This paper presents a class of packing problems where circles may be placed either inside or outside other circles, the whole set being packed in a rectangle. This corresponds to a practical problem of packing tubes in a container. Before being inserted in the container, tubes may be put inside other tubes in a recursive fashion. A variant of the greedy randomized adaptive search procedure is proposed for tackling this problem, and its performance is assessed in a set of benchmark instances.

Melting is a major step in plasticating single screw extrusion, but most of the existing phenomenological know how was gathered by performing Maddock-type experiments with homopolymers. Given the current widespread industrial use of polymer blends, it is worth determining whether the same mechanisms and mathematical models apply, or whether different sequences develop. This work reports the results of Maddock-type experiments using a PA6/PP blend, both in its immiscible and compatibilized varieties. A melting mechanism combining the features of the classical Tadmor mechanism and of the dispersed melting mechanism, also previously reported in the literature, was observed.

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A prototype modular single screw extruder fitted with a screw extracting device is used to monitor melting of an immiscible polymer blend (PP/PA6, with different weight ratios) in this widely used processing equipment. As anticipated, the phenomena observed are much more complex than those involved in extruding PP or PA6, when the well known Maddock/Tadmor mechanism is valid. Consequently a hybrid melting mechanism, involving Maddock/Tadmor and Dispersive melting sequences, is proposed.

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