Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Spiral capacitor calculation using FEniCS   The paper shows how to optimize a water level sensor consisting of a cylinder
with spiraling metal stripes on the side, using a powerful Python library
FEniCS. It is shown how to reduce a 3D Laplace equation to a 2D, using a
spiraling coordinate system; how to specify the correct boundary conditions for
an open region; how to convert the partial differential equation to a
variational form for FEniCS; and how to calculate the capacitance. Then the
FEniCS code is shown that solves the Laplace equation and calculates the
capacitance. The further numeric experiments show that there is an optimal
combination of the spiral frequency and the width of the stripes that maximizes
the sensitivity of the sensor. The Python code is given to calculate the
optimum.

5
The categories of this paper are: gr-qc
30
The categories of this paper are: q-alg
16
The categories of this paper are: stat
23
The categories of this paper are: solv-int
3
The categories of this paper are: physics
13
The categories of this paper are: quant-ph
33
The categories of this paper are: plasm-ph
35
The categories of this paper are: mtrl-th
17
The categories of this paper are: q-fin
37
The categories of this paper are: supr-con
18
The categories of this paper are: econ
4
The categories of this paper are: cond-mat
9
The categories of this paper are: nlin
21
The categories of this paper are: adap-org
6
The categories of this paper are: astro-ph
36
The categories of this paper are: cmp-lg