Dr. Raphael Blumenfeld, Cambridge Hydrodynamics, Princeton, NJ
4 PM, Thursday, October 24, 1996
Room 101, Olin Physical Laboratory
A new theoretical approach is presented for the study of surface growth and is discussed in the context of interfaces growing in two-dimensional Laplacian fields. In this case, the interface dynamics are shown to be Hamiltonian with the Hamiltonian being directly related to the potential field. By mapping the growing region conformally onto the unit disk, the problem is converted to the dynamics of a many-body system. The Hamiltonian structure allows to introduce surface effects as a field, where particles and antiparticles can be excited. Such an excitation corresponds to tip-splitting along the interface. By analysing the statistical mechanics of the many-body system morphological features of the interface are predicted and discussed. The theory is applied to calculate the distribution of the curvature and the moments of the growth probability distribution along the interface. Using a dilute gas approximation, the distribution of the curvature is shown to develop algebraic tails, thus predicting the onset of fractality from first-principles. Application to other surface growth dynamics is discussed.