Ensemble correlation function computation by multiplication

1967 ◽  
Vol 55 (1) ◽  
pp. 116-116
Author(s):  
T.R. O'Meara
Keyword(s):  
Correlation Function ◽  
Function Computation ◽  
Ensemble Correlation

Increasing the Efficiency of Using Hardware Resources for Time-Frequency Correlation Function Computation

2014 ◽  
Vol 1040 ◽  
pp. 969-974 ◽  
Author(s):  
Valeriy V. Avramchuk ◽  
E.E. Luneva ◽  
Alexander G. Cheremnov
Keyword(s):  
Fourier Transform ◽  
Correlation Function ◽  
Fast Fourier Transform ◽  
Sample Size ◽  
Optimal Number ◽  
Computing Technique ◽  
Frequency Correlation ◽  
Time Frequency ◽  
Function Computation ◽  
Fixed Base

In the article the techniques of increasing efficient of using multi-core processors for the task of calculating the fast Fourier transform were considered. The fast Fourier transform is led on the basis of calculating a time time-frequency correlation function. The time-frequency correlation function allows increasing the information content of the analysis as compared with the classic correlation function. The significant computational capabilities are required to calculate the time-frequency correlation function, that by reason of the necessity of multiple computing fast Fourier transform. For computing the fast Fourier transform the Cooley-Tukey algorithm with fixed base two is used, which lends itself to efficient parallelization and is simple to implement. Immediately before the fast Fourier transform computation the procedure of bit-reversing the input data sequence is used. For algorithm of calculating the time-frequency correlation function parallel computing technique was used that experimentally allowed obtaining the data defining the optimal number of iterations for each core of the CPU, depending on the sample size. The results of experiments allowed developing special software that automatically select the effective amount of subtasks for parallel processing. Also the software provides the choice of sequential or parallel computations mode, depending on the sample size and the number of frequency intervals in the calculation of time-frequency correlation function.

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.

scholarly journals Investigation of local maxima of the modified modular correlation function

2020 ◽  
Vol 1515 ◽  
pp. 042105
Author(s):  
D M Malinichev ◽  
E A Melnikova ◽  
Y V Prus
Keyword(s):  
Correlation Function ◽  
Local Maxima

A Rheo-optical Investigation into the Viscoelastic Moduli of Acidified Milk Gel

1999 ◽  
Vol 9 (6) ◽  
pp. 246-253 ◽  
Author(s):  
E. O. Arikainen ◽  
J. C. Earnshaw ◽  
A. Wehling ◽  
E. Waghorne
Keyword(s):  
Correlation Function ◽  
Mean Square Displacement ◽  
Slow Motion ◽  
Casein Micelle ◽  
Optical Investigation ◽  
Viscoelastic Moduli ◽  
Decay Times ◽  
Delay Times ◽  
Intensity Correlation Function ◽  
Viscoelastic Modulus

Abstract Diffusing wave spectroscopy (DWS) in the backscattering geometry was employed to observe the evolution of the intensity correlation function during the acidification of skimmed milk by gluconic-δ-lactone (GDL). At the stage when the formation of casein particle gel is largely complete the correlation function at shorter decay times reveals the local structural arrest of the casein micelles, whereas at longer delay times it illustrates the hindered slow motion of casein micelle aggregates. We use the principles of the approach suggested by Mason, Gang and Weitz, linking the optically measured mean square displacement, <Δr2(t)>, of the microscopic particles in a dense colloid to its viscoelastic properties, to provide an estimate of the frequency dependent viscoelastic modulus of the acidified milk gel (AMG). We compare the viscoelastic moduli measured by the conventional mechanical rheometry with the optically measured ones. The results of the two different experimental methods are found to be in reasonable agreement.

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