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Hard-sphere jamming through the lens of linear optimization.

Claudia Artiaco1, Rafael Díaz Hernández Rojas2, Giorgio Parisi2,3

  • 1Department of Physics, KTH Royal Institute of Technology, Stockholm 106 91, Sweden.

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A new algorithm, CALiPPSO, efficiently generates jammed hard-sphere (HS) packings by treating jamming as an optimization problem. This method ensures isostaticity and mechanical equilibrium, aiding the study of jamming transitions in finite dimensions.

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Area of Science:

  • Physics
  • Statistical Mechanics
  • Computational Physics

Background:

  • The jamming transition is a critical phenomenon observed across diverse physical systems, including granular matter, foams, and glasses.
  • While mean-field theories accurately describe jamming in infinite dimensions, finite-dimensional systems present significant numerical challenges.
  • Existing methods are unsuitable for hard-sphere (HS) systems due to their zero interaction energy by construction.

Purpose of the Study:

  • To develop a numerical method for generating jammed hard-sphere (HS) packings in finite dimensions.
  • To overcome the limitations of energy minimization algorithms for HS systems.
  • To provide a tool for exploring the jamming transition in systems beyond the infinite-dimensional limit.

Main Methods:

  • Recasting the jamming of hard spheres (HS) as a constrained optimization problem.
  • Introducing the CALiPPSO algorithm, which solves a series of linear optimization problems.
  • Analyzing the force balance conditions and properties of optimal solutions to prove isostaticity and mechanical equilibrium.

Main Results:

  • The CALiPPSO algorithm successfully generates jammed HS packings without effective potentials.
  • Analytical proof demonstrates that the generated packings are always isostatic and in mechanical equilibrium.
  • Numerical simulations show the algorithm probes the free-energy landscape, aligning with mean-field predictions.

Conclusions:

  • CALiPPSO offers an effective approach to studying jamming transitions in finite-dimensional hard-sphere systems.
  • The algorithm provides a means to achieve mechanical equilibrium and isostaticity in HS packings.
  • This work facilitates further investigation into the complex physics of jamming in realistic systems.