The hard core of soft matter: sphere systems in soft material (Q5962794)

The short paper gives a review of the problem of packing of large ensembles of spherical particles. This is a topic which is rather interesting and challenging not only for its mathematical content, but also for various physical applications. In particular, molecular dynamics, crystallography, thermodynamics, fluid dynamics, and rigid body systems are involved, to mention only a few of them.NEWLINENEWLINEWe know, since the times of Kepler and Gauss, that the hexagonal and the face-centered cubic packings play an important role under all regular packings by minimizing the volume or maximizing the density. Immediately other questions arise. What about irregular packings? What shall be minimized/maximized? The energy? Or the entropy? Or what else? And what are the interactions between the spheres? Are they governed by potentials like Lennard-Jones? Or can we assume just rigid spheres that do not interact otherwise?NEWLINENEWLINEAlso, the process of generating such packings has a substantial influence on the result. Are they jammed or pressed or shaken, or are they randomly created by computer algorithms?NEWLINENEWLINEThe paper gives an overview of such problems and their different aspects. As such, one cannot expect much details and satisfying explanations rather than hints and further references for reading. It gives the impression that the topic is not only rather demanding and challenging, but also rich in applications, both known and still unknown ones.