Growth Patterns in Physical Sciences and Biology

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Jaun-Manuel Garcia-Ruiz, Enrique Louis, P. Meakin, Leonard M. Sander
Springer Science & Business Media, Dec 6, 2012 - Science - 429 pages
During the past decade interest in the formation of complex disorderly patterns far from equilibrium has grown rapidly. This interest has been stim ulated by the development of new approaches (based primarily on fractal geometry) to the quantitative description of complex structures, increased understanding of non-linear phenomena and the introduction of a variety of models (such as the diffusion-limited aggregation model) that provide paradigms for non-equilibrium growth phenomena. Advances in computer technology have played a crucial role in both the experimental and theoret ical aspects of this enterprise. Substantial progress has been made towards the development of comprehensive understanding of non-equilibrium growth phenomena but most of our current understanding is based on simple com puter models. Pattern formation processes are important in almost all areas of science and technology, and, clearly, pattern growth pervades biology. Very often remarkably similar patterns are found in quite diverse systems. In some case (dielectric breakdown, electrodeposition, fluid-fluid displacement in porous media, dissolution patterns and random dendritic growth for example) the underlying causes of this similarity is quite well understood. In other cases (vascular trees, nerve cells and river networks for example) we do not yet know if a fundamental relationship exists between the mechanisms leading the formation of these structures.
 

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Contents

Fractal Growth and Morphological Change in Bacterial Colony Formation
2
Preliminary Observations
11
Amoebae Aggregation in Dictyoselium Discoideum
21
The Fractal Nature of Common Patterns
29
Study of SelfAffine Fractal Surfaces with STM
37
Dynamic Scaling in Surface Growth Phenomena
45
MBE Growth and Surface Diffusion
57
Growth in Systems with Quenched Disorder
65
Scaling Properties of Average Diffusion Limited Aggregation Clusters
221
Adaptive Cluster Growth Models
233
The Double Layer Impedance at SelfSimilar Surfaces
245
Multifractals
257
Complex Anatomies from Deterministic
267
Mechanisms of Biological Pattern Formation and Constraints Imposed by Growth
277
Growth Patterns in Fracture
289
On the Stability of Growth with a Threshold
299

Kinetic Roughening with Algebraically Distributed Noise Amplitudes
77
Experiment and Models
85
WaitingTime Formulation of Surface Growth and Mapping to Directed
99
Scaling Far From Thermal Equilibrium
109
Discrete Potential Flow Simulation of a Premixed Flame Front
119
Fractal Landscapes in Physics and Biology
127
Interface Kinetics and Oscillatory Growth in Directional Solidification of Binary
137
Ionic Concentration and Electric Field in Fractal Electrodeposition
153
Properties of the Morphologies Envelope in a Diffusion Limited Growth
163
Growth Patterns in Zinc Electrodeposition
173
Natural Viscous Fingering
183
Fibonacci Sequences in DiffusionLimited Aggregation
191
Growth in a Channel
203
Self Organized Criticality in Simple Growth Models
213
Evidence for Universality in Transients
307
2D Manifolds Arising from Local Interactions
315
Simulating Radiate Accretive Growth Using Iterative Geometric Constructions
331
Phyllotaxis as a SelfOrganized Growth Process
341
Stochastic GinzburgLandau Equations
353
DYNAMICAL SYSTEMS
361
Order Pattern Selection and Noise in Low Dimensional Systems
373
Pattern Formation in Extended Continuous Systems
381
Role of Catalysis on the Evolution of ErrorProne SelfReplicative Molecules
393
Molecular QuasiSpecies in Hopfield Replication Landscapes
401
The Practical Measurement of Fractal Parameters
417
Index
425
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