Numerical simulations of soft-core frictionless disks in two dimensions are carried out to study the behavior of a simple liquid as a function of temperature T, packing fraction φ, and uniform applied shear strain rate γ[over ·]. Inferring the hard-core limit from our soft-core results, we find that it depends on the two parameters φ and T/γ[over ·]. Here T/γ[over ·]→0 defines the athermal limi...

We theoretically study the magnetization relaxation of Ising spins distributed randomly in a $d$-dimension homogeneous and Gaussian profile under soft-core two-body interaction potential $\ensuremath{\propto}1/[1+{(r/{R}_{c})}^{\ensuremath{\alpha}}]$ $(\ensuremath{\alpha}\ensuremath{\ge}d)$, where $r$ is interspin distance ${R}_{c}$ radius. The dynamics starts with all polarized transverse dire...