NUMERICAL SOLUTION OF THE INTERRELATED DIFFERENTIAL EQUATION OF MOTION IN PHONON ENGINEERING
In this work, we study numeric calculations of phonon modes in nanostructures. The motion equation of atoms in a crystal with some simplification, results in a second order ordinary differential equation and two interrelated second order differential equations for 3 polarizations according to 3 dimensions. Although first equation can easily be solved, the next two interrelated equations cannot be solved by usual numerical methods. Based on discretization, a new technique is proposed for studying the motion equations. The results are presented by dispersion curves for shear, dilatational, and flexural modes of phonons.
Keywords:
numeric approximation Eigenvalue problem, dispersion curve.,
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- ISSN: 2146-1147
- Başlangıç: 2010
- Yayıncı: Turkic World Mathematical Society