Difference between revisions of "User:Tohline/Appendix/Ramblings/Nonlinar Oscillation"
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=Radial Oscillations in Pressure-Truncated n = 5 Polytropes= | =Radial Oscillations in Pressure-Truncated n = 5 Polytropes= | ||
<font color="red">[24 August 2016 | <font color="red">[Comment by Joel Tohline on 24 August 2016]</font> Over the past few weeks, I have been putting together a [[User:Tohline/SSC/FreeEnergy/PowerPoint#Supporting_Derivations_for_Free-Energy_PowerPoint_Presentation|powerpoint presentation]] that summarizes what I've learned, especially over 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 [[User:Tohline/SSC/FreeEnergy/PowerPoint#Figure3|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 | 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 that (nonlinear) oscillation might be. | ||
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== | ==Review of Internal Structure== | ||
Revision as of 13:59, 25 August 2016
Radial Oscillations in Pressure-Truncated n = 5 Polytropes
[Comment by Joel Tohline on 24 August 2016] Over the past few weeks, I have been putting together a powerpoint presentation that summarizes what I've learned, especially over 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 that (nonlinear) oscillation might be.
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