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Pair Partitioning in time reversal acoustics

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.