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Double‐wall nanotube as vibrational system: Mathematical approach
Author(s) -
Shubov Marianna A.,
RojasArenaza Miriam
Publication year - 2008
Publication title -
mathematical methods in the applied sciences
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.719
H-Index - 65
eISSN - 1099-1476
pISSN - 0170-4214
DOI - 10.1002/mma.1001
Subject(s) - resolvent , mathematics , operator (biology) , perturbation (astronomy) , van der waals force , boundary value problem , perturbation theory (quantum mechanics) , mathematical analysis , generator (circuit theory) , boundary (topology) , physics , quantum mechanics , chemistry , biochemistry , power (physics) , repressor , molecule , transcription factor , gene
In this paper, we present a recently developed mathematical model for short double‐wall carbon nanotubes. The model is governed by a system of four hyperbolic equations representing the two Timoshenko beams coupled through the Van der Waals forces. The system is equipped with a four‐parameter family of the boundary conditions and can be reduced to an evolution equation. This equation defines a strongly continuous semi‐group. Spectral properties of the semi‐group generator are presented in the paper. We show that it is an unbounded non‐selfadjoint operator with compact resolvent. Moreover, this operator is a relatively compact perturbation of a certain selfadjoint operator. Copyright © 2008 John Wiley & Sons, Ltd.