Polarization and moment tensors. With applications to inverse problems and effective medium theory

Polarization and moment tensors. With applications to inverse problems and effective medium theory
~
Ammari H., Kang H.

This book presents important recent developments in mathematical and computational methods used in impedance imaging and the theory of composite materials. The methods involved come from various areas of pure and applied mathematics, such as potential theory, PDEs, complex analysis, and numerical methods. The unifying thread in this book is the use of generalized polarization and moment tensors. The main approach is based on modern layer potential techniques. By augmenting the theory with interesting practical examples and numerical illustrations, the exposition brings simplicity to the advanced material. An introductory chapter covers the necessary basics.With its extensive list of references and open problems, the book should enhance accessibility to specialized literature and stimulate progress in the fields of impedance imaging and composite materials. Graduate students and researchers in applied mathematics will benefit from this book. Researchers in engineering and physics might also find this book helpful.

# Hardcover: 316 pages
# Publisher: Springer; 1 edition (July 18, 2007)
# Language: English
# ISBN-10: 0387715657
# ISBN-13: 978-0387715650
# Product Dimensions: 9.2 x 6.1 x 0.8 inches

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Tensors in Image Processing and Computer Vision (Advances in Pattern Recognition) (Hardcover)

Tensors in Image Processing and Computer Vision (Advances in Pattern Recognition) (Hardcover)
~ Aja-Fernandez S., et al.

Details

# Hardcover: 470 pages
# Publisher: Springer; 1 edition (July 14, 2009)
# Language: English
# ISBN-10: 1848822987
# ISBN-13: 978-1848822986

Description

Tensor signal processing is an emerging field with important applications to computer vision and image processing.

This book presents the state of the art in this new branch of signal processing, offering a great deal of research and discussions by leading experts in the area. The wide-ranging volume offers an overview into cutting-edge research into the newest tensor processing techniques and their application to different domains related to computer vision and image processing.

This comprehensive text will prove to be an invaluable reference and resource for researchers, practitioners and advanced students working in the area of computer vision and image processing.

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Visualization and Processing of Tensor Fields: Advances and Perspectives (Mathematics and Visualization)

Visualization and Processing of Tensor Fields: Advances and Perspectives (Mathematics and Visualization)
by: David Laidlaw, Joachim Weickert

Details

# Hardcover: 376 pages
# Publisher: Springer; 1 edition (April 21, 2009)
# Language: English
# ISBN-10: 3540883770
# ISBN-13: 978-3540883777

Description

Visualisation and Processing of Tensor Fields provides researchers an inspirational look at how to process and visualize complicated 2D and 3D images known as tensor fields. Tensor fields are the natural representation for many physical quantities; they can describe how water moves around in the brain, how gravity varies around the earth, or how materials are stressed and deformed. With its numerous color figures, this book helps the reader understand both the underlying mathematics and the applications of tensor fields. The reader also will learn about the most recent research topics and open research questions.

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A Brief on Tensor Analysis (Undergraduate Texts in Mathematics)

A Brief on Tensor Analysis (Undergraduate Texts in Mathematics)
by: James G. Simmonds

Details

# Hardcover: 112 pages
# Publisher: Springer; 2nd edition (July 31, 1997)
# Language: English
# ISBN-10: 038794088X
# ISBN-13: 978-0387940885

Description

This new edition is intended for third and fourth year undergraduates in Engineering, Physics, Mathematics, and the Applied Sciences, and can serve as a springboard for further work in Continuum Mechanics or General Relativity. Starting from a basic knowledge of calculus and matrix algebra, together with fundamental ideas from mechanics and geometry, the text gradually develops the tools for formulating and manipulating the field equations of Continuum Mechanics. The mathematics of tensor analysis is introduced in well-separated stages: the concept of a tensor as an operator; the representation of a tensor in terms of its Cartesian components; the components of a tensor relative to a general basis, tensor notation, and finally, tensor calculus. The physical interpretation and application of vectors and tensors are stressed throughout. Though concise, the text is written in an informal, non-intimidating style enhanced by worked-out problems and a meaningful variety of exercises. The new edition includes more exercises, especially at the end of chapter IV. Furthermore, the author has appended a section on Differential Geometry, the essential mathematical tool in the study of the 2-dimensional structural shells and 4-dimensional general relativity.

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Introduction to Tensor Calculus and Continuum Mechanics

Introduction to Tensor Calculus and Continuum Mechanics
by: J. H. Heinbockel

Details

# Paperback: 432 pages
# Publisher: Trafford Publishing (December 19, 2001)
# Language: English
# ISBN-10: 1553691334
# ISBN-13: 978-1553691334

Description

Introduction to Tensor Calculus and Continuum Mechanics is an advanced College level mathematics text. The first part of the text introduces basic concepts, notations and operations associated with the subject area of tensor calculus. The material presented is developed at a slow pace with a detailed explanation of the many tensor operations. The first half of the text concludes with an introduction to the application of tensor concepts to differential geometry and relativity. The second half of the text presents applications of tensors to areas from continuum mechanics. Tensor calculus is applied to the areas of dynamics, elasticity, fluids, electricity and magnetism. Many of the basic equations from physics, engineering and science are developed which makes the text an excellent reference work. The second half of the text concludes with an introduction to quaternions, multivectors and Clifford algebra.

There are four Appendices. The Appendix A contains units of measurements from the Systeme International d'Unites along with some selected physical constants. The Appendix B contains a listing of Christoffel symbols of the second kind associated with various coordinate systems. The Appendix C is a summary of useful vector identities. The Appendix D contains solutions to selected exercises. The text has numerous illustrative worked examples and over 450 exercises.

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