Fermi-Jagla model: Difference between revisions

Revision as of 10:48, 5 October 2017

The Fermi-Jagla model is a smooth variant of the Jagla model. It is given by (Eq. 1 in ^[1]):

\Phi _{12}(r)=\epsilon _{0}\left[\left({\frac {a}{r}}\right)^{n}+{\frac {A_{0}}{1+\exp \left[{\frac {A_{1}}{A_{0}}}({\frac {r}{a}}-A_{2})\right]}}-{\frac {B_{0}}{1+\exp \left[{\frac {B_{1}}{B_{0}}}({\frac {r}{a}}-B_{2})\right]}}\right]

There is a relation between the Fermi function and hyperbolic tangent:

{\frac {1}{e^{x}+1}}={\frac {1}{2}}-{\frac {1}{2}}\tanh {\frac {x}{2}}

Using this relation one can show that Fermi-Jagla model is equivalent to the generalised Fomin potential (which has scientific priority).

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 The '''Fermi-Jagla model''' is a smooth variant of the [[Ramp model | Jagla model]]. It is given by (Eq. 1 in <ref>[http://dx.doi.org/10.1021/jp205098a Joel Y. Abraham, Sergey V. Buldyrev, and Nicolas Giovambattista "Liquid and Glass Polymorphism in a Monatomic System with Isotropic, Smooth Pair Interactions", Journal of Physical Chemistry B '''115''' pp. 14229-14239 (2011)]</ref>):
-:<math>\Phi_{12}(r) = \epsilon_0 \left[ \left( \frac{a}{r} \right)^n + \frac{A_0}{1+\exp \left[ \frac{A_1}{A_0} \frac{r}{a-A_2} \right]} - \frac{B_0}{1+\exp \left[ \frac{B_1}{B_0} \frac{r}{a-B_2} \right]}  \right]</math>
+:<math>\Phi_{12}(r) = \epsilon_0 \left[ \left( \frac{a}{r} \right)^n + \frac{A_0}{1+\exp \left[ \frac{A_1}{A_0} (\frac{r}{a}-A_2) \right]} - \frac{B_0}{1+\exp \left[ \frac{B_1}{B_0} (\frac{r}{a}-B_2) \right]}  \right]</math>
 There is a relation between the Fermi function and hyperbolic tangent: