of the total dust abundance of nearby galaxies in [@2012MNRAS.423...38M]. A17 also predicted a variation of grain size distribution along the galactic radius. [@2017MNRAS.469..870H] took advantage of the grain size information in A17 and investigated the temporal and spatial variation of extinction curves. They also examined the dependence of extinction curves on metallicity. They found that extinction curves become steeper at the intermediate age and metallicity when the dust abundance is strongly modified by the accretion of gas-phase metals, and at low densities where shattering is more efficient than coagulation. Using the same simulation, [@2018MNRAS.474.1545C] calculated the abundance of H$_2$ and CO in a consistent manner with the dust abundance and grain size distribution, which govern the grain-surface reaction rates and UV shielding. They found that H$_2$ is not a good tracer of SFR at low metallicity because H$_2$-rich regions are limited to dense compact regions.

The above framework with the two-size approximation has also been applied to cosmological simulations [@2018MNRAS.478.4905A; @2018MNRAS.479.2588G; @2019MNRAS.484.1852A; @2019MNRAS.485.1727H]. For example, [@2018MNRAS.478.4905A] explained the observed relation between dust-to-gas ratio and metallicity, the evolution of the comoving dust mass density in the Universe, and the radial profile of dust surface density around massive galaxies. [@2019MNRAS.485.1727H], using 