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Significant interest in the investigation of systems with discontinuous trajectories is explained by the development of equipment in which significant role is played by impulsive control systems and impulsive computing systems. Impulsive systems are also encountered in numerous problems of natural sciences described by mathematical models with conditions reflecting the impulsive action of external forces with pulses whose duration can be neglected. Differential equations with set-valued right-hand side arise in the investigation of evolution processes in the case of measurement errors, inaccuracy or incompleteness of information, action of bounded perturbations, violation of unique solvability conditions, etc. Differential inclusions also allow one to describe the dynamics of controlled processes and are widely used in the theory of optimal control. This monograph is devoted to the investigation of impulsive differential equations with set-valued and discontinuous right-hand sides. It is intended for researchers, lecturers, postgraduate students, and students of higher schools specialized in the field of the theory of differential equations, the theory of optimal control, and their applications.
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In this book, a distinguished expert introduces plasma physics from the ground up, presenting it as a comprehensible field that can be grasped largely on the basis of physical intuition and qualitative reasoning, similar to other fields of physics. Plasmas are ionized gases that can be found in a hydrogen bomb explosion, the confinement chamber of an experimental fusion reactor, the solar corona, the aurora borealis, the interstellar medium, and the immediate vicinity of a gravitational black hole. Not surprisingly, plasma physics appears to consist of numerous topics arising independently from astrophysics, fusion physics, and other practical applications, and hence it remains a field poorly understood even by many astrophysicists. But, in fact, most of these topics can be approached from the same perspective, with a simple, physical intuition. Selecting simple examples and presenting them in a simultaneously intuitive and rigorous manner, Russell Kulsrud guides readers through a careful derivation of the results and allows them to think through the physics for themselves. Thus, they are better prepared for complex cases and more general results. The first eleven chapters present topics by their importance to plasma physics while the last three chapters emphasize the field's astrophysical applications, applying the results accrued earlier. Throughout, many problems illustrate the field's applications. Based on a course the author taught for many years, Plasma Physics for Astrophysics is intended for graduate students as well as for working astrophysicists.
Plasma astrophysics. --- Accretion disk. --- Alfven time. --- Bessel function. --- Braginski equations. --- Charge neutrality. --- Compression. --- Contour integration. --- Critical drift velocity. --- Dalembertian solution. --- Debye length. --- Downstream region. --- Earth's magnetic field. --- Entropy. --- Faraday rotation. --- Flux freezing. --- Guide field. --- Helicity spectrum. --- Impact parameter. --- Ion acoustic mode. --- Jump conditions. --- Laplace transform. --- Magnetic reconnection. --- Magnetic tension. --- Maxwell distribution. --- Ohm's law. --- Parallel viscosity. --- Quasi neutrality. --- Shocks. --- Solar flare. --- Topology.
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