Mathematical essays on growth and the emergence of form / edited by Peter L. Antonelli.

Format:

Book

Contributor:

Antonelli, Peter L.

Language:

English

Subjects (All):

Biomathematics.

Developmental biology--Mathematics.

Developmental biology.

Morphogenesis--Mathematics.

Morphogenesis.

Ecology--Mathematics.

Ecology.

Physical Description:

1 online resource (355 p.)

Edition:

1st ed.

Place of Publication:

Edmonton, Alta., Canada : University of Alberta Press, c1985.

Language Note:

English

Summary:

Of interest to theoretical biologists, as well as mathematicians, physical scientists or anyone concerned with problems in growth, chemical ecology and the developmental biology of form, these essays on biological modelling by American, British and Canadian researchers provide an interesting geometric excursion to the frontiers of contemporary mathematical biology.

Contents:

""Contents""; ""Contributors""; ""Preface""; ""Acknowledgements""; ""Introduction""; ""References""; ""MECHANICS""; ""1 Hamiltonian Statistical Mechanics and Biological Order: Problems and Progress""; ""1.1 Introduction""; ""1.2 Hamiltonian Dynamics for a Layered Statistical Mechanics""; ""1.3 Generalized Liouville Equations for Layered Statistical Mechanics""; ""1.4 Discussion""; ""Acknowledgements""; ""References""; ""2 Primary Productivity and the Ecology of Sessile Organisms""; ""2A Non-Euclidean Allometry and the Growth of Forests and Corals""

""2B Starfish Predation of a Growing Coral Reef Community""""2C Competition and Productivity in Aquatic Plant Communities: Experiments and Theories""; ""2D A Mathematical Model of Chemical Defense of Apparent Plants Against Insects""; ""2E A Mathematical Model of Multiple Tannin Defense of Apparent Plants Against Insects""; ""2F Autotoxin Production in Some Symbiotical Plant Communities Is Unstable""; ""3 On the Mathematical Foundations of Growth Mechanics""; ""3A Solving Geodesic Equations in Space of Locally Constant Connections""

""3B On the Mathematical Theory of Volterra-Hamilton Systems""""3C A Note on Passive Volterra-Hamilton Systems""; ""FIELD THEORY""; ""4 Positional Information in Imaginal Discs: A Cartesian Coordinate Model""; ""4.1 Theory of Pattern Formation in Embryonic Development""; ""4.2 The System: Imaginal Discs in Drosophila""; ""4.3 Positional Information in Imaginal Discs""; ""4.4 Compartment Formation""; ""4.5 Evidence from Pattern Mutants""; ""References""; ""5 Developing Organisms as Self-Organizing Fields""; ""5.1 Introduction""; ""5.2 Organisms as Fields""

""5.3 A Field Description of the Typical Cleavage Process""""5.4 A Variational Principle for Cleavage Planes""; ""5.5 Fields and Self-Organization""; ""5.6 Generation and Regeneration""; ""5.7 Structuralist Biology""; ""Acknowledgements""; ""References""; ""Table 1""; ""6 Remarks on Emergence in Physics and Biology""; ""6.1 Introduction""; ""6.2 Global Aspects of Quantum Physics""; ""6.3 Field Expression of Quantum Globality""; ""6.4 Discussion""; ""References""; ""7 Pattern Formation and Morphogenetic Fields""; ""7.1 Introduction""; ""7.2 The Imaginal Wing Disk of Drosophila Melanogaster""

""7.3 Modelling the Initial Stages of Embryogenesis""""7.4 Pattern Formation in Protozoa""; ""Acknowledgements""; ""References""; ""8 Transformations of Quadrilaterals, Tensor Fields, and Morphogenesis""; ""8.1 Introduction""; ""8.2 The Symmetric Tensor Field as a Coordinate Grid for Deformation""; ""8.3 Vector Components of Shape Change for a Quadrilateral""; ""8.4 The Purely Inhomogeneous Transformation as a Mapping""; ""8.5 Tensor Fields and Morphogenetic Explanation: Some Speculations""; ""Acknowledgements""; ""References""; ""THE HISTORICAL RECORD""

""9 Principes de Biologie Mathematique (Principles of Mathematical Biology)""

Notes:

Description based upon print version of record.

Includes bibliographies.

ISBN:

1-4593-0401-2

1-4175-9310-5