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Quasicrystalline three-dimensional foams.

S J Cox1, F Graner, R Mosseri

  • 1Department of Mathematics, Aberystwyth University, SY23 3BZ, United Kingdom.

Journal of Physics. Condensed Matter : an Institute of Physics Journal
|January 6, 2017
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Summary
This summary is machine-generated.

We numerically studied quasiperiodic foams as candidates for space-partitioning. One foam structure approached the minimal surface area solution for the Kelvin problem, offering new insights into space-filling geometries.

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Area of Science:

  • Materials Science
  • Computational Physics
  • Geometry

Background:

  • The Kelvin problem seeks the optimal partition of 3D space into equal volumes with minimal surface area.
  • Quasiperiodic structures offer complex, non-repeating geometries that may provide novel solutions.
  • Frank-Kasper phases are known quasiperiodic structures with potential applications in materials science.

Purpose of the Study:

  • To numerically investigate quasiperiodic foams derived from Frank-Kasper phases.
  • To evaluate these foams as candidates for solving the Kelvin problem.
  • To explore the geometric properties influencing space-partitioning efficiency.

Main Methods:

  • Generation of quasiperiodic foams as duals of Frank-Kasper phases.
  • Numerical simulation and analysis of foam structures.
  • Comparison with known periodic candidates for the Kelvin problem.

Main Results:

  • One computed quasiperiodic foam structure closely approximates the minimal surface area requirement of the Kelvin problem.
  • This structure slightly exceeds the surface area of the best known periodic Weaire-Phelan candidate.
  • A correlation was identified between normalized bubble surface area and the deviation in the number of faces per bubble.

Conclusions:

  • Quasiperiodic foams present promising, albeit not yet optimal, candidates for the Kelvin problem.
  • The identified correlation offers insights into the geometric factors governing minimal surface area partitions.
  • Further research into quasiperiodic structures could lead to breakthroughs in space-partitioning problems.