Topography Influence on the Lake Equations in Bounded Domains

We investigate the influence of the topography on the lake equations which describe the two-dimensional horizontal velocity of a three-dimensional incompressible flow. We show that the lake equations are structurally stable under Hausdorff approximations of the fluid domain and L ^p perturbations of the depth. As a byproduct, we obtain the existence of a weak solution to the lake equations in the case of singular domains and rough bottoms. Our result thus extends earlier works by Bresch and Métivier treating the lake equations with a fixed topography and by Gérard-Varet and Lacave treating the Euler equations in singular domains.     

Maximal f-Vectors of Minkowski Sums of Large Numbers of Polytopes

It is known that in the Minkowski sum of r polytopes in dimension d, with r<d, the number of vertices of the sum can be as high as the product of the number of vertices in each summand. However, the number of vertices for sums of more polytopes was unknown so far.     

Probing defect species on real surfaces from the analysis of the spectral profile of admolecules

The analysis of changes in the vibrational spectrum of infrared active molecules adsorbed on a ionic surface containing point or extended defects can be an efficient method to determine the nature and density of surface defects. We study the infrared response of ammonia molecules deposited on a ionic surface of MgO containing charge vacancies and dipolar defects in various concentrations and distributions and show significant changes assigned to the defects signature. A Monte Carlo approach is used to randomly deposit the probe molecules on the surface displaying random or regularly arranged defects at low temperature.     

COMPORTEMENT COMPARE DE L'EPICHLORHYDRINE,DE L'EPIBROMHYDRINE ET DE LEURS HOMOLOGUES VIS A VIS DU METHYLENETRIPHENYLPHOSPHORANE

Abstract

Condensation of methylenetriphenylphosphorane with epihalohydrines (X = Cl or Br) leads to 2,2-dihydro-2,2,2,-triphenyl-3,4-methano-1,2-oxaphospholane. The first step of this reaction depends on the nature of the halogene: a) attack on the epoxide group with X = Cl; b) attack on the halogenated function when X = Br. With 1-halogeno 2,3-epoxy butanes the reaction occurs according to b) and gives 2,2-dihydro-2,2,2-triphenyl-3,4-methano-5-methyl-1,2-oxaphospholane.     

Collision cell pressure effect on CID spectra pattern using triple quadrupole instruments: a RRKM modeling

Control of the ion internal energy in mass spectrometry is needed to establish a workable mass spectral library. The purpose of this study is to understand and to compare the pressure effects on the collision‐induced dissociation (CID) spectrum pattern recorded using triple quadrupole instruments. The monoprotonated Leucine enkephalin [YGGFL, H⁺] was used as a thermometer molecule to calibrate the electrospray ionization (ESI) and the CID internal energies deposited on the molecular species and the time scale of ion decompositions. The survival yield and the ratio of a₄/b₄ fragment ions were mainly monitored. The energy uptake for the ESI source geometry used in our study has no impact on the CID spectrum fingerprint. The collision cell pressure for the [YGGFL, H⁺] has a major influence on the SY curves slope and on the experimental time scale. To demonstrate the pressure effect on internal energy distribution, three models (threshold, thermal and collisional) based on RRKM theory were built using the Masskinetics software. As a result, the limit of each model is discussed, and the investigation demonstrates that the thermal model, using truncated Maxwell‐Boltzmann internal energy distribution, is well‐suited for simulating the experimental data at high pressure widely used in the analytical conditions. Copyright © 2013 John Wiley & Sons, Ltd.