title: Statistics of frictional families.
abstract: We develop a theoretical description for mechanically stable frictional packings in terms of the difference between the total number of contacts required for isostatic packings of frictionless disks and the number of contacts in frictional packings, m=Nc0 - Nc. The saddle order m represents the number of unconstrained degrees of freedom that a static packing would possess if friction were removed. Using a novel numerical method that allows us to enumerate disk packings for each m, we show that the probability to obtain a packing with saddle order m at a given static friction coefficient μ, Pm(μ), can be expressed as a power series in μ. Using this form for Pm(μ), we quantitatively describe the dependence of the average contact number on the friction coefficient for static disk packings obtained from direct simulations of the Cundall-Strack model for all μ and N.
authors.affiliation: Department of Physics, Yale University, New Haven, Connecticut 06520-8120, USA.
authors.forename: Tianqi
authors.initials: T
authors.lastname: Shen
authors.affiliation: Department of Physics, Yale University, New Haven, Connecticut 06520-8120, USA and Department of Mechanical Engineering & Materials Science, Yale University, New Haven, Connecticut 06520-8260, USA.
authors.forename: Stefanos
authors.initials: S
authors.lastname: Papanikolaou
authors.affiliation: Department of Physics, Yale University, New Haven, Connecticut 06520-8120, USA and Department of Mechanical Engineering & Materials Science, Yale University, New Haven, Connecticut 06520-8260, USA and Department of Applied Physics, Yale University, New Haven, Connecticut 06520-8120, USA.
authors.forename: Corey S
authors.initials: CS
authors.lastname: O'Hern
authors.affiliation: Department of Mechanical Engineering & Materials Science, Yale University, New Haven, Connecticut 06520-8260, USA and Benjamin Levich Institute and Physics Department, The City College of the City University of New York, New York, New York 10031, USA.
authors.forename: Mark D
authors.initials: MD
authors.lastname: Shattuck