Double‐wall nanotube as vibrational system: Mathematical approach | Zendy

Shubov Marianna A. | Zendy; RojasArenaza Miriam | Zendy

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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.

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