DSB seminar "Thermodynamically viable fractional wave equations for power law attenuation in viscoelastic media" by Sverre Holm

Many complex media of great practical interest, such as in medical ultrasound and sediment acoustics, display an attenuation that increases with a power law as a function of frequency. Usually measurements can only be taken over a limited frequency range, while fractional wave equations model attenuation over all frequencies. There is therefore some freedom in how the models behave outside of this limited interval, and many different fractional wave equations have been proposed.

In addition, it is desirable that a wave equation models physically viable media and for that two conditions have to be satisfied. The first is causality, and the second is a criterion that comes from thermodynamic considerations and implies that the relaxation modulus is a completely monotonic function. The latter implies that attenuation asymptotically cannot rise faster than frequency raised to the first power. These criteria will be explained and used to evaluate several of the fractional wave equations that exist.

Invited minisymposium presentation at SIAM Computer Science and Engineering conference, Atlanta, Georgia, 27.2-3.3.2017