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商品コード: 9780387877099

The Mathematics and Mechanics of Biological Growth

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分野別 > 数学 > 応用数学

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書名

The Mathematics and Mechanics of Biological Growth
著者・編者 Goriely, A.
出版社/発行元 Springer
発行年/月 2017年6月   
装丁 Hardcover
ページ数/巻数 666 ページ
ISBN 978-0-387-87709-9
発送予定 海外倉庫よりお取り寄せ 2-3週間以内に発送します

 

Desciption

 

This monograph presents a general mechanical theory for biological growth. It provides both a conceptual and a technical foundation for the understanding and analysis of problems arising in biology and physiology. The theory and methods is illustrated on a wide range of examples and applications.

A process of extreme complexity, growth plays a fundamental role in many biological processes and is considered to be the hallmark of life itself. Its description has been one of the fundamental problems of life sciences, but until recently, it has not attracted much attention from mathematicians, physicists, and engineers. The author herein presents the first major technical monograph on the problem of growth since D’Arcy Wentworth Thompson’s 1917 book On Growth and Form.

The emphasis of the book is on the proper mathematical formulation of growth kinematics and mechanics. Accordingly, the discussion proceeds in order of complexity and the book is divided into five parts. First, a general introduction on the problem of growth from a historical perspective is given. Then, basic concepts are introduced within the context of growth in filamentary structures. These ideas are then generalized to surfaces and membranes and eventually to the general case of volumetric growth. The book concludes with a discussion of open problems and outstanding challenges.

Thoughtfully written and richly illustrated to be accessible to readers of varying interests and background, the text will appeal to life scientists, biophysicists, biomedical engineers, and applied mathematicians alike.

 

Contents:

 

Part I Introduction: Where It All Starts
1 Basic Aspects of Growth
2 Mechanics and Growth
3 Discrete Computational Models

Part II Filament Growth: A One-Dimensional Theory
4 Growing on a Line
5 Elastic Rods
6 Morphoelastic Rods

Part III Surface Growth: A Two-Dimensional Theory
7 Accretive Growth
8 Membranes and Shells
9 Growing Membranes
10 Morphoelastic Plates

Part IV Volumetric Growth: A Three-Dimensional Theory
11 Nonlinear Elasticity
12 The Kinematics of Growth
13 Balance Laws
14 Evolution Laws and Stability
15 Growing Spheres
16 Growing Cylinders

Part V Conclusion: Where It Does Not End
17 Ten Challenges

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