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Summary
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Investigating sphere interactions, this study reveals that in 3D, fragmented bearing domains, not a sharp line, minimize energy dissipation. This novel state features a spanning network of non-slipping contacts, driven by increased degrees of freedom.

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Area of Science:

  • Physics
  • Materials Science
  • Mechanical Engineering

Background:

  • Spheres in a bearing state roll without slip.
  • Systems with two different bearing states on opposite sides are studied.
  • Energy dissipation in such systems is investigated.

Purpose of the Study:

  • To find configurations of lowest energy dissipation in systems of touching spheres with opposing bearing states.
  • To analyze the effect of different friction models (viscous vs. Coulomb) on energy dissipation.
  • To explore the behavior of these systems in two and three dimensions.

Main Methods:

  • Simulating systems of touching spheres under different bearing conditions.
  • Analyzing energy dissipation based on viscous damping constants and Coulomb friction coefficients.
  • Comparing 2D and 3D configurations to identify differences in minimum energy states.

Main Results:

  • In 2D with Coulomb friction, a sharp line (minimum cut) separates bearing states.
  • In 3D, intermediate bearing domains form a fragmented structure, not a sharp cut.
  • This 3D fragmented state, energetically favorable, features a spanning network of non-slipping contacts.

Conclusions:

  • Three-dimensional systems exhibit novel, fragmented states of minimum energy dissipation.
  • The increased degrees of freedom in 3D allow for complex, synchronized bearing states.
  • The findings challenge simple minimum-cut models and reveal intricate contact dynamics.