In The Oxford handbook of philosophy of physics. Oxford University Press. pp. 255-286 (2013)

Authors
Robert W. Batterman
University of Pittsburgh
Abstract
This paper examines a fundamental problem in applied mathematics. How can one model the behavior of materials that display radically different, dominant behaviors at different length scales. Although we have good models for material behaviors at small and large scales, it is often hard to relate these scale-based models to one another. Macroscale models represent the integrated effects of very subtle factors that are practically invisible at the smallest, atomic, scales. For this reason it has been notoriously difficult to model realistic materials with a simple bottom-up-from-the-atoms strategy. The widespread failure of that strategy forced physicists interested in overall macro-behavior of materials toward completely top-down modeling strategies familiar from traditional continuum mechanics. The problem of the ``tyranny of scales'' asks whether we can exploit our rather rich knowledge of intermediate micro- scale behaviors in a manner that would allow us to bridge between these two dominant methodologies. Macroscopic scale behaviors often fall into large common classes of behaviors such as the class of isotropic elastic solids, characterized by two phenomenological parameters---so-called elastic coefficients. Can we employ knowledge of lower scale behaviors to understand this universality---to determine the coefficients and to group the systems into classes exhibiting similar behavior?
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Naturalness, the Autonomy of Scales, and the 125GeV Higgs.Porter Williams - 2015 - Studies in History and Philosophy of Science Part B: Studies in History and Philosophy of Modern Physics 51:82-96.
Non-Factive Understanding: A Statement and Defense.Yannick Doyle, Spencer Egan, Noah Graham & Kareem Khalifa - 2019 - Journal for General Philosophy of Science / Zeitschrift für Allgemeine Wissenschaftstheorie 50 (3):345-365.
Reduction, Emergence, and Renormalization.Jeremy Butterfield - 2014 - Journal of Philosophy 111 (1):5-49.
Biology Meets Physics: Reductionism and Multi-Scale Modeling of Morphogenesis.Sara Green & Robert Batterman - 2017 - Studies in History and Philosophy of Science Part C: Studies in History and Philosophy of Biological and Biomedical Sciences 7161:20-34.

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