A quantitative theory-versus-experiment comparison for the intense laser dissociation of H2+

A detailed theory-versus-experiment comparison is worked out for H$_2^+$ intense laser dissociation, based on angularly resolved photodissociation spectra recently recorded in H.Figger's group. As opposite to other experimental setups, it is an electric discharge (and not an optical excitation) that prepares the molecular ion, with the advantage for the theoretical approach, to neglect without lost of accuracy, the otherwise important ionization-dissociation competition. Abel transformation relates the dissociation probability starting from a single ro-vibrational state, to the probability of observing a hydrogen atom at a given pixel of the detector plate. Some statistics on initial ro-vibrational distributions, together with a spatial averaging over laser focus area, lead to photofragments kinetic spectra, with well separated peaks attributed to single vibrational levels. An excellent theory-versus-experiment agreement is reached not only for the kinetic spectra, but also for the angular distributions of fragments originating from two different vibrational levels resulting into more or less alignment. Some characteristic features can be interpreted in terms of basic mechanisms such as bond softening or vibrational trapping.Comment: submitted to PRA on 21.05.200

Local solvability and regularity results for a class of semilinear elliptic problems in nonsmooth domains

summary:We consider a class of semilinear elliptic problems in two- and three-dimensional domains with conical points. We introduce Sobolev spaces with detached asymptotics generated by the asymptotical behaviour of solutions of corresponding linearized problems near conical boundary points. We show that the corresponding nonlinear operator acting between these spaces is Frechet differentiable. Applying the local invertibility theorem we prove that the solution of the semilinear problem has the same asymptotic behaviour near the conical points as the solution of the linearized problem if the norms of the given right hand sides are small enough. Estimates for the difference between the solution of the semilinear and of the linearized problem are derived

Computation of 3D vertex singularities for linear elasticity: Error estimates for a finite element method on graded meshes

This paper is concerned with the computation of 3D vertex singularities of anisotropic elastic fields with Dirichlet boundary conditions, focusing on the derivation of error estimates for a finite element method on graded meshes. The singularities are described by eigenpairs of a corresponding operator pencil on spherical polygonal domains. The main idea is to introduce a modified quadratic variational boundary eigenvalue problem which consists of two self-adjoint, positive definite sesquilinear forms and a skew-Hermitean form. This eigenvalue problem is discretized by a finite element method on graded meshes. Based on regularity results for the eigensolutions estimates for the finite element error are derived both for the eigenvalues and the eigensolutions. Finally, some numerical results are presented

Differential expression of the EGF-TM7 family members CD97 and EMR2 in lipid-laden macrophages in atherosclerosis, multiple sclerosis and Gaucher disease

The members of the epidermal growth factor (EGF)-transmembrane (TM)7 family of adhesion class G-protein coupled receptors are abundantly expressed by cells of the myeloid lineage. A detailed investigation of their expression by functional subsets of activated macrophages is still lacking. Therefore, we determined the expression of CD97, EGF module-containing mucin-like receptor (EMR)2 and EMR3 by monocyte-derived macrophages experimentally polarized in vitro. This was compared to three types of disease-associated lipid-laden macrophages displaying an alternatively activated phenotype in situ. Polarization in vitro towards classically activated M1 versus alternatively activated M2 extremes of macrophage activation did not result in a congruent regulation of EGF-TM7 receptor mRNA and protein except for a down-regulation of CD97 by IL-10. In contrast, macrophages handling lipid overload in vivo displayed differences in the expression of CD97 and EMR2. While foamy macrophages in atherosclerotic vessels expressed both CD97 and EMR2, foam cells in multiple sclerosis brain expressed CD97, but only little EMR2. Foam cell formation in vitro by oxidized LDL and myelin did not affect CD97 or EMR2 expression. Gaucher spleen cells accumulating glucosylceramide expressed very high levels of CD97 and EMR2. These findings indicate that complex cellular expression programmes rather than activation modes regulate the expression of EGF-TM7 receptors in macrophages. (C) 2010 Elsevier B.V. All rights reserve