  We use molecular dynamics simulations of a model three-dimensional
particulate gel, to investigate the linear viscoelastic response. The numerical
simulations are combined with a novel test protocol (the optimally- windowed
chirp or OWCh), in which a continuous exponentially-varying frequency sweep
windowed by a tapered cosine function is applied. The mechanical response of
the gel is then analyzed in the Fourier domain. We show that i) OWCh leads to
an accurate computation of the full frequency spectrum at a rate significantly
faster than with the traditional discrete frequency sweeps, and with a
reasonably high signal-to-noise ratio, and ii) the bulk viscoelastic response
of the microscopic model can be described in terms of a simple mesoscopic
constitutive model. The simulated gel response is in fact well described by a
mechanical model corresponding to a fractional Kelvin-Voigt model with a single
Scott-Blair (or springpot) element and a spring in parallel. By varying the
viscous damping and the particle mass used in the microscopic simulations over
a wide range of values, we demonstrate the existence of a single master curve
for the frequency dependence of the viscoelastic response of the gel that is
fully predicted by the constitutive model. By developing a fast and robust
protocol for evaluating the linear viscoelastic spectrum of these soft solids,
we open the path towards novel multiscale insight into the rheological response
for such complex materials.
