Statistics of nodal points of in-plane random waves in elastic media.
We consider the nodal points (NPs) u=0 and v=0 of the in-plane vectorial displacements u=(u,v) which obey the Navier-Cauchy equation. Similar to the Berry conjecture of quantum chaos, we present the in-plane eigenstates of chaotic billiards as the real part of the superposition of longitudinal and transverse plane waves with random phases. By an average over random phases we derive the mean density and correlation function of NPs. Consequently we consider the distribution of the nearest distances between NPs.
Maksimov
Dmitrii N
DN
Institute of Physics, Academy of Sciences, 660036 Krasnoyarsk, Russia.
Sadreev
Almas F
AF