Application of Quaternion Neural Network to Time Reversal Based Nonlinear Elastic Wave Spectroscopy

Abstract

Identification of crack positions or anomalies in materials using the time reversal based nonlinear elastic wave spectroscopy (TR-NEWS) is an established method. We propose a system using transducers which emit forward propagating solitonic wave and time-reversed propagating solitonic wave produced by memristers placed on a side of a rectangle and scattered by cracks in the material and received by receivers which are placed on the opposite side of the rectangle. By minimizing the difference of the scattered forward propagating wave and the scattered TR wave, we get information of the position of the crack by using the neural network technique. Route of the solitons are expressed by 2 dimensional projective quaternion functions, and parameters for getting the optimal route from signals are expected to be reduced. We consider the wave is expressed by a soliton which is conformal, and discuss symmetry protected topological impurities and gravitational effects using the Atiyah-Patodi-Singer's index theorem.

arXiv comment16 pages, 19 figures

References in corpus (9)

• Quantum Spin Hall Effect in Graphene
• $Z_2$ Topological Order and the Quantum Spin Hall Effect
• Classification of topological insulators and superconductors in three spatial dimensions
• Novel Symmetry Classes in Mesoscopic Normal-Superconducting Hybrid Structures
• Revisiting time reversal and holography with spacetime transformations
• Electromagnetic and gravitational responses and anomalies in topological insulators and superconductors
• The "Parity" Anomaly On An Unorientable Manifold
• Bulk-edge correspondence, spectral flow and Atiyah-Patodi-Singer theorem for the Z2-invariant in topological insulators
• A Closer Look at Gluons