Hard-sphere jamming through the lens of linear optimization.

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.