Amorphous radial frustration and water-like anomalies in a ramp-shoulder fluid.

We investigate the thermodynamic, structural, and dynamic behavior of a three-dimensional coarse-grained ramp-shoulder fluid derived from effective interactions between polymer-grafted nanoparticles. The interaction combines a softened repulsive ramp with a shallow attractive shoulder, stabilizing competing local organizations over a broad pressure interval. Molecular dynamics simulations reveal density, diffusion, and structural anomalies together with crystalline, amorphous, and fluid regions in the phase diagram. Unlike conventional isotropic core-softened fluids, the anomalous hierarchy becomes partially decoupled: the density anomaly extends beyond the structural anomaly, while the diffusion anomaly becomes closely connected to amorphization and shell migration processes. Analysis of radial distribution functions, excess entropy, translational and orientational order, and coordination-shell organization shows that the anomalies are not controlled solely by shell competition. Instead, they emerge from cooperative radial restructuring in a regime where radial correlations increase without the development of crystalline orientational order. The results indicate that the detailed shape of the softened interaction region strongly influences the structural pathways explored under compression, leading to a regime of amorphous radial frustration associated with anomalous diffusion and frustrated shell reorganization.