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Least Action Principle Of Crystal Formation Of Dense Packing Type And Kepler's Conjecture

Least Action Principle Of Crystal Formation Of Dense Packing Type And Kepler's Conjecture by W Y Hsiang
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US$ 163.00
The dense packing of microscopic spheres (i.e. atoms) is the basic geometric arrangement in crystals of mono-atomic elements with weak covalent bonds, which achieves the optimal "known density" of p/√18. In 1611, Johannes Kepler had already "conjectured" that p/√18 should be the optimal "density" of sphere packings. Thus, the central problems in the study of sphere packings are the proof of Kepler's conjecture that p/√18 is the optimal density, and the establishing of the least action principle that the hexagonal dense packings in crystals are the geometric consequence of optimization of density. This important book provides a self-contained proof of both, using vector algebra and spherical geometry as the main techniques and in the tradition of classical geometry.

Contents:

  • The Basics of Euclidean and Spherical Geometries and a New Proof of the Problem of Thirteen Spheres
  • Circle Packings and Sphere Packings
  • Geometry of Local Cells and Specific Volume Estimation Techniques for Local Cells
  • Estimates of Total Buckling Height
  • The Proof of the Dodecahedron Conjecture
  • Geometry of Type I Configurations and Local Extensions
  • The Proof of Main Theorem I
  • Retrospects and Prospects

    Readership: Researchers in classical geometry and solid state physics.

  • World Scientific Publishing Company; January 2001
    425 pages; ISBN 9789812384911
    Read online, or download in secure PDF format
    Title: Least Action Principle Of Crystal Formation Of Dense Packing Type And Kepler's Conjecture
    Author: W Y Hsiang
     
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