17 research outputs found
Rheology of cellulose/1,5-diazabicyclo[4.3.0]non-5-enium propionate solutions and shaping into aerogel beads
International audienc
Rheology of cellulose/1,5-diazabicyclo[4.3.0]non-5-enium propionate solutions and shaping into aerogel beads
International audienc
On the Frobenius integrability of certain holomorphic p-forms
Abstract. The goal of this note is to exhibit the integrability properties (in the sense of the Frobenius theorem) of holomorphic p-forms with values in certain line bundles with nonpositive curvature on a compact Kähler manifold. There are in fact very strong restrictions, both on the holomorphic form and on the curvature of the line bundle. In particular, these observations provide interesting information on the structure of projective manifolds which admit a contact structure: either they are Fano manifolds or they are biholomorphic to the projectivization of the cotangent bundle of another suitable projective manifold. 1. Main results Recall that a holomorphic line bundle L on a compact complex manifold is said to be pseudo-effective if c1(L) contains a closed positive (1, 1)-current T, or equivalently, if L possesses a (possibly singular) hermitian metric h such that the curvature current T = Θh(L) = −i∂ ∂ log h is nonnegative. Our main result is Main Theorem. Let X be a compact Kähler manifold. Assume that there exists a pseudo-effective line bundle L on X and a nonzero holomorphic section θ ∈ H0 (X, Ω p X ⊗ L−1), where 0 � p � n = dimX. Let Sθ be the coherent subsheaf of germs of vector fields ξ in the tangent sheaf TX, such that the contraction iξθ vanishes. Then Sθ is integrable, namely [Sθ, Sθ] ⊂ Sθ, and L has flat curvature along the leaves of the (possibly singular) foliation defined by Sθ. Before entering into the proof, we discuss several consequences. If p = 0 or p = n, the result is trivial (with Sθ = TX and Sθ = 0, respectively). The most interesting case is p = 1. Corollary 1. In the above situation, if the line bundle L → X is pseudoeffective and θ ∈ H 0 (X, Ω 1 X ⊗ L−1) is a nonzero section, the subsheaf Sθ defines a holomorphic foliation of codimension 1 in X, that is, θ ∧ dθ = 0. We now concentrate ourselves on the case when X is a contact manifold, i.e. dim X = n = 2m + 1, m � 1, and there exists a form θ ∈ H 0 (X, Ω 1 X ⊗ L−1), called the contact form, such that θ ∧(dθ) m ∈ H 0 (X, KX ⊗L −m−1) has no zeroes. Then Sθ is a codimension 1 locally free subsheaf of TX and there are dual exact2 Frobenius integrability of certain holomorphic p-forms sequence
Improving the dynamics of Northern Hemisphere high-latitude vegetation in the ORCHIDEE ecosystem model
Processes that describe the distribution of vegetation and ecosystem
succession after disturbance are an important component of dynamic global
vegetation models (DGVMs). The vegetation dynamics module (ORC-VD) within
the process-based ecosystem model ORCHIDEE (Organizing Carbon and Hydrology
in Dynamic Ecosystems) has not been updated and evaluated since many years
and is known to produce unrealistic results. This study presents a new
parameterization of ORC-VD for mid- to high-latitude regions in the Northern
Hemisphere, including processes that influence the existence, mortality and
competition between tree functional types. A new set of metrics is also
proposed to quantify the performance of ORC-VD, using up to five different
data sets of satellite land cover, forest biomass from remote sensing and
inventories, a data-driven estimate of gross primary productivity (GPP) and
two gridded data sets of soil organic carbon content. The scoring of ORC-VD
derived from these metrics integrates uncertainties in the observational
data sets. This multi-data set evaluation framework is a generic method that
could be applied to the evaluation of other DGVM models. The results of the
original ORC-VD published in 2005 for mid- to high-latitudes and of the new
parameterization are evaluated against the above-described data sets.
Significant improvements were found in the modeling of the distribution of
tree functional types north of 40° N. Three additional sensitivity
runs were carried out to separate the impact of different processes or
drivers on simulated vegetation distribution, including soil freezing which
limits net primary production through soil moisture availability in the root
zone, elevated CO<sub>2</sub> concentration since 1850, and the effects of
frequency and severity of extreme cold events during the spin-up phase of
the model
A decomposition theorem for singular spaces with trivial canonical class of dimension at most five
International audienc