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The Tyranny of Scales

Batterman, Robert W. (2011) The Tyranny of Scales. [Preprint]

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    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- (or meso-) 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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    Item Type: Preprint
    Keywords: Models, Statistical Mechanics, Hydrodynamics, Continuum Mechanics, Renormalization Group, Homogenization, Universality, Explanation
    Subjects: Specific Sciences > Physics > Classical Physics
    Specific Sciences > Physics > Condensed Matter
    General Issues > Explanation
    Specific Sciences > Mathematics
    General Issues > Models and Idealization
    Specific Sciences > Physics > Statistical Mechanics/Thermodynamics
    Depositing User: Robert Batterman
    Date Deposited: 20 Jun 2011 14:49
    Last Modified: 20 Jun 2011 14:49
    Item ID: 8678
    URI: http://philsci-archive.pitt.edu/id/eprint/8678

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