Fermi-Jagla model - Revision history

Carl McBride: Added a recent publication

2018-03-12T13:19:56Z

Added a recent publication

← Older revision		Revision as of 15:19, 12 March 2018
Line 12:		Line 12:
	;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]]

80.250.179.2 at 08:48, 5 October 2017

2017-10-05T08:48:45Z

← Older revision		Revision as of 10:48, 5 October 2017
Line 1:		Line 1:
	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} \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:		There is a relation between the Fermi function and hyperbolic tangent:

Carl McBride: replaced "introduced earlier" with "scientific priority"

2014-01-24T12:37:18Z

replaced "introduced earlier" with "scientific priority"

← Older revision		Revision as of 14:37, 24 January 2014
Line 3:		Line 3:
	:<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 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 show that Fermi-Jagla model is equivalent to [[Fomin potential]] ~~introduced earlier~~.		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/>

Fomin314 at 11:29, 24 January 2014

2014-01-24T11:29:05Z

← Older revision		Revision as of 13:29, 24 January 2014
Line 7:		Line 7:
	:<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 ~~connect the~~ Fermi-Jagla model ~~with the~~ [[Fomin potential]].		Using this relation one can show that Fermi-Jagla model is equivalent to [[Fomin potential]] introduced earlier.
	==References==		==References==
	<references/>		<references/>

Carl McBride: Slight tidy + added an internal link

2014-01-23T11:41:01Z

Slight tidy + added an internal link

← Older revision		Revision as of 13:41, 23 January 2014
Line 5:		Line 5:
	There is a relation between Fermi function and hyperbolic tangent:		There is a relation between Fermi function and hyperbolic tangent:

	:<math>\frac{1}{1+e^x}=\frac{1}{2}-\frac{1}{2}tanh(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 deduce Fermi-Jagla model to Fomin potential introduced earlier and described in another section of this site.~~

			Using this relation one can connect the Fermi-Jagla model with the [[Fomin potential]].
	==References==		==References==
	<references/>		<references/>

Fomin314 at 17:42, 22 January 2014

2014-01-22T17:42:36Z

← Older revision		Revision as of 19:42, 22 January 2014
Line 2:		Line 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>		:<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:

			:<math>\frac{1}{1+e^x}=\frac{1}{2}-\frac{1}{2}tanh(x/2)</math>

			Using this relation one can deduce Fermi-Jagla model to Fomin potential introduced earlier and described in another section of this site.

	==References==		==References==

Carl McBride: Created page with "The '''Fermi-Jagla model''' is a smooth variant of the Jagla model. It is given by (Eq. 1 in [http://dx.doi.org/10.1021/jp205098a Joel Y. Abraham, Sergey..."

2013-04-25T13:13:09Z

Created page with "The '''Fermi-Jagla model''' is a smooth variant of the Jagla model. It is given by (Eq. 1 in <ref>[http://dx.doi.org/10.1021/jp205098a Joel Y. Abraham, Sergey..."

New page

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>

==References==
<references/>
;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)]

[[category: models]]