Combined discrete and continual approaches in biological modelling

목차 (Table of Contents)

• CONTENTS
• 1 Introduction = 1
• 1.1 The ‘Attracting Nature’ of Nature = 1
• 1.2 The Mathematics of Self-Organization = 2
• 1.3 Frozen Kinetics or the Large River Effect = 4
• 1.4 Variable Potentials = 7
• 1.5 Lessons to Be Learned from the Dynamics of a Myrmecochorous Plant Community = 9
• 1.6 Adiabatic Approximation = 10
• 1.6.1 Continuous or Discrete Modeling = 11
• 1.6.2 Continuous and Discrete Modeling in Multidimensional Space = 13
• 1.7 Disadvantages of the Continuous Approach = 14
• 1.8 Lessons to Be Learned from the Adhesive System of Insects = 17
• 1.9 Lessons to Be Learned from Hairy Spatulate Contact Structures = 20
• References = 23
• 2 Various Methods of Pattern Formation = 25
• 2.1 A Simple Theory of Phase Transitions and Pattern Formation = 26
• 2.2 Automatic Blocking of the Nucleation and Freezing of the Process = 30
• 2.3 Large-Scale Structure of the Fluctuating Field : Universality and Scaling = 33
• 2.4 Chemical Appearance of Fractal Surfaces = 36
• 2.5 Mathematical Creation of Fractal Surfaces = 41
• 2.6 The Combination of Discrete and Continuous Techniques = 47
• References = 52
• 3 Clusterization of Biological Structures with High Aspect Ratio = 53
• 3.1 Adhesion without Clusterization Due to a Material Gradient = 54
• 3.1.1 Fibrillar Adhesive Systems of Insect Feet = 54
• 3.1.2 Structure and Material Properties of Insect Setae = 56
• 3.1.3 Mathematical Model of Insect Setae with Gradients of Mechanical Properties = 57
• 3.1.4 Functional Significance of Gradients of Material Properties = 63
• 3.2 Adhesion without Clusterization Due to a Non-uniformly Distributed 3D Structure = 64
• 3.2.1 Hierarchical Structure of the Gecko Adhesive Setae = 64
• 3.2.2 Mathematical Model of Contact Formation by Gecko Setae = 66
• 3.2.3 Functional Significance of a Non-uniform Geometry = 68
• 3.3 Adhesion with Clustering Behavior = 73
• 3.3.1 Carbon Nanotube Arrays as an Approach to Bioinspired Adhesives = 73
• 3.3.2 Mathematical Model of the Clustering of Nanotube Arrays = 75
• 3.3.3 Functional Significance of CNT Clusterization in Multiple Attachment–Detachment Cycles = 78
• References = 83
• 4 Contact Between Biological Attachment Devices and Rough Surfaces = 87
• 4.1 The Role of Dimension in the Adhesive Properties of Spatula-Like Biological Attachment Devices = 90
• 4.1.1 The Significance of Roughness with Regard to Attachment Capabilities = 90
• 4.1.2 Contact Formation with Numerically Generated Rough Surfaces = 93
• 4.1.3 Contact Formation on Rough Surfaces Created by Gaussian Convolution = 97
• 4.1.4 Contact Formation with Real Substrates of Different Roughness = 99
• 4.1.5 Biological Consequences of Roughness-Dependent Attachment Capabilities = 101
• 4.2 Shear-Induced Adhesion of Biological Spatula-Like Attachment Devices = 102
• 4.2.1 Microscopical Examination of Various Spatulae = 105
• 4.2.2 Numerical Modeling of the Shear-Induced Contact of Spatulae with Rough Surfaces = 106
• 4.2.3 Implications for Biological Systems = 111
• 4.3 Wet Attachment and Loss of the Fluid from the Adhesive Pads in Contact with the Substrate = 112
• 4.3.1 Attraction Based on Liquid Bridges = 112
• 4.3.2 Microscopic Examination of Insect Prints with Wet Adhesion = 113
• 4.3.3 Fluid Loss Model = 114
• 4.3.4 Influence of Various Factors on the Fluid Distribution = 118
• 4.3.5 Discussion of the Numerically Obtained Results and Biological Consequences = 121
• 4.4 Self-Alignment System of an Adhesive Fruit = 123
• 4.4.1 The Plant Commicarpus helenas in Nature = 123
• 4.4.2 Numerical Model of Commicarpus Adhesion to Rough Surfaces = 125
• 4.4.3 Biological Significance of the Obtained Results = 135
• References = 136
• 5 Anisotropic Friction in Biological Systems = 143
• 5.1 Frictional-Anisotropy-Based Mechanical Systems in Biology = 144
• 5.1.1 Numerical Model of Anisotropic Friction in Propulsion and Particle Transport = 147
• 5.1.2 Typical Temporal Development and Mean Values of Forces = 148
• 5.1.3 Main Results and Biological Implications = 151
• 5.2 Anisotropic Surface Nanostructures of Snake Skin = 154
• 5.2.1 Modeling of the Frictional Behavior of Snake Skin = 155
• 5.2.2 Mean Friction Forces of Snake Skin and Their Variations = 157
• 5.3 Snake Locomotion with Change of Body Shape Based on the Friction Anisotropy of the Ventral Skin = 160
• 5.3.1 Dynamic Change of Frictional Interactions = 161
• 5.3.2 Experimental Observations = 162
• 5.3.3 Numerical Model of Snake-Like Motion = 162
• 5.3.4 Biological Interpretation of the Numerical Results = 170
• References = 172
• 6 Mechanical Interlocking of Biological Fasteners = 177
• 6.1 Co-opted Contact Pairs in Arresting Systems of Insects = 177
• 6.1.1 Some Arresting Structures Observed in Biological Systems = 179
• 6.1.2 Continuous Model of an Arresting System = 180
• 6.1.3 Discrete Model of an Arresting System and Dynamic Simulations = 185
• 6.1.4 Biological and Biomimetic Significance of the Obtained Results = 188
• 6.2 Mechanical Interlocking and Unzipping in Bird Feathers = 190
• 6.2.1 General Properties of Bird Feathers = 190
• 6.2.2 Basic Experimental Results = 191
• 6.2.3 Modeling of Feather Unzipping = 193
• 6.2.4 Recovery of Ruptured Feathers = 197
• References = 201
• 7 Biomechanics at the Microscale = 205
• 7.1 Model of Penile Propulsion in a Chrysomelid Beetle = 206
• 7.1.1 CLSM Examination of the Genitalia of Cassida rubiginosa = 207
• 7.1.2 Simplified Model of the Flagellum and the Helical Spermathecal Duct = 208
• 7.1.3 The Stiffness Gradient of the Beetle Penis Facilitates Propulsion in the Female Spermathecal Duct = 214
• 7.1.4 Comparison of the Model Results and Microscopical Observations = 220
• 7.2 Slow Viscoelastic Response of Resilin = 221
• 7.2.1 General Properties and Biological Importance of Resilin = 221
• 7.2.2 Physical Properties of Resilin and Experimental Methods = 222
• 7.2.3 Two Procedures for Modeling the Experimental Results = 224
• References = 231
• 8 Nanoscale Pattern Formation in Biological Surfaces = 235
• 8.1 Snake Skin Surface Nanostructures = 236
• 8.1.1 Correlation Analysis of the Nanostructures of Moth Eye and Snake Skin = 238
• 8.1.2 Correlation Analysis of Numerically Generated Structure Arrangements = 242
• 8.2 3D Pattern Formation of Colloid Spheres in the Water-Repellent Cerotegument of Whip-Spiders = 243
• 8.2.1 Water Repellence and Ultrastructure of Certain Granules in the Whip-Spider Cerotegument = 244
• 8.2.2 Numerical Simulation of the Colloidal Self-assembly of Cerotegument Structures = 246
• 8.2.3 Discussion of the Results and Their Biological Significance = 258
• 8.3 Numerical Simulation of the Pattern Formation of Springtail Cuticle Nanostructures = 259
• 8.3.1 Biological and Chemical Background of Pattern Formation in Springtail Cuticle = 260
• 8.3.2 Numerical Model of the Pattern Formation in Springtail Cuticle = 262
• 8.3.3 Discussion of the Results and Biological Significance = 270
• References = 271
• 9 Ecology and Evolution = 275
• 9.1 Long-Term Dynamics of Ant-Species-Dependent Plant Seeds = 276
• 9.1.1 Myrmecochorous Plant Community = 276
• 9.1.2 Temporal Development of the Forest Ecosystem = 278
• 9.1.3 Integral Values of Time-Depending Behavior and Their Biological Interpretation = 282
• 9.1.4 Discussion of the Modeling Results = 286
• 9.2 Influence of Aggregation Behavior on Predator–Prey Interactions = 289
• 9.2.1 Numerical Model of Interactions Between a Predator and Aggregated Prey ' 291
• 9.2.2 Model Behavior in a “Flat” World = 295
• 9.2.3 Model Behavior in a “Cylindrical World” = 298
• 9.2.4 Biological Consequences of Motion in Worlds of Different Topologies = 302
• References = 304
• Index = 309