  Using molecular dynamics simulations, we study a liquid model which consists
of particles interacting via a spherically-symmetric two-scale Jagla ramp
potential with both repulsive and attractive ramps. The Jagla potential
displays anomalies similar to those found in liquid water, namely expansion
upon cooling and an increase of diffusivity upon compression, as well as a
liquid-liquid (LL) phase transition in the region of the phase diagram
accessible to simulations. The LL coexistence line, unlike in
tetrahedrally-coordinated liquids, has a positive slope, because of the
Clapeyron relation, corresponding to the fact that the high density phase (HDL)
is more ordered than low density phase (LDL). When we cool the system at
constant pressure above the critical pressure, the hydrodynamic properties
rapidly change from those of LDL-like to those of HDL-like upon crossing the
Widom line. The temperature dependence of the diffusivity also changes rapidly
in the vicinity of the Widom line, namely the slope of the Arrhenius plot
sharply increases upon entering the HDL domain. The properties of the glass
transition are different in the two phases, suggesting that the less ordered
phase (LDL) is fragile, while the more ordered phase (HDL) is strong, which is
consistent with the behavior of tetrahedrally-coordinated liquids such as water
silica, silicon, and BeF$_2$.
