Mathematics of a Double-Walled Carbon Nanotube Model: Asymptotic and Spectral Analysis,   Miriam Rojas-Arenaza ,   University of New Hampshire ,  Fri, 3 July, 2009,   2:00 p.m. A-233


During my talk, I will present a recently developed mathematical model for a double-walled carbon nanotube. The model is given as a system of two Timoshenko beams coupled through the Van der Waals forces. Mathematically, it is a system of two coupled hyperbolic partial differential equations equipped with a four-parameter family of dynamical boundary conditions. The system has been reduced to an evolution equation with a non-selfadjoint matrix differential operator that is a dynamics generator. Asymptotic and spectral properties of this generator will be presented in the talk. We proved that it is an unbounded nonselfadjoint operator with compact resolvent, and that the set of complex eigenvalues of the dynamic generators asymptotically splits into four individual spectral branches, which is consistent with the physics of the model. The asymptotical distribution of the eigenvalues along each branch will be discussed.