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The Mathematics and Mechanics of Biological Growth - Alain Goriely

The Mathematics and Mechanics of Biological Growth (eBook)

(Autor)

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2017 | 1st ed. 2017
XXII, 646 Seiten
Springer New York (Verlag)
978-0-387-87710-5 (ISBN)
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This monograph presents a general mathematical 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 are 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.   



This monograph presents a general mathematical 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 are 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.   

Basic aspects of growth.- Mechanics and growth.- Discrete computational models.- Growing on a line.- Elastic rods.- Morphoelastic rods.- Accretive growth.- Membranes and shells.- Growing membranes.- Morphoelastic plates.- Nonlinear elasticity.- The kinematics of growth.- Balance laws.- Evolution laws and stability.- Growing spheres.- Growing cylinders.- Ten challenges.- References.- Index.

Erscheint lt. Verlag 29.5.2017
Reihe/Serie Interdisciplinary Applied Mathematics
Zusatzinfo XXII, 646 p. 341 illus.
Verlagsort New York
Sprache englisch
Themenwelt Mathematik / Informatik Mathematik Angewandte Mathematik
Naturwissenschaften Biologie Genetik / Molekularbiologie
Naturwissenschaften Biologie Zellbiologie
Naturwissenschaften Physik / Astronomie Angewandte Physik
Naturwissenschaften Physik / Astronomie Mechanik
Schlagworte Balance Laws • Biological growth • Evolution laws • Filament growth • Mathematical Biology • Mechanical biology • Morphoelasticity • Morphogenesis • Physiology • Volumetric growth
ISBN-10 0-387-87710-X / 038787710X
ISBN-13 978-0-387-87710-5 / 9780387877105
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