Relaxation at Critical Points: Deterministic and Stochastic Theory.

Abstract

A generalized critical point is characterized by totally non-linear dynamics. The deterministic and stochastic theory of relaxation is formulated at such a point. Canonical problems are used to motivate the general solutions. In the deterministic theory, at the critical point certain modes have polynomial (rather than exponential) growth or decay. The stochastic relaxation rates can be calculated in terms of various incomplete special functions. Three examples are considered. First, a substrate inhibited reaction (marginal type dynamical system). Second, the relaxation of a mean field ferromagnet. A result is obtained that generalizes the work of Griffiths et al. Third, the relaxation of a critical harmonic oscillator, is considered.

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Document Details

Document Type
Technical Report
Publication Date
Jun 01, 1978
Accession Number
ADA058540

Entities

People

  • Marc Mangel

Organizations

  • Center for Naval Analyses

Tags

Communities of Interest

  • C4I
  • Energy and Power Technologies
  • Human Systems
  • Materials and Manufacturing Processes

DTIC Thesaurus Topics

  • Business Administration
  • Chemical Reactions
  • Differential Equations
  • Diffusion
  • Eigenvalues
  • Eigenvectors
  • Equations
  • Information Processing
  • Information Science
  • Nonlinear Dynamics
  • Operations Research
  • Oscillators
  • Physics
  • Polynomials
  • Statistical Mechanics
  • Steady State
  • Ussr

Fields of Study

  • Physics

Readers

  • Mathematical Modeling and Probability Theory.
  • Quantum spin resonance or Electron Paramagnetic Resonance spectroscopy.