Wave equations, dispersion relations, and van Hove singularities for applications of doublet mechanics to ultrasound propagation in bio- and nanomaterials |
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Authors: | Wu Junru Layman Christopher Liu Jun |
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Institution: | Department of Physics, University of Vermont, Burlington, Vermont 05405, USA. Jun-Ru.Wu@uvm.edu |
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Abstract: | A fundamental mathematical framework for applications of Doublet Mechanics to ultrasound propagation in a discrete material is introduced. A multiscale wave equation, dispersion relation for longitudinal waves, and shear waves are derived. The van Hove singularities and corresponding highest frequency limits for the Mth-order wave equations of longitudinal and shear waves are determined for a widely used microbundle structure. Doublet Mechanics is applied to soft tissue and low-density polyethylene. The experimental dispersion data for soft tissue and low-density polyethylene are compared with results predicted by Doublet Mechanics and an attenuation model based on a Kramers-Kronig relation in classical continuum mechanics. |
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