User:Tohline/SSC/FreeEnergy/PowerPoint
Supporting Derivations for Free-Energy PowerPoint Presentation
The derivations presented here are an extension of our accompanying free-energy synopsis. These additional details proved to be helpful while developing an overarching PowerPoint presentation.
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General Free-Energy Expression
We're considering a free-energy function of the following form:
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<math>~\mathfrak{G}^*_\mathrm{type}</math> |
<math>~=</math> |
<math>~-ax^{-1} + b x^{-3/n} + c x^{-3/j} + \mathfrak{G}_0 \, .</math> |
As we have shown, setting,
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<math>~\frac{\partial \mathfrak{G}^*_\mathrm{type}}{\partial x}</math> |
<math>~=</math> |
<math>~0</math> |
generates a mathematical statement of virial equilibrium, namely,
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