Atlanta, GA | Posted: January 1, 1998
Stephan Luckhaus is the director of the Mathematical Institute at the University of Leipzig. He has also served as chair at the University of Bonn. His areas of interest are free boundary value problems, mathematical imaging and phase transitions many-body systems.
In a continuum physics setting, phase changes that involve either a latent heat or concentration jumps across the phase interface have been modelled by the Stefan problem. In more than one dimension the resulting equation or system can only be solved excluding metastable phenomena like undercooling. In order to explain these phenomena, surface tension, i.e., interface curvature and velocity, has been introduced into the equations. This goes under the name Gibbs Thompson law. Methods from minimal surface theory are used to construct solutions for these systems. But again there are phenomena, nucleation for example, which are not explained by the theory. The hope is that using stochastic lattice models in approprite scaling limits one may find a solution to this problem, but this has not yet been done.