Ebook: Universalities in Condensed Matter: Proceedings of the Workshop, Les Houches, France, March 15–25,1988

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.

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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.
Content:
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 Schr?dinger 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
Front Matter....Pages 109-112
Magnetic Frustration and Pairing in Doped Lathanum Cuprate....Pages 23-23
Front Matter....Pages 113-116
On the Shape of Trees: Tools to Describe Ramified Patterns....Pages 117-117
Scaling and Universality in Multifractal Growth Processes....Pages 118-124
Theory of Fractal Growth....Pages 125-128
The Hunt for Universality in Fracture....Pages 129-131
Multifractal Viscous Fingering and Non-Newtonian Growth....Pages 132-135
Scattering by Fractal Structures....Pages 136-141
Capillary Aggregation at an Interface....Pages 142-145
Kinetics of Aggregation in a Sheared Dispersion of Macroscopic Spheres....Pages 146-149
Reaction-Limited Aggregation: Recent Simulation Results....Pages 150-152
Cluster-Cluster Aggregation of Magnetic Particles....Pages 153-158
Diffusion Limited Aggregation on the Torus....Pages 159-161
Filtered Operators and Ultrametricity....Pages 162-164
Front Matter....Pages 165-167
Random Multiplicative Processes and Multifractals....Pages 169-169
Universal Properties of Multifractal Moments: Analogies with Critical Phenomena....Pages 170-175
Multifractal Analysis in the Circle Map: Analogies with Critical Phenomena....Pages 176-182
Correlations in Multifractals....Pages 183-187
Bulk and Surface Exponents at the d=2 ?-Point....Pages 188-190
Rough Surfaces: Scaling Theory and Universality....Pages 191-192
Computer Simulation of Random Ballistic Deposition....Pages 193-198
Front Matter....Pages 199-205
Scaling Properties of Soft Thermal Turbulence in Rayleigh-B?nard Convection....Pages 207-207
The Organization of Chaos by Periodic Orbits: Topological Universality of Complex Systems....Pages 208-212
Some Results on Lyapunov Exponents for Products of Random Matrices....Pages 213-215
Relevance of Classical Chaos in Quantum Mechanics....Pages 216-219
Intermittency and Equilibrium Measures in Dynamical Systems....Pages 220-223
Chaos in a Model of Random Neural Networks....Pages 224-228
Phase Transitions on Strange Attractors and Fractal Aggregates....Pages 229-232
Diffusion of Passive Scalars in Fluid Flows: Maps in Three Dimensions....Pages 233-235
Gap Road: Main Properties....Pages 236-241
Dynamics and Damage Spreading in Cooperative Systems: A Numerical Search for Universality....Pages 242-245
Universality in Relaxation of Disordered Systems....Pages 246-249
Back Matter....Pages 250-256
....Pages 257-258