Statistical Mechanics of Athermal Packings: Incorporating Basin Volumes

ORAL

Abstract

We present a first principles formalism for the statistical mechanics of athermal packings subject to driving beyond the weak limit. Edwards hypothesized a statistical mechanics of flat measure associated with packings explored at fixed density. This ensemble has been found to work well in the limit of very weak (but non-zero) driving. Beyond the weak driving limit, the probability measures associated with jammed states become proportional to the volume of basins of attractions associated with the packings on the density landscape. We propose here, a statistical mechanics which takes into consideration the volume of basins of attraction under certain approximations. Further, the statistical mechanics takes into account the protocol by writing the partition function in terms of an integral over protocol dependent generalized coordinates. This will allow an extremum principle to determine states, in these out of equilibrium systems.

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Authors

  • Ashwin S. S.

    Departments of Mechanical Engineering \& Materials Science and Physics, Yale University

  • Jerzy Blawzdziewicz

    Texas Tech University, Mechanical Engineering,Texas Tech University

  • Corey O'Hern

    Yale University, Departments of Mechanical Engineering \& Materials Science, and Physics, Yale University, Mechanical Engineering \& Materials Science, and Physics, Yale University, Departments of Mechanical Engineering and Physics, Yale University, Departments of Mechanical Engineering \& Materials Science and Physics, Yale University, Departments of Mechanical Engineering \& Materials Science and Physics, Yale University, New Haven, Connecticut 06520, Department of Mechanical Engineering \& Materials Science, Yale University, Yale University, Dpt of Mechanical Engineering

  • Mark Shattuck

    Benjamin Levich Institute and Physics Department, The City College of the New York, Benjamin Levich Institute and Physics Department, The City College of the City University of New York, New York, New York 10031, Benjamin Levich Institute and Department of Physics, City College of New York of the City University of New York, Benjamin Levich Institute and Physics Department, The City College of the City University of New York