Propagation of transient acoustic waves in layered porous media: Fractional equations for the scattering operators

Nonlinear Dynamics

Volumn 38, Issue 1-4, 2004, Pages 181-190

  Depollier, Claude ^a   Fellah, Zine El Abidine ^b   Fellah, Mohamed ^c  

^a UNIVERSITÉ DU MAINE   (France)

^b INSERM   (France)

^c UNIVERSITY OF SCIENCES AND TECHNOLOGY HOUARI BOUMEDIENE   (Algeria)

Author keywords

Fractional calculus; Wave splitting

Indexed keywords

ACOUSTIC WAVE PROPAGATION; ACOUSTIC WAVE SCATTERING; FLUID STRUCTURE INTERACTION; FOURIER TRANSFORMS; MATHEMATICAL MODELS; MATHEMATICAL OPERATORS; PHYSICAL PROPERTIES; POROUS MATERIALS; PROBLEM SOLVING; TIME DOMAIN ANALYSIS; WAVE EQUATIONS;

FRACTIONAL CALCULUS; FRACTIONAL TELEGRAPH EQUATIONS; SCATTERING OPERATORS; WAVE SPLITTING;

ACOUSTIC WAVES;

EID: 15544385900     PISSN: 0924090X     EISSN: None     Source Type: Journal    
DOI: 10.1007/s11071-004-3754-8     Document Type: Conference Paper

References (16)

1. Fellah, Z. E. A. and Depollier, C., 'Transient acousticwave propagation in rigid porous media: A time-domain approach', Journal of the Acoustical Society of America 107, 2000, 683-688.
2. Johnson, D. L., 'Recent developpments in the acoustic properties of porous media', in Proceedings of the International School of Physics "Enrico Fermi" Course XCIII Frontiers in Physical Acoustics, D. Sette(ed.), North Holland, 1986, pp. 255-290.
3. Allard, J. F., Propagation of Sound in Porous Media: Modeling Sound Absorbing Materials, Chapman & Hall, London, 1993, pp. 255-290.
4. Lafarge, D., Lemarnier, P., Allard, J. F., and Tarnow, V., 'Dynamic compressibility of air in porous structures at audible frequencies', Journal of the Acoustical Society of America 102, 1997, 1995-2006.
5. Johnson, D. L., Koplik, J., and Dashen, R., 'Theory of dynamic permeability and tortuosity in fluid-saturated porous media', Journal of Fluid Mechanics 176, 1987, 379-402.
6. Champoux, Y. and Allard, J. F., 'Dynamic tortuosity and bulk modulus in air-saturated porous media', Journal of Applied Physics 70, 1991, 1975-1979.
7. Samko, S. G., Kilbas, A. A., and Marichev, O. I., Fractional Integrals and Derivatives, Gordon andBreach, Yverdon, Swittzerland, 1993.
8. Hanyga, A. and Rok, V., 'Wave propagation in micro-heterogeneous porous media: A model based on an integro-differential waveequation', Journal of the Acoustical Societyof America 107, 2000, 2965-2972.
9. Cascaval, R. C., Eckstein, E. C., Frota, C. L., Goldstein, J. A., 'Fractional telegraph equations', Journal of Mathematic Analysis and Application 276, 2002, 145-159.
10. Kristensson, G. and Krueger, R. J., 'Direct and inverse scattering in the time domain for a dissipative wave equation: I. Scatteringoperators', Journal of MathematicalPhysics 27, 1986, 1667-1682; Kristensson, G. and Krueger, R. J., 'Direct and inverse scattering in the time domain for a dissipative wave equation: II. Simultaneous reconstruction of dissipation and phase velocity profiles', Journal of Mathematical Physics 27, 1986, 1683-1693.
11. Kristensson, G. and Krueger, R. J., 'Direct and inverse scattering in the time domain for a dissipative wave equation: I. Scatteringoperators', Journal of MathematicalPhysics 27, 1986, 1667-1682; Kristensson, G. and Krueger, R. J., 'Direct and inverse scattering in the time domain for a dissipative wave equation: II. Simultaneous reconstruction of dissipation and phase velocity profiles', Journal of Mathematical Physics 27, 1986, 1683-1693.
12. Courant, R. and Hilbert, D., Methods of Mathematical Physics, Vol. 2, Interscience, New York, 1962.
13. Stokes, G. C., 'On the intensity of the light reflected and transmitted through a pile of plates', in Mathematical and Physical Papers, Vol. 2, Cambridge University Press, Cambridge, 1883.
14. Fellah, Z. E. A., Depollier, C., and Fellah, M., in preparation.
15. Kirsh, A. and Kress, R., 'Two methods for solvingthe inverse acoustic scattering problem', Inverse Problems 4, 1988, 749-770.
16. Weng, C. C., Waves and Fields in Inhomogeneous Media, IEEE Press, New York, 1995.