Stephen H. Davis

Theory of Solidification

Cambridge Monographs on Mechanics

Description

The processes of freezing and melting were present at the beginnings of the Earth and
continue to dominate the natural and industrial worlds. The solidification of a liquid or the
melting of a solid involves a complex interplay of many physical effects. This book presents in a
systematic way the field of continuum solidification theory based on instability
phenomena. An understanding of the physics is developed by using examples of increasing
complexity with the object of creating a deep physical insight applicable to more complex
problems. Applied mathematicians, engineers, physicists, and materials scientists will all find
this volume of interest.

Chapter Contents

1. Introduction; 2. Pure substances; 3. Binary substances; 4. Nonlinear theory for directional
solidification; 5. Anisotrophy; 6. Disequilibrium; 7. Dendrites; 8. Eutectics; 9. Microscale fluid flow;
10. Mesoscale fluid flow; 11. Phase-field models.

ISBN: 0-521-65080-1
Binding: Hardback
Pages: 350
Figures: 242 line diagrams 32
half-tones 4 tables

Edited by Peter Harman, Simon Mitton

Cambridge Scientific Minds

Description

Since the 'scientific revolution' of the seventeenth century, a great number of distinguished
scientists and mathematicians have been associated with the University of Cambridge.
Cambridge Scientific Minds provides a portrait of some of the most eminent scientists associated
with the University over the past 400 years, including accounts of the work of three of the
greatest figures in the entire history of science, Isaac Newton, Charles Darwin and James Clerk
Maxwell. The chronological balance reflects the increasing importance of science in the recent
history of the University. The book comprises personal memoirs and historical essays,
including contributions by leading Cambridge scientists. Cambridge Scientific Minds will be of
interest not only to graduates of the University, science students and historians of science, but to
anyone wishing to gain an insight into some of the greatest scientific minds in history.

Chapter Contents

Introduction Peter Harman; 1. William Gilbert Stephen Pumfrey; 2. William Harvey Andrew
Cunningham; 3. Isaac Newton Rupert Hall; 4. William Whewell Richard Yeo; 5. Adam Sedgwick
David Oldroyd; 6. Charles Babbage Anthony Hyman; 7. Charles Darwin Peter Bowler; 8.
Stokes and Kelvin David Wilson; 9. James Clerk Maxwell Simon Schaffer; 10. Russell and
Whitehead Ivor Grattan-Guinness; 11. Thomson and Rutherford Brian Pippard; 12. Gowland
Hopkins Harmke Kamminga; 13. Sherrington and Adrian Tilli Tansey; 14. Hardy and Littlewood
Robin Wilson; 15. Arthur Eddington Malcolm Longair; 16. Paul Dirac Helge Kragh; 17. Alan
Turing Andrew Hodges; 18. Crick and Watson Robert Olby; 19. Mary Cartwright Tom Kvrner; 20.
Joseph Needham Gregory Blue; 21. Molecular Biology Max Perutz; 22. Radioastronomy Antony
Hewish; 23. Stephen Hawking Simon Mitton.

ISBN: 0-521-78100-0
Binding: Hardback
ISBN: 0-521-78612-6
Binding: Paperback
Pages: 240
Figures: 14 half-tones 1 figure

D. Kaminski, R. B. Paris

Asymptotics and Mellin-Barnes Integrals

Encyclopedia of Mathematics and its Applications

Description

Asymptotics and Mellin-Barnes Integrals provides an account of the use and properties of a type of
complex integral representation that arisesfrequently in the study of special functions
typically of interest in classical analysis and　mathematical physics. After developing the
properties of these integrals, their use in　determining the asymptotic behaviour of special
functions is detailed. Although such integrals　have a long history, the book's account includes
recent research results in analytic number theory　and hyperasymptotics. The book also fills a gap
in the literature on asymptotic analysis and　special functions by providing a thorough account
of the use of Mellin-Barnes integrals that is　otherwise not available in other standard
references on asymptotics.

Chapter Contents

1. Introduction; 2. Fundamental results; 3.　Properties of Mellin transforms; 4. Applications of
Mellin transforms; 5. Asymptotic expansions; 6.　The Stokes phenomenon and hyperasymptotics;
7. Multiple Mellin-Barnes integrals; 8. Application　to some special functions.

ISBN: 0-521-79001-8
Binding: Hardback
Pages: 400
Figures: 69 line diagrams 2 half-tones

W. Lawvere, R. Rosebrugh

Sets for Mathematics

Description

This volume has arisen from courses given by　the authors to students at the State University of
New York at Buffalo. The aim is to give an　elementary view of set theory which will be useful
to readers without a substantial background in　math. The approach taken by the authors is
grounded in their own interests in category　theory. This gives the book a character that is
different from other books at a similar level and　will make it of interest to readers already
acquainted with set theory.

Chapter Contents

1. Abstract sets and mappings; 2. Sums,　monomorphisms and parts; 3. Finite inverse
limits; 4. Colimits, epimorphisms and the axiom　of choice; 5. Mapping sets and exponentials; 6.
Summary of the axioms and an example of　variable sets; 7. Consequences and uses of
exponentials; 8. More on power sets; 9.　Introduction to a variable set; 10. Models of
additional variation; A. Logic as the algebra of　parts; B. The axiom of choice; C. Definitions,
symbols, the Greek alphabet.

ISBN: 0-521-80444-2
Binding: Hardback
ISBN: 0-521-01060-8
Binding: Paperback
Pages: 250