Open Access
March 2007 Complete Time-Reversed Refocusing in Reflection with an Acoustic Lagrangian Model
Daniel G. Alfaro Vigo, Adolfo G. S. Correia, André Nachbin
Commun. Math. Sci. 5(1): 161-185 (March 2007).


Discrete reflection-transmission acoustic models are introduced and analysed regarding their underlying physical properties. Namely, phenomena related to multiple scattering as encountered in the underlying continuous model. Moreover, the discrete models are designed so that computational experiments can be performed effciently. Each discrete model is expressed through its corresponding reflection-transmission matrix establishing a connection with lattice models encountered in the Physics literature. Their connections with the continuous acoustic model are discussed in detail. In particular we show how a Goupillaud medium can arise from a stable discretization of a more general random medium. Related physical phenomena are studied computationally. In particular reflection-transmission properties of waves in a rapidly varying random medim, which are valid over long propagation distances. By using a long computational domain, in a regime where we have Anderson localization, the energy of an incoherently scattered signal is entirely reflected back and, by time-reversal, completely recompressed into the smooth initial data. Experiments are also performed in a regime where separation of scales fails to hold. Another new result is the time-reversed refocusing, in reflection, of a wave train in the form of a bit stream. The bit stream is scrambled by reflection and unscrambled through time reversal. The robustness of the time-reversed refocusing phenomenon is outstanding.


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Daniel G. Alfaro Vigo. Adolfo G. S. Correia. André Nachbin. "Complete Time-Reversed Refocusing in Reflection with an Acoustic Lagrangian Model." Commun. Math. Sci. 5 (1) 161 - 185, March 2007.


Published: March 2007
First available in Project Euclid: 5 April 2007

zbMATH: 1139.35371
MathSciNet: MR2310638

Primary: 35L05 , 60H15 , 74J20

Keywords: Asymptotic theory , Inhomogeneous media , Time reversal

Rights: Copyright © 2007 International Press of Boston

Vol.5 • No. 1 • March 2007
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