Penetrable sphere model: Difference between revisions
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where <math>\Phi_{12}(r)</math> is the [[intermolecular pair potential]], <math>\epsilon</math> is the hight of the repulsive core, <math>r</math> is the distance between site 1 and site 2 <math>r := |\mathbf{r}_1 - \mathbf{r}_2|</math> and <math>\sigma</math> is the radius of the core. Note: an earlier, different, penetrable sphere model was proposed, but is now known as the [[Widom-Rowlinson model]]. This model can be seen as the limiting case of the | where <math>\Phi_{12}(r)</math> is the [[intermolecular pair potential]], <math>\epsilon</math> is the hight of the repulsive core, <math>r</math> is the distance between site 1 and site 2 <math>r := |\mathbf{r}_1 - \mathbf{r}_2|</math> and <math>\sigma</math> is the radius of the core. Note: an earlier, different, penetrable sphere model was proposed, but is now known as the [[Widom-Rowlinson model]]. This model can be seen as the limiting case of the [[Gaussian overlap model]] where <math>n \rightarrow \infty</math>. In the limit <math>\epsilon \rightarrow \infty</math> one has the [[hard sphere model]]. | ||
[[Gaussian overlap model]] where <math>n \rightarrow \infty</math>. | |||
==References== | ==References== | ||
<references/> | <references/> | ||
[[category: models]] | [[category: models]] | ||
Latest revision as of 11:28, 23 May 2017
The penetrable sphere model is given by [1]:
- Failed to parse (SVG (MathML can be enabled via browser plugin): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle \Phi_{12}\left( r \right) = \left\{ \begin{array}{ccc} \epsilon & ; & r < \sigma \\ 0 & ; & r \ge \sigma \end{array} \right. }
where Failed to parse (SVG (MathML can be enabled via browser plugin): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle \Phi_{12}(r)} is the intermolecular pair potential, Failed to parse (SVG (MathML can be enabled via browser plugin): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle \epsilon} is the hight of the repulsive core, Failed to parse (SVG (MathML can be enabled via browser plugin): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle r} is the distance between site 1 and site 2 Failed to parse (SVG (MathML can be enabled via browser plugin): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle r := |\mathbf{r}_1 - \mathbf{r}_2|} and Failed to parse (SVG (MathML can be enabled via browser plugin): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle \sigma} is the radius of the core. Note: an earlier, different, penetrable sphere model was proposed, but is now known as the Widom-Rowlinson model. This model can be seen as the limiting case of the Gaussian overlap model where Failed to parse (SVG (MathML can be enabled via browser plugin): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle n \rightarrow \infty} . In the limit Failed to parse (SVG (MathML can be enabled via browser plugin): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle \epsilon \rightarrow \infty} one has the hard sphere model.