Buldyrev and Stanley model

The Buldyrev and Stanley model consists of a double shoulder plus a square well (Ref. 1 Eq. 1):

$\Phi _{12}\left(r\right)=\left\{{\begin{array}{ccc}\infty &;&r<a\\U_{1}&;&a\leq r<b_{1}\\U_{2}&;&b_{1}\leq r<b_{2}\\-U_{A}&;&b_{2}\leq r<c\\0&;&r\geq c\end{array}}\right.$

where $\Phi _{12}(r)$ is the intermolecular pair potential, $r:=|\mathbf {r} _{1}-\mathbf {r} _{2}|$, 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 c>b_2>b_1>a} 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 U_A>0} .

References

1. Sergey V. Buldyrev and H. Eugene Stanley "A system with multiple liquid–liquid critical points", Physica A 330 pp. 124-129 (2003)