Sophia University

About: Sophia University is a education organization based out in Tokyo, Japan. It is known for research contribution in the topics: Nonlinear system & Catalysis. The organization has 4986 authors who have published 7657 publications receiving 106567 citations. The organization is also known as: Jōchi Daigaku.

Discontinuous Dynamical Systems

Abstract: This chapter discusses analysis and design problems of discontinuous dynamic systems represented by differential equations with discontinuous right-hand side. After a brief review of discontinuous dynamic systems, which is summarized in Section 16.1, Filippov framework including solution and some analyzing tools for control system design is explained in Section 16.2. Furthermore, a feedback design problem is investigated in Section 16.3 for a class of nonlinear systems which have cascaded structure. Section 16.4 demonstrates an application example of stability analysis for PD controlled mechanical systems.

The Second Born Corrections to the Electrical and Thermal Conductivities of Dense Matter in the Liquid Metal Phase

Abstract: The second Born corrections to the electrical and thermal conductivities are calculated for the dense matter in the liquid metal phase for various elemental compositions of astrophysical importance. Inclusion up to the second Born corrections is sufficiently accurate for the Coulomb scattering of the electrons by the atomic nuclei with Z 26. Our approach is semianalytical and is in contrast to that of the previous authors who have used fully numerical values of the cross section for the Coulomb scattering of the electron by the atomic nucleus. The merit of the present semianalytical approach is that this approach allows us to obtain the results with a reliable Z dependence and ρ dependence. The previous fully numerical approach has made use of the numerical values of the cross section for the scattering of the electron off the atomic nucleus for a limited number of Z-values, Z = 6, 13, 29, 50, 82, and 92, and for a limited number of electron energies, 0.05, 0.1, 0.2, 0.4, 0.7, 1, 2, 4, and 10 MeV. Our study, however, has confirmed that the previous results are sufficiently accurate. They are recovered if the terms higher than the second Born terms are taken into account. We make a detailed comparison of the present results with those of the previous authors. The numerical results are parameterized in the form of analytic formulae that would facilitate practical use of the results. We also extend our calculations to the case of mixtures of nuclear species.