منابع مشابه
A method for dense packing discovery
The problem of packing a system of particles as densely as possible is foundational in the field of discrete geometry and is a powerful model in the material and biological sciences. As packing problems retreat from the reach of solution by analytic constructions, the importance of an efficient numerical method for conducting de novo (from-scratch) searches for dense packings becomes crucial. I...
متن کاملPacking and Covering Dense Graphs
Let d be a positive integer. A graph G is called d-divisible if d divides the degree of each vertex of G. G is called nowhere d-divisible if no degree of a vertex of G is divisible by d. For a graph H, gcd(H) denotes the greatest common divisor of the degrees of the vertices of H. The H-packing number of G is the maximum number of pairwise edge disjoint copies of H in G. The H-covering number o...
متن کاملDense packing on uniform lattices
We study the Hard Core Model on the graphs G obtained from Archimedean tilings i.e. configurations in {0,1} with the nearest neighbor 1’s forbidden. Our particular aim in choosing these graphs is to obtain insight to the geometry of the densest packings in a uniform discrete set-up. We establish density bounds, optimal configurations reaching them in all cases, and introduce a probabilistic cel...
متن کاملUnderstanding shape entropy through local dense packing.
Entropy drives the phase behavior of colloids ranging from dense suspensions of hard spheres or rods to dilute suspensions of hard spheres and depletants. Entropic ordering of anisotropic shapes into complex crystals, liquid crystals, and even quasicrystals was demonstrated recently in computer simulations and experiments. The ordering of shapes appears to arise from the emergence of directiona...
متن کاملDense Packing of Patterns in a Permutation
We study the length Lk of the shortest permutation containing all patterns of length k. We establish the bounds e−2k2 < Lk ≤ (2/3 + o(1))k2 . We also prove that as k → ∞, there are permutations of length (1/4+o(1))k2 containing almost all patterns of length k.
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ژورنال
عنوان ژورنال: Physical Review E
سال: 2010
ISSN: 1539-3755,1550-2376
DOI: 10.1103/physreve.82.056707