Crystal Growth and Fluid Mechanics Problems in Directional Solidification

Our work in directional solidification has been in the following areas: (1) Dynamics of dendrites including rigorous mathematical analysis of the resulting equations; (2) Examination of the near-structurally unstable features of the mathematically related Hele-Shaw dynamics; (3) Numerical studies of steady temperature distribution in a vertical Bridgman device; (4) Numerical study of transient effects in a vertical Bridgman device; (5) Asymptotic treatment of quasi-steady operation of a vertical Bridgman furnace for large Rayleigh numbers and small Biot number in 3D; and (6) Understanding of Mullins-Sererka transition in a Bridgman device with fluid dynamics is accounted for.