Penetration of waves in global stochastic conducting media

Fisher and Shannon Functionals for Hyperbolic Diffusion

“…In Figure 3, we show the complexity measure C(t) for the solution to the TE. While this measure for the Wiener process is a constant as shown in (11), for the TE, this measure is a non-trivial function of time. Parameters of the TE are as in Figures 1 and 2, i.e., τ = 5 and v = 1.…”

“…Extensions of the present approach can also be conducted when the rate of absorption of energy (characterized by the parameter τ −1 ) has time fluctuations (noise) [11]. In this case, the general interest lies in averaging statistical objects over realizations of disorder (time fluctuations in the rate τ −1 ).…”

“…Advances in understanding wave propagation in a conducting medium were achieved through the analysis of the telegrapher's equation (TE), which originally appeared in the study of electromagnetic fields in waveguides [1][2][3]. This hyperbolic diffusion equation has been used in different areas of research, including the hyperbolic heat equation [4], generalized Cattaneo-Fick equations [5,6], neuroscience [7,8], biomedical optics [9], electromagnetic analysis in multilayered conductor planes [10], penetration of waves in complex conducting media [11], asymptotic diffusion from Boltzmann anisotropic scattering [12][13][14], TE in 2D and 3D for engineers problems [15], describing cosmic microwave background radiation with spherically hyperbolic diffusion [16,17], finite-velocity diffusion in heterogeneous media [18][19][20][21], as well as in the damping and propagation of surface gravity waves on a random bottom [22].…”