Universality class of three-dimensional localization of elastic waves
In plain words
Sound waves in a random network of welded metal beads have been seen to stop spreading, which is Anderson localization of elastic waves. Multifractal intensity patterns at the transition have been measured, but whether its critical exponent matches the electron transition, despite two kinds of waves (compression and shear) that convert into each other, is untested.
Precise statement
Ultrasound (MHz frequencies) in 3D networks of brazed aluminum beads, where localization was reported from transmission statistics and dynamic coherent backscattering. Quantity: the critical exponent $\nu$ and the multifractal spectrum of intensity at the mobility edge, for vector elastic waves with coupled longitudinal and transverse modes. An answer is $\nu$ and the multifractal exponents with uncertainties small enough to test the orthogonal-class values ($\nu\ \text{approximately}\ 1.57$).
What would settle it
Frequency-resolved scaling of transmission and backscattering near the mobility edge in samples of several thicknesses, compared with numerics of the elastic wave equation in the same geometry.
Status in the literature
Localization was reported in 2008 (Hu et al., Nature Physics), multifractality in 2009 (Faez et al., PRL) and a mobility gap in 2016 (Cobus et al., PRL); the critical exponent $\nu$ has not been measured with an uncertainty that tests the orthogonal class.