Non-destructive characterisation of fine grained samples: assessment of insitu micro-XRD of primitive meteorite matrix

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Basic properties of nonsmooth Hormander's vector fields and Poincare's inequality

We consider a family of vector fields defined in some bounded domain of R^p, and we assume that they satisfy Hormander's rank condition of some step r, and that their coefficients have r-1 continuous derivatives. We extend to this nonsmooth context some results which are well-known for smooth Hormander's vector fields, namely: some basic properties of the distance induced by the vector fields, the doubling condition, Chow's connectivity theorem, and, under the stronger assumption that the coefficients belong to C^{r-1,1}, Poincare's inequality. By known results, these facts also imply a Sobolev embedding. All these tools allow to draw some consequences about second order differential operators modeled on these nonsmooth Hormander's vector fields.Comment: 60 pages, LaTeX; Section 6 added and Section 7 (6 in the previous version) changed. Some references adde

Suppression of cell-spreading and phagocytic activity on nano-pillared surface: in vitro experiment using hemocytes of the colonial ascidian Botryllus schlosseri.

Nano-scale nipple array on the body surface has been described from various invertebrates including endoparasitic and mesoparasitic copepods, but the functions of the nipple array is not well understood. Using the hydrophilized nanopillar sheets made of polystyrene as a mimetic material of the nipple arrays on the parasites\u2019 body surface, we assayed the cell spreading and phagocytosis of the hemocytes of the colonial ascidian Botryllus schlosseri. On the pillared surface, the number of spreading amebocytes and the number of phagocytizing hemocytes per unit area were always smaller than those on the flat surface (Mann-Whitney test, p < 0.05 - 0.001), probably because the effective area for the cell attachment on the pillared surface is much smaller than the area on the flat sheet. The present results supports the idea that the nipple array on the parasites' body surface reduces the innate immune reaction from the host hemocytes

Approximations of Sobolev norms in Carnot groups

This paper deals with a notion of Sobolev space $W^{1,p}$ introduced by J.Bourgain, H.Brezis and P.Mironescu by means of a seminorm involving local averages of finite differences. This seminorm was subsequently used by A.Ponce to obtain a Poincar\'e-type inequality. The main results that we present are a generalization of these two works to a non-Euclidean setting, namely that of Carnot groups. We show that the seminorm expressd in terms of the intrinsic distance is equivalent to the $L^p$ norm of the intrinsic gradient, and provide a Poincar\'e-type inequality on Carnot groups by means of a constructive approach which relies on one-dimensional estimates. Self-improving properties are also studied for some cases of interest

Harnack inequality and regularity for degenerate quasilinear elliptic equations

We prove Harnack inequality and local regularity results for weak solutions of a quasilinear degenerate equation in divergence form under natural growth conditions. The degeneracy is given by a suitable power of a strong $A_\infty$ weight. Regularity results are achieved under minimal assumptions on the coefficients and, as an application, we prove $C^{1,\alpha}$ local estimates for solutions of a degenerate equation in non divergence form

Oxygen isotopic and petrological constraints on the origin and relationship of IIE iron meteorites and H chondrites

New oxygen isotopic measurements of IIEs and H chondrites are indistinguishable — strengthening a possible common origin for these groups. Combining oxygen results with mineralogy, the nature of their parent body or bodies can be explored

Oxygen Isotopic Constraints on the Number and Origin of Basaltic Achondrite Parent Bodies

Our data show that HED meteorites have a homogeneous oxygen isotopic composition consistent with a magma ocean on Vesta. Ibitira, Asuka 881394, Pasamonte, and NWA 1240 probably come from separate parent asteroids

Emittance sharing and exchange driven by linear betatron coupling in circular accelerators

The influence of linear betatron coupling due to constant-in-time skew quadrupolar fields on the transverse emittances is discussed using both a simplified model of a smooth circular accelerator and a more realistic strong-focusing lattice with localized sources of coupling (thin lens). New formulas for the coupled transverse emittances are derived that include the initial emittances, the coupling strengths, and the tune distance from the resonance. By using the more powerful Lie algebra and the resonance driving terms formalism, equivalent formulas are derived that provide a better understanding of some counterintuitive effects, otherwise not understandable in the smooth approximation. The new formulas have been tested both numerically and experimentally by using data of the CERN Proton Synchrotron showing a remarkable agreement