Many of us have been fascinated as children by soap bubbles and soap films. Their shapes and colours are beautiful and they are great fun to pay with. With no les intensity, scientists and mathematicians have been interested in the properties of bubbles and films throughout scientific history. In this book David Lovett describes the properties of soap films and soap bubbles. He then uses their properties to illustrate and elucidate a wide range of physical principles and scientific phenomena in a way that unifies different concepts. The book will appeal not only to students and teachers at school and university but also to readers with a general scientific interest and to researchers studying soap films. For the most part simple school mathematics is used. Sections containing more advanced mathematics have been placed in boxes or appendices and can be omitted by readers without the appropriate mathematical background. The text is supported with * Over 100 diagrams and photgraphs. * Details of practical experiments that can be performed using simple household materials. * Computer programs that draw some of the more complicated figures or animate sequences of soap film configurations. * A bibliography for readers wishing to delve further into the subject. David Lovett is a lecturer in physics at the University of Essex. His research interests include Langmiur-Blodgett thin films and the use of models as teaching aids in physics. He has been interested in soap films since 1978 and has made a number of original contributions to the subject, particularly in the use of models which change their dimensions and their analogy with phase transitions. He has published three other books including ITensor Properties of Crystals (Institute of Physics Publishing 1989). John Tilley is also a lecturer in physics at the University of Essex with research interests in theoretical solid-state physics and soap films. He is coauthor of Superfluidity and Superc

Nature tries to minimize the surface area of a soap film through the action of surface tension. The process can be understood mathematically by using differential geometry, complex analysis, and the calculus of variations. This book employs ingredients from each of these subjects to tell the mathematical story of soap films. The text is fully self-contained, bringing together a mixture of types of mathematics along with a bit of the physics that underlies the subject. The development is primarily from first principles, requiring no advanced background material from either mathematics or physics. Through the Maple applications, the reader is given tools for creating the shapes that are being studied. Thus, you can "see" a fluid rising up an inclined plane, create minimal surfaces from complex variables data, and investigate the "true" shape of a balloon. Oprea also includes descriptions of experiments and photographs that let you see real soap films on wire frames. The theory of minimal surfaces is a beautiful subject, which naturally introduces the reader to fascinating, yet accessible, topics in mathematics. Oprea's presentation is rich with examples, explanations, and applications. It would make an excellent text for a senior seminar or for independent study by upper-division mathematics or science majors.

Ordinary foams such as the head of a glass of beer and more exotic ones such as solid metallic foams raise many questions for the physicist and have attracted a substantial research community in recent years. The present book describes the results of extensive experiments, computer simulations, and theories in an authoritative yet informal style, making ample use of illustrations and photographs. As an introduction to the whole field of the physics of foams it puts a strong emphasis on liquids while also including solid foams. Simple, idealized models are adopted and their consequences explored. Specific topics include: structure, drainage, rheology, conductivity, and coarsening. A minimum of mathematics is used. Theory and experiment are described together at every stage. A guide to further reading is provided through carefully selected references. This is a complete and coherent introduction to the subject which no other modern text currently offers.

This book is a collection of articles studying various Steiner tree prob lems with applications in industries, such as the design of electronic cir cuits, computer networking, telecommunication, and perfect phylogeny. The Steiner tree problem was initiated in the Euclidean plane. Given a set of points in the Euclidean plane, the shortest network interconnect ing the points in the set is called the Steiner minimum tree. The Steiner minimum tree may contain some vertices which are not the given points. Those vertices are called Steiner points while the given points are called terminals. The shortest network for three terminals was first studied by Fermat (1601-1665). Fermat proposed the problem of finding a point to minimize the total distance from it to three terminals in the Euclidean plane. The direct generalization is to find a point to minimize the total distance from it to n terminals, which is still called the Fermat problem today. The Steiner minimum tree problem is an indirect generalization. Schreiber in 1986 found that this generalization (i.e., the Steiner mini mum tree) was first proposed by Gauss.

Mathematics and engineering are inevitably interrelated, and this interaction will steadily increase as the use of mathematical modelling grows. Although mathematicians and engineers often misunderstand one another, their basic approach is quite similar, as is the historical development of their respective disciplines. The purpose of this Math Primer is to provide a brief introduction to those parts of mathematics which are, or could be, useful in engineering, especially bioengineering. The aim is to summarize the ideas covered in each subject area without going into exhaustive detail. Formulas and equations have not been avoided, but every effort has been made to keep them simple in the hope of persuading readers that they are not only useful but also accessible. The wide range of topics covered includes introductory material such as numbers and sequences, geometry in two and three dimensions, linear algebra, and the calculus. Building on these foundations, linear spaces, tensor analysis and Fourier analysis are introduced. All these concepts are used to solve problems for ordinary and partial differential equations. Illustrative applications are taken from a variety of engineering disciplines, and the choice of a suitable model is considered from the point of view of both the mathematician and the engineer. This book will be of interest to engineers and bioengineers looking for the mathematical means to help further their work, and it will offer readers a glimpse of many ideas which may spark their interest.

Design in engineering and science has often been inspired by nature. This has been more evident in recent years, after a period during which our civilization thought in terms of taming rather than working in harmony with nature. The consequences of that approach are still with us and have resulted in a world increasingly homogenized, lacking in biodiversity and with increased pollution. Mankind has been slow to learn and even slower to apply the lessons that nature offers, in spite of the urgency of our predicament. This book contains papers presented at the fourth International Conference on Comparing Design in Nature with Science and Engineering . The emphasis of this Volume is on engineering and architectural applications and on biomimetics, reflecting in some measure current interest in finding environmentally friendly solutions which also optimize the use of natural resources. The contributions have been arranged into the following topics: Biomimetics; Shape and Form in Engineering Nature; Nature and Architectural Design; Natural Materials and Surfaces; Complexity; and Education.

Here, Andrew Glassner opens his notebook and invites readers into a wide range of stimulating explorations of art, nature and computer graphics. The text is accessible and informal, alongside images illustrating topics from Celtic knotwork and lightning to soap bubbles.