Sentence examples for optimal sphere from inspiring English sources

3) HCP and FCC are optimal packings for infinite 3D spaces, but, to our knowledge, there is no mathematical proof for what is the optimal sphere packing for a finite-sized 3D space, such as typical laboratory arenas and rooms.

The total volume of an ITEX tube is about 300 μL, and the sorbent bed takes up 160 μL, which results in about 118 μL of the sorbent material, if an optimal sphere packing is assumed, ensuing a total void volume of about 180 to 190 μL.

In this case the fabrication of well-ordered colloidal monolayers is particularly challenging as the optimal spheres are <200 nm diameter, which requires proper control of the assembly conditions at the air water interface.

For example, the benchmark results show that optimal bounding spheres for inputs with tens of millions of points can be computed in just a few milliseconds.

end{aligned}Remarkably this bound is optimal for the sphere in dimensions three and five.

For the infinite cylinder and the finite sphere, optimal solutions can be quite different from the "magical" overlap.

This factor is but a simple geometrical factor which cares the optimal radius of a sphere inside eight octahedra arranged at right angles and has been quite useful to explain major physical properties such as transport and magnetic properties in cubic, tetragonal, and orthorhombic colossal magnetoresistance.

10.7554/eLife.05913.003 Figure 2. Regular optimal solutions to the sphere packing problem in 3D.

The iteration numbers are optimal for the hot spheres, but not for the cold ones, the CRC of which continues to slowly improve with the iteration number (see Appendix 2 for the convergence rate).

The optimal retraction distances for spheres and tubes that help the method achieve the second-order accuracy are found to be around 0.30 and −0.47 times of the lattice spacing, respectively.

The radial-based importance sampling (RBIS) method, excluding a β-sphere from the sampling domain, is extended with an efficient adaptive scheme to determine the optimal radius β of the sphere.