The evolution of a crystal surface: Analysis of a one-dimensional step train connecting two facets in the ADL regime

We study the evolution of a monotone step train separating two facets of a crystal surface. The model is one-dimensional and we consider only the attachment-detachment-limited regime. Starting with the well-known ODEs for the velocities of the steps, we consider the system of ODEs giving the evolution of the “discrete slopes.” It is the l²-steepest-descent of a certain functional. Using this structure, we prove that the solution exists for all time and is asymptotically self-similar. We also discuss the continuum limit of the discrete self-similar solution, characterizing it variationally, identifying its regularity, and discussing its qualitative behavior. Our approach suggests a PDE for the slope as a function of height and time in the continuum setting. However, existence, uniqueness, and asymptotic self-similarity remain open for the continuum version of the problem.     

Triplet-triplet interaction in a nearly one dimensional molecular crystal: Application to 1,4-dibromonaphtalene

The effect of a magnetic field (6 kG) on the delayed fluorescence in a 1,4-Dibromonaphtalene at 300 K and 20 K is analysed using a new approach of calculation of the triplet-triplet annihilation rate constant. The agreement of the best fit between experiment and theory allows reaching at 300 K and 20 K respectively the lifetimes and the interaction constant of the triplets pairs. Received 12 March 1999 and Received in final form 27 April 2000