High-dimensional sphere packing and the modular bootstrap
نویسندگان
چکیده
منابع مشابه
Caging of a d-dimensional sphere and its relevance for the random dense sphere packing.
We analyze the caging of a hard sphere (i.e., the complete arrest of all translational motions) by randomly distributed static contact points on the sphere surface for arbitrary dimension d>/=1, and prove that the average number of uncorrelated contacts required to cage a sphere is (d)=2d+1. Computer simulations, which confirm this analytical result, are also used to model the effect of corr...
متن کاملThe sphere packing problem
Hales, T.C., The sphere packing problem, Journal of Computational and Applied Mathematics 44 (1992) 41-76. The sphere packing problem asks whether any packing of spheres of equal radius in three dimensions has density exceeding that of the face-centered-cubic lattice packing (of density IT/V%). This paper sketches a solution to this problem.
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A brief report on recent work on the sphere-packing problem. 1991 Mathematics Subject Classification: 52C17
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In this paper we consider the Online Bin Packing Problem in three variants: Circles in Squares, Circles in Isosceles Right Triangles, and Spheres in Cubes. The two first ones receive an online sequence of circles (items) of different radii while the third one receive an online sequence of spheres (items) of different radii, and they want to pack the items into the minimum number of unit squares...
متن کاملSphere Packing Lecture
What is the most space-efficient way to stack spheres in three-dimensional space? Although the answer is obvious, a rigorous proof has eluded mathematicians for centuries, having only recently been found by Hales in 1998, who used an immense computerized proof-by-exhaustion. The more general problem of packing (n-1)-spheres into n-dimensional Euclidean (or other) space is still only poorly unde...
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ژورنال
عنوان ژورنال: Journal of High Energy Physics
سال: 2020
ISSN: 1029-8479
DOI: 10.1007/jhep12(2020)066