A dependency is seen between mixing time and the higher order moments of length scale distribution, viz., skewness and kurtosis and a generalized correlation has been built up for important types of equipment and associated flow parameters.
A linear mixed-effects model analysis (fixed factor) revealed statistically significant differences (p<0.01) in the transport rates between the wild type and all mutant genotypes, between the d6pk single mutants and the higher order d6pk mutants as well as between the d6pk01 double mutant and the d6pk012 triple mutant.
Step 3. The positive integer 'm' can be determined by considering the homogeneous balance between the highest order derivatives and the nonlinear terms appearing in Eq. (10).
Step 3. Determine the positive integer N in Eq. (6) by considering the homogeneous balance between the highest order derivatives and the nonlinear terms in Eq. (5).
By balancing the order between the highest order derivative term and nonlinear term in Eq. (13), we can obtain m = 2. So, we have U = a 0 + a 1 ( D ξ α G G ) + a 2 ( D ξ α G G ) 2. (15).
Considering the homogeneous balance between the highest order derivatives and the nonlinear terms in (13), we get U = α 0 + α 1 ϕ + α 2 ϕ 2 + α 3 ϕ + α 4 ϕ 2 , (14).
Considering the homogeneous balance between the highest order derivative and the nonlinear term in (24), we have U = α 0 + α 1 ϕ + α 2 ϕ 2 + α 3 ϕ + α 4 ϕ 2 , (25).
where a j, i, i = − m j, …, 0, 1, …, m j, j = 1, 2, …, k are constants to be determined later, the positive integer m j can be determined by considering the homogeneous balance between the highest order derivatives and nonlinear terms appearing in (9), G = G satisfies the fractional Jacobi elliptic equation denoted by (1).
