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We examine the influence of the shape of dynamical heterogeneities on the Stokes-Einstein (SE) and Stokes-Einstein-Debye (SED) relations in quasi-two-dimensional suspensions of colloidal ellipsoids. For ellipsoids with repulsive interactions, both SE and SED relations are violated at all area fractions. On approaching the glass transition, however, the extent to which this violation occurs changes beyond a crossover area fraction. Quite remarkably, we find that it is not just the presence of dynamical heterogeneities but their change in the shape from stringlike to compact that coincides with this crossover. On introducing a suitable short-range depletion attraction between the ellipsoids, associated with the lack of morphological evolution of dynamical heterogeneities, the extent to which the SE and SED relations are violated remains unchanged even for deep supercooling.

Our extended electrical conductivity and viscosity measurements have revealed a general fractional power relation between them in pure and mixed ionic melts: $\ensuremath{\sigma}T\ensuremath{\propto}(T/\ensuremath{\eta}{)}^{m}$ ( $m\phantom{\rule{0ex}{0ex}}=\phantom{\rule{0ex}{0ex}}0.8\ifmmode\pm\else\textpm\fi{}0.1$ for all melts) where $\ensuremath{\eta}$ is a shear viscosity of a melt. This relation has been observed in 9 orders of magnitude range of viscosity for the well known ionic melt ${\mathrm{Ca}}_{2}{\mathrm{K}}_{3}({\mathrm{NO}}_{3}{)}_{7}$. This fractional interdependence is considered to be a macroscopic manifestation of a basic difference in elementary mechanisms of charge and momentum transport in ionic melts.

We study the breakdown of the Stokes-Einstein (SE) and Debye-Stokes-Einstein (DSE) relations for translational and rotational motion in a prototypical model of a network-forming liquid, the ST2 model of water. We find that the emergence of ``fractional'' SE and DSE relations at low temperature is ubiquitous in this system, with exponents that vary little over a range of distinct physical regimes. We also show that the same fractional SE relation is obeyed by both mobile and immobile dynamical heterogeneities of the liquid.