Shallow water model for aluminium electrolysis cells with variable top and bottom

The MHD wave instability in commercial cells for electrolytic aluminium production is often described using ‘shallow water’ models. The model [1] is extended for a variable height cathode bottom and anode top to account for realistic cell features. The variable depth of the two fluid layers affects the horizontal current density, the wave development and the stability threshold. Instructive examples for the 500 kA cell are presented.

Moment decay rates of solutions of stochastic differential equations

The objective of this paper is to investigate the p-ίh moment asymptotic stability decay rates for certain finite-dimensional Itό stochastic differential equations. Motivated by some practical examples, the point of our analysis is a special consideration of general decay speeds, which contain as a special case the usual exponential or polynomial type one, to meet various situations. Sufficient conditions for stochastic differential equations (with variable delays or not) are obtained to ensure their asymptotic properties. Several examples are studied to illustrate our theory.

Performance analysis of a register insertion ring with a variable size buffer

There has been a recent revival of interest in the register insertion (RI) protocol because of its high throughput and low delay characteristics. Several variants of the protocol have been investigated with a view to integrating voice and data applications on a single local area network (LAN). In this paper the performance of an RI ring with a variable size buffer is studied by modelling and simulation. The chief advantage of the proposed scheme is that an efficient but simple bandwidth allocation scheme is easily incorporated. Approximate formulas are derived for queue lengths, queueing times, and total end-to-end transfer delays. The results are compared with previous analyses and with simulation estimates. The effectiveness of the proposed protocol in ensuring fairness of access under conditions of heavy and unequal loading is investigated.