Asymptotic solutions of the Dirichlet problem for the heat equation at a characteristic point

The Dirichlet problem for the heat equation in a bounded domain G⊂Rn+1 is characteristic because there are boundary points at which the boundary touches a characteristic hyperplane t=c, where c is a constant. For the first time, necessary and sufficient conditions on the boundary guaranteeing that the solution is continuous up to the characteristic point were established by Petrovskii (1934) under the assumption that the Dirichlet data are continuous. The appearance of Petrovskii’s paper was stimulated by the existing interest to the investigation of general boundary-value problems for parabolic equations in bounded domains. We contribute to the study of this problem by finding a formal solution of the Dirichlet problem for the heat equation in a neighborhood of a cuspidal characteristic boundary point and analyzing its asymptotic behavior.Задача Діріхлє для рівняння тєплопровідності в обмеженій області G⊂Rn+1 є характеристичною, оскільки існують граничні точки, в яких границя є дотичною до характеристичної гіперплощини t=c, де c є сталою. I. Г. Петров-ський (1934) уперше встановив необхідні та достатні умови на границю, що гарантують неперервність розв'язку аж до характеристичної точки за умови, що дані Діріхле є неперервними. Поява даної роботи була викликана постійним інтересом до вивчення загальних граничних задач для рівнянь параболічного типу в обмежених областях. Наш внесок у вивчення цієї проблеми полягає в побудові формального розв'язку задачі Діріхле для рівняння теплопровідності в околі гострокінцевої характеристичної граничної точки та дослідженні його асимптотичного характеру

The new analysis of the KLOE data on the phi->eta pi0 gamma decay

In this paper we present the fit to the recent high-statistical KLOE data on the phi -> eta pi^0 gamma decay. This decay mainly goes through the a_0 gamma intermediate state. The obtained results differ from those of the previous fits: data prefer a high a_0 mass and a considerably large a_0 coupling to the K\bar K}.Comment: 11 pages, 2 figure

Database of satellite polarimetry

We present the electronic database (EAR-SA-COMPIL-3-SATPOL-V1.0, NASA Planetary Data System), involving 2355 published and 105 unpublished results in planetary satellite polarimetry. The database contains 2460 measurements of linear polarization of planetary satellites, including fifteen measurements of polarization for the Martian satellites (Phobos and Deimos), 2318 measurements for five Jovian satellites (Io, Europa, Ganymede, Callisto, and Himalia), 127 measurements for two Saturnian satellites (Titan and Iapetus). Broad-band measurements within the spectral region 233-850 nm are presented. The range of phase angles is 0.1°-154° . The geometric conditions of observations (phase angle, planetographic longitude and latitude of the target disk centre seen by the observer, and position angle of the scattering plane) are calculated for given moments of time according to the JPL Horizons ephemeris system. We have compiled nineteen references to the published papers and some unpublished sources. The data are provided in a tabular ASCII format. The database can be used as the observational basis for detailed theoretical modelling, interpretation of the phase-angle and spectral dependence of polarization, and for selecting future space-mission targets

Light Scalar Mesons from Phi to Psi

The following topics are considered. 1) Confinement, chiral dynamics, and light scalar mesons. 2) Chiral shielding of the $\sigma(600)$. 3) The $\phi$ meson radiative decays about nature of light scalar resonances. 4) The $J/\psi$ decays about nature of light scalar resonances. 5) The $a_0(980)\to\gamma\gamma$ and $f_0(980)\to\gamma\gamma$ decays about nature of light scalar resonances. 6) New round in $\gamma\gamma\to\pi^+\pi^-$, the Belle data. Arguments in favor of the four-quark model of the $a_0(980)$ and $f_0(980)$ mesons are given.Comment: 7 pages, 7 figures. Talk presented by N.N. Achasov at the International Workshop "e+e- Collisions from Phi to Psi", February 27--March 2, 2006, BINP, Novosibirsk, Russian Federatio

Polarimetry of Saturnian satellite Enceladus

We present results of polarimetric observations of Saturn's moon Enceladus carried out from April 14, 2010 to April 13, 2013 in WR spectral band (550-750 nm). We used 2.6-m telescope equipped with a one-channel photoelectric photometer-polarimeter (Crimean Astrophysical Observatory). The measurements were performed at phase angles ranging from 1.65° to 5.71°. The phase-angle dependence of linear polarization of Enceladus was obtained using the results of our observations. Results obtained are discussed in terms of existing models of light scattering by regolith surfaces

Polarimetric observations of the Galilean satellites near opposition in 2011

We present results of the new polarimetric observations of the Galilean satellites Io, Ganymede, Europe, and Callisto carried out on October 21 - November 1, 2011. We used 1.25m telescope equipped with the UBVRI double image chopping photoelectric polarimeter, 2.6m Shain telescope equipped with a one-channel photoelectric photometer-polarimeter, 1m RCC telescope equipped with a one-channel photoelectric photometer-polarimeter (Crimean Astrophysical Observatory, Ukraine), and 0.7m telescope equipped with a one-channel photoelectric photometer-polarimeter (Chuguev Observational Station of Astronomical Institute of Karazin Kharkiv National University, Ukraine). The measurements were performed at phase angles ranging from 0.34° to 2.12°. Our new observations fully confirmed the presence of the polarization opposition effect for high-albedo satellites Io, Europa, and Ganymede at phase angles less than 2° . Within the accuracy of the measurements we did not detect the polarization opposition effect for moderate-albedo satellite Callisto

Nonlinear Spin Dynamics in Nuclear Magnets

A method is developed for solving nonlinear systems of differential, or integrodifferential, equations with stochastic fields. The method makes it possible to give an accurate solution for an interesting physical problem: What are the peculiarities of nonlinear spin dynamics in nonequilibrium nuclear magnets coupled with a resonator? Evolution equations for nuclear spins are derived basing on a Hamiltonian with dipole interactions. The ensemble of spins is coupled with a resonator electric circuit. Seven types of main relaxation regimes are found: free induction, collective induction, free relaxation, collective relaxation, weak superradiance, pure superradiance, and triggered superradiance. The initial motion of spins can be originated by two reasons, either by an imposed initial coherence or by local spin fluctuations due to nonsecular dipole interactions. The relaxation regimes caused by the second reason cannot be described by the Bloch equations. Numerical estimates show good agreement with experiment.Comment: 1 file, 47 pages, LaTe

Pioneers of Adsorption Science 3. Professor A. V. Kiselev

A short account is given of the life and work of Andrej Vladimirovich Kiselev (1908–1984). Kiselev was born and educated in Moscow, Russia. He was appointed assistant professor in the M.V. Lomonosov Moscow State University in 1943 and became professor of physical chemistry in 1951. Thereafter, he directed the work of two large groups of research scientists, in laboratories of the M.V. Lomonosov Moscow State University and the Institute of Physical Chemistry of the USSR Academy of Sciences. Kiselev's prodigious research output, over a period of about 30 years, was of great international importance and included theoretical and experimental studies on the specificity of physical adsorption, chromatography and the surface properties of carbons, oxides and zeolites