A number of aperture distributions are tested: log-normal and power-law distributions (from narrow to broad), and one where the aperture is proportional to the fracture length.
Our new TP- and TE-statistic should also be useful for other applications in the natural sciences as a powerful non-parametric test for power-laws and exponentials.
As a preliminary test for power law behavior, T1ρ2 was plotted against γB1 for various BSA and tissue samples.
Statistical tests on the fitted power-law exponent and the calculated compliances were done in SPSS version 16 for Windows.
In the power law test, we calculated the p′-value for the best power-law fit for the empirical data set.
Open image in new window Fig. 8 Power curve showing laminar and turbulent regimes for the Power-Law fluids tested.
Since information on fracture apertures, especially in the subsurface, is limited, we test power-law distributions (from narrow to broad), log-normal distributions (from narrow to broad), and one case in which the aperture is proportional to the fracture length.
Here, a refined higher order shear and normal deformation theory is presented for exponential (E), power-law (P) and sigmoid (S) functionally graded material (FGM) plates on elastic foundation.
Not all the cases examined above are tested here: For the cases with power-law aperture distributions, we examine α = 1.001, 2, and 6; for the cases of log-normal aperture distributions, we examine σ = 0.1, 0.2, and 0.6; we also test the cases where the aperture is proportional to the fracture length.
If the aperture distribution is broad enough (α ≤ 2 for power-law aperture distributions and σ ≥ 0.4 for log-normal aperture distributions), most of the fractures can be eliminated without significantly reducing the effective permeability.
