Global Analysis of the Flows of Fluids with Pressure-Dependent Viscosities

 To describe the flows of fluids over a wide range of pressures, it is necessary to take into account the fact that the viscosity of the fluid depends on the pressure. That the viscosity depends on the pressure has been verified by numerous careful experiments. While the existence of solutions local-in-time to the equations governing the flows of such fluids are available for small, special data and rather unrealistic dependence of the viscosity on the pressure, no global existence results are in place. Our interest here is to establish the existence of weak solutions for spatially periodic three-dimensional flows that are global in time, for a large class of physically meaningful viscosity-pressure relationships. (Accepted May 1, 2002) Published online November 15, 2002 Communicated by S. S. ANTMAN     

DNA Effect on Cis–Trans Equilibrium and Fluorescent Properties of 3,3′-Diethyl-9-thiomethylthiacarbocyanine Iodide in Aqueous Solution

The influence of DNA on the cis–trans equilibrium and fluorescent properties of 3,3-diethyl-9-thiomethylthiacarbocyanine iodide (DTTC) in a phosphate buffer (pH 7) was studied by various photochemical techniques. The interaction of dye molecules with DNA leads to the formation of stable noncovalently bonded complexes. Data obtained from DTTC absorption and fluorescence spectra suggest that complexation proceeds primarily through the cis-form of the dye. Complexation with DNA leads to a substantial increase in the quantum yield of the triplet state of DTTC molecules. The rate constant for quenching the dye triplet state by oxygen turned out to be significantly lower than the diffusion-controlled value.     

Study of the absorption spectra and ionic equilibria of cationic-anionic polymethine dyes

The absorption spectra of a number of cationic-anionic polymethine dyes in polar, low-polarity, and nonpolar solvents were studied. It was established that in polar solvents the absorption spectra represent the sum of the absorption spectra of the cation and anion, whereas in nonpolar and low-polarity solvents, in many cases the appearance of a short-wave absorption band is observed, due to interaction of the chromophores of the cation and anion in ion pairs. In solvents of intermediate polarity (for example, in chloroform and ethyl acetate), a concentration dependence of the absorption spectra is observed, determined by the equilibria of ionic dissociation. The ionic dissociation constants of a number of cationic-anionic dyes in chloroform and ethyl acetate were determined by a conductometric method. The thermodynamic data obtained are compared with the spectral data.N. N. Semenov Institute of Chemical Physics, Russian Academy of Sciences, 117977 Moscow. Translated fromIzvestiya Akademii Nauk, Seriya Khimicheskaya, No. 11, pp. 2524–2532, November, 1992.     

Hydrogen transfer from ketyl radicals to nitroxyl radicals

The transfer of an H atom from a ketyl radical (KR) to a nitroxyl radical is the sole reaction occurring between benzophenone or acetone KR and nitroxyl radicals (NR). The rate constants (k_H) of the reaction of the KR of substituted benzophenones with the NR-4-hydroxy-2,2,6,6-tetramethylpiperidine-1oxyl and 4-oxo-2,2,6,6-tetramethylpiperidine-1-oxyl in various solvents were measured by the pulse photolysis method. In low-viscosity solvents (up to 1-2 cP), the values of k_H are not limited by the diffusion of the reagents. The k_H values decrease with increase in the Hammet's -constants of the substituents in the KR and with decrease in the reduction potential of the NR, which indicates a charge transfer from the KR to NR in the transition state of the reaction. A cyclic structure was proposed for the transition state. The reaction is characterized by a low isotopic effect (k_H/k_D=1.4–1.5). The dependence of log k_H on the solvation parameter of the solvent E_t(30) is V-shaped in character.Translated from Izvestiya Akademii Nauk SSSR, Seriya Khimicheskaya, No. 5, pp. 999–1003, May, 1990.     

Cis-trans-isomerization of cationic-anionic polymethine dyes

The effect of solvent polarity and ion pair formation oncis-trans-isomerization of cationic-anionic polymethine dyes and of related simple cationic and anionic dyes is studied by flash photolysis. The change in the rate constant for reversecis-trans- isomerization of photoisomers due to the interaction of a cation with an anion in an ion pair is observed in nonpolar solvents. A drop in the yield of the photoisomers to zero is observed for a number of cationic-anionic dyes in weakly polar and nonpolar solvents which is possibly due to steric hindrances in the photoisomerization process in ion pairs.Translated fromIzvestiya Akademii Nauk. Seriya Khimicheskaya, No. 4, pp. 719–724, April, 1993.     

Energy transfer in the course of triplet state quenching of aromatic hydrocarbons by nitroxyl radicals

Quenching of triplet states of aromatic hydrocarbons by nitroxyl radicals has been investigated by the flash photolysis method. There are two different mechanisms of triplet quenching: quenching occurs via enhanced intersystem crossing on exchange interaction with the radical for the triplet states of aromatic hydrocarbons which have low triplet energy (E_T < 14700 cm^?1); for very high triplet energies, energy transfer from the triplet molecule to the nitroxyl radical occurs. The energy of the excited nitroxyl radical was estimated to be 18000 cm^?1.     

Synthesis,spectral properties,and conformations of nonlinear cross-conjugated polyenes containing pyrane or dihydropyridine fragment

New cross-conjugated ω,ω′-dimethylaminopolyenes containing the central pyrane or N-methyldihydropyridine fragment were synthesized. In new compounds, the interaction of the aminopolyene chromophores occurs through the dicyanomethylidene, 1-cyano-1-(4-nitrophenyl)methylidene, or 1,3-dioxoindan-2-ylidene groups in position 4 of the heterocycle. The conformation of the synthesized compounds was determined by 2D ¹H NMR spectroscopy (NOESY and ROESY): the chromophores are arranged at an acute or obtuse angle in the structures with the pyrane or dihydropyridine fragment, respectively. The conformational differences in polyenes result in a drastic change in their spectral properties: for the dyes with an acute angles between the chromophores, the long-wavelength absorption band is less intense, as a rule, than the shorter-wavelength band, while the situation is opposite for the compounds with an obtuse angle. The absorption spectra of the synthesized compounds with dinitrile and other acceptor groups lie in a longer-wavelength region than the absorption spectra of the corresponding compounds with carbonyl acceptor groups. The central bridging substituent NMe decreases the energy of interaction of the chromophores.     

<Emphasis Type="Italic">meso</Emphasis>-substituted polymethine dyes as efficient spectral and fluorescent probes for biomacromolecules

It is shown that meso-substituted polymethine dyes are promising spectral and fluorescent probes for biomacromolecules. Some dyes are recommended for application in real biological objects and were used for analysis of extracellular media of the eye.     

Guided modes of integrated optical guides. A mathematical study

A waveguide in integrated optics is defined by its refractiveindex. The guide is assumed to be invariant in the propagationdirection while in the transverse direction it is supposed tobe a compact perturbation of an unbounded stratified medium.We are interested in the modes guided by this device, whichare waves with a transverse energy confined in a neighbourhoodof the perturbation. Our goal is to analyse the existence of such guided modes. Underthe assumptions of weak guidance the problem reduces to a two-dimensionaleigenvalue problem for a scalar field. The associated operatoris unbounded, selfadjoint, and bounded from below. Its spectrumconsists of the discrete spectrum corresponding to the guidedmodes and of the essential spectrum corresponding to the radiationmodes. We present existence results of guided modes and an asymptoticstudy at high frequencies, which shows that contrarily to thecase of optical fibers, the number of guided modes can remainbounded. The major tools are the min-max principle and comparisonof results between different eigenvalue problems. The originalityof the present study lies in the stratified character of theunbounded reference medium.