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Universal hidden order in amorphous cellular geometries.

Michael A Klatt1,2, Jakov Lovrić3,4,5, Duyu Chen6

  • 1Institute of Stochastics, Karlsruhe Institute of Technology (KIT), Englerstr. 2, 76131, Karlsruhe, Germany.

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Researchers optimized space-partitioning using the Quantizer problem, finding disordered, hyperuniform states independent of initial conditions. These findings suggest new amorphous materials with unique physical properties.

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Area of Science:

  • Computational geometry
  • Materials science
  • Statistical physics

Background:

  • Partitioning space into cells with specific geometric properties is crucial across scientific disciplines.
  • The Quantizer problem focuses on optimizing the moment of inertia of Voronoi cells for 'sphere-like' shapes.

Purpose of the Study:

  • To investigate the Quantizer problem using Lloyd's algorithm.
  • To characterize the resulting space-partitioning states and their properties.

Main Methods:

  • Application of Lloyd's centroidal Voronoi diagram algorithm.
  • Analysis of structure factors and density fluctuations.

Main Results:

  • The algorithm converges to disordered states within deep local minima.
  • These states exhibit universality, independent of initial conditions.
  • Anomalous suppression of long-wavelength density fluctuations leads to effective hyperuniformity.

Conclusions:

  • The study identifies universal amorphous hyperuniform states.
  • Findings encourage the exploration of novel cellular materials with distinct physical characteristics.