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.

Multiple attractors of host-parasitoid models with integrated pest management strategies: eradication, persistence and outbreak

Host-parasitoid models including integrated pest management (IPM) interventions with impulsive effects at both fixed and unfixed times were analyzed with regard to host-eradication, host-parasitoid persistence and host-outbreak solutions. The host-eradication periodic solution with fixed moments is globally stable if the host's intrinsic growth rate is less than the summation of the mean host-killing rate and the mean parasitization rate during the impulsive period. Solutions for all three categories can coexist, with switch-like transitions among their attractors showing that varying dosages and frequencies of insecticide applications and the numbers of parasitoids released are crucial. Periodic solutions also exist for models with unfixed moments for which the maximum amplitude of the host is less than the economic threshold. The dosages and frequencies of IPM interventions for these solutions are much reduced in comparison with the pest-eradication periodic solution. Our results, which are robust to inclusion of stochastic effects and with a wide range of parameter values, confirm that IPM is more effective than any single control tactic.

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.

Predicting the relationship between reliability and geometric parameters of cu column bumped flip-chips

Cu column bumping is a novel flip chip packaging technique that allows Cu columns to be bonded directly with the dies. It has eliminated the under-bump-metallurgy (UBM) fonnation step of the traditional flip chip manufacturing process. This bumping technique has the potential benefits of simplifying the flip chip manufacturing process, increasing productivity and the UO counts. In this paper, a study of reliability of Cu column bumped flip chips will be presented. Computer modelling methods have been used to predict the shape of solder joints and the response of flip chips to cyclic thermal-mechanical loading. The accumulated plastic strain energy at the corner solder joints has been used as an indicator of the solder joint reliability. Models with a wide range of design parameters have been compared for their reliability. The design parameters that have been investigated are the copper column height and radius, PCB pad radius, solder volume and Cu column wetting height. The relative importance ranking of these parameters has been obtained. The Lead-free solder material 96.5Sn3.5Ag has been used in this modelling work.

Ontological considerations of time, meta-predicates and temporal propositions

A natural approach to representing and reasoning about temporal propositions (i.e., statements with time-dependent truth-values) is to associate them with time elements. In the literature, there are three choices regarding the primitive for the ontology of time: (1) instantaneous points, (2) durative intervals and (3) both points and intervals. Problems may arise when one conflates different views of temporal structure and questions whether some certain types of temporal propositions can be validly and meaningfully associated with different time elements. In this paper, we shall summarize an ontological glossary with respect to time elements, and diversify a wider range of meta-predicates for ascribing temporal propositions to time elements. Based on these, we shall also devise a versatile categorization of temporal propositions, which can subsume those representative categories proposed in the literature, including that of Vendler, of McDermott, of Allen, of Shoham, of Galton and of Terenziani and Torasso. It is demonstrated that the new categorization of propositions, together with the proposed range of meta-predicates, provides the expressive power for modeling some typical temporal terms/phenomena, such as starting-instant, stopping-instant, dividing-instant, instigation, termination and intermingling etc.