This work presents the concepts, methods and applications of kinetic theory to rarefied gas dynamics. After introducing the basic tools, Carlo Cercignani treats problems in plane geometry using all the approximation techniques. He later uses these same techniques to deal with two- and three-dimensional problems. The models include not only monatomic but also polyatomic gases, mixtures, chemical reactions. A special chapter is devoted to evaporation and condensation phenomena. Each section is accompanied by helpful problems. The book can be used in a range of graduate courses in aerospace...

This work presents the concepts, methods and applications of kinetic theory to rarefied gas dynamics. After introducing the basic tools, Carlo Cercignani treats problems in plane geometry using all the approximation techniques. He later uses these same techniques to deal with two- and three-dimensional problems. The models include not only monatomic but also polyatomic gases, mixtures, chemical reactions. A special chapter is devoted to evaporation and condensation phenomena. Each section is accompanied by helpful problems. The book can be used in a range of graduate courses in aerospace...

High Speed Flow covers subsonic and supersonic flight, shock waves, high-speed aerofoils, and temperature changes. Starting from first principles, the book gives complete and elementary derivations of all results, and takes the reader to research level in the subject. C.J. Chapman includes many exercises and an extensive bibliography, providing access to the entire literature from 1860 to the present, with over two hundred items published since 1990. An extensive set of formulae on thermodynamics and oblique shock waves is also included.

Astronomers have long noted that the Earth does not rotate uniformly about an axis fixed in the planet, that both the length-of-day and the direction of the rotation axis vary periodically and irregularly by small amounts. These variations are an immediate consequence of the Earth not being a rigid body. In this book Professor Lambeck discusses the irregular nature of this motion and the geophysical mechanisms responsible for it. A complete analysis of these causes requires a discussion of solid Earth physics, magnetohydrodynamics, oceanography and meteorology. The study of the Earth's...

Instability of flows and their transition to turbulence are widespread phenomena in engineering and the natural environment. They are important in applied mathematics, astrophysics, biology, geophysics, meteorology, oceanography, physics, and engineering. This is a graduate-level textbook to introduce these phenomena by modeling them mathematically, and describing numerical simulations and laboratory experiments. The visualization of instabilities is emphasized with many figures. Many worked examples and exercises for students illustrate the ideas of the text. Readers are assumed to be fluent...

This is the first comprehensive introduction to collocation methods for the numerical solution of initial-value problems for ordinary differential equations, Volterra integral and integro-differential equations, and various classes of more general functional equations. It guides the reader from the "basics" to the current state-of-the-art level of the field, describes important problems and directions for future research, and highlights methods. The analysis includes numerous exercises and applications to the modelling of physical and biological phenomena.

Jon Lee focuses on key mathematical ideas leading to useful models and algorithms, rather than on data structures and implementation details, in this introductory graduate-level text for students of operations research, mathematics, and computer science. The viewpoint is polyhedral, and Lee also uses matroids as a unifying idea. Topics include linear and integer programming, polytopes, matroids and matroid optimization, shortest paths, and network flows. Problems and exercises are included throughout as well as references for further study.

This book describes the remarkable connections that exist between the classical differential geometry of surfaces and modern soliton theory. The authors also explore the extensive body of literature from the nineteenth and early twentieth centuries by such eminent geometers as Bianchi, Darboux, Backlund, and Eisenhart on transformations of privileged classes of surfaces which leave key geometric properties unchanged. Prominent amongst these are Backlund-Darboux transformations with their remarkable associated nonlinear superposition principles and importance in soliton theory.

Providing a basic foundation for advanced graduate study and research in the mechanics of solids, this treatise develops systematically the fundamentals of finite inelastic deformations of heterogeneous materials. The book combines the mathematical precision of solid mechanics with the physics-based micro-structural knowledge of materials science, presenting a coherent picture of finite inelastic deformation of single and polycrystalline metals.

Many practical applications require the reconstruction of a multivariate function from discrete, unstructured data. This book gives a self-contained, complete introduction into this subject. It concentrates on truly meshless methods such as radial basis functions, moving least squares, and partitions of unity. The book starts with an overview on typical applications of scattered data approximation, coming from surface reconstruction, fluid-structure interaction, and the numerical solution of partial differential equations. It then leads the reader from basic properties to the current state of...