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In the present work, a compact, fast, and yet accurate algorithm is developed to calculate the numerical values of the Ambartsumian-Chandrasekhar's H -function for isotropic scattering and its moments on the basis of the double exponential (DE) formula of Takahashi and Mori (RIMS, Kyoto Univ., 9:721, 1974). The main improvement made in the new method is an elimination of the iterative procedure for automatic adjustment of the step-size of integrations carried out with the DE-formula. Instead, a set of optimal values for the upper limit of integration T max and the number of division points N T to specify the step-size of the quadrature is predetermined for calculations of the H -function with a 15-digit accuracy, and also another for the evaluations of the moments with an accuracy of 14-digits or better. FORTRAN90 subroutines HFISCA for the H -function and HFMOMENT for the moments of arbitrary degrees are subsequently constructed (their source codes and a driver together with a sample set of output are shown in Appendix of this paper). Tables of sample calculations of the H -function and its moments of degree −1 through 6 carried out by these programs are also presented. The routines HFISCA and HFMOMENT should prove useful not only in astrophysical applications but also in other disciplines of science such as the electron transports in condensed matter and remote-sensing data analyses. A request for a copy of the Fortran 90 source code of the program can be made by writing to kawabata@rs.kagu.tus.ac.jp. [ABSTRACT FROM AUTHOR]

In this paper uniform convergences of the two-dimensional exponential integral functions are investigated. We also study the continuity, integrability and asymptotic behaviour of these functions. [ABSTRACT FROM AUTHOR]

The time-evolution of polymer spherulite formation in the melt was investigated by Hv light scattering. The Hv scattering gives both the 'four-leaf clover pattern' and isotropic scattering independent of azimuthal angle. The isotropic scattering from spherulites of isotactic polystyrene is measured over a wide range of crystallization: from bundles to a matured spherulite. Correlation length is obtained from the isotropic scattering. In the early stage of spherulite growth, the correlation length increases in proportion to crystallization time and reaches maximum value of about 1 µm. Hence, the isotropic scattering is attributed to the bundles. The correlation length is the size of the bundles. The bundles grow and successively evolve to spherulites by branching. In the late stage, a matured spherulite grows. However, the correlation length decreases to a value of about 0.6 µm and remains unchanged. By re-examination of the lattice model of Yoon and Stein, the model is found applicable to matured spherulites. The correlation length in matured spherulites is suggested to be the distance between branches of a bundle. The length agrees to a distance between screw dislocations in a crystal grown from the polymer melt. [ABSTRACT FROM AUTHOR]

The effect of isotropic scattering in a two‐phase zone on the velocity of boundaries, thickness of the transitional zone, and distribution of the solid phase over the two‐phase zone thickness in the course of solidification of a semitransparent material is considered. A generalized model of phase transition in a semitransparent medium is used. The results of numerical calculations show that radiation scattering can exert a significant effect on the structure and size of the two‐phase zone and also on heat transfer (temperature gradient) in the crystal being formed. [ABSTRACT FROM AUTHOR]