Gradient correlation

Becke, A. D., 1992b, Density Functional Thermochemistry. II. The Effect of the Perdew-Wang Generalized-Gradient Correlation Correction , J. Chem. Phys., 97, 9173. 

In homogeneous, locally isotropic turbulence the velocity-gradient correlation terms in (2.127) simplify to (Pope 2000)... 

Scalar correlation at the diffusive scales can be measured by the scalar-gradient correlation function ... 

In order to illustrate how the multi-variate SR model works, we consider a case with constant Re>. = 90 and Schmidt number pair Sc = (1, 1/8). If we assume that the scalar fields are initially uncorrelated (i.e., pup 0) = 0), then the model can be used to predict the transient behavior of the correlation coefficients (e.g., pap(i)). Plots of the correlation coefficients without (cb = 0) and with backscatter (Cb = 1) are shown in Figs. 4.14 and 4.15, respectively. As expected from (3.183), the scalar-gradient correlation coefficient gap(t) approaches l/yap = 0.629 for large t in both figures. On the other hand, the steady-state value of scalar correlation pap depends on the value of Cb. For the case with no backscatter, the effects of differential diffusion are confined to the small scales (i.e., (), / h and s)d) and, because these scales contain a relatively small amount of the scalar energy, the steady-state value of pap is close to unity. In contrast, for the case with backscatter, de-correlation is transported back to the large scales, resulting in a lower steady-state value for p p. 

Gross, T.S., Edwards, J.L., et.al. (1997) Strain gradients correlate with sites of periosteal bone formation. Journal of Bone and Mineral Research 12 982-8... 

The one-electron Kohn-Sham equations were solved using the Vosko-Wilk-Nusair (VWN) functional [27] to obtain the local potential. Gradient correlations for the exchange (Becke fimctional) [28] and correlation (Perdew functional) [29] energy terms were included self-consistently. ADF represents molecular orbitals as linear combinations of Slater-type atomic orbitals. The double- basis set was employed and all calculations were spin unrestricted. Integration accuracies of 10 -10 and 10 were used during the single-point and vibrational frequency calculations, respectively. The cluster size chosen for Ag or any bimetallic was... 

Measurements from the in vivo invasion assay have been shown to correlate with the metastatic properties of cancer cells in a xenograft model of breast cancer, with more metastatic cells invading 15-fold more efficiently than less metastatic cancer cells in response to an EGF gradient, correlating with their in vitro chemotactic responses to EGF (10). Transgenic models of breast cancer have also been examined, and the invasiveness of breast cancer cells to chemoattractants such as TGF-a and heregulin among others was evaluated in the polyoma Middle T model (11). 

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