Uniqueness in the water-wave problem for bodies intersecting the free surface at arbitrary anglesL'unicité du problème des ondes de surface pour les corps qui intersectent la surface libre sous des angles arbitraires

This Note deals with the linearized water-wave problem involving a surface-piercing cylinder in water of infinite depth. A solution to this problem is proved to be unique for all values of the radian frequency when the cylinder intersecting the free surface at arbitrary angles is subjected to certain geometric arrangements. To cite this article: N. Kuznetsov, C. R. Mecanique 332 (2004).     

On the fundamental sloshing frequency in the ice-fishing problemSur la fréquence de ballottement principale dans le problème de la glace avec trous pour pêcher

The sloshing problem is considered in a half-space covered by a rigid dock with apertures. The dependence of the fundamental sloshing frequency on the shape of the free surface region is studied. It is proved that the inequality holds between the fundamental eigenvalues corresponding to two different regions if some conditions are fulfilled. These conditions are verified for particular classes of regions of a fixed area in order to demonstrate that the disk yields the maximum of the fundamental eigenvalue for each of these classes. On the other hand, examples of regions are constructed for which the fundamental eigenfrequency is larger than that for the circular aperture of the same area and even as large as one wishes. To cite this article: V. Kozlov, N. Kuznetsov, C. R. Mecanique 330 (2002) 723–728.     

Synthesis and characterization of phosphates in molten systems Cs2O-P2O5-CaO-M2O3 (M—Al, Fe, Cr)

The crystallization of complex phosphates from the melts of Cs₂O-P₂O₅-CaO-M^III₂O₃ (M^III—Al, Fe, Cr) systems have been investigated at fixed value Cs/P molar ratios equal to 0.7, 1.0 and 1.3 and Са/Р=0.2 and Ca/М^III=1. The fields of crystallization of CsCaP₃O₉, β-Ca₂P₂O₇, Cs₂CaP₂O₇, Cs₃CaFe(P₂O₇)₂, Ca₉M^III(PO₄)₇ (M^III—Fe, Cr), Cs_0.63Ca_9.63Fe_0.37(PO₄)₇ and CsCa₁₀(PO₄)₇ were determined. Obtained phosphates were investigated using powder X-ray diffraction and FTIR spectroscopy. Novel whitlockite-related phases CsCa₁₀(PO₄)₇ and Cs_0.63Ca_9.63Fe_0.37(PO₄)₇ have been characterized by single crystal X-ray diffraction: space group R3c, a=10.5536(5) and 10.5221(4) Å, с=37.2283(19) and 37.2405(17) Å, respectively.     

One-photon photophysics and two-photon absorption of 4-[9,9-di(2-ethylhexyl)-7-diphenylaminofluoren-2-yl]-2,2':6',2'-terpyridine and their platinum chloride complexes

The synthesis, one-photon photophysics and two-photon absorption (2PA) of three dipolar D-π-A 4-[9,9-di(2-ethylhexyl)-7-diphenylaminofluoren-2-yl]-2,2':6',2'-terpyridine and their platinum chloride complexes with different linkers between the donor and acceptor are reported. All ligands exhibit (1)π,π* transition in the UV and (1)π,π*/(1)ICT (intramolecular charge transfer) transition in the visible regions, while the complexes display a lower-energy (1)π,π*/(1)CT (charge transfer) transition in the visible region in addition to the high-energy (1)π,π* transitions. All ligands and the complexes are emissive at room temperature and 77 K, with the emitting excited state assigned as the mixed (1)π,π* and (1)CT states at RT. Transient absorption from the ligands and the complexes were observed. 2PA was investigated for all ligands and complexes. The two-photon absorption cross-sections (σ(2)) of the complexes (600-2000 GM) measured by Z-scan experiment are much larger than those of their corresponding ligands measured by the two-photon induced fluorescence method. The ligand and the complex with the ethynylene linker show much stronger 2PA than those with the vinylene linker.     

Assessment of the electronic structure of 2,2'-pyridylpyrrolides as ligands

The ligand class 2,2'-pyridylpyrrolide is surveyed, both for its structural features and its electronic structure, when attached to monovalent K, Cu, Ag, Au, and Rh. The influence of pyrrolide ring substituents is studied, as well as the question of push/pull interaction between the pyridyl and pyrrolide halves. The π donor ability of the pyrrolide is found to be less than that of an analogous phenyl. However, in contrast to the phenyl analog, the HOMO is pyrrolide π in character for pyridylpyrrolide complexes of copper and rhodium, while it is conventionally metal localized for planar, d(8) rhodium pyridylphenyl. Monovalent three-coordinate copper complexes show great deviations from Y-shaped toward T-shaped structures, including cases where the pyridyl ligand bonds only weakly.     

Relation between two-photon absorption and dipolar properties in a series of fluorenyl-based chromophores with electron donating or electron withdrawing substituents

We investigate two-photon absorption (2PA) in a series of fluorenyl-based 9,9-diethyl-2-ethynyl-7-((4-R-phenyl)ethynyl)-9,9a-dihydro-4aH-fluorene chromophores with R being various electron donating (ED) and electron withdrawing (EW) groups. We use wavelength-tunable femtosecond laser pulses to measure the 2PA cross sections in the lowest dipole-allowed transition and show that the substituents with stronger ED or EW character enhance the peak 2PA cross section (up to σ(2) ～ 60-80 GM) while the neutral substituents lead to smaller cross sections, σ(2) < 10 GM. We apply two-level approximation to establish a quantitative relation between the 2PA in the pure electronic transition (0-0) and the corresponding change of the permanent electric dipole moment upon the excitation (Δμ). This relation is elucidated by comparing Δμ values obtained from the 2PA measurements with quantum-chemical calculations and with measurements of solvatochromic shifts in a series of solvents. We show that the calculated Δμ correlate well with the values obtained from the 2PA spectroscopy. The Δμ values obtained from the solvatochromic shifts agree well with the above two methods for the chromophores with neutral or weak EW or ED substituents. On the other hand, stronger EW or ED end groups give much larger Stokes shifts, which lead to an overestimation of the Δμ values. We tentatively attribute this effect to the excitation-induced electronic density change occurring predominantly at the substituent side of the molecule, which causes the effective point dipole associated with the Δμ to interact more strongly with the surrounding solvent.