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The Mathematics and Mechanics of Biological Growth
Taschenbuch von Alain Goriely
Sprache: Englisch

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Beschreibung
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.
Zusammenfassung

Presents a mathematical theory to quantify and model biological growth processes

Shows how mechanics and geometry are coupled during growth and how complex forms and morphological patterns may arise due to instabilities

Illustrated with simple examples and detailed biological applications

Includes supplementary material: [...]

Inhaltsverzeichnis
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.
Details
Erscheinungsjahr: 2018
Fachbereich: Allgemeines
Genre: Mathematik
Rubrik: Naturwissenschaften & Technik
Medium: Taschenbuch
Seiten: 668
Reihe: Interdisciplinary Applied Mathematics
Inhalt: xxii
646 S.
341 s/w Illustr.
646 p. 341 illus.
ISBN-13: 9781493979110
ISBN-10: 1493979116
Sprache: Englisch
Ausstattung / Beilage: Paperback
Einband: Kartoniert / Broschiert
Autor: Goriely, Alain
Auflage: Softcover reprint of the original 1st ed. 2017
Hersteller: Springer US
Springer New York
Interdisciplinary Applied Mathematics
Maße: 235 x 155 x 36 mm
Von/Mit: Alain Goriely
Erscheinungsdatum: 27.07.2018
Gewicht: 0,996 kg
preigu-id: 114151911
Zusammenfassung

Presents a mathematical theory to quantify and model biological growth processes

Shows how mechanics and geometry are coupled during growth and how complex forms and morphological patterns may arise due to instabilities

Illustrated with simple examples and detailed biological applications

Includes supplementary material: [...]

Inhaltsverzeichnis
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.
Details
Erscheinungsjahr: 2018
Fachbereich: Allgemeines
Genre: Mathematik
Rubrik: Naturwissenschaften & Technik
Medium: Taschenbuch
Seiten: 668
Reihe: Interdisciplinary Applied Mathematics
Inhalt: xxii
646 S.
341 s/w Illustr.
646 p. 341 illus.
ISBN-13: 9781493979110
ISBN-10: 1493979116
Sprache: Englisch
Ausstattung / Beilage: Paperback
Einband: Kartoniert / Broschiert
Autor: Goriely, Alain
Auflage: Softcover reprint of the original 1st ed. 2017
Hersteller: Springer US
Springer New York
Interdisciplinary Applied Mathematics
Maße: 235 x 155 x 36 mm
Von/Mit: Alain Goriely
Erscheinungsdatum: 27.07.2018
Gewicht: 0,996 kg
preigu-id: 114151911
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