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A simple, analytic and exact condition is found for TE resonances of dielectric spheres. This condition reduces to the `magnetic wall' condition for large spheres, and to the Richtmyer condition when total reflection takes place. The resonant frequency shifts slightly in the absence of an external radiation source. The TM resonance is also discussed. These results are fundamental to the study of optical resonance.

The standard Green function method is used to model the spatial and angular distributions of THG scattering by micro-droplets. These distributions are found to depend critically on the size of the droplets. However, the THG peaks around and are of comparable magnitudes and stable. These results are compared with experimental observations and the prediction of the surface charge model.

Molecular-dynamics simulations suggest that in 2D screened Coulomb solids melt when the r.m.s. displacement of particles in local co-ordinate systems exceeds ~ 10% of the lattice period, close to the Lindemann criterion in 3D. This criterion is over-estimated in the co-operative motion model, but under-estimated in the Einstein model, because during melting a 2D solid is a mixture of both ordered and disordered phases.