Soil Medium Electromagnetic Scattering Model for the Study of Wireless Underground Sensor Networks

In recent years, there has been keen interest in the area of Internet of Things connected underground, and with this is the need to fully understand and characterize their operating environment. In this paper, a model, based on the Peplinski principle, for the propagation of waves in soils that takes into account losses attributable to the presence of local inhomogeneity is proposed. In the work, it is assumed that the inhomogeneities are obstacles such as stones or pebbles, of moderate size, all identical and randomly distributed in space. A new wave number is obtained through a combination of the multiple scattering theory and the Peplinski principle. Since the latter principle considers the propagation in a homogeneous medium (without obstacles), the wave number it provides is inserted into the one resulting from the former, the multiple scattering theory. The effective wave number thus obtained is compared numerically with that of Peplinski alone on the one hand and with that of multiple scattering alone on the other hand. The phase velocity and the loss tangent are analyzed against the particle concentration at the low-frequency Rayleigh limit condition ( k a ≲ 0.1 ) and against the frequency at two particle concentrations ( c = 0.2 and c = 0.4 ), two particle radii ( a = 0.55 cm and a = 1.10 cm), and 5% and 50% volumetric water content of the soil. Path losses are also compared to each other to examine the effects on transmission of soil containing obstacles. The results obtained suggest that the proposed model has better accuracy in estimating the wave number than previously used schemes.

Multiple Scattering Theory for Strong Scattering Heterogeneous Elastic Continua with Triaxial Inhomogeneities: Theoretical Fundamentals and Applications

The geometry of mesoscopic inhomogeneities plays an important role in determining the macroscopic propagation behaviors of elastic waves in a heterogeneous medium. Non-equiaxed inhomogeneities can lead to anisotropic wave velocity and attenuation. Developing an accurate scattering theory to describe the quantitative relation between the microstructure features and wave propagation parameters is of fundamental importance for seismology and ultrasonic nondestructive characterization. This work presents a multiple scattering theory for strongly scattering elastic media with general tri-axial heterogeneities. A closed analytical expression of the shape-dependent singularity of the anisotropic Green’s tensor for the homogeneous reference medium is derived by introducing a proper non-orthogonal ellipsoidal coordinate. Renormalized Dyson’s equation for the coherent wave field is then derived with the help of Feynman’s diagram technique and the first-order-smoothing approximation. The exact dispersion curves and the inverse Q-factors of coherent waves in several representative medium models for the heterogeneous lithosphere are calculated numerically. Numerical results for small-scale heterogeneities with the aspect ratio varying from 1 to 7 show satisfactory agreement with those obtained from real earthquakes. The results for velocity dispersion give rise to a novel explanation to the formation mechanism of different seismic phases. The new model has potential applications in seismology and ultrasonic microstructure characterization.

Multiple scattering theory of non-Hermitian sonic second-order topological insulators

Topological phases of sound enable unconventional confinement of acoustic energy at the corners in higher-order topological insulators. These unique states which go beyond the conventional bulk-boundary correspondence have recently been extended to non-Hermitian wave physics comprising finite crystal structures including loss and gain units. We use a multiple scattering theory to calculate these topologically trapped complex states that agree very well to finite element predictions. Moreover, our semi-numerical tool allows us to compute the spectral dependence of corner states in the presence of defects, illustrating the limits of the topological resilience of these confined non-Hermitian acoustic states.