Acoustic precursor wave propagation in viscoelastic media

Abstract

Precursor field theory has been developed to describe the dynamics of electromagnetic field evolution in causally attenuative and dispersive media. In Debye dielectrics, the so-called Brillouin precursor exhibits an algebraic attenuation rate that makes it an ideal pulse waveform for communication, sensing, and imaging applications. Inspired by these studies in the electromagnetic domain, the present paper explores the propagation of acoustic precursors in dispersive media, with emphasis on biological media. To this end, a recently proposed causal dispersive model is employed, based on its interpretation as the acoustic counterpart of the Cole¿Cole model for dielectrics. The model stems from the fractional stress¿strain relation, which is consistent with the empirically known frequency power-law attenuation in viscoelastic media. It is shown that viscoelastic media described by this model, including human blood, support the formation and propagation of Brillouin precursors. The amplitude of these precursors exhibits a sub-exponential attenuation rate as a function of distance, actually being proportional to z(-p), where z is the distance traveled within the medium and 0.5 <p < 1. The precursors identified in this work facilitate the design of optimal waveforms for propagation in complex media, creating new possibilities for acoustic-pulse-based communication and imaging systems.

Algebraic Conditions for Stability Analysis of Linear Time‐Invariant Distributed Order Dynamic Systems: A Lagrange Inversion Theorem Approach

“…This formula could be used in (5) to make utilizing Lagrange inversion theorem easier in some aspects. In fact, relation (7) paves the way to construct the Taylor series of the inverse function by merely using the Taylor series coefficients of the main function.…”

“…Fractional calculus is a generalization of classical calculus, which includes non-integer order differential operators. This calculus has found various applications in several scientific fields since its emergence, including applications in biology [1,2], economics [3] and viscoelastic materials [4,5]. Today, fractional calculus is frequently encountered in diffusion equations [6][7][8], and it is widely used in electrical circuit theory and design [9,10], as well as control systems [11][12][13][14][15][16].…”