We have developed an analytical method to determine the coefficient of thermal expansion (CTE) for single wall carbon nanotubes (CNTs). We have found that all CTEs are negative at low and room temperature and become positive at high temperature. As the CNT diameter decreases, the range of negative CTE shrinks. The CTE in radial direction of the CNT is less than that in the axial direction for armchair CNTs, but the opposite holds for zigzag CNTs. The radial CTE is independent of the CNT helicity, while the axial CTE shows a strong helicity dependence.

Classical molecular dynamics is applied to study the energy dissipation (the Q factor) of the cantilever-type beam oscillators of single wall and double-walled carbon nanotubes (CNTs). The study finds that the Q factor of the CNT beam oscillator varies with the temperature T following the 1/T(0.36) dependence. For single wall CNT, the Q factor drops from 2 x 10(5) at 0.05 K to 1.5 x 10(3) at 293 K. The study further reveals that the weak interlayer binding strength and the interlayer commensurance significantly increases the energy dissipation in the double-walled CNT oscillator.

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We have developed an accurate atomic-scale finite element method ͑AFEM͒ that has exactly the same formal structure as continuum finite element methods, and therefore can seamlessly be combined with them in multiscale computations. The AFEM uses both first and second derivatives of system energy in the energy minimization computation. It is faster than the standard conjugate gradient method which uses only the first order derivative of system energy, and can thus significantly save computation time especially in studying large scale problems. Woven nanostructures of carbon nanotubes are proposed and studied via this new method, and strong defect insensitivity in such nanostructures is revealed. The AFEM is also readily applicable for solving many physics related optimization problems.

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