Adiabatic elimination and reduced probability distribution functions in spatially extended systems with a fluctuating control parameter

Journal Article · Wed Aug 01 04:00:00 EDT 2001 · Physical Review E

DOI:https://doi.org/10.1103/PhysRevE.64.026120· OSTI ID:40277012

Drolet, Franc ois; Vinals, Jorge

We obtain the stationary probability distribution functions of the order parameter near onset for the one-dimensional real Ginzburg-Landau and Swift-Hohenberg equations with a fluctuating control parameter. A perturbative expansion in the intensity of the fluctuations leads to a hierarchy of Fokker-Planck equations for conditional probability distribution functions that relate components of the order parameter that evolve in different time scales. Successive integration leads to a Fokker-Planck equation for the slowest mode, which we solve analytically for the models studied. In all cases, the probability distribution function above onset is of the form P(A{sub 0}){proportional_to}A{sub 0}{sup {delta}}e{sup -{gamma}A{sub 0}{sup 2}}, where A{sub 0} is the slow component of the order parameter and the values of {delta} and {gamma} depend explicitly on the intensity of the fluctuations. Knowledge of P(A{sub 0}) allows the calculation of an effective bifurcation threshold and of the moments of A{sub 0} above threshold.

• Sponsoring Organization: (US)
• DOE Contract Number: FG05-95ER14566
• OSTI ID: 40277012
• Journal Information: Physical Review E, Journal Name: Physical Review E Journal Issue: 2 Vol. 64; ISSN 1063-651X
• Publisher: The American Physical Society
• Country of Publication: United States
• Language: English

Related Subjects

71 CLASSICAL AND QUANTUM MECHANICS
GENERAL PHYSICS
BIFURCATION
DISTRIBUTION FUNCTIONS
FLUCTUATIONS
FOKKER-PLANCK EQUATION
ORDER PARAMETERS
PROBABILITY