A fundamental solution due to a periodic point force in the interior of an elastic half-space

The fundamental solution for a periodic point force in the interior of a three-dimensional, homogeneous, isotropic, elastic half-space is derived. The method of synthesis and superposition is employed to obtain the solution in the Laplace transform as well as the frequency domain. These correspond to the dynamic equivalent of Mindlin's static half-space point force solutions. It is reduced, for certain limiting conditions, to the dynamic equivalent of Boussinesq's and Cerruti's problems of a normal and tangential periodic point force respectively, on the boundary of a half-space. Also, static solutions of Mindlin, Boussinesq and Cerruti are recovered for small frequency parameters. Finally, results are presented and compared with other available solutions.     

Possible Evidence of Long-Term Oscillations in the Solar Atmosphere

We have obtained the temporal correlation function, Q(t), from time sequences of Caii K filtergrams and Dopplergrams from Antarctica, Taiwan Oscillation Network (TON) and Solar and Heliospheric Observatory (SOHO). Q(t) gives the time evolution of the pattern under examination, supergranulation in this case. It has been found that Q(t) shows oscillatory signals of both 5-min and long-term periods. The 5-min oscillations are suppressed by averaging the images over 10 min. An exponential decay curve which represents the lifetime trend of supergranules, is fitted to Q(t) and subtracted out. The Q(t) residuals thus obtained contain the oscillatory component and are then subjected to a periodogram analysis. Significant periodicities in the range of 1.4–10 hours have been noted. The causes of these oscillations are not fully known at present, but the instrumental and atmospheric factors can be ruled out, pointing to solar origin. Various possibilities are discussed. Some of the observed periodicities may be considered as probable candidates for long-term oscillations in the Sun, such as the elusive gravity modes.     

Persistent 22-year cycle in sunspot activity: Evidence for a relic solar magnetic field

We use the recently presented group sunspot number series to show that a persistent 22-year cyclicity exists in sunspot activity throughout the entire period of about 400 years of direct sunspot observations. The amplitude of this cyclicity is about 10% of the present sunspot activity level. A 22-year cyclicity in sunspot activity is naturally produced by the 22-year magnetic polarity cycle in the presence of a relic dipole magnetic field. Accordingly, a persistent 22-year cyclicity in sunspot activity gives an evidence for the existence of such a relic magnetic field in the Sun. The stable phase and the roughly constant amplitude of this cyclicity during times of very different sunspot activity level strongly support this interpretation.     

Investigation of Barred Galaxies. VII. Comparative Statistics of SB and SA Galaxies. Near and Mid-IR Regions

The near and mid-IR properties of barred and unbarred spiral galaxies are discussed on the basis of complete samples that were compiled earlier. The two types of spirals are shown not to differ from one another in emission power in the near and mid-IR ranges. Multiple regression and principal component analysis have been applied to investigate near and mid-IR properties of SB and SA galaxies, particularly their relation to X-ray and radio continuum emissions. There are definite differences between SB and SA spirals in the near and mid-IR. In the case of SB galaxies, the compactness of 10 m emission is closely related to the J - H color index, and the redder J - H color corresponds to relatively more extended emission at 10 m. It is assumed that these are caused by the bar itself, which stimulates enhanced star formation in a barred galaxy with respect to unbarred spiral.     

A Negative Branch of Polarization for Comets and Atmosphereless Celestial Bodies and the Light Scattering by Aggregate Particles

Optical observations of comets and atmosphereless celestial bodies show that a change of sign of the linear polarization of scattered light from negative to positive at phase angles less than 20° is typical of the cometary coma, as well as of the regolith of Mercury, the Moon, planetary satellites, and asteroids. To explain a negative branch of polarization, this research suggests a unified approach to the treatment of cometary-dust particles and regolith grains as aggregate forms. A composite structure of aggregate particles resulting in the interaction of composing structural elements (monomers) in the light-scattering process is responsible for the negative polarization at small phase angles, if the monomer sizes are comparable to the wavelength. The characteristics of single scattering of light calculated for aggregates of this kind turned out to be close to the properties observed for cometary dust. Unlike the cometary coma, the regolith is an optically semi-infinite medium, where the interaction between particles is significant. To find the reflectance characteristics of regolith, the radiative-transfer equation should be solved for a regolith layer. In this case, the interaction between scatterers can be modeled to a certain extent by representing the regolith grains as aggregate structures consisting of several or many elements. Although real regolith grains are much larger than the particles considered here, laboratory measurements have shown that it is precisely the surface irregularities comparable to the wavelength that cause a negative branch of polarization. The main observed features of the phase and spectral dependence of the linear polarization of light scattered from comets and atmosphereless celestial bodies, which are due to the difference of the elementary scatterers in composition, size, and structure, can be successfully explained using the aggregate model of particles.     

Did Predictions of the Maximum Sunspot Number for Solar Cycle 23 Come True?

For solar cycle 23, the maximum sunspot number was predicted by several workers, and the range was very wide, 80–210. Cycle 23 started in 1996 and seems to have peaked in 2000, with a smoothed sunspot number maximum of 122. From about 20 predictions, 8 were within 122±20. There is an indication that a long-term oscillation of 80–100 years may be operative and might have peaked near cycle 20 (1970), and sunspot maxima in cycles in the near future may be smaller and smaller for the next 50 years or so and rebound thereafter in the next 50 years or so.