Differential Variance Analysis: a direct method to quantify and visualize dynamic heterogeneities.

Many amorphous materials show spatially heterogenous dynamics, as different regions of the same system relax at different rates. Such a signature, known as Dynamic Heterogeneity, has been crucial to understand the nature of the jamming transition in simple model systems and is currently considered very promising to characterize more complex fluids of industrial and biological relevance. Unfortunately, measurements of dynamic heterogeneities typically require sophisticated experimental set-ups and are performed by few specialized groups. It is now possible to quantitatively characterize the relaxation process and the emergence of dynamic heterogeneities using a straightforward method, here validated on video microscopy data of hard-sphere colloidal glasses. We call this method Differential Variance Analysis (DVA), since it focuses on the variance of the differential frames, obtained subtracting images at different time-lags. Moreover, direct visualization of dynamic heterogeneities naturally appears in the differential frames, when the time-lag is set to the one corresponding to the maximum dynamic susceptibility. This approach opens the way to effectively characterize and tailor a wide variety of soft materials, from complex formulated products to biological tissues.