EffectiveWaves
A Julia package for calculating, processing and plotting waves travelling in heterogeneous materials. The focus is on ensemble averaged waves.
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At present, the packages calculates effective wavenumbers, wave transimission and wave reflection from random particulate materials in two-dimensions, see arXiv preprint for details on the mathematics, or these notes for the formulas.
Installation
Type into Julia:
using Pkg
Pkg.clone("https://github.com/arturgower/EffectiveWaves.jl.git")
using EffectiveWaves
Documentation
- STABLE — documentation of the most recently tagged version.
- DEVEL — documentation of the in-development version.
Simple example
Effective wavenumbers for two species randomly (uniformly) distributed in Glycerol.
#where: ρ = density, r = radius, c = wavespeed, and volfrac = volume fraction
const WaterDistilled= Medium(ρ=0.998*1000, c = 1496.0)
const Glycerol = Medium(ρ=1.26*1000, c = 1904.0)
species = [
Specie(ρ=WaterDistilled.ρ,r=30.e-6, c=WaterDistilled.c, volfrac=0.1),
Specie(ρ=Inf, r=100.0e-6, c=2.0, volfrac=0.2)
]
# background medium
background = Glycerol
Calculate effective wavenumbers:
# angular frequencies
ωs = LinRange(0.01,1.0,60)*30.0e6
wavenumbers = wavenumber_low_volfrac(ωs, background, species)
speeds = ωs./real(wavenumbers)
attenuations = imag(wavenumbers)
For a list of possible materials go to src/materials.jl.
More examples
For more examples and details go to docs/src/examples/.
Acknowledgements and contributing
This library was originally written by Artur L Gower. Contributions are very welcome.
References
[1] Gower AL, Smith MJ, Parnell WJ, Abrahams ID. Reflection from a multi-species material and its transmitted effective wavenumber. Proc. R. Soc. A. 2018 Apr 1;474(2212):20170864.
[2] Gower, Artur L., William J. Parnell, and I. David Abrahams. "Multiple waves propagate in random particulate materials." SIAM Journal on Applied Mathematics 79.6 (2019): 2569-2592.
[3] Gower, Artur L., I. David Abrahams, and William J. Parnell. "A proof that multiple waves propagate in ensemble-averaged particulate materials." Proceedings of the Royal Society A 475.2229 (2019): 20190344.