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

Flow in a double-film-fed fluid bead between contra-rotating rolls, Part 2: bead break and flooding

Two-dimensional flow is considered in a fluid bead located in the gap between a pair of contra-rotating cylinders and bounded by two curved menisci. The stability of such bead flows with two inlet films, and hence no contact line, are analysed as the roll speed ratio S is increased. One of the inlet films can be regarded as an ‘input flux’ whilst the other is a ‘returning film’ whose thickness is specified as a fraction [zeta] of the outlet film on that roll. The flow is modelled via lubrication theory and for Ca [double less-than sign] 1, where Ca represents the capillary number, boundary conditions are formally developed that account for S [not equal] 1 and the non-constant gap. It is shown that there is a qualitative difference in the results between the single and double inlet film models unless small correction terms to the pressure drops at the interfaces are taken into account. Futhermore, it is shown that the inclusion of these small terms produces an O(1) effect on the prediction of the critical value of S at which bead break occurs. When the limits of the returning film fraction are examined it is found that as [zeta] [rightward arrow] 0 results are in good agreement with those for the single inlet film. Further it is shown for a fixed input flux that as [zeta] [rightward arrow] 1 a transition from bead break to upstream flooding of the nip can occur and multiple two-dimensionally stable solutions exist. For a varying input flux and fixed and ‘sufficiently large’ values of [zeta] there is a critical input flux &[lambda]macr;([zeta]) such that as S is increased from zero: (i) bead break occurs for [lambda] < &[lambda]macr;; (ii) upstream flooding occurs for [lambda] > &[lambda]macr;; (iii) when [lambda] = &[lambda]macr; the flow becomes neutrally stable at a specific value of S beyond which there exist two steady solutions (two-dimensionally stable) leading to bead break and upstream flooding, respectively

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