The relationship between the Wigner-Weyl kinetic formalism and the complex geometrical optics method

The relationship between two different asymptotic techniques developed in order to describe the propagation of waves beyond the standard geometrical optics approximation, namely, the Wigner-Weyl kinetic formalism and the complex geometrical optics method, is addressed. More specifically, a solution of the wave kinetic equation, relevant to the Wigner-Weyl formalism, is obtained which yields the same wavefield intensity as the complex geometrical optics method. Such a relationship is also discussed on the basis of the analytical solution of the wave kinetic equation specific to Gaussian beams of electromagnetic waves propagating in a ``lens-like'' medium for which the complex geometrical optics solution is already available.Comment: Extended version comprising two new section

Non-commutative integrable systems on bb-symplectic manifolds

In this paper we study non-commutative integrable systems on $b$-Poisson manifolds. One important source of examples (and motivation) of such systems comes from considering non-commutative systems on manifolds with boundary having the right asymptotics on the boundary. In this paper we describe this and other examples and we prove an action-angle theorem for non-commutative integrable systems on a $b$-symplectic manifold in a neighbourhood of a Liouville torus inside the critical set of the Poisson structure associated to the $b$-symplectic structure

Manifolds associated with (Z2)n(Z_2)^n-colored regular graphs

In this article we describe a canonical way to expand a certain kind of $(\mathbb Z_2)^{n+1}$-colored regular graphs into closed $n$-manifolds by adding cells determined by the edge-colorings inductively. We show that every closed combinatorial $n$-manifold can be obtained in this way. When $n\leq 3$, we give simple equivalent conditions for a colored graph to admit an expansion. In addition, we show that if a $(\mathbb Z_2)^{n+1}$-colored regular graph admits an $n$-skeletal expansion, then it is realizable as the moment graph of an $(n+1)$-dimensional closed $(\mathbb Z_2)^{n+1}$-manifold.Comment: 20 pages with 9 figures, in AMS-LaTex, v4 added a new section on reconstructing a space with a $(Z_2)^n$-action for which its moment graph is a given colored grap

Photochemical reactions of cyanoacetylene and dicyanoacetylene: Possible processes in Titan's atmosphere

Titan has an atmosphere which is subject to dramatic chemical evolution due mainly to the dramatic effect of the UV flux from the Sun. The energetic solar photons and other particles are converting the methane-nitrogen atmosphere into the unsaturated carbon compounds observed by the Voyager probes. These same solar photons are also converting some of these unsaturated reaction products into the aerosols observed in the atmosphere which obscure the view of the surface of Titan. In particular, the photochemical reactions of cyanoacetylene, dicyanoacetylene, acetylene and ethylene may result in the formation of the higher hydrocarbons and polymers which result in the aerosols observed in Titan's atmosphere. Polymers are the principal reaction products formed by irradiation of cyanoacetylene and dicyanoacetylene. Irradiation of cyanoacetylene with 185 nm of light also yields 1,3,5-tricyanobenzene while irradiation at 254 nm yields 1,2,4-tricyanobenzene and tetracyano cyclooctatetraenes. Photolyses of mixtures of cyanoacetylene and acetylene yields mono- and di- cyanobenzenes. The 1-Cyanocyclobutene is formed from the photochemical addition of cyanoacetylene with ethylene. The photolysis of dicyanoacetylene with acetylene yields 2,3-dicyano-1,3-butadiene and 1,2-dicyanobenzene. Tetracyano cyclooctatetraene products were also observed in the photolysis of mixtures of dicyanoacetylene and acetylene with 254 nm light. The 1,2-Dicyano cyclobutene is obtained from the photolysis dicyanoacetylene and ethylene. Reaction mechanisms will be proposed to explain the observed photoproducts

Searching for Trans Ethyl Methyl Ether in Orion KL

We report on the tentative detection of $trans$ Ethyl Methyl Ether (tEME), $t-CH_3CH_2OCH_3$, through the identification of a large number of rotational lines from each one of the spin states of the molecule towards Orion KL. We also search for $gauche$-$trans$-n-propanol, $Gt-n-CH_3CH_2CH_2OH$, an isomer of tEME in the same source. We have identified lines of both species in the IRAM 30m line survey and in the ALMA Science Verification data. We have obtained ALMA maps to establish the spatial distribution of these species. Whereas tEME mainly arises from the compact ridge component of Orion, Gt-n-propanol appears at the emission peak of ethanol (south hot core). The derived column densities of these species at the location of their emission peaks are $\leq(4.0\pm0.8)\times10^{15} cm^{-2}$ and $\leq(1.0\pm0.2)\times10^{15} cm^{-2}$ for tEME and Gt-n-propanol, respectively. The rotational temperature is $\sim100 K$ for both molecules. We also provide maps of $CH_3OCOH$, $CH_3CH_2OCOH$, $CH_3OCH_3$, $CH_3OH$, and $CH_3CH_2OH$ to compare the distribution of these organic saturated O-bearing species containing methyl and ethyl groups in this region. Abundance ratios of related species and upper limits to the abundances of non-detected ethers are provided. We derive an abundance ratio $N(CH_3OCH_3)/N(tEME)\geq150$ in the compact ridge of Orion.Comment: Accepted in A&A Letter

Resorption of Natural Calcium Carbonate by Avian Osteoclasts In Vitro

Osteoclasts isolated from the endosteum of 2.5 to 3-week chick tibia were cultured on glass coverslips or natural CaC03 (Tridacna) wafers for 2 and 4 days. The cells were exposed to the pH-dependent dye, acridine orange, and fluorescence was measured by a light microscope photometer. Fluorescence intensity values were higher in cells adherent to Tridacna wafers than in those incubated on glass after 2 and 4 days of culture (three and two-fold, respectively). Moreover, osteoclasts on Tridacna wafers were more flattened and were found to produce resorption pits. Acid production by osteoclasts cultured on Tridacna wafers was stimulated with 10-8 M parathyroid hormone and inhibited with 10-7 M acetazolamide or 10-7 M hydroxybenezoyl thiophene sulfonamide, as shown by changes in intensity of acridine orange fluorescence after 30, 60 and 120 minutes of treatment. These results indicate that osteoclasts cultured on natural CaC03 wafers mimic the behavior of osteoclasts cultured on other substrates. Further, the capacity to acidify was enhanced in cells cultured on CaC03 wafers. These results indicate that natural CaC03 Tridacna wafers provide a suitable substrate for osteoclasts in culture and demonstrate that carbonic anhydrase plays a role in carbonated substrate resorption

On the geometry of mixed states and the Fisher information tensor

In this paper, we will review the co-adjoint orbit formulation of finite dimensional quantum mechanics, and in this framework, we will interpret the notion of quantum Fisher information index (and metric). Following previous work of part of the authors, who introduced the definition of Fisher information tensor, we will show how its antisymmetric part is the pullback of the natural Kostant-Kirillov-Souriau symplectic form along some natural diffeomorphism. In order to do this, we will need to understand the symmetric logarithmic derivative as a proper 1-form, settling the issues about its very definition and explicit computation. Moreover, the fibration of co-adjoint orbits, seen as spaces of mixed states, is also discussed.Comment: 27 pages; Accepted Manuscrip

Network Synthesis

Contains research objectives and reports on two research projects

Base manifolds for fibrations of projective irreducible symplectic manifolds

Given a projective irreducible symplectic manifold $M$ of dimension $2n$, a projective manifold $X$ and a surjective holomorphic map $f:M \to X$ with connected fibers of positive dimension, we prove that $X$ is biholomorphic to the projective space of dimension $n$. The proof is obtained by exploiting two geometric structures at general points of $X$: the affine structure arising from the action variables of the Lagrangian fibration $f$ and the structure defined by the variety of minimal rational tangents on the Fano manifold $X$