Pair Partitioning in time reversal acoustics

TL;DR

This paper introduces the Pair Partitioning method, inspired by quantum Trotter strategies, to simulate time reversal acoustics in coupled oscillators, enhancing understanding of robustness and energy dissipation in the process.

Contribution

It presents a novel Pair Partitioning algorithm for coupled oscillators, extending time reversal acoustics analysis with a Trotter-inspired approach and dissipation considerations.

Findings

The method effectively models time reversal in coupled oscillators.

It provides a formal basis for including energy dissipation.

The approach demonstrates stability against medium inhomogeneities.

Abstract

Time reversal of acoustic waves can be achieved efficiently by the persistent control of excitations in a finite region of the system. The procedure, called Time Reversal Mirror, is stable against the inhomogeneities of the medium and it has numerous applications in medical physics, oceanography and communications. As a first step in the study of this robustness, we apply the Perfect Inverse Filter procedure that accounts for the memory effects of the system. In the numerical evaluation of such procedures we developed the Pair Partitioning method for a system of coupled oscillators. The algorithm, inspired in the Trotter strategy for quantum dynamics, obtains the dynamic for a chain of coupled harmonic oscillators by the separation of the system in pairs and applying a stroboscopic sequence that alternates the evolution of each pair. We analyze here the formal basis of the method and discuss his extension for including energy dissipation inside the medium.