Padé approximations for identification of air bubble volume from temperature- or frequency-dependent permittivity of a two-component mixture

Inverse Problems in Science and Engineering

Volumn 16, Issue 4, 2008, Pages 425-445

  Zhang, Dali ^a   Cherkaev, Elena ^b  

^a UNIVERSITY OF CALGARY   (Canada)

^b UNIVERSITY OF UTAH   (United States)

Author keywords

Effective complex permittivity; Ellipsoidal inclusion; Pade approximations; Spectral representation; Two component composite

Indexed keywords

ETHANOL; IDENTIFICATION (CONTROL SYSTEMS); MIXTURES; NUMERICAL METHODS; PARAMETER ESTIMATION; PERMITTIVITY; PERMITTIVITY MEASUREMENT; POLYNOMIAL APPROXIMATION; SPECTRUM ANALYSIS; TITRATION;

AIR BUBBLING; COMPLEX PERMITTIVITY (CP); COMPLEX-PERMITTIVITY MEASUREMENTS; CONSTRAINED MINIMIZATION PROBLEM; EFFECTIVE PERMITTIVITY; FREQUENCY DEPENDENT; MICRO GEOMETRIES; NUMERICA L RESULTS; OBLATE SPHEROIDAL INCLUSIONS; PADE' APPROXIMATION; PREDICTED VALUES; SPECTRAL FUNCTIONS; STRUCTURAL PARAMETERS; TWO-COMPONENT; TWO-COMPONENT MIXTURES;

VOLUME FRACTION;

EID: 46149084931     PISSN: 17415977     EISSN: 17415985     Source Type: Journal    
DOI: 10.1080/17415970701529213     Document Type: Article

References (32)

1. McPhedran, R.C., McKenzie, D.R. and Milton, G.W., 1982, Extraction of structural information from measured transport properties of composites. Applied Physics A, 29, 19-27.
2. McPhedran, R.C. and Milton, G.W., 1990, Inverse transport problems for composite media. Materials Research Society Symposium Proceedings, 195, 257-274.
3. Cherkaeva, E. and Golden, K.M., 1998, Inverse bounds for microstructural parameters of a composite media derived from complex permittivity measurements. Waves in Random Media, 8, 437-450.
4. Tripp, A.C., Cherkaeva, E. and Hulen, J., 1998, Bounds on the complex conductivity of geophysical mixtures. Geophysical Prospecting, 46(6), 589-601.
5. Bergman, D.J., 1978, The dielectric constant of a composite material - A problem in classical physics. Physical Reports C, 43, 377-407.
6. Bergman, D.J., 1980, Exactly solvable microscopic geometries and rigorous bounds for the complex dielectric constant of a two-component composite material. Physical Review Letters, 44, 1285.
7. Bergman, D.J., 1982, Rigorous bounds for the dielectric constant of a two-component composite. Annalen der Physik, 138, 78.
8. Bergman, D.J., 1993, Hierarchies of Stieltjes functions and their application to the calculation of bounds for the dielectric constant. SIAM, Journal on Applied Mathematics, 53(4), 915-930.
9. Golden, K. and Papanicolaou, G., 1983, Bounds on effective parameters of heterogeneous media by analytic continuation. Communications in Mathematical Physics, 90, 473-491.
10. Milton, G.W., 1980, Bounds on the complex dielectric constant of a composite material. Applied Physics Letters, 37(3), 300-302.
11. Milton, G.W., 1981, Bounds on the complex permittivity of a two-component composite material. Journal of Applied Physics, 52(8), 5286-5293.
12. Milton, G.W., 2002, Theory of Composites (Cambridge: Cambridge Press).
13. Cherkaev, E., 2001, Inverse homogenization for evaluation of effective properties of a mixture. Inverse Problems, 17, 1203-1218.
14. Cherkaev, E. and Zhang, D., 2003, Coupling of the effective properties of a random mixture through the reconstructed spectral representation, ETOPIM Proceedings. Physica B: Physics of Condensed Matter, 338, 16-23.
15. Day, A.R. and Thorpe, M.F., 1996, The spectral function of random resistor networks. Journal of Physics: Condensed Matter, 8, 4389-4409.
16. Day, A.R. and Thorpe, M.F., 1999, The spectral function of composites: the inverse problem. Journal of Physics: Condensed Matter, 11, 2551-2568.
17. Tuncer, E., 2005, Extracting the spectral density function of a binary composite without a priori assumptions. Physical Review B, 71, 012101.
18. Zhang, D. and Cherkaev, E., Reconstruction of spectral function from effective permittivity of a composite material using rational function approximations, to be submitted.
19. Tikhonov, A.N. and Arsenin, V.Y., 1977, Solutions of Ill-posed Problems (New York: Willey).
20. Caflisch, R.E., Miksis, M.J. Papanicolaou, G.C. and Ting, L., 1985, Effective equations for wave propagation in bubbly liquids. Journal of Fluid Mechanics, 153, 259-273.
21. Chang, A.T.C. and Wilheit, T.T., 1979, Remote sensing of atmospheric water vapor, liquid water, and wind speed at ocean surface by passive microwave techniques from the Nimbus 5 satellite. Radio Science, 14, 793-802.
22. Duraiswami, R., Prabhukumar, S. and Chahine, G.L., 1998, Bubble counting using an inverse acoustic scattering method. Journal of the Acoustical Society of America, 104(5), 2699-2717.
23. Kafesaki, M., Penciu, R.S. and Economou, E.N., 2000, Air bubbles in water: a strongly multiple scattering medium for acoustic waves. Physical Review Letter, 84(26), 6050-6053.
24. Rzasa, M.R. and Plaskowski, A., 2003, Application of optical tomography for measurements of aeration parameters in larger water tanks. Measurement Science and Technology, 14, 199-204.
25. Cubaud, T., Tatineni, M., Zhong, X. and Ho, C.M., 2005, Bubble dispenser in microfluidic devices. Physical Review E, 72, 037302.
26. Kristensson, G., Rikte, S. and Sihvola, A., 1998, Mixing formulas in the time domain. Journal of the Optical Society of America A, 15(5), 1411-1422.
27. Torquato, S., 2002, Random Heterogeneous Materials. Microstructure and Macroscopic Properties (New York: Springer-Verlag).
28. Sihvola, A., 1999, Electromagnetic Mixing Formulas and Applications, IEE Electromagnetic Waves Series, Vol. 47 (London: Institution of Electrical Engineers).
29. Maxwell Garnett, J.C., 1904, Color in metal glasses and in metallic films. Philosophical Transactions of the Royal Society of London, A203, 385-420.
30. Baker, G.A. Jr and Graves-Morris, P., 1996, Padé Approximations, 2nd Edn (Cambridge: Cambridge University Press).
31. Fierro, R.D., Golub, G.H., Hansen, P.C. and O'Leary, D.P., 1997, Regularization by truncated total least squares. SIAM Journal on Scientific Computing, 18(4), 1223-1241.
32. Golub, G.H., Hansen, P.C. and O'Leary, D.P., 1999, Tikhonov regularization and total least squares. SIAM Journal on Matrix Analysis and Applications, 21(1), 185-194.