Abstract
An approximate solution of the Dyson equation related to a stochastic Helmholtz equation, which describes the acoustic dynamics of a three-dimensional isotropic random medium with elastic tensor fluctuating in space, is obtained in the framework of the Random Media Theory. The wavevector-dependence of the self-energy is preserved, thus allowing a description of the acoustic dynamics at wavelengths comparable with the size of heterogeneity domains. This in turn permits to quantitatively describe the mixing of longitudinal and transverse dynamics induced by the medium's elastic heterogeneity and occurring at such wavelengths. A functional analysis aimed to attest the mathematical coherence and to define the region of validity in the frequency-wavevector plane of the proposed approximate solution is presented, with particular emphasis dedicated to the case of disorder characterized by an exponential decay of the covariance function.
Highlights
Most materials we encounter on a daily basis, such as glasses, polycrystalline aggregates, ceramics, composites, geophysical materials, and concrete can be classified as heterogeneous materials, being composed by domains with different physical characteristics
We propose an approximate solution of the vectorial Dyson equation, which takes into account in an approximate form terms of the Neumann-Liouville series up to the second order, introducing corrective terms to the Born Approximation
The Mixing of Polarizations Beyond the Born Approximation We introduce an approximate method (GBA) for the calculation of (q, ω)
Summary
Most materials we encounter on a daily basis, such as glasses, polycrystalline aggregates, ceramics, composites, geophysical materials, and concrete can be classified as heterogeneous materials, being composed by domains with different physical characteristics. In the so-called Rayleigh region, i.e., for values of wavelength (λ) of elastic excitations much lower than the characteristic size (a) of inhomogeneity domains, the phase velocity of acoustic modes shows a softening with respect to its hydrodynamic value (retardation). It is observed, a strong increase of the acoustic wave attenuation (Rayleigh scattering), the two quantities being related to each other by Kramers-Kroning relations [11]. The basic analytical instrument to describe the ensemble averaged elastodynamic
Sign-in/Register to view highlights & summary Sign-in/Register to access full text options 
Talk to us
Join us for a 30 min session where you can share your feedback and ask us any queries you have
Schedule a call
