We illustrate how theta constant identities are a tool. Let S be 2 copies of the positive integers congruent to 0 mod 7 and one copy of the remaining positive integers. The talk requires no previous experience with theta functions. We also discuss the Rogers-Ramanujan identity and the Macdonald identities from representations of Lie algebras. Abstract Emulsions are viscoelastic suspensions of microscopic droplets in a bulk fluid phase, and are present in numerous biological systems and industrial applications.
Important examples are blood flow and oil processing and recovery.
The rheological and mechanical properties of emulsions are strongly affected by the phenomena that occur at the drop microscale, such as drop breakup and coalescence. The numerical simulations are based on a mesh discretization capable of describing complex geometries. We demonstrate, by quantitative comparison to the experimental results, that numerical simulations are an accurate and powerful tool for the investigation of complex microstructures. We apply the numerical methods to the investigation of drop breakup in steady flows. The case of quasi-steady crystal growth is a fundamental problem both in phase transitions and in diffusion dominated growth.