We consider the two-dimensional solidification/melting (one problem being the time-reversal of the other) of dendrites in an imposed hydrodynamic flow with a stagnation point. Complex variable methods are used, and a new class of solutions is presented (neglecting surface effects at the interface). These solutions can exhibit the interesting phenomenon of transient singularity formation in the dendrite boundary; a cusp forms in the boundary, but then instantly smooths and the solution can be continued.
All Science Journal Classification (ASJC) codes
- Statistical and Nonlinear Physics
- Mathematical Physics
- Condensed Matter Physics
- Applied Mathematics
- Hydrodynamic flow