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The terahertz frequency absorption spectra of DNA molecules reflect low-frequency internal helical vibrations involving rigidly bound subgroups that are connected by the weakest bonds, including the hydrogen bonds of the DNA base pairs, and/or non-bonded interactions. Although numerous difficulties make the direct identification of terahertz phonon modes in biological materials very challenging, recent studies have shown that such measurements are both possible and useful. Spectra of different DNA samples reveal a large number of modes and a reasonable level of sequence-specific uniqueness. This chapter utilizes computational methods for normal mode analysis and theoretical spectroscopy to predict the low-frequency vibrational absorption spectra of short artificial DNA and RNA. Here the experimental technique is described in detail, including the procedure for sample preparation. Careful attention was paid to the possibility of interference or etalon effects in the samples, and phenomena were clearly differentiated from the actual phonon modes. The results from Fourier-transform infrared spectroscopy of DNA macromolecules and related biological materials in the terahertz frequency range are presented. In addition, a strong anisotropy of terahertz characteristics is demonstrated. Detailed tests of the ability of normal mode analysis to reproduce RNA vibrational spectra are also conducted. A direct comparison demonstrates a correlation between calculated and experimentally observed spectra of the RNA polymers, thus confirming that the fundamental physical nature of the observed resonance structure is caused by the internal vibration modes in the macromolecules. Application of artificial neural network analysis for recognition and discrimination between different DNA molecules is discussed.

The tri-dimensional acoustic wave propagation in general anisotropic piezoelectric crystals is analyzed by adopting generalized characteristic theory. The characteristic differential equations and compatible relations along bicharacteristics are deduced. Instead of degenerated to 2D plane and using Umov-Poynting vector or ray method, the explicit expressions for phonons along an arbitrary direction in general anisotropic piezoelectric solids are obtained through the characteristic relations. The focusing patterns in piezoelectric crystals with different symmetry are discussed with the purpose to disclose the evolution rules of phonon focusing along with the increase of the material anisotropy.