Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Analytic solution of an oscillatory migratory alpha^2 stellar dynamo   Analytic solutions of the mean-field induction equation predict a
nonoscillatory dynamo for homogeneous helical turbulence or constant alpha
effect in unbounded or periodic domains. Oscillatory dynamos are generally
thought impossible for constant alpha. We present an analytic solution for a
one-dimensional bounded domain resulting in oscillatory solutions for constant
alpha, but different (Dirichlet and von Neumann or perfect conductor and
vacuum) boundary conditions on the two boundaries. We solve a second order
complex equation and superimpose two independent solutions to obey both
boundary conditions. The solution has time-independent energy density. On one
end where the function value vanishes, the second derivative is finite, which
would not be correctly reproduced with sine-like expansion functions where a
node coincides with an inflection point. The field always migrates away from
the perfect conductor boundary toward the vacuum boundary, independently of the
sign of alpha. The obtained solution may serve as a benchmark for numerical
dynamo experiments and as a pedagogical illustration that oscillatory migratory
dynamos are possible with constant alpha.

27
The categories of this paper are: comp-gas
0
The categories of this paper are: hep-ph
23
The categories of this paper are: solv-int
20
The categories of this paper are: acc-phys
30
The categories of this paper are: q-alg
31
The categories of this paper are: ao-sci
25
The categories of this paper are: patt-sol
13
The categories of this paper are: quant-ph
10
The categories of this paper are: q-bio
35
The categories of this paper are: mtrl-th
29
The categories of this paper are: funct-an
24
The categories of this paper are: dg-ga
34
The categories of this paper are: chem-ph
19
The categories of this paper are: eess
4
The categories of this paper are: cond-mat
18
The categories of this paper are: econ