Compact expressions for spherically averaged position and momentum densities

Compact expressions for spherically averaged position and momentum density integrals are given in terms of spherical Bessel functions (j(n)) and modified spherical Bessel functions (i(n)), respectively. All integrals required for ab initio calculations involving s, p, d, and f-type Gaussian functions are tabulated, highlighting a neat isomorphism between position and momentum space formulae. Spherically averaged position and momentum densities are calculated for a set of molecules comprising the ten-electron isoelectronic series (Ne-CH₄) and the eighteen-electron series (Ar-SiH₄, F₂-C₂H₆).This work was supported by an Australian Research Council grant to Professor Peter Gill Grant No. DP0664466

Apports des méthodes fréquentielle et temporelle dans l'étude des instabilités de frottement responsables du crissement

International audienceIn order to model and understand friction-induced vibration phenomenon, two approaches are compared in this article: temporal approach and modal approach. This analysis has been made on a simplified system composed of two beams in contact. Modal approach consists in calculating eigenvalues of the friction coupled system. Instabilities appear when a pair of modes merges. Eigenvalues with positive real parts are identified as potentially unstable modes. Temporal approach calculates the evolution of displacements, velocities, accelerations, forces ... One speaks about instabilities when stick or separation zones appear in the contact surfaces. With this approach frequencies which are excited during instability are obtained. Results have been compared and both methods give coherent and complementary results

Friction-induced instabilities: modal, transient analysis and experimental validation

International audienceThe vibrations generated at the interface between the two bodies in friction are responsible for various noises such as squealing, juddering, hammering, hooting, etc. In order to model and understand friction-induced vibration phenomenon, two types of analysis, modal analysis and transient analysis, are compared in this article. This study has been made on a simplified system composed of two beams in contact. In modal analysis, instabilities appear when a pair of modes merges. Eigenvalues with positive real parts are identified as potentially unstable modes. In transient analysis, one speaks about instabilities when stick or separation zones appear in the contact surfaces. Results have been compared and both analysis give coherent and complementary results. An experimental validation has been made and shows a good correlation between experimental and numerical results

Role of methylotrophy during symbiosis between Methylobacterium nodulans and Crotalaria podocarpa

Some rare leguminous plants of the genus Crotalaria are specifically nodulated by the methylotrophic bacterium Methylobacterium nodulans. In this study, the expression and role of bacterial methylotrophy were investigated during symbiosis between M. nodulans, strain ORS 2060(T), and its host legume, Crotalaria podocarpa. Using lacZ fusion to the mxaF gene, we showed that the methylotroph genes are expressed in the root nodules, suggesting methylotrophic activity during symbiosis. In addition, loss of the bacterial methylotrophic function significantly affected plant development. Indeed, inoculation of M. nodulans nonmethylotroph mutants in C. podocarpa decreased the total root nodule number per plant up to 60%, decreased the whole-plant nitrogen fixation capacity up to 42%, and reduced the total dry plant biomass up to 46% compared with the wild-type strain. In contrast, inoculation of the legume C. podocarpa with nonmethylotrophic mutants complemented with functional mxa genes restored the symbiotic wild phenotype. These results demonstrate the key role of methylotrophy during symbiosis between M. nodulans and C. podocarpa

Crystal Graphs and qq-Analogues of Weight Multiplicities for the Root System AnA_n

We give an expression of the $q$-analogues of the multiplicities of weights in irreducible \sl_{n+1}-modules in terms of the geometry of the crystal graph attached to the corresponding U_q(\sl_{n+1})-modules. As an application, we describe multivariate polynomial analogues of the multiplicities of the zero weight, refining Kostant's generalized exponents.Comment: LaTeX file with epic, eepic pictures, 17 pages, November 1994, to appear in Lett. Math. Phy