scholarly journals Evaluation of the Time Correlation Function for the Kuramoto-Sivashinsky Equation with a Projection Operator Method

2006 ◽  
Vol 116 (1) ◽  
pp. 47-59 ◽  
Author(s):  
Makoto Okamura
Keyword(s):  
Correlation Function ◽  
Projection Operator ◽  
Operator Method ◽  
Time Correlation ◽  
Time Correlation Function ◽  
Projection Operator Method ◽  
Sivashinsky Equation

An improved hierarchy for turbulent magnetized plasma Part 1. Theory

1972 ◽  
Vol 7 (2) ◽  
pp. 337-362
Author(s):  
Eldon J. Linnebur ◽  
Terry Kammash
Keyword(s):  
Magnetic Field ◽  
Correlation Function ◽  
Time Dependence ◽  
Projection Operator ◽  
Kinetic Equations ◽  
Time Correlation ◽  
Time Correlation Function ◽  
Turbulent Plasma ◽  
Magnetized Plasma ◽  
Consistent Manner

The kinetic equations for infinite homogeneous turbulent plasma in a magnetic field are analyzed using a projection operator which allows the time dependence to be maintained in a more exact and consistent manner than has been possible heretofore. By introducing approximations on the multi-time correlation function rather than the fluctuations, as is conventionally done, a hierarchy of equations is obtained which predicts different behaviour for the system especially in connexion with wave-wave interations. These effects are further highlighted by showing how the present results reduce to those obtained by various authors.

Rate Constants, Reactive Flux

2018 ◽  
Author(s):  
Niels Engholm Henriksen ◽  
Flemming Yssing Hansen
Keyword(s):  
Correlation Function ◽  
Rate Constant ◽  
Cross Sections ◽  
Time Correlation ◽  
Time Correlation Function ◽  
Exact Expression ◽  
Reaction Cross ◽  
Dividing Surface ◽  
Definition Of ◽  
Reactive Flux

This chapter discusses a direct approach to the calculation of the rate constant k(T) that bypasses the detailed state-to-state reaction cross-sections. The method is based on the calculation of the reactive flux across a dividing surface on the potential energy surface. Versions based on classical as well as quantum mechanics are described. The classical version and its relation to Wigner’s variational theorem and recrossings of the dividing surface is discussed. Neglecting recrossings, an approximate result based on the calculation of the classical one-way flux from reactants to products is considered. Recrossings can subsequently be included via a transmission coefficient. An alternative exact expression is formulated based on a canonical average of the flux time-correlation function. It concludes with the quantum mechanical definition of the flux operator and the derivation of a relation between the rate constant and a flux correlation function.

Two-body dynamics in fluids as probed by interaction-induced light scattering

1981 ◽  
Vol 59 (10) ◽  
pp. 1504-1509 ◽  
Author(s):  
U. Balucani ◽  
R. Vallauri
Keyword(s):  
Correlation Function ◽  
Light Scattering ◽  
Time Correlation ◽  
Time Correlation Function ◽  
Simulation Experiments ◽  
Particle Pairs ◽  
Body Dynamics ◽  
Atomic Fluids ◽  
Relative Dynamics

The relative dynamics of particle pairs in fluids is investigated both theoretically and by simulation experiments. The physical implications of this analysis are important in all interaction-induced phenomena and illustrated in the case of the pair time correlation function relevant to collision-induced light scattering in atomic fluids.

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