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major void: 5 23 h 48 m −24° 39′ 53.0 34.8 Aquarius/Sculptor: major void SRSS1 Void 3 (Sculptor Void) 6 3 h 56 m −20° 11′ 56.5 32.0 Eridanus: major void: 7 3 h 17 m −11° 40′ 77.2 25.5 Eridanus: major void: 8 23 h 20 m −12° 32′ 83.9 27.8 Aquarius: major void: 9 3 h 06 m −13° 47′ 114.6 39.0 Eridanus: major void: 10 0 h 26 ...
There are two simple regular lattices that achieve this highest average density. They are called face-centered cubic (FCC) (also called cubic close packed) and hexagonal close-packed (HCP), based on their symmetry. Both are based upon sheets of spheres arranged at the vertices of a triangular tiling; they differ in how the sheets are stacked ...
[citation needed] In a close-packed structure there are 4 atoms per unit cell and it will have 4 octahedral voids (1:1 ratio) and 8 tetrahedral voids (1:2 ratio) per unit cell. [1] The tetrahedral void is smaller in size and could fit an atom with a radius 0.225 times the size of the atoms making up the lattice.
Here there is a choice between separating the spheres into regions of close-packed equal spheres, or combining the multiple sizes of spheres into a compound or interstitial packing. When many sizes of spheres (or a distribution ) are available, the problem quickly becomes intractable, but some studies of binary hard spheres (two sizes) are ...
Void content in composites is represented as a ratio, also called void ratio, where the volume of voids, solid material, and bulk volume are taken into account.Void ratio can be calculated by the formula below where e is the void ratio of the composite, V v is the volume of the voids, and V t is the volume of the bulk material.
where is the void ratio, is the porosity, V V is the volume of void-space (gases and liquids), V S is the volume of solids, and V T is the total (or bulk) volume. This figure is relevant in composites , in mining (particular with regard to the properties of tailings ), and in soil science .
There is a large theory of special functions which developed out of statistics and mathematical physics. A modern, abstract point of view contrasts large function spaces , which are infinite-dimensional and within which most functions are 'anonymous', with special functions picked out by properties such as symmetry , or relationship to harmonic ...
Another generalization is to calculate the number of coprime integer solutions , to the inequality m 2 + n 2 ≤ r 2 . {\displaystyle m^{2}+n^{2}\leq r^{2}.\,} This problem is known as the primitive circle problem , as it involves searching for primitive solutions to the original circle problem. [ 9 ]