Velocity Selection in two-dimensional Dendritic Growth

The applet is a preliminary version and shall be further improved in the future.

Button "Ivantsov":
The Ivantsov parabola is drawn. P denotes the Peclet number and xN sets the x-range in which the N collocation points are chosen.

Button "solve":
The integro-differential equation below is solved for some specified anisotropy alpha and some specified dimensionless capillarity length d.

Button "select":
The slope at the tip as a function of d is plotted. dA and dB set the d-range and m sets the number of points for which the integro-differential equation is solved. Solvability theory proposes that the largest root is the selected steady-state.

Example:
xN=0.4 , N=11 , P=1.0 , d=0.014 , alpha=0.227

The source code is available here.