Cross-correlation functions in two-dimensional and three-dimensional colloidal crystals

2001 ◽  
Vol 115 (23) ◽  
pp. 10945-10954 ◽  
Author(s):  
Yuichi N. Ohshima ◽  
Koushi E. Hatakeyam ◽  
Motoi Satake ◽  
Yumi Homma ◽  
Ryosuke Washidzu ◽  
...  
Keyword(s):  
Correlation Functions ◽  
Cross Correlation ◽  
Three Dimensional ◽  
Colloidal Crystals ◽  
Two Dimensional

Pattern Classification for GIS Base on GK Clustering Algorithm

2013 ◽  
Vol 448-453 ◽  
pp. 1955-1958
Author(s):  
Hui Wang ◽  
Xiu Wei Li ◽  
Yu Xin Yun ◽  
Hai Yan Yuan
Keyword(s):  
Pattern Classification ◽  
Cross Correlation ◽  
Clustering Algorithm ◽  
Partial Discharge ◽  
Three Dimensional ◽  
Pulse Amplitude ◽  
Correlation Factor ◽  
Two Dimensional ◽  
Clustering Method

Four typical defects in GIS for PD detection are proposed, and the pulse, amplitude, phases, number of PD has been used to form the three-dimensional PQN matrix. Based on the PQN matrix, three two-dimensional distributions of Hqmax~Phi, Hqmean~Phi and Hn~Phi can be achieved. Then the new GK clustering method is introduced to separate the four different defects according to separate the four different partial discharge defects in gas in GIS, according to the parameters of Skewness (Sk), Kurtosis (Ku), number of peaks (Pe), cross-correlation factor (CC) and the discharge factor Q.

scholarly journals Two-dimensional turbulence cross-correlation functions in the edge of NSTX

2017 ◽  
Vol 24 (10) ◽  
pp. 102509 ◽  
Author(s):  
S. J. Zweben ◽  
D. P. Stotler ◽  
F. Scotti ◽  
J. R. Myra
Keyword(s):  
Correlation Functions ◽  
Cross Correlation ◽  
Two Dimensional

scholarly journals An experimental investigation on Lagrangian correlations of small-scale turbulence at low Reynolds number

2007 ◽  
Vol 574 ◽  
pp. 405-427 ◽  
Author(s):  
MICHELE GUALA ◽  
ALEXANDER LIBERZON ◽  
ARKADY TSINOBER ◽  
WOLFGANG KINZELBACH
Keyword(s):  
Reynolds Number ◽  
Time Scales ◽  
Correlation Functions ◽  
Time Scale ◽  
Cross Correlation ◽  
Strain Tensor ◽  
Three Dimensional ◽  
Small Scale ◽  
Production Term ◽  
Long Time

Lagrangian auto- and cross-correlation functions of the rate of strain s2, enstrophy ω2, their respective production terms −sijsjkski and ωiωjsij, and material derivatives, Ds2/Dt and Dω2/Dt are estimated using experimental results obtained through three-dimensional particle tracking velocimetry (three-dimensional-PTV) in homogeneous turbulence at Reλ=50. The autocorrelation functions are used to estimate the Lagrangian time scales of different quantities, while the cross-correlation functions are used to clarify some aspects of the interaction mechanisms between vorticity ω and the rate of strain tensor sij, that are responsible for the statistically stationary, in the Eulerian sense, levels of enstrophy and rate of strain in homogeneous turbulent flow. Results show that at the Reynolds number of the experiment these quantities exhibit different time scales, varying from the relatively long time scale of ω2 to the relatively shorter time scales of s2, ωiωjsij and −sijsjkski. Cross-correlation functions suggest that the dynamics of enstrophy and strain, in this flow, is driven by a set of different-time-scale processes that depend on the local magnitudes of s2 and ω2. In particular, there are indications that, in a statistical sense, (i) strain production anticipates enstrophy production in low-strain–low-enstrophy regions (ii) strain production and enstrophy production display high correlation in high-strain–high-enstrophy regions, (iii) vorticity dampening in high-enstrophy regions is associated with weak correlations between −sijsjkski and s2 and between −sijsjkski and Ds2/Dt, in addition to a marked anti-correlation between ωiωjsij and Ds2/Dt. Vorticity dampening in high-enstrophy regions is thus related to the decay of s2 and its production term, −sijsjkski.

NMR imaging of fluids in porous solids

1990 ◽  
Vol 333 (1632) ◽  
pp. 441-452 ◽  
Keyword(s):  
Correlation Functions ◽  
Spin Echo ◽  
Three Dimensional ◽  
Porous Solids ◽  
Nmr Imaging ◽  
Two Dimensional ◽  
Related Property ◽  
Reservoir Rocks ◽  
Hydrocarbon Reservoir ◽  
Internal Structures

The principles governing the NMR behaviour of 1 H-containing fluids permeating porous solids, such as hydrocarbon reservoir rocks, are outlined. The additional capabilities of NMR imaging methods for characterizing these systems is considered. Experimental results are presented for NMR imaging applied to a model porous solid (alumina) and natural sandstone and limestone rocks, saturated with aqueous phases. Both three-dimensional and slice-selected two-dimensional FT spin echo methods are used and the images demonstrate the capability of NMRI in these systems to reveal internal structures of the porous solids. Simple strategies for characterizing the spatial heterogeneity of these materials in terms of histograms and correlation functions are proposed and a general pixel fitting program is used to examine some of the data in terms of such histograms and related property maps.

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