Dynamic length scales and feedback from long-time structural relaxation ina simple liquid

Liquid can sustain shear waves up to a minimum wavenumber, indicating solid -like behaviour over short length scales. With the increase of density this critical wavenumber decreases, indicating a growth of a dynamic length sca le. The speed of the propagating shear waves goes to zero approaching a cri tical wavenumber. The maximum wavelength shows an initial enhancement appro aching the mode-coupling transition and finally grows at a slower rate as t he sharp transition is cut off. The growth of this dynamic length scale in the supercooled regime is studied using the transverse correlation function and by computing the feedback effects of dynamic correlation in an extende d mode-coupling model where the structure factor of the liquid is used as a n input.