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.

In the present research, the aqueous suspensions of nano-sized YSZ particles were prepared using a common and available dispersant (Dolapix CE64) at different pH values and their stability were evaluated through the sedimentation height, viscosity measurement, and microstructural observation. Different amounts of dispersant were tested and the optimum percentage was examined by measuring the vi...

To investigate whether any parameter other than packing density determines the quality of packing in a folded protein, the contribution of van der Waals interactions between hydrophobic core residues to protein stability at fixed packing density is investigated experimentally in this study. To this end, we employed a novel sequence variation scheme called “residue shuffling”, defined as permuta...

We have investigated the efficiency of packing by calculating intramolecular packing density above and below peptide planes of internal beta-pleated sheet residues in five globular proteins. The orientation of interest was chosen to allow study of regions that are approximately perpendicular to the faces of beta-pleated sheets. In these locations, nonbonded van der Waals packing interactions pr...

Aneurysm models were used to study the density of packing after coil embolization. Platinum coils were introduced until the point of minimally dense packing, indicated by aneurysmal circulatory exclusion. Packing was continued up to the point of maximal density, indicated by protrusion into the parent artery. Volumetric ratios (coil volume/aneurysmal volume) were calculated for minimally and ma...

The packing of uniform fine spherical particles ranging from 1 to 1000 microm has been simulated by means of discrete particle simulation. The packing structure is analyzed, facilitated by the well established Voronoi tessellation. The topological and metric properties of Voronoi polyhedra are quantified as a function of particle size and packing density. The results show that as particle size ...

In protein evolution, due to functional and biophysical constraints, the rates of amino acid substitution differ from site to site. Among the best predictors of site-specific rates are solvent accessibility and packing density. The packing density measure that best correlates with rates is the weighted contact number (WCN), the sum of inverse square distances between a site's C α and the C α of...