Wednesday, February 20th, 2013
2:00pm - 3:00pm, in McCormack 2-116

Miriam Rojas-Arenaza

UMass Boston

Mathematical Analysis of a Double-Walled Carbon Nanotube Model

Abstract: Carbon nanotubes are considered outstanding candidates for innovation and promotion of emerging technologies due to their remarkable chemical, mechanical, and physical properties. Mathematical models are needed that capture the nature of the responses of these structures under a variety of physical conditions. Viewing a double-walled carbon nanotube as a system of two nested Timoshenko beams connected through the relatively weak Van der Waals forces, we study the spectral properties of the linear non-selfadjoint operator arising from this model, introducing a coupled hyperbolic system of four PDE equipped with a four parameter family of dynamical boundary conditions. Asymptotic and spectral properties of this generator will be present in the talk. We show that it is an unbounded nonselfadjoint operator with compact resolvent. We show that the set of complex eigenvalues of the dynamics generator asymptotically splits into four distinct spectral branches, which is consistent with the physics of the model. We discuss the asymptotical distribution of the eigenvalues along each branch.