Ramp model

The model:

Failed to parse (syntax error): {\displaystyle u(r) = \left\{ \infty & {\rm if}\; r < \sigma W_r - (W_r-W_a)\frac{r-\sigma}{d_a-\sigma} {\rm if}\;\sigma\leq r \leq d_a W_a - W_a\frac{r-d_a}{d_c-d_a} & {\rm if}\;d_a < r \leq d_c 0 {if}\; r > d_c \right} where $W_{r}>0$ and $W_{u}<0$.

References

• P. C. Hemmer and G. Stell "Fluids with Several Phase Transitions", Physical Review Letters 24 pp. 1284 - 1287 (1970)
• G. Stell and P. C. Hemmer, "Phase Transitions Due to Softness of the Potential Core", Journal of Chemical Physics' 56, pp. 4274-4286 (1972)
• E. A. Jagla "Core-softened potentials and the anomalous properties of water", Journal of Chemical Physics' 111, pp. 8980-8986 (1999)