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A cloud resolving model in spectral weak temperature gradient mode is used to explore systematically the response of mean convective rainfall to variations tropical environmental conditions. A very large fraction of the variance in modeled rainfall is explained by three variables, the surface moist entropy flux, the instability index (a measure of low to midlevel moist convective instability), and the saturation fraction (a kind of column-averaged relative humidity). The results of these calculations are compared with the inferred rainfall from 37 case studies of convection over the tropical west Pacific, the tropical Atlantic, and the Caribbean, as well as in the NCEP FNL analysis and the ERA-Interim reanalysis. The model shows significant predictive skill in all of these cases. However, it consistently overpredicts precipitation by about a factor of three, due possibly to simplifications made in the model. These calculations also show that the saturation fraction is not a predictor of rainfall in the case of strong convection. Instead, saturation fraction covaries with the precipitation as a result of a moisture quasi-equilibrium process.

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We show that supersymmetry and inflation, in a broad class of models, generically lead to formation of primordial black holes (PBHs) that can account for dark matter. Supersymmetry predicts a number of scalar fields that develop a coherent condensate along the flat directions of the potential at the end of inflation. The subsequent evolution of the condensate involves perturbative decay, as well as fragmentation into Q-balls, which can interact by some long-range forces mediated by the scalar fields. The attractive scalar long-range interactions between Q-balls facilitates the growth of Q-balls until their ultimate collapse to black holes. For a flat direction lifted by supersymmetry breaking at the scale Λ ∼ 100 TeV, the black hole masses are of the order of (M 3 Planck/Λ2) ∼ 1022 g, in the allowed range for dark matter. Similar potentials with a lower scale Λ (not necessarily associated with supersymmetry) can result in a population of primordial black holes with larger masses, which can explain some recently reported microlensing events.

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