Colloquium Salvatore Torquato
When: Friday 6 September 2013
Where: Ceres building, CE0.31, TU/e campus
In the first part of this presentation I will show how inverse statistical-mechanical techniques can be used to challenge conventional wisdom about the nature of classical low-temperature states of matter. A number of questions are posed that have surprising answers. Can low-coordinated crystal structures, such as solid forms of carbon (e.g., graphene or diamond crystal structures) be the ground states of many-particle interactions that involve only non-directional (isotropic) pair potentials? Are there single-component many-particle systems characterized by isotropic pair potentials that possess exotic low-temperature bulk properties, such as negative thermal expansion or negative Poisson's ratio? Can ground states ever be disordered? In other words, can cooling a liquid to absolute zero result in a completely disordered many-particle configuration (as opposed to the usual crystal ground state)? I will show that the answers to all of these questions are in the affirmative, and have fundamental and practical implications. I then will turn my attention to dense packings of convex and concave solids (particles) in three-dimensional Euclidean space. Over the past decade there has been increasing interest in the effects of particle shape on the characteristics of dense particle packings, since they are of fundamental interest and can lead to more realistic models of granular media, nanostructured materials, and tissue architecture. We have formulated organizing principles to obtain dense particle packings based on characteristics of the particle shape and symmetry.
In the second part of this presentation, I will discuss two-phase random heterogeneous materials, which abound in nature and in synthetic situations. Examples of such natural materials include geologic media, animal and plant tissue, bone, blood and lungs; synthetic materials include all types of composites, colloids, concrete, packed beds and gels. It is a challenge to relate the macroscopic transport and mechanical properties of such materials to the underlying structure at the "microscopic" scale. I will begin with a brief description of rigorous methods to link the macroscopic properties of heterogeneous materials to various correlation functions that statistically characterize the media. I then consider two intriguing inverse problems. The first concerns the reconstruction of two-phase random media using limited microstructural information as measured by statistical correlation functions. I describe a general procedure that we have formulated to reconstruct general digitized random heterogeneous materials that is simple to implement and can incorporate any type and number of correlation functions. The second inverse problem concerns the optimal design of material microstructures to achieve desirable macroscopic properties, which puts no constraints on the allowable topologies.