Numerical Methods in the Study of Critical Phenomena [E-Book] : Proceedings of a Colloquium, Carry-le-Rouet, France, June 2–4, 1980 / edited by Jean Della Dora, Jacques Demongeot, Bernard Lacolle.
Demongeot, Jacques, (editor)
Dora, Jean Della, (editor) / Lacolle, Bernard, (editor)
Berlin, Heidelberg : Springer, 1981
X, 272 p. online resource.
Springer Series in Synergetics ; 9
Full Text
Table of Contents:
  • 1. Mathematical Methods
  • 1.1 Study of Singularities
  • Padé-Hermite Approximants
  • Somme Comments About the Numerical Utilization of Factorial Series
  • to Real Quasianalytic Classes and Continuation Problems
  • 1.2 Critical Phenomena in Dynamical Systems
  • Groups Transformations and Critical Asymptotics Applications to Non-Linear Differential and Partial Derivative Equations
  • Antecedent Invariant Curves of an Endomorphism. Influence Domain of a Stable Cycle Coexisting with an Isolated Stable Invariant Curve
  • Topological Entropy As a Measure of Dynamic Chaos in Endomorphisms
  • Topological Entropy of Markov Processes for a C0-Endomorphism of the Interval
  • Sequential Iteration of Threshold Functions
  • Some Properties of Second Order Dynamic Systems with Parametric Resonances
  • 2. Applications in Physics
  • 2.1 Critical Phenomena in Solid-State Physics
  • On the Bifurcation of Certain Kam Tori in the Standard Mapping
  • MO Stochasticity Criterion
  • Singularities in Saw Numerical Simulations
  • Monte Carlo Measurement of the Single Vortex Free Energy in the Kosterlitz-Thouless Theory
  • Algebraic Method for the Computation of the Partition Functions of Spin Glasses and Numerical Study of the Distributions of Zeros
  • Percolation and Gelation by Additive Polymerization
  • Ground State Structure of the Random Frustration Model in Two Dimensions
  • Line Defects and the Glass Transition
  • Universality in Size-Effects in 2D Percolation
  • 2.2 Use of Renormalisation Techniques
  • The Phenomenological Renormalization Method
  • Computation of the Yang-Lee Edge Singularity in Ising Models
  • Real-Space Renormalization-Group Method for Quantum Systems: Application to Quantum Frustration in Two Dimensions
  • Yang-Lee Edge Singularity by Real Space Renormalization Group
  • 3. Applications in Biology
  • Numerical Determination of a Periodical Solution of Discontinuous Type, near a Singular Point, for a Neurophysiological Model
  • On the Relation Between the Logical Structure of Systems and Their Ability to Generate Multiple Steady States or Sustained Oscillations
  • Critical Delays in Logical Asynchronous Models
  • 4. Applications in Chemistry
  • A Simulation Technique for Studying Critical Properties of Chemical Dissipative Systems
  • Critical Paths and Passes: Application to Quantum Chemistry
  • 5. Non-Physical Applications of Statistical Mechanics
  • Telephone Network: Statistical Mechanics and Non-Random Connecting Procedures
  • The Thermodynamic Formalism in Population Biology
  • Asymptotic Inference for Markov Random Fields on Zd
  • List of Contributors.