Stability and cycles in a cobweb model with heterogeneous expectations

We investigate the dynamics of a cobweb model with heterogeneous beliefs, generalizing the example of Brock and Hommes (1997). We examine situations where the agents form expectations by using either rational expectations, or a type of adaptive expectations with limited memory defined from the last two prices. We specify conditions that generate cycles. These conditions depend on a set of factors that includes the intensity of switching between beliefs and the adaption parameter. We show that both Flip bifurcation and Neimark-Sacker bifurcation can occur as primary bifurcation when the steady state is unstable.

Heterogeneous nucleation of Mg-Al alloys

Grain size is one of the most important microstructural characteristics determining the mechanical properties and therefore the service performance of polycrystalline materials. Heterogeneous nucleation involves the addition or in situ formation of potent nuclei in the system to promote nucleation events, leading to a fine grain structure. This paper reports experimental results using graphite and SiC as potential grain refining agents to form in situ nuclei for Mg in Mg-Al alloys, and demonstrates the key role of Al4C3 in grain refilling this important alloy system. This insight will contribute to the design and development of the most cost effective, eco-friendly grain refining agents for Mg-Al alloys. (c) 2006 Acta Materialia Inc. Published by Elsevier Ltd. All rights reserved.