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We investigate the equation of state, diffusion coefficient, and structuralorder of a family of spherically-symmetric potentials consisting of a hard coreand a linear repulsive ramp. This generic potential has two characteristiclength scales: the hard and soft core diameters. The family of potentials isgenerated by varying their ratio, $\lambda$. We find negative thermal expansion(thermodynamic anomaly) and an increase of the diffusion coefficient uponisothermal compression (dynamic anomaly) for $0\leq\lambda<6/7$. As in water,the regions where these anomalies occur are nested domes in the ($T, \rho$) or($T, P$) planes, with the thermodynamic anomaly dome contained entirely withinthe dynamic anomaly dome. We calculate translational and orientational orderparameters ($t$ and $Q_6$), and project equilibrium state points onto the ($t,Q_6$) plane, or order map. The order map evolves from water-like behavior tohard-sphere-like behavior upon varying $\lambda$ between 4/7 and 6/7. Thus, wetraverse the range of liquid behavior encompassed by hard spheres ($\lambda=1$)and water-like ($\lambda\sim4/7$) with a family of tunablespherically-symmetric potentials by simply varying the ratio of hard tosoft-core diameters. Although dynamic and thermodynamic anomalies occur almostacross the entire range $0\leq\lambda\leq1$, water-like structural anomalies(i.e., decrease in both $t$ and $Q_6$ upon compression and strictly correlated$t$ and $Q_6$ in the anomalous region) occur only around $\lambda=4/7$.Water-like anomalies in structure, dynamics and thermodynamics arise solely dueto the existence of two length scales, orientation-dependent interactions beingabsent by design.Comment: total 21 pages, 6 figure

Family of tunable spherically symmetric potentials that span the range from hard spheres to waterlike behavior