Fermi-Jagla model: Difference between revisions
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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>): | 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 | :<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 Fermi function and hyperbolic tangent: | There is a relation between the Fermi function and hyperbolic tangent: | ||
:<math>\frac{1}{e^x+1}=\frac{1}{2}-\frac{1}{2}\tanh \frac{x}{2}</math> | :<math>\frac{1}{e^x+1}=\frac{1}{2}-\frac{1}{2}\tanh \frac{x}{2}</math> | ||
Using this relation one can | Using this relation one can show that Fermi-Jagla model is equivalent to the generalised [[Fomin potential]] (which has scientific priority). | ||
==References== | ==References== | ||
<references/> | <references/> | ||
;Related reading | ;Related reading | ||
*[http://dx.doi.org/10.1063/1.4790404 Shaina Reisman and Nicolas Giovambattista "Glass and liquid phase diagram of a polyamorphic monatomic system", Journal of Chemical Physics '''138''' 064509 (2013)] | *[http://dx.doi.org/10.1063/1.4790404 Shaina Reisman and Nicolas Giovambattista "Glass and liquid phase diagram of a polyamorphic monatomic system", Journal of Chemical Physics '''138''' 064509 (2013)] | ||
*[https://doi.org/10.1063/1.5017105 Saki Higuchi, Daiki Kato, Daisuke Awaji, and  Kang Kim "Connecting thermodynamic and dynamical anomalies of water-like liquid-liquid phase transition in the Fermi–Jagla model", Journal of Chemical Physics '''148''' 094507 (2018)] | |||
[[category: models]] | [[category: models]] | ||
Latest revision as of 15:19, 12 March 2018
The Fermi-Jagla model is a smooth variant of the Jagla model. It is given by (Eq. 1 in [1]):
![{\displaystyle \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]}](https://wikimedia.org/api/rest_v1/media/math/render/svg/9e746e236c78fd9fcd2bb0ff5f1e8194cb9581a8)
There is a relation between the Fermi function and hyperbolic tangent:
Using this relation one can show that Fermi-Jagla model is equivalent to the generalised Fomin potential (which has scientific priority).
References[edit]
- Related reading
- Shaina Reisman and Nicolas Giovambattista "Glass and liquid phase diagram of a polyamorphic monatomic system", Journal of Chemical Physics 138 064509 (2013)
- Saki Higuchi, Daiki Kato, Daisuke Awaji, and  Kang Kim "Connecting thermodynamic and dynamical anomalies of water-like liquid-liquid phase transition in the Fermi–Jagla model", Journal of Chemical Physics 148 094507 (2018)