  We study the onset of rigidity near the glass transition (GT) in a
short-chain polymer melt modelled by a bead-spring model, where all beads
interact with Lennard-Jones potentials. The properties of the system are
examined above and below the GT. In order to minimize high cooling-rate effects
and computational times, equilibrium configurations are reached via isothermal
compression. We monitor quantities such as the heat capacity C_P, the
short-time diffusion constants D, the viscosity \eta, and the shear modulus;
the time-dependent shear modulus G(t) is compared with the shear modulus \mu
obtained from an externally applied instantaneous shear. We give a detailed
analysis of the effects of such shearing on the system, both locally and
globally. It is found that the polymeric glass only displays long-time rigid
behavior below a temperature T_1, where T_1<T_G. Furthermore, the linear and
non-linear relaxation regimes under applied shear are discussed.
