# Tagged Questions

0answers
71 views

### Formal definitions for a few lattice packing invariants

I'm a bit hesitant to post this question here because it regards definitions that are likely trivial, and please note that I'm cross-posting this question from Math.Stackexchange (posted nine days ...
1answer
158 views

### Is there an “accepted” jamming limit for hard spheres placed in the unit cube by random sequential adsorption?

I have a unit cube, and operating in the continuum limit (i.e. not on a lattice), I sequentially place spheres of some radius $r$ inside the cube until a filled volume "jamming limit" ...
1answer
385 views

### Optimal fitting of spheres in a cylinder.

how to find the minimum height and width of a cylinder containing n identical spheres?
2answers
682 views

### The kissing number of a square, cube, hypercube?

How many nonoverlapping unit squares can (nonoverlappingly) touch one unit square? By "nonoverlapping" I mean: not sharing an interior point. By "touch" I mean: sharing a boundary point. ...
2answers
460 views

### What is the largest possible thirteenth kissing sphere?

It is well-known that it is impossible to arrange 13 spheres of unit radius all tangent to another unit sphere without their interiors intersecting. This was apparently the subject of disagreement ...
2answers
648 views

### Average degree of contact graph for balls in a box

Imagine you dump congruent, hard, frictionless balls in a box, letting gravity compress the balls into a stable configuration (I believe such configurations are called jammed.) Assume the box ...
5answers
515 views

### covering by spherical caps

Consider the unit sphere $\mathbb{S}^d.$ Pick now some $\alpha$ (I am thinking of $\alpha \ll 1,$ but I don't know how germane this is). The question is: how many spherical caps of angular radius ...