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Area of Science:

  • Physics
  • Materials Science
  • Computational Science

Background:

  • Maximally random jammed (MRJ) particle packings are key models for understanding glasses due to their disorder and rigidity.
  • Predicting packing density (ϕMRJ) for frictionless particles remains a significant theoretical challenge, even for simple shapes like spheres and disks.

Purpose of the Study:

  • To derive a highly accurate formula for MRJ densities for a broad range of 2D frictionless packings.
  • To investigate MRJ densities in binary convex superdisks, which interpolate between circles and squares.

Main Methods:

  • Utilizing a geometric-structure approach to develop the predictive formula.
  • Incorporating specific attributes of MRJ states and a novel organizing principle.
  • Comparing derived predictions with extensive computer-simulation data across various parameters (semi-axis ratio α and concentration x).

Main Results:

  • The derived formula shows excellent agreement with computer simulations for MRJ densities across a wide parameter space.
  • In the monodisperse circle limit, the predicted ϕMRJ of 0.834 closely matches the recent numerical discovery of 0.827.
  • Predictions for non-circular monodisperse superdisks indicate achievable MRJ densities lower than previously thought possible with standard protocols.

Conclusions:

  • The new formula provides a robust theoretical tool for predicting MRJ densities in diverse 2D packing systems.
  • The findings validate the geometric-structure approach and offer a stringent test for theories of disordered matter.
  • This work advances the understanding of glass physics and the fundamental properties of jammed matter.