Pair Partitioning In Time Reversal Acoustics

Abstract

Time reversal of acoustic waves can be achieved ef_ciently by the persistent control of excitations
in a _nite 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 _rst 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 sequency 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.