Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Analytical proof of Schottky Conjecture for multi-stage field emitters   Schottky Conjecture is analytically proved for multi-stage field emitters
consisting on the superposition of rectangular or trapezoidal protrusions on a
line under some specific limit. The case in which a triangular protrusion is
present on the top of each emitter is also considered as an extension of the
model. The results presented here are obtained via Schwarz-Christoffel
conformal mapping and reinforce the validity of Schottky Conjecture when each
protrusion is much larger than the ones above it, even when an arbitrary number
of stages is considered. Moreover, it is showed that it is not necessary to
require self-similarity between each of the stages in order to ensure the
validity of the conjecture under the appropriate limits.

33
The categories of this paper are: plasm-ph
5
The categories of this paper are: gr-qc
17
The categories of this paper are: q-fin
34
The categories of this paper are: chem-ph
25
The categories of this paper are: patt-sol
6
The categories of this paper are: astro-ph
21
The categories of this paper are: adap-org
18
The categories of this paper are: econ
32
The categories of this paper are: atom-ph
8
The categories of this paper are: hep-ex
30
The categories of this paper are: q-alg
23
The categories of this paper are: solv-int
2
The categories of this paper are: math
20
The categories of this paper are: acc-phys
0
The categories of this paper are: hep-ph
29
The categories of this paper are: funct-an