Venting of gas explosion through relief ducts: interaction between internal and external explosions.

Relief ducts fitted to venting openings is a widespread configuration in the industrial practice. The presence of a duct has been reported to severely increase the violence of the vented explosion posing a problem for the proper design of the venting device. Several studies have reported the leading importance--in the whole complex explosion phenomenology--of a secondary explosion in the duct. Modern approaches in the study of simply vented explosions (without ducts) have focused on the study of the interaction between internal and external explosion as a key issue in the mechanisms of pressure generation. The issue is even more relevant when a duct is fitted to the vent due the confined nature of the external explosion. In this work the interaction between internal and external events is experimentally investigated for gas explosions vented through a relief duct. The work has aimed at studying mechanisms underlying the pressure rise of this venting configuration. The study has put the emphasis on the mutual nature of the interaction. A larger scale than laboratory has been investigated allowing drawing results with a greater degree of generality with respect to data so far presented in literature.

The hard-hexagon model and Rogers-Ramanujan type identities.

In regime II of Baxter's solution of the hard-hexagon model [Baxter, R. J. (1980) J. Phys. A 13, L61-L70], he presents six conjectures identifying certain one-dimensional partition functions with infinite products. An outline of the proof of these conjectures is given here.

MacMahon's conjecture on symmetric plane partitions.

In 1898, P. A. MacMahon conjectured that the generating function for symmetric plane partitions with at most s rows and each part at most j has an especially simple closed form. An outline of the proof of this conjecture is given here.

An analytic generalization of the rogers-ramanujan identities for odd moduli.

A (k - 1)-fold Eulerian series expansion is given for II(1 - q(n))(-1), where the product runs over all positive integers n that are not congruent to 0,i or - i modulo 2k + 1. The Rogers-Ramanujan identities are the cases k = i = 2 and k = i + 1 = 2.