Abstract
This talk will look at a ubiquitous methodology in condensed matter physics and materials science that aims to understand bulk behaviors of many-body systems. The focus is on finding and characterizing structures that exist at scales in between the so-called fundamental or atomic, and that of the continuum. I will argue that such multiscale techniques provide justification and explanation for the continued use of effective theories in various theoretical contexts. My focus is on the role played by so-called “representative volume elements,” or RVEs, in homogenization theory. At everyday, continuum scales, a material like a steel beam looks reasonably homogenous. However, if we zoom in, we will begin to see structure that are hidden at everyday, naked-eye length scales. In order to model the main, important features of the piece of steel at these shorter length scales, scientists employ RVEs. RVEs are statistically representative of features of a material at some particular spatial scale. Importantly, RVEs (1) are scale-relative, that is, the actual characteristic lengths of the structures in an RVE can vary considerably, and (2) are always considered to be continua. These features of RVEs lead to both a unified methodological approach for modeling materials as varied as steel, wood, water, and gases; and, they provide methodological constraints that guide modeling strategies. I illustrate these features of RVEs by looking at examples where one can determine effective values for material parameters describing bulk behaviors. These include parameters like Young’s modulus for elastic materials and transport coefficients such as thermal and electrical conductivity. I will emphasize how little the values for these effective parameters depend on lowest scale/fundamental features of the systems; or, in other words, how effective parameters succeed in being autonomous from the fundamental features of the systems. Upper-scale phenomena of the sort I will consider in this talk often display a remarkable insensitivity to changes in lower-scale details. This is, of course, a hallmark of effective theories. Using these lessons from RVE modeling techniques, I will further discuss how reductive strategies, and those that emphasize the role of fundamentality in justifying the use of a multiscale modeling technique, ignore the autonomy of effective theories and why ignoring that autonomy inhibits multiscale modeling.
