Mathematical essays on growth and the emergence of form

Contents......Page 6
Contributors......Page 12
Preface......Page 14
Acknowledgements......Page 16
Introduction......Page 18
References......Page 22
MECHANICS......Page 24
1.1 Introduction......Page 26
1.2 Hamiltonian Dynamics for a Layered Statistical Mechanics......Page 32
1.3 Generalized Liouville Equations for Layered Statistical Mechanics......Page 44
Acknowledgements......Page 61
References......Page 62
2 Primary Productivity and the Ecology of Sessile Organisms......Page 66
2A Non-Euclidean Allometry and the Growth of Forests and Corals......Page 68
2B Starfish Predation of a Growing Coral Reef Community......Page 82
2C Competition and Productivity in Aquatic Plant Communities: Experiments and Theories......Page 102
2D A Mathematical Model of Chemical Defense of Apparent Plants Against Insects......Page 114
2E A Mathematical Model of Multiple Tannin Defense of Apparent Plants Against Insects......Page 124
2F Autotoxin Production in Some Symbiotical Plant Communities Is Unstable......Page 132
3 On the Mathematical Foundations of Growth Mechanics......Page 138
3A Solving Geodesic Equations in Space of Locally Constant Connections......Page 140
3B On the Mathematical Theory of Volterra-Hamilton Systems......Page 148
3C A Note on Passive Volterra-Hamilton Systems......Page 188
FIELD THEORY......Page 190
4.1 Theory of Pattern Formation in Embryonic Development......Page 192
4.2 The System: Imaginal Discs in Drosophila......Page 193
4.3 Positional Information in Imaginal Discs......Page 194
4.4 Compartment Formation......Page 201
4.5 Evidence from Pattern Mutants......Page 203
References......Page 205
5.1 Introduction......Page 208
5.2 Organisms as Fields......Page 211
5.3 A Field Description of the Typical Cleavage Process......Page 212
5.4 A Variational Principle for Cleavage Planes......Page 213
5.5 Fields and Self-Organization......Page 216
5.6 Generation and Regeneration......Page 219
5.7 Structuralist Biology......Page 220
References......Page 222
Table 1......Page 223
6.1 Introduction......Page 224
6.2 Global Aspects of Quantum Physics......Page 225
6.3 Field Expression of Quantum Globality......Page 227
6.4 Discussion......Page 228
References......Page 229
7.1 Introduction......Page 230
7.2 The Imaginal Wing Disk of Drosophila Melanogaster......Page 231
7.3 Modelling the Initial Stages of Embryogenesis......Page 237
7.4 Pattern Formation in Protozoa......Page 240
References......Page 243
8.1 Introduction......Page 244
8.2 The Symmetric Tensor Field as a Coordinate Grid for Deformation......Page 246
8.3 Vector Components of Shape Change for a Quadrilateral......Page 255
8.4 The Purely Inhomogeneous Transformation as a Mapping......Page 261
8.5 Tensor Fields and Morphogenetic Explanation: Some Speculations......Page 279
References......Page 287
THE HISTORICAL RECORD......Page 290
9A PART I – The Bases of the Theory of the Struggle for Existence......Page 292
9B PART II – The General Laws of the Struggle for Existence......Page 314
10 Principes de Philosophie Zoologique (Principles of Zoological Philosophy)......Page 334