Although the concept of random close packing with an almost universal packing fraction of approximately 0.64 for hard spheres was introduced more than half a century ago, there are still ongoing ...

Imagine placing oranges or tennis balls into a rigid container. How can the balls be arranged such that they occupy the largest volume fraction of the container, otherwise known as the largest packing ...

newsletter signup To make the notion of random packing more consistent and mathematically precise, Torquato and his colleagues have introduced the concept of what they call a “maximally random jammed” ...

At each stage of the packing of a closed interval K, a random number of random open intervals (the packing objects) are placed in that part of K which is as yet unoccupied. No overlapping between the ...

We consider two random sequential packing processes in which spheres of unit radius are randomly attached to the surface of a fixed unit sphere. Independent random spheres are generated and added ...

In math, the search for optimal patterns never ends. The sphere-packing problem — which asks how to cram balls into a (high-dimensional) box as efficiently as possible — is no exception. It has ...