Evaluation of hydraulic performance indices for retention ponds

Comprehensive hydraulic analysis of sediment retention ponds is commonly achieved through interpretation of residence time distribution and derivation of indices associated with short-circuiting and mixing. However, the availability of various indices indicates the need for careful selection of the most appropriate indices. This study compares some of the commonly used hydraulic performance indices, together with a new short-circuiting index, τ5, for five different flow regimes in a model sediment retention pond. The results show that τ5 was the best measure for short-circuiting. Among the mixing indices, only the Morril index correctly represented the physical behaviour of the experiments. In addition, two hydraulic efficiency indices, λ and a moment index (MI) were assessed and showed a good correlation with the short-circuiting and mixing indices, but MI was more reproducible than λ. Based on these results, this study recommends using τ5, Morril index and MI for analysis of hydraulic performance in sediment retention ponds.

A finite element analysis of idealized damage in beam structures

The strain energy damage index (SEDI) and a nominally similar parameter called SEDI2 are reported to be insensitive to the magnitude of the underlying damage in beams, although they do help to locate the damage itself. A new damage-sensitive parameter, the modal moment index (MMI), is introduced. It is shown that the MMI also ‘jumps’ at the location of damage in the beam. In addition, it is established that the magnitude of the MMI is closely related to the decrease in relative modulus. It is concluded hence that the MMI seems to be a damage-sensitive parameter with potential for application in experimental modal analysis.

The moment index of minima

For a random variable (RV) X its moment index κ(X) ≡ sup{κ : E(|X|κ) < ∞} lies in 0 ≤ κ (X) ≤∞; it is a critical quantity and finite for heavy-tailed RVs. The paper shows that κ (min(X, Y)) ≥ κ(X) + κ (Y) for independent non-negative RVs X and Y. For independent non-negative ‘excess' RVs Xs and Ys whose distributions are the integrated tails of X and Y, κ (X) + κ (Y) ≤ κ (min(Xs, Ys)) + 2 ≤ κ (min(X, Y)). An example shows that the inequalities can be strict, though not if the tail of the distribution of either X or Y is a regularly varying function.

The moment index of minima

For a random variable (RV) X its moment index κ(X) ≡ sup{κ : E(|X| κ ) &lt; ∞} lies in 0 ≤ κ (X) ≤∞; it is a critical quantity and finite for heavy-tailed RVs. The paper shows that κ (min(X, Y)) ≥ κ(X) + κ (Y) for independent non-negative RVs X and Y. For independent non-negative ‘excess' RVs Xs and Ys whose distributions are the integrated tails of X and Y, κ (X) + κ (Y) ≤ κ (min(Xs, Ys )) + 2 ≤ κ (min(X, Y)). An example shows that the inequalities can be strict, though not if the tail of the distribution of either X or Y is a regularly varying function.

Some interesting features of charged particles produced in high-energy hadron–emulsion collisions

The emission characteristics of secondary charged particles produced in 400 GeV proton–emulsion interactions were compared with those obtained at other energies. The results revealed that the angular distribution of grey particles does not depend on the nature and energy of the projectile. The dependence of the average multiplicity of the grey, black, shower, and heavily ionizing tracks on the mass of the target nucleus (A) and the nature and energy of the projectiles are also examined. The ratio of the valance quarks in pions (π−) and protons (p) was found to be almost equal to the ratio of the grey particles produced in π−–A and p–A collisions at the same energy. The values of the normalized moments of the multiplicity distributions of charged shower particles in different Nh intervals were found to be nearly the same. However, this value increased with increasing values of the moment index, K. Finally, the values of the normalized and central moments were almost equal for both p–p and p–A interactions.