The emergent collective phenomena of structure and elasticity in architecturally complex media

Department Colloquia

Speaker: Paul Goldbart, Georgia Tech
Date & Time: November 14, 2013 16:00 - 17:00
Location: UBC, Hennings 201
Local Contact: Robert Raussendorf
Intended Audience: Undergraduate

Launched before the atomic hypothesis held sway, the conventional theory of elasticity is a spectacular intellectual achievement. A continuum-level theory, it furnishes scientists and engineers with a powerful, internally consistent toolkit for determining how architecturally simple (i.e., regular) solid media such as crystals respond macroscopically to imposed stresses, whilst encoding the underlying microscopic details of the atomic realm economically, via a handful of numerical parameters. Solids that are architecturally complex (i.e., highly irregular) at the atomic or molecular level (such as vulcanized rubber, gels and glasses) are also commonly addressed using conventional elasticity theory. However, the irregularity of these media at the microscopic level raises new issues, not only of elasticity but also of structure: In what way do the elastic “constants” of such media fluctuate across a sample? Do such media strain non-affinely in response to imposed stresses? Are there regional variations in the thermal position-fluctuations of the constituent atoms? And, more generally, can the structure and elasticity of architecturally complex solids be viewed as emergent collective phenomena, determinable from their underlying, microscopic thermal motion and characterizable by some suitable continuum theory? I shall explain the essential elements of a microscopic approach to the physical properties of architecturally complex media, pioneered by Sam Edwards in the mid-1970s, which has given rise to our modern continuum-based notions of structure and elasticity for irregular solids. At the heart of this microscopic approach is an extension of statistical mechanics that enables the handling of architecturally complex media, with their two distinct classes of microscopic random variables: the (equilibrating) atomic coordinates and the (fixed) descriptors of the architectural complexity. Edwards’ bold extrapolation hints at a continuum theory for complex media whose mathematical form would be hard to divine without this microscopic intervention: the fields of this continuum theory are curious entities, depending on a continuously tunable number of copies of the three-dimensional position-vector. This tunability permits the encoding and determination of detailed statistical information about the emergent, spatially heterogeneous structure and elasticity of complex solids.