User:Tohline/Appendix/Ramblings/Nonlinar Oscillation
Radial Oscillations in Pressure-Truncated n = 5 Polytropes
[24 August 2016; comment by Joel Tohline] Over the past few weeks, I have been putting together a powerpoint presentation that summarizes what I've learned over, especially, the last several years about turning points — and their relative positioning with respect to points of dynamical instability — along equilibrium sequences. One key finding, which is illustrated in Figure 3 of that discussion, is that the transition from stable to unstable systems along the n = 5 sequence occurs after, rather than at, the pressure maximum of the sequence. This means that, in the immediate vicinity of the pressure maximum, two stable equilibrium configurations exist with the same <math>~(K, M_\mathrm{tot}, P_e) </math> but different radii. Perhaps this means that, in the absence of dissipation, and without the need for a driving mechanism, a permanent oscillation between these two states can be activated.
Upon further thought, it occurred to me that a careful examination of the internal structure of both models — especially relative to one another — might reveal what the eigenvector of the oscillation might be.
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