Pulsation theory is discussed in light of recent improvements in the theory of radiative transfer and hydrodynamics with applications to Cepheids, RR Lyrae, and W Virginis stars.

Covering both radial and nonradial oscillations, this book includes not only a thorough treatment of the basic theory of stellar pulsation but also a comprehensive synthesis of the most recent work done in this area. Originally published in 1980. The Princeton Legacy Library uses the latest print-on-demand technology to again make available previously out-of-print books from the distinguished backlist of Princeton University Press. These editions preserve the original texts of these important books while presenting them in durable paperback and hardcover editions. The goal of the Princeton Legacy Library is to vastly increase access to the rich scholarly heritage found in the thousands of books published by Princeton University Press since its founding in 1905.

This book discusses analytic and asymptotic methods relevant to radiative transfer in dilute media, such as stellar and planetary atmospheres. Several methods, providing exact expressions for the radiation field in a semi-infinite atmosphere, are described in detail and applied to unpolarized and polarized continuous spectra and spectral lines. Among these methods, the Wiener–Hopf method, introduced in 1931 for a stellar atmospheric problem, is used today in fields such as solid mechanics, diffraction theory, or mathematical finance. Asymptotic analyses are carried out on unpolarized and polarized radiative transfer equations and on a discrete time random walk. Applicable when photons undergo a large number of scatterings, they provide criteria to distinguish between large-scale diffusive and non-diffusive behaviors, typical scales of variation of the radiation field, such as the thermalization length, and specific descriptions for regions close and far from boundaries. Its well organized synthetic view of exact and asymptotic methods of radiative transfer makes this book a valuable resource for both graduate students and professional scientists in astrophysics and beyond.

This tract gives a simple but rigorous treatment of some of the mathematical problems that arise in the theory of the transfer of radiation through the atmosphere of a star. Similar problems occur in the theory of the diffusion of neutrons and in the study of temperature-wave flow in solids; so the solutions found in one theory can often be applied in the others. Dr Busbridge's starting-point is the equation of transfer. The first section provides the auxiliary mathematics, and the second discusses the Milne equations. Some unsolved and incompletely solved problems are considered in an appendix. The language and notation of astrophysics is used throughout, for brevity and simplicity, but translation into other notations is usually fairly easy. Over the years the subject had grown considerably, and several outstanding problems have been solved, though the total amount of rigorous work is small. This tract will help to clear up confusions which exist and will provide an introduction to some of the more powerful mathematical techniques available.

Radiative transfer theory describes the interaction of radiation with scattering and absorbing media. It has applications in neutron transport, atmospheric physics, heat transfer, molecular imaging, and so on. In steady state, the radiative transfer equation is an integro-differential equation of five independent variables. This high dimensionality and presence of integral term present a serious challenge when one tries to solve the equation numerically. Over the past 50 years, several techniques for solving the radiative transfer equation have been introduced. One among them is to use approximations of RTE. Various approximations of RTE have been proposed in the literature. These include, but are certainly not limited to, the delta-Eddington approximation, the Fokker-Planck approximation, the Boltzmann-Fokker-Planck approximation, the generalized Fokker-Planck approximation, the Fokker-Planck-Eddington approximation and the generalized Fokker-Planck-Eddington approximation. The Fokker-Planck approximation and differential approximation have received particular attention in the literature due to their relatively high accuracy, relatively low computational cost, and flexibility to potential large scale parallel computing. In this thesis we present a well-posed result for the Fokker-Planck equation that may be used to approximate the radiative transfer equation in highly forward-peaked media. Then we study the differential approximation of radiative transfer (RT/DA) equations. Well-posedness of these approximations is studied. A convergent iteration method for the RT/DA equation is presented. Then we turn to a study of RT/DA based inverse problems. The inverse problems are ill-posed and regularization is needed in solving the inverse problems. We present an existence result for solutions of regularized formulations of the inverse problems. Finally examples are included to illustrate numerical results in solving the inverse problems.

Covering both radial and nonradial oscillations, this book includes not only a thorough treatment of the basic theory of stellar pulsation but also a comprehensive synthesis of the most recent work done in this area. Originally published in 1980. The Princeton Legacy Library uses the latest print-on-demand technology to again make available previously out-of-print books from the distinguished backlist of Princeton University Press. These editions preserve the original texts of these important books while presenting them in durable paperback and hardcover editions. The goal of the Princeton Legacy Library is to vastly increase access to the rich scholarly heritage found in the thousands of books published by Princeton University Press since its founding in 1905.

The authors expound on non-traditional phenomena for transfer theory, which are nevertheless of considerable interest in wave measurements, and bring the advances of transfer theory as close as possible to the practical needs of those working in all areas of wave physics. The book opens with a historical overview of the topic, then moves on to examine the phenomenological theory of radiative transport, blending traditional theory with original ideas. The transport equation is derived from first principles, and the ensuing discussion of the diffraction content of the transport equation and non-classical radiometry is illustrated by practical examples from various fields of physics. Popular techniques of solving the transport equation are discussed, paying particular attention to wave physics and computing the coherence function. The book also examines various problems which are no longer covered by the traditional radiative transfer theory, such as enhanced backscattering and weak localization phenomena, nonlinear transport problems and kinetic equations for waves. This monograph bridges the gap between the simple power balance description in radiative transfer theory and modern coherence theory. It will be of interest to researchers and professionals working across a wide range of fields from optics, acoustics and radar theory to astrophysics, radioastronomy and remote sensing, as well as to students in these areas.