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.     

Tuneable Sagnac comb filter including two wave retarders

In this paper we study theoretically and experimentally a wavelength-tuneable Sagnac birefringence filter. The device is a Sagnac interferometer including a symmetric fibre coupler and a length of high-birefringence fibre in the loop. A wave retarder is inserted at each end of the birefringent fibre for absolute wavelength tuning. We show theoretically that wavelength tuning through wave plate orientation ensuring constant amplitude of the filtering function is possible only if a minimum of two wave retarders are included in the setup. The position of the transmission peaks then varies linearly with the angle of one of the retarders and can be adjusted over one entire channel spacing. This happens only when a quarter-wave retarder and a half-wave retarder are used, if the former is oriented at 45° with respect to the fibre birefringence axes, while the orientation of the latter serves as the adjustment parameter. The theoretical predictions are confirmed by the experimental results.     

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.     

Identification tree based on fragmentation rules for structure elucidation of organophosphorus esters by electrospray mass spectrometry

Organophosphorus compounds have played important roles as pesticides, chemical warfare agents and extractors of radioactive material. Structural elucidation of phosphonates poses a particular challenge because their initial forms can be hydrolyzed, thus, degradation products may predominate in samples acquired in the field. The analysis of non‐volatile organophosphorus compounds and their degradation products is possible using electrospray tandem mass spectrometry ESI‐MS/MS. Here, we present a generic strategy that allows the unambiguous identification of substituents for two families of organophosphorus compounds: the phosphonates and phosphates. General fragmentation rules were deduced based on the study of decomposition pathways of 55 organophosphorus esters, including examples found in the literature. Multistage MS (MSⁿ) experiments at high resolution in a hybrid mass spectrometer provide accurate mass measurements, whereas collision‐induced dissociation experiments in a triple quadrupole give access to small fragment ions. The creation of a specific nomenclature for each possible structure of organophosphorus compound, depending on the alkyl side chain linked to the oxygen, was achieved by applying these fragmentation rules. This led to the creation of an ‘identification tree’ based upon the unique consecutive decomposition pathways uncovered for each individual compound. Hence, seven structural motifs were created that orient an unequivocal identification using the ‘identification tree’. Despite the similar structures of the ensemble of phosphate and phosphonate esters, distinct identifications based upon characteristic neutral losses and diagnostic fragment ions were possible in all cases. Copyright © 2013 John Wiley & Sons, Ltd.     

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.