We consider three-dimensional clusters of equal-volume bubbles packed around a central bubble and calculate their energy and optimal shape. We obtain the surface area and bubble pressures to improve on existing growth laws for three-dimensional bubble clusters. We discuss the possible number of bubbles that can be packed around a central one: the "kissing problem," here adapted to deformable ob...

For nearly 150 years, it has been recognized that cell shape strongly influences the orientation of the mitotic cleavage plane (e.g., Hofmeister, 1863). However, we still understand little about the complex interplay between cell shape and cleavage-plane orientation in epithelia, where polygonal cell geometries emerge from multiple factors, including cell packing, cell growth, and cell division...

The relationship between the size of the substituents of aryl groups in a series of fifteen 6,9,12,15,18-pentaaryl-1-hydro[60]fullerenes and the solid-state structures and packing motifs of these compounds has been analyzed. Pentaarylfullerenes have a characteristic "badminton shuttlecock" shape that causes several derivatives to crystallize into columnar stacks. However, many pentaarylfulleren...

We consider three-dimensional clusters of equal-volume bubbles packed around a central bubble and calculate their energy and optimal shape. We obtain the surface area and bubble pressures to improve on existing growth laws for three-dimensional bubble clusters. We discuss the possible number of bubbles that can be packed around a central one: the “kissing problem”, here adapted to deformable ob...

Truss lattices are common in a wide variety of engineering applications, due to their high ratio strength versus relative density. They used both as the interior support for other structures, and structures on own. Using 3D sphere packing, we propose set methods generating truss that fill B-rep models, polygonal or (trimmed) NURBS based, arbitrary shape. Once packing spheres has been establishe...

Three-dimensional discrete numerical simulation is used to investigate the properties of close-packed frictionless granular assemblies as a function of particle polydispersity and shape. Unlike some experimental results, simulations show that disordered packings of pinacoids (eight-face convex polyhedra) achieve higher solid fraction values than amorphous packings of spherical or rounded partic...