Dependence of local modulus estimates on microstructure and scale ratio

Determine how the distribution of local modulus estimates obtained from repeated active-microrheology measurements depends on the material microstructure and on the ratio of probe size to heterogeneity length scale.

Background

The paper uses Bayesian inference to estimate local elastic moduli from creep-recovery measurements of a probe moving through a spatially heterogeneous viscoelastic material. Because the probe size is comparable to the heterogeneity length scale, each measurement responds to a weighted average of the surrounding modulus rather than to a pointwise value. Repeated measurements at different locations therefore produce a distribution of local modulus estimates that reflects both the underlying microstructure and the probe's spatial averaging.

For the heterogeneous field examined in the paper, the mean of the local estimates agrees with an independently computed effective shear modulus, while the distribution is narrower than the full range of the modulus field. The authors explicitly leave unresolved how this distribution changes with the details of the microstructure and with the ratio between probe size and heterogeneity length scale.