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Throughout his life Lewis Fry Richardson made many inspirational
contributions to various disciplines. Often his ideas were ahead of
contemporary thinking, and preceded the technical means necessary
for their practical implementation. He is best known for his wealth
of important work on meteorology, and his groundbreaking
application of mathematics to the causes of war, though his field
of interest was in no way limited to these topics, and various
aspects of psychology and mathematical approximation also benefited
from his unique approach. The originality of Richardson's research
can be seen in this collection of all his important papers in the
behavioural sciences.
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 in linear algebra, advanced calculus, elementary theory of ordinary differntial equations, complex variable and the elements of fluid mechanics. The book is aimed at graduate students, but is very useful for specialists in other fields.
A coherent treatment of nonlinear systems covering chaos, fractals, and bifurcation, as well as equilibrium, stability, and nonlinear oscillations. The systems treated are mostly of difference and differential equations. The author introduces the mathematical properties of nonlinear systems as an integrated theory, rather than simply presenting isolated fashionable topics. The topics are discussed in as concrete a way as possible, worked examples and problems are used to motivate and illustrate the general principles. More advanced parts of the text are denoted by asterisks, thus making it ideally suited to both undergraduate and graduate courses.
A 'soliton' is a localized nonlinear wave of permanent form which
may interact strongly with other solitons so that when they
separate after the interaction they regain their original forms.
This textbook is an account of the theory of solitons and of the
diverse applications of the theory to nonlinear systems arising in
the physical sciences. The essence of the book is an introduction
to the method of inverse scattering. Solitary waves, cnoidal waves,
conservation laws, the initial-value problem for the Korteweg-de
Vries equation, the Lax method, the sine-Gordon equation and
Backlund transformations are treated. The book will be useful for
research workers who wish to learn about solitons as well as
graduate students in mathematics, physics and engineering.
This book begins with a basic introduction to three major areas of hydrodynamic stability: thermal convection, rotating and curved flows, and parallel shear flows. There follows a comprehensive account of the mathematical theory for parallel shear flows. A number of applications of the linear theory are discussed, including the effects of stratification and unsteadiness. The emphasis throughout is on the ideas involved, the physical mechanisms, the methods used, and the results obtained. Wherever possible, the theory is related to both experimental and numerical results. A distinctive feature of the book is the large number of problems it contains. These problems (for which hints and references are given) not only provide exercises for students but also provide many additional results in a concise form.
The Navier-Stokes equations were firmly established in the 19th
Century as the system of nonlinear partial differential equations
which describe the motion of most commonly occurring fluids in air
and water, and since that time exact solutions have been sought by
scientists. Collectively these solutions allow a clear insight into
the behavior of fluids, providing a vehicle for novel mathematical
methods and a useful check for computations in fluid dynamics, a
field in which theoretical research is now dominated by
computational methods. This 2006 book draws together exact
solutions from widely differing sources and presents them in a
coherent manner, in part by classifying solutions via their
temporal and geometric constraints. It will prove to be a valuable
resource to all who have an interest in the subject of fluid
mechanics, and in particular to those who are learning or teaching
the subject at the senior undergraduate and graduate levels.
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 in linear algebra, advanced calculus, elementary theory of ordinary differntial equations, complex variable and the elements of fluid mechanics. The book is aimed at graduate students, but is very useful for specialists in other fields.
Solitons: An Introduction discusses the theory of solitons and its diverse applications to nonlinear systems that arise in the physical sciences. Drazin and Johnson explain the generation and properties of solitons, introducing the mathematical technique known as the Inverse Scattering Tranform. Their aim is to present the essence of inverse scattering clearly, rather than rigorously or completely. Thus, the prerequisites are merely what is found in standard courses on mathematical physics and more advanced material is explained in the text with useful references to further reading given at the end of each chapter. Worked examples are frequently used to help the reader follow the various ideas and the exercises at the end of each chapter not only contain applications but also test understanding. Answers, or hints to their solution, are given at the end of the book. Sections and exercises that contain more difficult material are indicated by asterisks.
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