Numerical analysis of spatial distortions in a single-grating chirped pulse amplification system

A numerical study of spatial distortions of a laser beam after propagation through an optical single-grating chirp pulse amplification (CPA) system was developed. This study is based on numerical simulation using the ray-tracing model from Rayica module of MATHEMATICA and it relates the behavior of the aberrated beam in terms of spatial distortions (eg. spatial chirp and pulse front tilt) in case of grating incident angle variation. The results are relevant for different applications which use CPA systems with needs of high quality laser beam profile.     

Cycloaddition versus amidation in reactions of 2-amino-2-oxoethyl-phenanthrolinium ylides to activated alkynes and alkenes

A comparative study regarding cycloaddition versus amidation reactions of 2-amino-2-oxoethyl-phenanthrolinium ylides to activated alkynes and alkenes is presented. The reaction pathway is different, depending on dipolarophile (with triple or double bond) and ylide structures. The monoenamidation reaction proved to be stereoselective leading to a Z-stereochemistry on the acrylate double bond. The structures of all newly synthesized compounds have been proved by spectral analysis (NMR and IR) and in some cases by X-ray diffraction.     

Comparison of POD reduced order strategies for the nonlinear 2D shallow water equations

This paper introduces tensorial calculus techniques in the framework of POD to reduce the computational complexity of the reduced nonlinear terms. The resulting method, named tensorial POD, can be applied to polynomial nonlinearities of any degree p. Such nonlinear terms have an online complexity of , where k is the dimension of POD basis and therefore is independent of full space dimension. However, it is efficient only for quadratic nonlinear terms because for higher nonlinearities, POD model proves to be less time consuming once the POD basis dimension k is increased. Numerical experiments are carried out with a two‐dimensional SWE test problem to compare the performance of tensorial POD, POD, and POD/discrete empirical interpolation method (DEIM). Numerical results show that tensorial POD decreases by 76× the computational cost of the online stage of POD model for configurations using more than 300,000 model variables. The tensorial POD SWE model was only 2 to 8× slower than the POD/DEIM SWE model but the implementation effort is considerably increased. Tensorial calculus was again employed to construct a new algorithm allowing POD/DEIM SWE model to compute its offline stage faster than POD and tensorial POD approaches. Copyright © 2014 John Wiley & Sons, Ltd.     

An indirect shooting method based on the POD/DEIM technique for distributed optimal control of the wave equation

This paper presents a fast numerical method, based on the indirect shooting method and Proper Orthogonal Decomposition (POD) technique, for solving distributed optimal control of the wave equation. To solve this problem, we consider the first‐order optimality conditions and then by using finite element spatial discretization and shooting strategy, the solution of the optimality conditions is reduced to the solution of a series of initial value problems (IVPs). Generally, these IVPs are high‐order and thus their solution is time‐consuming. To overcome this drawback, we present a POD indirect shooting method, which uses the POD technique to approximate IVPs with smaller ones and faster run times. Moreover, in the presence of the nonlinear term, to reduce the order of the nonlinear calculations, a discrete empirical interpolation method (DEIM) is applied and a POD/DEIM indirect shooting method is developed. We investigate the performance and accuracy of the proposed methods by means of 4 numerical experiments. We show that the presented POD and POD/DEIM indirect shooting methods dramatically reduce the CPU time compared to the full indirect shooting method, whereas there is no significant difference between the accuracy of the reduced and full indirect shooting methods.     

On nano-scale hydrodynamic lubrication models

Current magnetic head sliders and other micromechanisms involve gas lubrication flows with gap thicknesses in the nanometer range and stepped shapes fabricated by lithographic methods. In mechanical simulations, rarefaction effects are accounted for by models that propose Poiseuille flow factors which exhibit singularities as the pressure tends to zero or +∞. In this Note we show that these models are indeed mathematically well-posed, even in the case of discontinuous gap thickness functions. Our results cover popular models that were not previously analyzed in the literature, such as the Fukui–Kaneko model and the second-order model, among others. To cite this article: G. Buscaglia et al., C. R. Mecanique 333 (2005).     

Water soluble complexes of methyl β-cyclodextrin and sulconazole nitrate

Complexation between methyl β-cyclodextrin (Me βCD) and sulconazole nitrate (SULC) was realized both under freeze drying and ultrasonication conditions. The process was carried out in solution and in solid state. In solution, the complexation was evaluated using solubility studies, nuclear magnetic resonance spectroscopy (¹H-NMR) and UV–Vis absorption studies. In the solid state, differential scanning calorimetry (DSC), and X-ray diffraction studies were used. Solubility studies indicate the existence of inclusion complexes between SULC and Me βCD. ¹H-NMR data showed that the inclusion complexes have different structures, according with the method we used for synthesis: for the freeze dried method the complex is obtained by complexation of dichlorobenzene ring of SULC into inner cavity of CD while for ultrasonication method the complex is obtained by complexation of imidazole graph of SULC into the CD molecule. DSC and X-ray studies bring supplementary information concerning the formation of complex Me βCD–SULC. As a result of the inclusion process into Me βCD, the solubility of SULC increase significant, being 10 times more comparative with the pure drug. We anticipate that these modifications will have a significant impact on the biological effects of the drug, making the SULC–Me βCD complex an appropriate candidate for a new drug delivery system.     

A spirobicyclic complex of Schmidpeter's ligand,bis(tetraphenylimidodiphosphinato)beryllium,Be(OPh2PNPPh2O)2, an inorganic analog of beryllium bis(β‐diketonates)

The crystal structure of bis(tetra‐phenylimidodiphosphinato)beryllium (as a benzene solvate), Be(OPh₂PNPPh₂O)₂. C₆H₆, was determined by X‐ray diffraction and compared with that of beryllium acetylacetonate, Be(OCMeCHCMeO)₂. The imidodiphosphinate is an inorganic spirobicyclic system, Be(OPNPO)₂, with tetrahedrally coordinated beryllium. Unlike the planar BeO₂C₃ rings in the acetylacetonate, the two six‐membered BeO₂P₂N inorganic rings are nonplanar and display a skew boat conformation. © 2000 John Wiley & Sons, Inc. Heteroatom Chem 11:244–248, 2000     

A refinement of the Brascamp–Lieb–Poincaré inequality in one dimension

In this short note, we give a refinement of the Brascamp–Lieb inequality in the style of the Houdré–Kagan extension for the Poincaré inequality in one dimension. This is inspired by works by Helffer and by Ledoux.     

NMR parameters in gapped graphene systems

We calculate the nuclear spin-lattice relaxation time and the Knight shift for the case of gapped graphene systems. Our calculations consider both the massive and massless gap scenarios. Both the spin-lattice relaxation time and the Knight shift depend on temperature, chemical potential, and the value of the electronic energy gap. In particular, at the Dirac point, the electronic energy gap has stronger effects on the system nuclear magnetic resonance parameters in the case of the massless gap scenario. Differently, at large values of the chemical potential, both gap scenarios behave in a similar way and the gapped graphene system approaches a Fermi gas from the nuclear magnetic resonance parameters point of view. Our results are important for nuclear magnetic resonance measurements that target the ¹³C active nuclei in graphene samples.