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An asymptotic‐numerical approach to the coronal loop problem
Author(s) -
Verhulst F.,
Zegeling P. A.
Publication year - 1990
Publication title -
mathematical methods in the applied sciences
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.719
H-Index - 65
eISSN - 1099-1476
pISSN - 0170-4214
DOI - 10.1002/mma.1670130507
Subject(s) - mathematics , singular perturbation , loop (graph theory) , mathematical analysis , perturbation (astronomy) , boundary value problem , boundary (topology) , physics , combinatorics , quantum mechanics
The coronal loop problem is characterized by mixed boundary conditions and the loop length condition, which is global. Using singular perturbation methods one can identify and construct two boundary layers at the base of the loop. Extending this to a combined asymptotic‐numerical treatment it is possible to construct two static solutions satisfying the same conditions; this unusual feature arises from the presence of the first boundary layer, which corresponds with a steep temperature gradient and an energy balance dominated by conduction and radiation losses.