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ERC

SOLLIQ Report Summary

Project ID: 291053
Funded under: FP7-IDEAS-ERC
Country: United Kingdom

Final Report Summary - SOLLIQ (Mathematics of solid and liquid crystals)

The project had two main themes:
(i) the prediction and understanding of microstructure arising from phase transformations in alloys arising from a change of shape of the underlying crystal lattice (so-called martensitic phase transformations). Two of the main novel outcomes were the development of a probabilistic model for the complex microstructure formation process with the aim of understanding power laws arising in acoustic emissions, and the extension of the nonlinear elasticity model to cover aspects of steels, whose large transformation strains and complex behaviour had previously seemed inaccessible. Other developments arising from the project were related to the dynamic formation of microstructure, to metastability arising from geometric incompatibility of parent and product phases, and to the understanding of complex interfaces and polycrystalline microstructure.

(ii) the study of mathematical models of liquid crystals and the relation between them. New directions developed during the project included the modelling of wall defects by allowing the director (which describes the mean orientation of the liquid crystal molecules) to jump across surfaces, the analysis of Onsager models in which the molecular orientations are described by a probability density, and the study of line defects and of defects in nematic shells.

In addition the project led to several related advances in the broad area of applied analysis.

Reported by

THE CHANCELLOR, MASTERS AND SCHOLARS OF THE UNIVERSITY OF OXFORD
United Kingdom
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