Growth Patterns in Physical Sciences and Biology: (304 NATO Science Series B:)

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.

Table of Contents:
Cell Colonies.- Fractal Growth and Morphological Change in Bacterial Colony Formation.- Interfacial Pattern Formation in Biological Systems: Preliminary Observations During Growth of Bacterial Colonies.- Amoebae Aggregation in Dictyoselium Discoideum.- The Fractal Nature of Common Patterns.- Surface and Interfaces.- Study of Self-Affine Fractal Surfaces with STM.- Dynamic Scaling in Surface Growth Phenomena.- MBE Growth and Surface Diffusion.- Growth in Systems with Quenched Disorder.- Kinetic Roughening with Algebraically Distributed Noise Amplitudes or Waiting Times.- Anomalous Surface Roughening: Experiment and Models.- Waiting-Time Formulation of Surface Growth and Mapping to Directed Polymers in a Random Medium.- Scaling Far From Thermal Equilibrium.- Discrete Potential Flow Simulation of a Premixed Flame Front.- Fractal Landscapes in Physics and Biology.- Interface Kinetics and Oscillatory Growth in Directional Solidification of Binary Mixtures.- Locally Interacting Cell Systems as Models for Carcinogenesis.- Properties of the Morphologies Envelope in a Diffusion Limited Growth.- Growth Patterns in Zinc Electrodeposition.- Natural Viscous Fingering.- Fibonacci Sequences in Diffusion-Limited Aggregation.- Pattern Formation in Screened Electrostatic Fields: Growth in a Channel and in Two Dimensions.- Self Organized Criticality in Simple Growth Models.- Scaling Properties of Average Diffusion Limited Aggregation Clusters.- Topological Considerations on Finger Dynamics in the Saffman-Taylor Problem..- Adaptive Cluster Growth Models.- The Double Layer Impedance at Self-Similar Surfaces.- Multifractals.- Angiogenesis and Vascular Networks: Complex Anatomies from Deterministic Non-Linear Physiologies.- Mechanisms of Biological Pattern Formation and Constraints Imposed byGrowth..- Growth Patterns in Fracture.- On the Stability of Growth with a Threshold.- Evidence for Universality in Transients.- Cellular Patterns.- Micelles and Foams: 2-D Manifolds Arising from Local Interactions.- Simulating Radiate Accretive Growth Using Iterative Geometric Constructions..- Phyllotaxis as a Self-Organized Growth Process.- Multiplicative Noise in Domain Growth: Stochastic Ginzburg-Landau Equations..- Dynamical Systems.- Bursting Intermittency and Microwave Popcorn: Comments on the “Reporting Out” of Neuron-Like Firing behavior.- Order, Pattern Selection and Noise in Low Dimensional Systems.- Pattern Formation in Extended Continuous Systems.- Self Replication.- Role of Catalysis on the Evolution of Error-Prone Self-Replicative Molecules.- Molecular Quasi-Species in Hopfield Replication Landscapes.- Self Organization.- Effects of Noise on Self-Organized Critical Phenomena.- Measurement and Characterization.- The Practical Measurement of Fractal Parameters.