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Passage through a barrier with a slowly increasing control parameter

Nicolis1, Nicolis

  • 1Institut Royal Meteorologique de Belgique, Avenue Circulaire 3, 1180 Brussels, Belgium.

Physical Review. E, Statistical Physics, Plasmas, Fluids, and Related Interdisciplinary Topics
|November 23, 2000
PubMed
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This study investigates bistable systems with noise and changing parameters, finding that a ramped control parameter alters state transition kinetics differently than predicted by classical theories.

Area of Science:

  • Physics
  • Physical Chemistry
  • Nonlinear Dynamics

Background:

  • Bistable systems exhibit two stable states separated by an energy barrier.
  • Noise and external parameters influence transitions between these states.
  • Classical Kramers theory describes barrier crossing rates in equilibrium systems.

Purpose of the Study:

  • To analyze the kinetics of transitions in a bistable system under noise and a slowly increasing control parameter.
  • To compare the system's behavior with predictions from the classical Kramers theory.

Main Methods:

  • Theoretical study of a bistable system.
  • Analysis of noise-induced transitions.
  • Investigation of systems with a time-dependent control parameter (ramped parameter).

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Main Results:

  • The presence of a ramp in the control parameter significantly impacts the probability distribution across the barrier.
  • Deviations from classical Kramers theory predictions were observed.
  • The kinetics of barrier crossing are altered by the ramped parameter.

Conclusions:

  • Classical Kramers theory may not accurately predict transition kinetics in bistable systems with ramped control parameters.
  • The study highlights the importance of considering dynamic parameter changes in understanding system behavior.