Universalities in Condensed Matter: Proceedings of the Workshop, Les Houches, France, March 15–25,1988 (Springer Proceedings in Physics, 32)

Universality is the property that systems of radically different composition and structure exhibit similar behavior. The appearance of universal laws in simple critical systems is now well established experimentally, but the search for universality has not slackened. This book aims to define the current status of research in this field and to identify the most promising directions for further investigations. On the theoretical side, numerical simulations and analytical arguments have led to expectations of universal behavior in several nonequilibrium systems, e.g. aggregation, electric discharges, and viscous flows. Experimental work is being done on "geometric" phase transitions, e.g. aggregation and gelation, in real systems. The contributions to this volume allow a better understanding of chaotic systems, turbulent flows, aggregation phenomena, fractal structures, and quasicrystals. They demonstrate how the concepts of renormalization group transformations, scale invariance, and multifractality are useful for describing inhomogeneous materials and irreversible phenomena. Front Matter....Pages I-X Front Matter....Pages 1-1 Hierarchy of Line Defects in Structures....Pages 2-5 Are There Universalities in Systems with Frustrated Local Order?....Pages 6-8 Contribution to the Theory of Quasicrystal Approximants....Pages 9-14 Beyond Quasiperiodicity: Scaling Properties of a Fourier Spectrum....Pages 15-18 The Fibonacci Chain Quasicrystal: An Exact Decimation Approach....Pages 19-22 Front Matter....Pages 23-23 Experimental Investigations of the Sol-Gel Transition....Pages 24-26 Conformation, Connectivity and Mechanical Properties of Polycondensates Near the Gel Point....Pages 27-34 Conformation and Dynamical Properties of Polymer Clusters in Concentrated Solution....Pages 35-42 Percolation and Dispersive Conduction in Fluid-Saturated Porous Media....Pages 43-51 Microscopic Observation of Critical Fluctuations: Fractal Aspects....Pages 52-56 Some Static and Dynamic Results for Walks on the Lattice....Pages 57-60 Problem of Universality in Phase Transitions in Low-Symmetry Systems....Pages 61-64 Exact Critical Properties of Two-Dimensional Polymer Networks from Conformal Invariance....Pages 65-79 A Hierarchical Schrödinger Operator....Pages 80-83 Universality and Nonuniversality in Frustrated Smectics....Pages 84-87 A Langevin Equation Approach to Sine-Gordon Soliton Diffusion with Application to Nucleation Rates....Pages 88-92 Disorder, Frustration and Critical Exponents....Pages 93-99 Universality Classes of Fluctuating Membranes....Pages 100-105 Diffusion Fronts of Interacting Particles....Pages 106-108 Static Scaling with T c Positive, Null or Negative....Pages 109-112 Front Matter....Pages 23-23 Magnetic Frustration and Pairing in Doped Lathanum Cuprate....Pages 113-116 Front Matter....Pages 117-117 On the Shape of Trees: Tools to Describe Ramified Patterns....Pages 118-124 Scaling and Universality in Multifractal Growth Processes....Pages 125-128 Theory of Fractal Growth....Pages 129-131 The Hunt for Universality in Fracture....Pages 132-135 Multifractal Viscous Fingering and Non-Newtonian Growth....Pages 136-141 Scattering by Fractal Structures....Pages 142-145 Capillary Aggregation at an Interface....Pages 146-149 Kinetics of Aggregation in a Sheared Dispersion of Macroscopic Spheres....Pages 150-152 Reaction-Limited Aggregation: Recent Simulation Results....Pages 153-158 Cluster-Cluster Aggregation of Magnetic Particles....Pages 159-161 Diffusion Limited Aggregation on the Torus....Pages 162-164 Filtered Operators and Ultrametricity....Pages 165-167 Front Matter....Pages 169-169 Random Multiplicative Processes and Multifractals....Pages 170-175 Universal Properties of Multifractal Moments: Analogies with Critical Phenomena....Pages 176-182 Multifractal Analysis in the Circle Map: Analogies with Critical Phenomena....Pages 183-187 Correlations in Multifractals....Pages 188-190 Bulk and Surface Exponents at the d=2 Θ-Point....Pages 191-192 Rough Surfaces: Scaling Theory and Universality....Pages 193-198 Computer Simulation of Random Ballistic Deposition....Pages 199-205 Front Matter....Pages 207-207 Scaling Properties of Soft Thermal Turbulence in Rayleigh-Bénard Convection....Pages 208-212 The Organization of Chaos by Periodic Orbits: Topological Universality of Complex Systems....Pages 213-215 Some Results on Lyapunov Exponents for Products of Random Matrices....Pages 216-219 Relevance of Classical Chaos in Quantum Mechanics....Pages 220-223 Intermittency and Equilibrium Measures in Dynamical Systems....Pages 224-228 Chaos in a Model of Random Neural Networks....Pages 229-232 Phase Transitions on Strange Attractors and Fractal Aggregates....Pages 233-235 Diffusion of Passive Scalars in Fluid Flows: Maps in Three Dimensions....Pages 236-241 Gap Road: Main Properties....Pages 242-245 Dynamics and Damage Spreading in Cooperative Systems: A Numerical Search for Universality....Pages 246-249 Universality in Relaxation of Disordered Systems....Pages 250-256 Back Matter....Pages 257-258