Suriname during the October 2005 GABRIEL campaign by simulating observations with a single-column chemistry and climate model (SCM) along a zonal transect. Simulated concentrations of O3 and NO as well as NO2 photolysis rates over the forest agree well with observations when a small soil-biogenic NO emission flux was applied. This suggests that the photochemical conditions observed during GABRIEL reflect a pristine tropical low-NOx regime. The SCM uses a compensation point approach to simulate nocturnal deposition and daytime emissions of acetone and methanol and produces daytime boundary layer mixing ratios in reasonable agreement with observations. The area average isoprene emission flux, inferred from the observed isoprene mixing ratios and boundary layer height, is about half the flux simulated with commonly applied emission algorithms. The SCM nevertheless simulates too high isoprene mixing ratios, whereas hydroxyl concentrations are strongly underestimated compared to observations, which can at least partly explain the discrepancy. Furthermore, the model substantially overestimates the isoprene oxidation products methlyl vinyl ketone (MVK) and methacrolein (MACR) partly due to a simulated nocturnal increase due to isoprene oxidation. This increase is most prominent in the residual layer whereas in the nocturnal inversion layer we simulate a decrease in MVK and MACR mixing ratios, assuming efficient removal of MVK and MACR. Entrainment of residual layer air masses, which are enhanced in MVK and MACR and other isoprene oxidation products, into the growing boundary layer poses an additional sink for OH which is thus not available for isoprene oxidation. Based on these findings, we suggest pursuing measurements of the tropical residual layer chemistry with a focus on the nocturnal depletion of isoprene and its oxidation products

The concentration of oleocanthal in olive oil waste

The aim of this study was to determine the concentration of oleocanthal in olive pomace waste and compare this to its concentration in extra-virgin olive oil (EVOO). The concentration of oleocanthal in freshly pressed EVOO and its subsequent waste was analysed at early, mid and late season harvests. Oleocanthal concentrations were quantified using high-performance liquid chromatography&ndash;mass spectrometry. In oil, oleocanthal concentration was as follows: 123.24 &plusmn; 6.48 mg kg&macr;&sup1;1 in early harvest, 114.20 &plusmn; 17.42 mg kg&macr;&sup1; in mid harvest and 152.22 &plusmn; 10.54 mg kg&macr;&sup1; in late harvest. Its concentration in waste was determined to be: 128.25 &plusmn; 11.33 mg kg&macr;&sup1; in early harvest, 112.15 &plusmn; 1.51mg kg&macr;&sup1; in mid harvest and 62.35 &plusmn; 8.00 mg kg&macr;&sup1; in late harvest. Overall, olive pomace waste is a valuable source of oleocanthal.<br /