Time-harmonic acoustic propagation in the presence of a shear flow

This work deals with the numerical simulation, by means of a finite element method, of the time-harmonic propagation of acoustic waves in a moving fluid, using the Galbrun equation instead of the classical linearized Euler equations. This work extends a previous study in the case of a uniform flow to the case of a shear flow. The additional difficulty comes from the interaction between the propagation of acoustic waves and the convection of vortices by the fluid. We have developed a numerical method based on the regularization of the equation which takes these two phenomena into account. Since it leads to a partially full matrix, we use an iterative algorithm to solve the linear system.     

A low-Mach number model for time-harmonic acoustics in arbitrary flows

This paper concerns the finite element simulation of the diffraction of a time-harmonic acoustic wave in the presence of an arbitrary mean flow. Considering the equation for the perturbation of displacement (due to Galbrun), we derive a low-Mach number formulation of the problem which is proved to be of Fredholm type and is therefore well suited for discretization by classical Lagrange finite elements. Numerical experiments are done in the case of a potential flow for which an exact approach is available, and a good agreement is observed.     

Kinetic Study on the Isomerization of Perindopril by HPLC

The isomerization of perindopril has been investigated using dynamics chromatography and an unified equation introduced by Trapp that was based on stochastic and theoretical plate models to determine the energies. The isomerization rate constants and Gibbs activation energies of isomerization are directly calculated from chromatographic peak parameters, i.e., retention times of the inter-converting species, peak width at half height, and relative plateau height. From the rate constant \( k_{1}^{ue} (T) \), measured at variable temperatures, the kinetic eyring activation parameters ΔG ^#, ΔH ^# and ΔS ^# of isomerization of perindopril were obtained. By variation of the flow rate of the mobile phase, the expected independence of the isomerization barrier from the chromatographic time scale was demonstrated for the first time. The relationships between peak shape and chromatographic conditions, such as flow rate, temperature, pH, organic modifier, and β-cyclodextrin, such as an additive, were investigated. In addition, an NMR investigation on perindopril was described.

     

Synthesis,spectroscopic and structural studies of 2,2,2-trifluoroethyl phosphorodiamidate complexes with tin(IV) chloride

The two octahedral complexes SnCl₄ · 2(O)P(NR₂)₂OCH₂CF₃ (R = Me (1) or Et (2)) have been prepared from SnCl₄ and the ligands (R₂N)₂P(O)OCH₂CF₃ in chloroform solution. Both adducts have been characterised by (³¹P and ¹¹⁹Sn) NMR, IR spectroscopy and elemental analysis. The NMR data show that the complexes exist as mixtures of cis and trans isomers in solution with the latter isomer being the predominant species. The structure of 1 has been determined by X-ray crystallography. Accordingly, the structure is centrosymmetric and the two ligands are bound trans to each other in the octahedral tin complex. DFT/B3LYP calculations show that trans configuration does indeed lead to the lowest energy species. Comparison of the structural, NMR and theoretical data of both complexes with those related to SnCl₄ · 2L (L = (Me₂N)₃P(O) and (Me₂N)₂P(O)F) further supports the important effects of the nature of the substituents in the ligand on the stereochemistry of the complex formed.     

Resonances of an elastic plate in a compressible confined fluid

We present a theoretical study of the resonances of a fluid–structureproblem, an elastic plate placed in a duct in the presence ofa compressible fluid. The case of a rigid plate has been largelystudied. Acoustic resonances are then associated to resonantmodes trapped by the plate. Due to the elasticity of the plate,we need to solve a quadratic eigenvalue problem in which theresonance frequencies k solve the equations (k) = k², where are the eigenvalues of a self-adjoint operator of the formA + kB. First, we show how to study the eigenvalues locatedbelow the essential spectrum by using the min–max principle.Then, we study the fixed-point equations. We establish sufficientconditions on the characteristics of the plate and of the fluidto ensure the existence of resonances. Such conditions are validatednumerically.     

Rapid analysis of NSAIDs binding to β-cyclodextrin using the simultaneous measurement of absorption and circular dichroism with a novel multi-cell low-volume device

One of the relatively recent and most widely used approaches to reduce side effects associated with the use of nonsteroidal anti-inflammatory drugs (NSAIDs) is the complexation of NSAIDs with Cyclodextrins (CyD). So far, CyD interaction with drugs is not well understood. There have been many reports along these lines; however, rarely do these studies exploit the full potential of optical techniques. The purpose of this work is to produce a versatile, compact, low-volume, routine apparatus for the simultaneous measurements of absorbance and circular dichroism (CD) which allows for the concurrent use of three different pathlengths for binding studies of NSAIDs/CyD as a function of pH. A new rotating multi-cell holder which holds four cells was designed and manufactured. The work was achieved using an effective novel method for binding titration employing four separate flow cells connected in series in a flow system involving a titration flask and a pump. The pK _a, binding constants, stoichiometry and structural co-conformations of NSAIDs/β-CyD complexes were elucidated and determined with accuracy. The system proved to be efficient and the analysis time was reduced to less than or equal to one fourth of total analysis time used in one-cell systems, with possible automation for high-throughput analysis.

Erratum to “Time harmonic wave diffraction problems in materials with sign-shifting coefficients” [J. Comput. Appl. Math. doi:10.1016/j.cam.2009.08.041]

We mention here an error in the statement of the configurations that are covered by the theory of T-coercivity presented in the paper “Time harmonic wave diffraction problems in materials with sign-shifting coefficients” [J. Comput. Appl. Math. doi:10.1016/j.cam.2009.08.041].     

Characterization and stereochemistry of alkyl 2-chloro-3-formylacrylates: Experimental NMR and theoretical DFT studies

The synthesis of alkyl 2-chloro-3-formylacrylates 1 from alkyl pyruvates was carried out using Vilsmeier reaction. The reaction is highly stereoselective and leads to a 95:5 mixture of Z and E stereoisomers. Both stereoisomers were characterized by ¹H and ¹³C NMR. In CDCl₃ solution, the NMR data, particularly the NOEDIFF experiments, show that the major species formed is the Z stereoisomer. Heating compound 1 in THF at reflux afforded the cyclic product 2 in 90 % yield. The interpretation of the experimental data were further supported by DFT/B3LYP calculations.     

Tris(dialkylamino)phosphine Chalcogenide Complexes of Tin(IV) Chloride: A Multinuclear (31P, 77Se,and 119Sn) NMR Characterization

Abstract

Four octahedral complexes of the type SnCl₄.2L [L = (R₂N)₃P(E): E = Se; R = Me(1), Et(2) and E = S; R = Me(3), Et(4)] have been studied in solution by multinuclear (³¹P, ⁷⁷Se, and ¹¹⁹Sn) NMR spectroscopy. ³¹P and ⁷⁷Se NMR data were informative of changes associated with complex formation. The solution structure of the complexes was confirmed by their ¹¹⁹Sn NMR spectra that showed two triplet features for each complex, attributed to a mixture of the expected cis and trans isomers. The triplet signal is due to the coupling with two equivalent phosphorus atoms, consistent with an octahedral geometry around the tin center. In addition, density functional theory (DFT)/B3LYP calculations have been carried out to support the interpretations of NMR data. The results are discussed and compared with those reported for related complexes.

GRAPHICAL ABSTRACT      

Synthesis, characterization and solution behaviour of phosphoryl complexes of tin tetrafluoride

The preparation and characterization of a series of octahedral complexes [SnF₄L₂] (L = (Me₂N)₃PO (1), L = (R₂N)₂P(O)F; R = Me (2); Et (3) or L = R₂NP(O)F₂; R = Me (4); Et (5)) are described. These new adducts have been characterised by multinuclear (¹⁹F, ³¹P and ¹¹⁹Sn) NMR, IR spectroscopy and elemental analysis. The NMR data particularly the ¹⁹F NMR spectra showed that the complexes exist in solution as mixtures of cis and trans isomers. The solution behaviour of the complexes studied by variable temperature NMR in the presence of excess ligand indicated that, unlike in the SnCl₄ analogues, the ligand exchange at room temperature is slow for 1–3 and fast only for 4 and 5. The metal–ligand exchange barriers in [SnF₄L₂] and [SnCl₄L₂] systems were estimated and compared. The results indicate that in addition to the difference in the Lewis acidity between SnF₄ and SnCl₄ the nature of the substituents (fluorine atoms) on the phosphorus atom of the ligand can contribute considerably to the lability of the complex obtained.