Computational Scattering Models for Elastic and Electromagnetic Waves in Particulate Media
Abstract
Numerical models were developed to simulate the propagation of elastic and electromagnetic waves in an arbitrary, dense dispersion of spherical particles. The scattering interactions were modeled with vector multipole fields using pure-orbital vector spherical harmonics, and solved using the full vector form of the boundary conditions. Multiple scattering was simulated by translating the scattered wave fields from one particle to another with the use of translational addition theorems, summing the multiple scattering contributions, and recalculating the scattering in an iterative fashion to a convergent solution. The addition theorems were rederived in this work using an integral method, and were shown to be numerically equivalent to previously published theorems. Both ordered and disordered collections of up to 5,000 spherical particles were used to demonstrate the ability of the scattering models to predict the spatial and frequency distributions of the transmitted waves. The results of the models show that they are qualitatively correct for many particle configurations and material properties, displaying predictable phenomena such as refractive focusing, mode conversion, and photonic band gaps. However, the elastic wave models failed to converge for specific frequency regions, possibly due to resonance effects. Additionally, comparison of the multiple scattering simulations with those using only single particle scattering showed that the multiple scattering computations are quantitatively inaccurate. The inaccuracies arise from nonconvergence of the translational addition theorems, introducing errors into the translated fields which minimize the multiple scattering contributions and bias the field amplitudes towards single scattering contributions. The addition theorems are shown to converge very slowly, and to exhibit plateaus in convergence behavior that can lead to false indications of convergence.
Document Details
- Document Type
- Technical Report
- Publication Date
- Jan 01, 2003
- Accession Number
- ADA420723
Entities
People
- Timothy Edwin Doyle
Organizations
- Utah State University