Stiff microscale forcing and solitary wave refocusing

Multiscale Modeling and Simulation

Volumn 3, Issue 3, 2005, Pages 680-705

  Muñoz Grajales, Juan Carlos ^a,b   Nachbin, André ^a  

^a IMPA   (Brazil)

^b UNIVERSIDAD DEL VALLE   (Colombia)

Author keywords

Inhomogeneous media; Refocusing; Solitary waves

Indexed keywords

COMPUTER SIMULATION; DIFFERENTIAL EQUATIONS; EIGENVALUES AND EIGENFUNCTIONS; MATHEMATICAL MODELS; NUMERICAL METHODS; POLYNOMIALS; SOLITONS;

INHOMOGENOUS MEDIA; REFOCUSING; SOLITARY WAVES;

ELECTROMAGNETIC WAVE PROPAGATION;

EID: 24644506765     PISSN: 15403459     EISSN: None     Source Type: Journal    
DOI: 10.1137/030602691     Document Type: Article

References (47)

1. D. G. Alfaro Vigo, J. P. Fouque, J. Garnier, and A. Nachbin, Robustness of time reversal for waves in time-dependent random media, Stochastic Process. Appl., 113 (2004), pp. 289-313.
2. M. Ash, W. Kohler, G. Papanicolaou, M. Postel, and B. White, Frequency content of randomly scattered signals, SIAM Rev., 33 (1991), pp. 519-625.
3. P. G. Baines, Topographic Effects in Stratified Flows, Cambridge University Press, Cambridge, UK, 1995.
4. G. Bal, G. Papanicolaou, and L. Ryzhik, Self-averaging in time reversal for the parabolic wave equation, Stoch. Dyn., 2 (2002), pp. 507-532.
5. P. Blomgren, G. Papanicolaou, and H. Zhao, Super-resolution in time-reversal acoustics, J. Acoust. Soc. Amer., 111 (2002), pp. 230-248.
6. L. Beryland and R. Burridge, The accuracy of the O'Doherty-Anstey approximation for wave propagating in highly disordered stratified media, Wave Motion, 21 (1995), pp. 357-373.
7. R. Burridge, G. Papanicolaou, and B. S. White. One-dimensional wave propagation in a highly discontinuous medium, Wave Motion, 10 (1988), pp. 19-44.
8. R. Burridge, G. Papanicolaou, P. Sheng, and B. White, Probing a random medium with a pulse, SIAM J. Appl. Math., 49 (1989), pp. 582-607.
9. J. F. Clouet and J. P. Fouque, A time-reversal method for an acoustical pulse propagating in randomly layered media, Wave Motion, 25 (1997), pp. 361-368.
10. A. Derode, P. Roux, and M. Fink, Robust acoustic time reversal with high-order multiple scattering, Phys. Rev. Lett., 75 (1995), pp. 4206-4209.
11. A. Derode, A. Tourin, and M. Fink, Random multiple scattering of ultrasound. II: Is time reversal a self-averaging process?, Phys. Rev. E, 64 (2001), paper 036606.
12. P. G. Drazin and R. S. Johnson, Solitons: An Introduction, Cambridge University Press, Cambridge, UK, 1989.
13. T. Driscoll, Schwarz-Christoffel Toolbox for Matlab, http://www. math.udel.edu/driscoll/software.
14. B. Engquist and A. Majda, Absorbing boundary conditions for the numerical simulation of waves, Math. Comp., 31 (1977), pp. 629-651.
15. European Centre for Medium-Range Weather Forecasts (ECMWF), Orography, Proceedings of a Workshop held at ECMWF, Reading, UK, 1998.
16. M. Fink, Time reversal mirrors, J. Phys. D: Appl. Phys., 26 (1993), pp. 1333-1350.
17. M. Fink, Time-reversed acoustics, Scientific American, November, 1999, pp. 67-93.
18. M. Fink and C. Prada, Eigenmodes of the time reversal operator: A solution to selective focusing in multiple-target media, Wave Motion, 20 (1994), pp. 151-163.
19. J.-P. Fouque and A. Nachbin, Time-reversed refocusing of surface water waves, Multiscale Model. Simul., 1 (2003), pp. 609-629.
20. J.-P. Fouque, J. Garnier, and A. Nachbin, Time reversal for dispersive waves in random media, SIAM J. Appl. Math., 64 (2004), pp. 1810-1838.
21. J. P. Fouque, J. Garnier, and A. Nachbin, Shock structure due to stochastic forcing and the time reversal of nonlinear waves, Phys. D, 195 (2004), pp. 324-346.
22. J. P. Fouque, J. Garnier, J. C. Muñoz, and A. Nachbin, Time reversing solitary waves, Phys. Rev. Lett., 92 (2004), paper 094502-1.
23. J.-P. Fouque and K. Sølna, Time-reversal aperture enhancement, Multiscale Model. Simul., 1 (2003), pp. 239-259.
24. T. Y. Hou, J. Lowengrub, and M. Shelley, Removing the stiffness from interfacial flows with surface tension, J. Comput. Phys., 114 (1994), pp. 312-338.
25. J. S. Kim, H. C. Song, and W. A. Kuperman, Adaptive time-reversal mirror, J. Acoust. Soc. Amer., 109 (2001), pp. 1817-1825.
26. W. A. Kuperman, W. S. Hodgkiss, H. C. Song, T. Akal, C. Ferla, and D. R. Jackson, Phase conjugation in the ocean: Experimental demonstration of an acoustic time reversal mirror, J. Acoust. Soc. Amer., 103 (1998), pp. 25-40.
27. P. Lewicki, R. Burridge, and G. Papanicolaou Pulse stabilization in a strongly heterogeneous layered medium, Wave Motion, 20 (1994), pp. 177-195.
28. P. Lewicki, R. Burridge, and M. V. de Hoop Beyond effective medium theory: Pulse stabilization for multimode wave propagation in high-contrast layered media, SIAM J. Appl. Math., 56 (1996), pp. 256-276.
29. C. C. Mei The Applied Dynamics of Ocean Surface Waves, John Wiley, New York, 1983.
30. J. C. Mũnoz Grajales, Dispersive Wave Attenuation and Refocusing Due to Disordered Orographic Forcing, Ph.D. thesis, Instituto de Matemática Pura e Aplicada, Rio de Janeiro, Brazil, 2002.
31. J. C. Muñoz Grajales and A. Nachbin Dispersive wave attenuation due to orographic forcing, SIAM J. Appl. Math., 64 (2004), pp. 977-1001.
32. A. Nachbin, A terrain-following Boussinesq system, SIAM J. Appl. Math., 63 (2003), pp. 905-922.
33. A. Nachbin, The localization length of randomly scattered water waves, J. Fluid Mech., 296 (1995), pp. 353-372.
34. A. Nachbin and V. Casulli, Water waves: Linear potential theory results validated with a hydrostatic Navier-Stokes model, in Mathematical and Numerical Aspects of Wave Propagation, J. A. DeSanto, ed., SIAM, Philadelphia, 1998, pp. 773-775.
35. A. Nachbin and K. Sølna, Apparent diffusion due to topographic microstructure in shallow waters, Phys. Fluids, 15 (2003), pp. 66-77.
36. J. Ndzie, Refocusing of a time-reversed acoustical pulse propagating in randomly layered media, J. Statist. Phys., 104 (2001), pp. 1253-1272.
37. O. Nwogu, Alternative form of Boussinesq equations for nearshore wave propagation, J. Waterway, Port, Coastal and Ocean Engineering, 119 (1993), pp. 618-638.
38. C. Pires and M. A. Miranda, Tsunami waveform inversion by adjoint methods, J. Geophys. Res., 106 (2001), pp. 19733-19796.
39. G. Papanicolaou, L. Ryzhik, and K. Sølna, Statistical stability in time reversal, SIAM J. Appl. Math., 64 (2004), pp. 1133-1155.
40. G. Papanicolaou and K. Sølna, Ray theory for a locally layered random medium, Waves Random Media, 10 (2000), pp. 155-202.
41. D. H. Peregrine, Long waves on a beach, J. Fluid Mech., 27 (1967), pp. 815-827.
42. C. Prada and M. Fink, Eigenmodes of the time reversal operator: A solution to selective focusing in multiple-target media, Wave Motion, 20 (1994), pp. 151-163.
43. K. Sølna, Stable Spreading of Acoustic Pulses Due to Laminated Microstructure, Ph.D. thesis, Department of Mathematics, Stanford University, 1997.
44. K. Sølna, Focusing of time-reversed reflections, Waves Random Media, 12 (2002), pp. 365-385.
45. M. Tanter, J. L. Thomas, F. Coulouvrat, and M. Fink, Breaking of time reversal invariance in nonlinear acoustics, Phys. Rev. E, 64 (2001), paper 016602.
46. G. Wei and J. Kirby, Time-dependent numerical code for extended Boussinesq equations, J. of Waterway, Port, Coastal and Ocean Engineering, 121 (1995), pp. 251-261.
47. G. B. Whitham, Linear and Nonlinear Waves, John Wiley, New York, 1974.