Order and disorder in energy minimization

zbMath1236.05058arXiv1003.3053MaRDI QIDQ3096702

Henry Cohn

Publication date: 11 November 2011

Full work available at URL: https://arxiv.org/abs/1003.3053

zbMATH Keywords

symmetryLeech latticeregular polytopesuniversal optimalitysphere packingpotential energy minimization\(E_{8}\)

Mathematics Subject Classification ID

Packing and covering in (n) dimensions (aspects of discrete geometry) (52C17) Lattice packing and covering (number-theoretic aspects) (11H31) Combinatorial aspects of packing and covering (05B40)

Related Items (11)

The Gaussian core model in high dimensions ⋮ Newton algorithm on constraint manifolds and the 5-electron Thomson problem ⋮ Spectrally optimized pointset configurations ⋮ Three-point bounds for energy minimization ⋮ Packing ovals in optimized regular polygons ⋮ Sphere packing bounds via spherical codes ⋮ Constrained shrinking dimer dynamics for saddle point search with constraints ⋮ Rigidity of spherical codes ⋮ Globally optimized packings of non-uniform size spheres in \(\mathbb {R}^{d}\): a computational study ⋮ Universal optimality of the \(E_8\) and Leech lattices and interpolation formulas ⋮ Anticoherent spin-2 states and spherical designs

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