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A charge distribution has spherical symmetry if the density of charge depends only on the distance from a point in space and not on the direction. In other words, if the system is rotated, it doesn't look different. For instance, if a sphere of radius R is uniformly charged with charge density ρ0, then the distribution has spherical symmetry. On the other hand, if a sphere of radius R is charged so that the top half of the sphere has a uniform charge density ρ1 and the bottom half has...
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Gauss's Law: Cylindrical Symmetry01:20

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A charge distribution has cylindrical symmetry if the charge density depends only upon the distance from the axis of the cylinder and does not vary along the axis or with the direction about the axis. In other words, if a system varies if it is rotated around the axis or shifted along the axis, it does not have cylindrical symmetry. In real systems, we do not have infinite cylinders; however, if the cylindrical object is considerably longer than the radius from it that we are interested in,...
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Hard spheres on the gyroid surface.

Tomonari Dotera1, Masakiyo Kimoto, Junichi Matsuzawa

  • 1Department of Physics, Kinki University, Higashi-Osaka 577-8502, Japan.

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Summary
This summary is machine-generated.

Hard spheres on a gyroid minimal surface self-organize entropically. This arrangement forms regular tessellations, analogous to hyperbolic tilings and Escher

Keywords:
ABC star polymerbicontinuous phasefluid–solid transitiongyroid surfacehard sphereshyperbolic tiling

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Area of Science:

  • Materials Science
  • Statistical Physics
  • Crystallography

Background:

  • Minimal surfaces, like the gyroid, offer unique geometric frameworks.
  • Understanding self-organization in confined geometries is crucial for materials design.

Purpose of the Study:

  • To investigate the entropic self-organization of hard spheres on a gyroid minimal surface.
  • To characterize the resulting sphere arrangements and their geometric properties.

Main Methods:

  • Utilizing Monte Carlo simulations to model hard sphere behavior.
  • Analyzing sphere packing using acceptance ratios and order parameters.

Main Results:

  • 48 out of 64 hard spheres per unit cell spontaneously organized on the gyroid surface.
  • The self-organized spheres formed regular tessellations exhibiting negative Gaussian curvature.
  • These tessellations are mathematically equivalent to hyperbolic tilings, such as Escher's Circle Limit IV.

Conclusions:

  • Entropic forces drive the self-organization of hard spheres on gyroid minimal surfaces.
  • The observed packing demonstrates a connection between physical self-assembly and mathematical hyperbolic geometry.
  • This provides a novel perspective on sphere packing in complex, curved environments.