Figure 1: The period ratio P_{1}/2P_{2} for a thin tube with exponential longitudinal structuring. The dashed curve corresponds to the numerically determined solution of the dispersion relations (9) and (10). The solid curve corresponds to the analytical approximation Eq. (46). | |
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Figure 2: The period ratio P_{1}/2P_{2} as a function of the density ratio of internal density at the loop apex to density at the loop base. The solid curve corresponds to the exponentially structured density profile, numerically determined by the solution of dispersion relations (9) and (10). Also shown for comparison are the results for a selection of other profiles, considering the linear profile (dashed line), the profile discussed by Dymova & Ruderman (2006a), Eq. (48) (dotted line), the profile (Eq. (50)) with kL=1 (dot-dashed line) and the profile discussed by Andries et al. (2005b) (Eq. (49), dot-dot-dashed line); for these profiles we have used the variational formulation. | |
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