Formation of a solid solution in the MgSiO3–MnSiO3 perovskite system

Experiments using laser-heated diamond anvil cells combined with synchrotron X-ray diffraction and SEM–EDS chemical analyses have confirmed the existence of a complete solid solution in the MgSiO₃–MnSiO₃ perovskite system at high pressure and high temperature. The (Mg, Mn)SiO₃ perovskite produced is orthorhombic, and a linear relationship between the unit cell parameters of this perovskite and the proportion of MnSiO₃ components incorporated seems to obey Vegard’s rule at about 50 GPa. The orthorhombic distortion, judged from the axial ratios of a/b and \( \sqrt{2}\,a/c, \) monotonically decreases from MgSiO₃ to MnSiO₃ perovskite at about 50 GPa. The orthorhombic distortion in (Mg_0.5, Mn_0.5)SiO₃ perovskite is almost unchanged with increasing pressure from 30 to 50 GPa. On the other hand, that distortion in (Mg_0.9, Mn_0.1)SiO₃ perovskite increases with pressure. (Mg, Mn)SiO₃ perovskite incorporating less than 10 mol% of MnSiO₃ component is quenchable. A value of the bulk modulus of 256(2) GPa with a fixed first pressure derivative of four is obtained for (Mg_0.9, Mn_0.1)SiO₃. MnSiO₃ is the first chemical component confirmed to form a complete solid solution with MgSiO₃ perovskite at the P–T conditions present in the lower mantle.     

Resolution Improvement of Solar Images

A method for the improvement of resolution in an observed solar image is proposed. A blind deconvolution method is used for restoration of an atmospherically-degraded solar image, and a super-resolution method is applied to its restored image to improve the resolution. It is confirmed that a blind deconvolution process can restore fine structures that are blurred in an observed image, and that the super-resolution process can make a cutoff frequency in a blind-deconvolved image higher. A time series of super-resolved images of a sunspot observed with the 70-cm Vacuum Tower Telescope at Teide Observatory is presented.     

15-digit accuracy calculations of Ambartsumian-Chandrasekhar’s $$-functions for four-term phase functions with the double-exponential formula

We have established an iterative scheme to calculate with 15-digit accuracy the numerical values of Ambartsumian-Chandrasekhar’s \(H\)-functions for anisotropic scattering characterized by the four-term phase function: the method incorporates some advantageous features of the iterative procedure of Kawabata (Astrophys. Space Sci. 358:32, 2015) and the double-exponential integration formula (DE-formula) of Takahashi and Mori (Publ. Res. Inst. Math. Sci. Kyoto Univ. 9:721, 1974), which proved highly effective in Kawabata (Astrophys. Space Sci. 361:373, 2016). Actual calculations of the \(H\)-functions have been carried out employing 27 selected cases of the phase function, 56 values of the single scattering albedo \(\varpi_{0}\), and 36 values of an angular variable \(\mu(= \cos\theta)\), with \(\theta\) being the zenith angle specifying the direction of incidence and/or emergence of radiation. Partial results obtained for conservative isotropic scattering, Rayleigh scattering, and anisotropic scattering due to a full four-term phase function are presented. They indicate that it is important to simultaneously verify accuracy of the numerical values of the \(H\)-functions for \(\mu<0.05\), the domain often neglected in tabulation. As a sample application of the isotropic scattering \(H\)-function, an attempt is made in Appendix to simulate by iteratively solving the Ambartsumian equation the values of the plane and spherical albedos of a semi-infinite, homogeneous atmosphere calculated by Rogovtsov and Borovik (J. Quant. Spectrosc. Radiat. Transf. 183:128, 2016), who employed their analytical representations for these quantities and the single-term and two-term Henyey-Greenstein phase functions of appreciably high degrees of anisotropy. While our results are in satisfactory agreement with theirs, our procedure is in need of a faster algorithm to routinely deal with problems involving highly anisotropic phase functions giving rise to near-conservative scattering.