Emergent Structures in Complex Systems

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This award will support research in emergent structures in a variety of many-body systems, including complex networks and soft matter. Response to shear deformation will be used to prove the existence and nature of such emergent structures, within simplified models. The main technique used will be variants of equilibrium statistical mechanics.Crystalline solids and other emergent structures are composed of components but exhibit their useful features, such as mechanical strength, only when the number of components is very large. For this reason, although such structures are widely modelled in the sciences there is as yet insufficient understanding of the complicated role played by the vast number of components. This award will support a newapproach to obtain effective mathematical control of the components in modelling these technologically important structures.