Deformations of modules of maximal grade and the Hilbert scheme at determinantal schemes

Let R be a polynomial ring and M a finitely generated graded R-module of maximal grade (which means that the ideal I_t(\cA) generated by the maximal minors of a homogeneous presentation matrix, \cA, of M has maximal codimension in R). Suppose X:=Proj(R/I_t(\cA)) is smooth in a sufficiently large open subset and dim X > 0. Then we prove that the local graded deformation functor of M is isomorphic to the local Hilbert (scheme) functor at X \subset Proj(R) under a week assumption which holds if dim X > 1. Under this assumptions we get that the Hilbert scheme is smooth at (X), and we give an explicit formula for the dimension of its local ring. As a corollary we prove a conjecture of R. M. Mir\'o-Roig and the author that the closure of the locus of standard determinantal schemes with fixed degrees of the entries in a presentation matrix is a generically smooth component V of the Hilbert scheme. Also their conjecture on the dimension of V is proved for dim X > 0. The cohomology H^i_{*}({\cN}_X) of the normal sheaf of X in Proj(R) is shown to vanish for 0 < i < dim X-1. Finally the mentioned results, slightly adapted, remain true replacing R by any Cohen-Macaulay quotient of a polynomial ring.Comment: 24 page

Crystal and magnetic structure of La_{1-x}Sr_{1+x}MnO_{4} : role of the orbital degree of freedom

The crystal and magnetic structure of La_{1-x}Sr_{1+x}MnO_4 (0<x<0.7) has been studied by diffraction techniques and high resolution capacitance dilatometry. There is no evidence for a structural phase transition like those found in isostructural cuprates or nickelates, but there are significant structural changes induced by the variation of temperature and doping which we attribute to a rearrangement of the orbital occupation.Comment: 8 pages, 6 figures, submitted to PR

Patterns of entropy production in dissolving natural porous media with flowing fluid

The tendency for irreversible processes to generate entropy is the ultimate driving force for structure evolution in nature. In engineering, entropy production is often used as an indicator for loss of usable energy. In this study, we show that the analysis of entropy production patterns can provide insight into the diverse observations from experiments that investigate porous medium dissolution in imposed flow field. We first present a numerical scheme for the analysis of entropy production in dissolving porous media. Our scheme uses a greyscale digital model for chalk (an extremely fine grained rock), that was obtained using X-ray nanotomography. Greyscale models preserve structural heterogeneities with very high fidelity. We focussed on the coupling between two types of entropy production: the percolative entropy, generated by dissipating the kinetic energy of fluid flow, and the reactive entropy, originating from the consumption of chemical free energy. Their temporal patterns pinpoint three stages of microstructural evolution. We then showed that local mixing deteriorates fluid channelisation by reducing local variations of reactant concentration. We also showed that microstructural evolution can be sensitive to the initial transport heterogeneities, when the macroscopic flowrate is low. This dependence on flowrate indicates the need to resolve the structural features of a porous system when fluid residence time is long

Stability of Landau-Ginzburg branes

We evaluate the ideas of Pi-stability at the Landau-Ginzburg point in moduli space of compact Calabi-Yau manifolds, using matrix factorizations to B-model the topological D-brane category. The standard requirement of unitarity at the IR fixed point is argued to lead to a notion of "R-stability" for matrix factorizations of quasi-homogeneous LG potentials. The D0-brane on the quintic at the Landau-Ginzburg point is not obviously unstable. Aiming to relate R-stability to a moduli space problem, we then study the action of the gauge group of similarity transformations on matrix factorizations. We define a naive moment map-like flow on the gauge orbits and use it to study boundary flows in several examples. Gauge transformations of non-zero degree play an interesting role for brane-antibrane annihilation. We also give a careful exposition of the grading of the Landau-Ginzburg category of B-branes, and prove an index theorem for matrix factorizations.Comment: 46 pages, LaTeX, summary adde

Syzygies in equivariant cohomology for non-abelian Lie groups

We extend the work of Allday-Franz-Puppe on syzygies in equivariant cohomology from tori to arbitrary compact connected Lie groups G. In particular, we show that for a compact orientable G-manifold X the analogue of the Chang-Skjelbred sequence is exact if and only if the equivariant cohomology of X is reflexive, if and only if the equivariant Poincare pairing for X is perfect. Along the way we establish that the equivariant cohomology modules arising from the orbit filtration of X are Cohen-Macaulay. We allow singular spaces and introduce a Cartan model for their equivariant cohomology. We also develop a criterion for the finiteness of the number of infinitesimal orbit types of a G-manifold.Comment: 28 pages; minor change

Constraining a hybrid volatility basis-set model for aging of wood-burning emissions using smog chamber experiments : A box-model study based on the VBS scheme of the CAMx model (v5.40)

In this study, novel wood combustion aging experiments performed at different temperatures (263 and 288 K) in a ∼ 7 m³ smog chamber were modelled using a hybrid volatility basis set (VBS) box model, representing the emission partitioning and their oxidation against OH. We combine aerosol–chemistry box-model simulations with unprecedented measurements of non-traditional volatile organic compounds (NTVOCs) from a high-resolution proton transfer reaction mass spectrometer (PTR-MS) and with organic aerosol measurements from an aerosol mass spectrometer (AMS). Due to this, we are able to observationally constrain the amounts of different NTVOC aerosol precursors (in the model) relative to low volatility and semi-volatile primary organic material (OM$_{sv}$), which is partitioned based on current published volatility distribution data. By comparing the NTVOC ∕ OM$_{sv}$ ratios at different temperatures, we determine the enthalpies of vaporization of primary biomass-burning organic aerosols. Further, the developed model allows for evaluating the evolution of oxidation products of the semi-volatile and volatile precursors with aging. More than 30 000 box-model simulations were performed to retrieve the combination of parameters that best fit the observed organic aerosol mass and O : C ratios. The parameters investigated include the NTVOC reaction rates and yields as well as enthalpies of vaporization and the O : C of secondary organic aerosol surrogates. Our results suggest an average ratio of NTVOCs to the sum of non-volatile and semi-volatile organic compounds of ∼ 4.75. The mass yields of these compounds determined for a wide range of atmospherically relevant temperatures and organic aerosol (OA) concentrations were predicted to vary between 8 and 30 % after 5 h of continuous aging. Based on the reaction scheme used, reaction rates of the NTVOC mixture range from 3.0 × 10$^{-11}$ to 4. 0 × 10$^{-11}$ cm³ molec$^{-1}$ s$^{-1}$. The average enthalpy of vaporization of secondary organic aerosol (SOA) surrogates was determined to be between 55 000 and 35 000 J mol$^{-1}$, which implies a yield increase of 0.03-0.06 % K$^{-1}$ with decreasing temperature. The improved VBS scheme is suitable for implementation into chemical transport models to predict the burden and oxidation state of primary and secondary biomass-burning aerosols