Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: On the equilibria of finely discretized curves and surfaces   Our goal is to identify the type and number of static equilibrium points of
solids arising from fine, equidistant $n$-discretrizations of smooth, convex
surfaces. We assume uniform gravity and a frictionless, horizontal, planar
support. We show that as $n$ approaches infinity these numbers fluctuate around
specific values which we call the imaginary equilibrium indices associated with
the approximated smooth surface. We derive simple formulae for these numbers in
terms of the principal curvatures and the radial distances of the equilibrium
points of the solid from its center of gravity. Our results are illustrated on
a discretized ellipsoid and match well the observations on natural pebble
surfaces.

0
The categories of this paper are: hep-ph
30
The categories of this paper are: q-alg
12
The categories of this paper are: nucl-th
5
The categories of this paper are: gr-qc
1
The categories of this paper are: cs
9
The categories of this paper are: nlin
16
The categories of this paper are: stat
24
The categories of this paper are: dg-ga
34
The categories of this paper are: chem-ph
6
The categories of this paper are: astro-ph
13
The categories of this paper are: quant-ph
25
The categories of this paper are: patt-sol
26
The categories of this paper are: bayes-an
17
The categories of this paper are: q-fin
3
The categories of this paper are: physics
20
The categories of this paper are: acc-phys