## Multivariate analysis of the dielectric response of materials modeled using networks of resistors and capacitors
Galvão, R. K. H., Kienitz, K. H., Hadjiloucas, S., Walker, G., Bowen, J., Soares, S. F. C. and Araújo, M. C. U.
(2013)
Full text not archived in this repository. It is advisable to refer to the publisher's version if you intend to cite from this work. See Guidance on citing. To link to this item DOI: 10.1109/TDEI.2013.6518970 ## Abstract/SummaryWe discuss the modeling of dielectric responses of electromagnetically excited networks which are composed of a mixture of capacitors and resistors. Such networks can be employed as lumped-parameter circuits to model the response of composite materials containing conductive and insulating grains. The dynamics of the excited network systems are studied using a state space model derived from a randomized incidence matrix. Time and frequency domain responses from synthetic data sets generated from state space models are analyzed for the purpose of estimating the fraction of capacitors in the network. Good results were obtained by using either the time-domain response to a pulse excitation or impedance data at selected frequencies. A chemometric framework based on a Successive Projections Algorithm (SPA) enables the construction of multiple linear regression (MLR) models which can efficiently determine the ratio of conductive to insulating components in composite material samples. The proposed method avoids restrictions commonly associated with Archie’s law, the application of percolation theory or Kohlrausch-Williams-Watts models and is applicable to experimental results generated by either time domain transient spectrometers or continuous-wave instruments. Furthermore, it is quite generic and applicable to tomography, acoustics as well as other spectroscopies such as nuclear magnetic resonance, electron paramagnetic resonance and, therefore, should be of general interest across the dielectrics community.
[1] S. K. Lyubutin, M. S. Pedos, A.V. Ponomarev, S. N. Rukin, B. G. Slovikovsky, S. N. Tsyranov, and P. V. Vasiliev, “High Efficiency Nanosecond Generator Based on Semiconductor Opening Switch, IEEE Trans. Dielectr. Electr. Insul. vol. 18, no. 4; August 2011 pp. 1221-1227,
[2] G.A.Mesyats, S.D. Korovin, V.V. Rostov, V.G. Shpak, and M.I. Yalandin, "The RADAN series of compact pulsed power generators and their applications," Proceedings of the IEEE, Volume: 92 , Issue: 7, Page(s): 1166 - 1179 (2004).
[3] P. Dedié, V. Brommer, A. Badel and P. Tixador, “Three-Stage Superconducting XRAM Generator, IEEE Trans. Dielectr. Electr. Insul., vol. 18, no. 4; August 2011, 1189-1193
[4] R. K. MaCrone, J. K. Nelson, R. C. Smith and L. S. Schadler. “The use of electron paramagnetic resonance in the probing of the nanodielectric interface,” IEEE Trans. Dielectr. Electr. Insul., vol. 15, pp. 197-204, 2008.
[5] V. Kozlov, and A. Turanov, “Transformer oil and Modern Physics,” IEEE Trans. Dielectr. Electr. Insul., vol. 19, no. 5 pp. 1485-1497, October 2012.
[6] J. Colmenero, A. Alegra, J. M. Alberdi, and F. Alvarez, “Dynamics of the α relaxation of a glass-forming polymeric system: Dielectric, mechanical, nuclear-magnetic-resonance, and neutron-scattering studies,” Phys. Rev. B vol. 44, pp. 7321–7329, 1991.
[7] T. R. Manley, “Thermal analysis of polymers”, Pure and Applied Chemistry, vol. 61, pp. 1353- 1360, 1989.
[8] P. K. Hopke, “The evolution of chemometrics”, Anal. Chim. Acta, vol. 500, pp. 365-377, 2003. [9] S. F. C. Soares, A. A. Gomes, A. R. Galvão Filho, M. C. U. Araújo and R. K. H. Galvão, “The successive projections algorithm”, Trends in Analytical Chemistry, vol. 42, pp. 84-98, 2013. [10] K. R. Beebe, R. J. Pell and B. Seasholtz, “Chemometrics: a Pratical Guide,” New York: John Wiley & Sons, 1998.
[11] A. Nicolson and G. Ross, “Measurement of intrinsic properties of materials by time domain techniques,” IEEE Trans. Instrum. Meas., vol IM-19, pp. 377-382, 1970.
[12] W. Weir, “Automatic measuremet of complex dielectric constant and permeability at microwave frequencies,” Proc. IEEE, vol 62, no 1, pp. 33-36, Jan. 1974.
[13] S. S. Stuchly, and M. Matuszewski, “A combined Total Reflection-Transmission Method in Application to Dielectric Spectoscopy,” IEEE Trans. Instrum. Meas., vol. IM-27, no 3, September 1978.
[14] D. Pailath and S. Chang, “Improved accuracy for dielectric data,” J. Phys. E., Sci. Instrum., vol 16, pp. 227-230, 1983.
[15] M.J. Harvilla, and D. P. Nyquist, “Electromagnetic Characterization of Layered Materials via Direct and De-embed methods,” IEEE Trans. Instrum. Meas., vol. 55, no 1, February 2006.
[16] A.G. Gorriti and E. C. Slob, “Synthesis of all known Analytical Permittivity Reconstruction Techniques of Nonmagnetic Materials from Reflection and Transmission Measurements,” IEEE Trans. Geosci. Remote Sens. Lett., vol. 2, no 4, October 2005.
[17] K. S. Cole, and R. H. Cole, “Dispersion and absorption in dielectrics, I. alternating current characteristics”, J. Chem. Phys., vol. 9, pp. 341-351, 1942.
[18] D. W. Davidson and R. H. Cole, ‘‘Dielectric Relaxation in Glycerol, Propylene Glycol, and N-Propanol,’’ J. Chem. Phys., vol. 19, pp. 1484-1490, 1951.
[19] Havriliak, S.; Negami, S., ‘‘A complex plane representation of dielectric and mechanical relaxation processes in some polymers,’’ Polymer vol. 8, pp. 161–210, 1967.
[20] H. Schafer, E. Sternin, R. Stannarius, M. Arndt, and F. Kremer, “Novel approach to the analysis of broadband dielectric spectra”, Phys. Rev. Lett., vol. 76, pp. 2177–2180, 1996.
[21] A. Bella, E. Laredo, and M. Grimau, “Distribution of relaxation times from dielectric spectroscopy using monte carlo stimulated annealing: Application to -pvdf”, Phys. Rev. B, vol. 60, pp. 12764–12774, 1999.
[22] E. Tuncer and J. R. Macdonald, “Comparison of methods for estimating continuous distributions of relaxation times”, J. Appl. Phys., vol. 99, p. 074106, 2006.
[23] H. Fröhlich “Theory of Dielectrics”, Oxford University Press, London 1949.
[24] A. K. Jonscher, “The universal dielectric response,” Nature, vol. 267, no. 5613, pp. 673-679, 1977.
[25] A. K. Jonscher, “Dielectric Relaxation in Solids,” Chelsea Dielectrics Press, London, 1983. [26] T. J. Lewis, “The dielectric behavior of non-crystalline solids”, Dielectric and Related Molecular Processes, vol. 3, pp. 186-218, 1977. [27] A.K. Jonscher, “Dielectric relaxation in solids,” J. Phys. D. Appl. Phys., vol. 32, R57-R70, 1999. [28] L. A. Dissado and R. M. Hill, “Non-exponential decay in dielectrics and dynamics of correlated systems”, Nature, vol. 279, 685-89, 1979.
[29] J. C. Dyre, “Some remarks on ac conduction in disordered solids,” Journal of Non-Crystalline Solids, vol. 135, pp. 219-226, 1991.
[30] W. Wieczorek, A. Zalewska, M. Siekierski and J. Przyluski, “Modelling the a.c. conductivity behaviour of composite polymeric electrolytes by the effective medium theory,” Solid State Ionics, vol. 86-88, pp. 357-362, 1996.
[31] D. L. Sidebottom, “Dimensionality dependence of the conductivity dispersion in ionic materials,” Physical Review Letters, vol. 83, pp. 983-986, 1999.
[32] D. L. Sidebottom, P. F. Green and R. K. Brow, “Comparison of KWW and Power Law. Analyses of an Ion-Conducting Glass,” Journal of Non-crystalline Solids, vol. 183 pp. 151-160 1995.
[33] D.L. Sidebottom, B. Roling and K. Funke, “Ionic conduction in solids: Comparing conductivity and modulus representations with regard to scaling properties,” Physical Review B, vol. 63, 024301
[34] A.S. Nowick and B.S. Lim, “Electrical relaxations: Simple versus complex ionic systems,” Physical Review B, vol. 63, 184115, 2001. [35] M. Creyssels, E. Falcon, and B. Castaing, “Scaling of ac electrical conductivity of powders under compression,” Physical Review B, vol. 77, 075135, 2008. [36] M. Kaushik, B. W.-H. Ng, B. M. Fischer, and D. Abbott, “Terahertz scattering by granular composite materials: An effective medium theory,” Appl. Phys. Lett., vol. 100, 011107, 2012.
[37] R. Bouamrane and D. P. Almond, “The emergent scaling phenomenon and the dielectric properties of random resistor-capacitor networks,” J. Physics: Condensed Matter, vol. 15, no 24, pp. 4089–4100, 2003.
[38] D. P. Almond, C. R. Bowen and D. A. S. Rees, “Composite dielectrics and conductors: simulation, characterization and design,” Journal of Physics D. Applied Physics, vol. 39, pp.1295-1304, 2006. [39] D. P. Almond, B. Vainas, N. F. Uvarov, “A new analysis of the bulk ac electrical response of ionic conductors,” Solid State Ionics, vol. 111, 253-261, 1998.
[40] B. Vainas, D. P. Almond, J. Luo and R. Stevens, “An evaluation of random R-C networks for modeling the bulk ac electrical response of ionic conductors,” Solid State Ionics, vol. 126, pp. 65-80, 1999.
[41] J. R. Macdonald, “Comparison of the universal dynamic response power-law fitting model for conducting systems with superior alternative models”, Solid State Ionics, vol. 133, 79-97, 2000.
[42] N. J. McCullen, D. P. Almond, C. J. Budd, and G. W. Hunt, “The robustness of the emergent scaling property of random RC network models of complex materials,” J. Phys. D: Appl. Phys., vol. 42, no. 6, pp. 64001.1– 64001.8, 2009.
[43] D. P. Almond, C. R. Bowen and D. A. S. Rees, “Composite dielectrics and conductors: simulation, characterization and design,” J. Phys. D: Appl. Phys., vol. 39, pp.1295-1304, 2006. [44] S. Panteny, R. Stevens and C.R. Bowen, “The frequency dependent permittivity and AC conductivity of random electrical networks,” Ferroelectrics, vol. 319, pp. 199-208, 2005.
[45] K. H. Kienitz, R. K. H. Galvão, S. Hadjiloucas, and R. J. M. Afonso, “Determining state equations from descriptor representations of dynamic systems,” Applied Mathematical Modelling (submitted).
[46] S. Hadjiloucas, G.C. Walker, J. W. Bowen and R.K.H. Galvão, “System identification algorithms for fast pulse spectroscopies,” Journal of Physics: Conference Series, vol. 310, paper 012002, 2011.
[47] R. K. H. Galvão, S. Hadjiloucas, K. H. Kienitz, H. M. Paiva, and R. J. M. Afonso, “Fractional Order Modeling of Large Three-Dimensional RC Networks,” IEEE Trans. Circuits and Systems I, (in press). [48] F. R. Barbosa, O. M. Almeida, A. P. S. Braga, M. A. B. Amora, “Application of an Artificial Neural Network in the Use of Physicochemical Properties as a Low Cost Proxy of Power Transformers DGA Data,” IEEE Trans. Dielectr. Electr. Insul., vol. 19, no. 1, pp. 239-246 February 2012. [49] R. A. Ghunem, K. Assaleh and A. H. El-Hag, “Artificial Neural Networks with Stepwise Regression for Predicting Transformer Oil Furan Content,” IEEE Trans. Dielectr. Electr. Insul., vol. 19, no. 2; pp. 414-420, April 2012.
[50] Z. Y. Wang, Y. L. Liu and P. J. Griffin, “A Combined ANN and expert system tool for transformer fault diagnosis”, IEEE Trans. Power Delivery, vol. 13, pp. 1224-1229, 1998. [51] M. Islam, T. Wu, and G. Ledwich, “A novel fuzzy logic approach to transformer fault diagnosis”, IEEE Trans. Dielectr. Electr. Insul., vol. 7, pp. 177-186, 2000. [52] K.F. Thang, R.K. Aggarwal, A.J. McGrail and D.G. Esp, “Analysis of power transformer dissolved gas data using the self-organizing map”, IEEE Trans. Power Delivery, vol. 18, pp. 1241-1248, 2008. [53] K. Shaban, A. H. El-Hag, and A. Matveev, “A Cascade of Artificial Neural Networks to Predict Transformers Oil Parameters”, IEEE Trans. Dielectr. Electrical Insul., vol. 16, pp. 516-523, 2009. [54] S. Fei, and Y. Sun, “Forecasting dissolved gases content in power transformer oil based on support vector machine with genetic algorithm”, Electric Power System Research, vol. 78, pp. 507-514, 2008. [55] E. Tuncer, B. Nettelblad, and S. M. Gubanski, “Non-debye dielectric relaxation in binary dielectric mixtures (50-50): Randomness and regularity in mixture topology,” J. Appl. Phys., vol. 92, pp. 4612–4624, 2002. [56] E. Tuncer, “Structure/property relationship in dielectric mixtures: application of the spectral density theory”, J. Phys. D: Appl. Phys., vol. 38, pp. 223–234, 2005. [57] J. R. Macdonald and J. C. Phillips, “Topological derivation of shape exponents for stretched exponential relaxation”, J. Chem. Phys., vol. 122, p. 074510, 2005.
[58] R.L. Hurt, and J. R. Macdonald, “Distributed circuit elements in impedance spectroscopy: a unified treatment of conductive and dielectric systems”, Solid State Ionics, vol. 20, 111-124, 1986. [59] H. G. Kranz, “Fundamentals in Computer Aided PD Processing, PD Pattern Recognition and Automated Diagnosis in GIS”, IEEE Trans. Dielectr. Electr. Insul., vol. 7, pp. 12-20, 2000. [60] H. Zhang, T.R. Blackburn, B. T. Phung and D. Sen, “A Novel Wavelet Transform Technique for On-line Partial Discharge Measurements. 1. WT Denoising Algorithm”, IEEE Trans. Dielectr. Electr. Insul., vol. 14, pp. 3-14, 2007. [61] D. Dey, B. Chatterjee, S. Chakravorti and S. Munshi, “Cross-wavelet transform as a new paradigm for feature extraction from noisy partial discharge pulses,” IEEE Trans. Dielectr. Electr. Insul., vol. 17, pp.157-166, 2010. [62] X. Ma, C. Zhou, and I. J. Kemp, “Automated Wavelet Selection and Thresholding for PD Detection”, IEEE Electr. Insul. Mag., vol. 18, no. 2, pp. 37-45, 2002. [63] J. Li, C. Cheng, T. Jiang and S. Grzybowski, “Wavelet De-noising of Partial Discharge Signals Based on Genetic Adaptive Threshold Estimation,” IEEE Trans. Dielectr. Electr. Insul., vol. 19, no. 2, 543-549, April 2012. [64] R. K. H. Galvão S. Hadjiloucas, J. W. Bowen and C. J. Coelho, “Optimal discrimination and classification of THz spectra in the wavelet domain,” Optics Express, vol. 11, 1462-1473 2003. [65] R. K. H. Galvão S. Hadjiloucas, V. M. Becerra and J. W. Bowen, ‘Subspace system identification framework for the analysis of multimoded propagation of THz-transient signals,” Meas. Sci. Technol., vol. 16, 1037-1053, 2005. [66] S. Hadjiloucas, G. C. Walker, J. W. Bowen and R. K. H. Galvão, “System identification algorithms for fast pulse spectroscopies,” J. Phys.: Conf. Series, vol. 310, paper 012002, 2011. [67] X. Yin, B. W.-H. Ng, B. Ferguson, D. Abbott and S. Hadjiloucas, “Auto-regressive Models of Wavelet Sub-bands for Classifying Terahertz Pulse Measurements,” Journal of Biological Systems vol. 15 (4), 551-571, 2007. [68] L. Hao, P. L. Lewin, J. A. Hunter, D. J. Swaffield, A. Contin, C. Walton and M. Michel, “Discrimination of Multiple PD Sources Using Wavelet Decomposition and Principal Component Analysis,” IEEE Trans. Dielectr. Electr. Insul., vol. 18, no. 5 pp. 1702-1711 October 2011. [69] A. Contin and S. Pastore, “Classification and Separation of Partial Discharge Signals by Means of their Auto-Correlation Function Evaluation”, IEEE Trans. Dielectr. Electr. Insul., vol. 16, pp. 1609- 1622, 2009. [70] L. Hao and P. L. Lewin, “Partial Discharge Source Discrimination using a Support Vector Machine,” IEEE Trans. Dielectr. Electr. Insul., vol. 17, pp. 189-197, 2010. [71] D, Evagorou, A, Kyprianou, P. L. Lewin, A. Stavrou, V. Efthymiou, A. C. Metaxas, and G. E. Georghiou, “Feature extraction of partial discharge signals using the wavelet packet transform and classification with a probabilistic neural network,” IET Science, Measurement and Technology, vol.4, No 3,177-192, 2010. [72] W. S. Zaengl, “Dielectric Spectroscopy in Time and Frequency Domain for HV Power Equipment, Part I: Theoretical Considerations”, IEEE Electr. Insul. Mag., vol. 19, No. 5, pp. 5-19, 2003. [73] S. J. Dodd, “A Deterministic Model for the Growth of Non-conducting Electrical Tree Structures,” Journal of Physics D: Appl. Phys., vol. 36, 129–141, 2003.
[74] K. Pearson, On lines and planes of closest fit to systems of points in space, Philosophical Magazine, vol. 2, no. 11, pp. 559-572, 1901.
[75] S. Wold, K. Esbensen and P. Geladi, “Principal Component Analysis”, Chemom. Intell. Lab. Syst., vol. 2, pp. 37-52, 1987.
[76] R. K. H. Galvão, M. C. U. Araújo, W. D. Fragoso, E. C. Silva, G. E. José, S. F. C. Soares, H. M. Paiva, “A variable elimination method to improve the parsimony of MLR models using the successive projections algorithm,” Chemom. Intell. Lab. Syst., vol. 92, pp. 83-91, 2008.
[77] D. P. Looze and J. S. Freudenberg, “Tradeoffs and limitations in feedback systems” In: W. S. Levine (ed.) The Control Handbook, Boca Raton: CRC Press, 1996.
[78] M.C.U. Araujo, T.C.B. Saldanha, R.K.H. Galvão, T. Yoneyama, H.C. Chame, V. Visani, “The successive projections algorithm for variable selection in spectroscopic multicomponent analysis,” Chemom. Intell. Lab. Syst., vol. 57, pp. 65-73, 2001. [79] H. M. Paiva, S. F. C. Soares, R. K. H. Galvão and M. C. U. Araújo, “A graphical user interface for variable selection employing the Successive Projections Algorithm”, Chemom. Intell. Lab. Syst., vol. 118, pp. 260-266, 2012.
[80] N. R. Draper and H. Smith, “Applied Regression Analysis,” 3rd ed., New York: John Wiley & Sons, 1998.
[81] J. Mayes and M. Sen, “Approximation of potential-driven flow dynamics in large-scale self-similar tree networks,” Proc. Royal Soc., A, Mathematical, Physical and Engineering Sciences, vol. 467, pp. 2810-2824, May 2011. [82] S. Hadjiloucas, R. K. H. Galvão and J. W. Bowen, “Analysis of spectroscopic measurements of leaf water content at THz frequencies using linear transforms,” J. Opt. Soc. Am. A vol. 19, 2495-2509, 2002. [83] I. J. Youngs, G. C. Stevens and A. S. Vaughan, “Trends in dielectrics research: an international review from 1980 to 2004,’’ J. Phys. D: Appl. Phys., vol.39, pp 1267-1276, 2006. [84] A. Wagner and H. Kliem, “Dispersive space charge relaxation in solid polymer electrolytes, I. Experimental system polyethylene oxide,’’ J. Appl. Phys., vol. 91, pp. 6630-6637, 2002. , [85] A. Wagner and H. Kliem, “Dispersive ionic space charge relaxation in solid polymer electrolytes, II. Model and simulation,’’ J. Appl. Phys., vol. 91, pp. 6638-6649, 2002. [86] J. K. Nelson and J. C. Fothergill, “Internal charge behaviour of nanocomposites”, Nanotechnology, vol. 15, pp. 586 - 595, 2004. [87] T. Tanaka, “Dielectric nanocomposites with insulating properties”, IEEE Trans. Dielectr. Electr. Insul., vol. 12, pp. 914-928, 2008., [88] T. J. Lewis, “Nanometric Dielectrics”, IEEE Trans. Dielectr. Electr. Insul., vol.1-5, pp. 812-825, 1994. [89] M. G. Danikas and T. Tanaka, “Nanocomposites: A review on electrical treeing and breakdown”, IEEE Electr. Insul. Mag., vol. 25, No. 4, pp. 19 - 25, 2009. [90] J. Y. Li, L. Zhang, and S. Ducharme, “Electric energy density of dielectric nanocomposites”, Appl. Phys. Lett., vol. 90, 132901, 2007. [91] M. Roy, J. K. Nelson, R. K. MacCrone and L. S. Schadler, “Candidate mechanisms controlling the electrical characteristics of silica/XLPE nanodielectrics”, J. Mater. Sci., vol. 42, pp. 3789-3799, 2007. [92] D. Kim, J. S. Lee, C. M. F. Barry and J. Mead, “Microscopic measurement of the degree of mixing for nanoparticles in polymer nanocomposites by TEM Images”, Microsc. Res. Techniq., vol. 70, pp. 539 - 546, 2007. [93] J. Leggoe, “Nth-nearest neighbor statistics for analysis of particle distribution data derived from micrographs”, Scripta Materialia, vol. 53, pp. 1263 - 1268, 2005. [94] T. Tanaka, M. Kozako, N. Fuse, and Y. Ohki, “Proposal of a multicore model for polymer nanocomposite dielectrics”, IEEE Trans. Dielectr. Electr. Insul., vol. 12, pp. 669 - 681, 2005. [95] A. Tewari, M. Dighe, and A.M. Gokhale, “Quantitative characterization of spatial arrangement of micropores in cast microstructures”, Materials Characterization, vol.40, pp.119-132, 1998.
[96] J. I. Hong, L. S. Schadler, R. W. Siegel, “Rescaled electrical properties of ZnO/low density polyethylene nanocomposites”, Appl. Phys. Lett., vol. 82, pp. 1956 - 1958, 2003. [97] C. Zou, J.C. Fothergill, and S.W. Rowe, “The effect of water absorption on the dielectric properties of epoxy nanocomposites”, IEEE Trans. Dielectr. Electr. Insul., vol. 15, pp. 106-117, 2008., [98] T. Hatakeyama, K. Nakamura and H. Hatakeyama, “Determination of bound water content in polymers by DTA, DSC and TG,” Thermochimica Acta, vol. 123, pp. 153-161, 1988. [99] H. Kliem, “Dielectric small signal response by protons in amorphous insulators,” IEEE Trans. Electr. Insul., vol. 24, pp. 185-197, 1989. [100] C. Calebrese, L. Hui, L. S. Schadler and J. K. Nelson, “A Review on the Importance of Nanocomposite Processing to Enhance Electrical Insulation,” IEEE Trans. Dielectr. Electr. Insul., vol. 18, no. 4; pp. 938-945 August 2011. [101] S. Lang and E. Tuncer, “Comparison of techniques for solving the laser intensity modulation method (limm) equation”, J. Electroceramics, vol. 21, pp. 827–830, 2008. [102] E. Tuncer and S. B. Lang, “Numerical extraction of distributions of space-charge and polarization from laser intensity modulation method”, Appl. Phys. Lett., vol. 86, p. 071107, 2005. [103] E. Tuncer, N. Bowler, I.J. Youngs and K.P. Lymer, Investigating low-frequency dielectric properties of a composite using the distribution of relaxation times technique, Philosophical magazine, vol. 86, No 16, 2359-2369, June 2006. [104] P. C. Dow, Jr., “An Analysis of Certain Errors in Electronic Differential Analyzers. II-Capacitor Dielectric Absorption”, IRE Trans. Elect. Comp., vol. 7, pp. 17-22, 1958. [105] C. Iorga, “Compartmental analysis of dielectric absorption in capacitors”, IEEE Trans. Dielectr. Electr. Insul., vol. 7, 187-192, 2000. [106] L. Ragni, “Unexpected Dielectric Behavior in Aluminum Wet Electrolytic Capacitors IEEE Trans. Dielectr. Electr. Insul., vol. 19, No. 1; February 2012 pp. 291-297. [107] H. Lustfeld, M. Reissel and B. Steffen “Magnetotomography and electric currents in a fuel cell”, Fuel Cells vol. 9 pp. 474–81, 2009.
[108] Archie, G.E.. “Classification of carbonate reservoir rocks and petrophysical considerations”, American Association of Petroleum Geologists Bulletin vol 36 No 2, 278–298, 1952.
[109] A.G. Redfield, “Relaxation theory: Density matrix formulation”, eMagRes, JohnWiley & Sons, March 2007
[110] J.R. Macdonald, “Surprising conductive- and dielectric-system dispersion differences and similarities for two Kohlrausch-related relaxation-time distributions”, J. Phys.: Condes. Matter, vol 18, 629-644, 2006.
[111] J.R. Macdonald, “Limiting electrical response of conductive and dielectric systems, stretched exponential behaviour, and discrimination between fitting models”, J.Appl. Phys., vol. 82, No. 2, 3962-3971, Oct.1997.
[112] R.F. Hamou, J.R. Macdonald and E. Tuncer, “Dispersive dielectric and conductive effects in 2D resistor-capacitor networks”, J. Phys.: Condes. Matter, vol 21, 025904, 2009.
[113] J.R. Macdonald, “New model for nearly constant dielectric loss in conductive systems: Temperature and concentration dependencies”, J. Chem. Phys., Vol 116, No 8, 3401-3409 Feb. 2002.
[114] J. R. Macdonald, “The response of systems with exponential distributions of activation energies for two classes of material temperature behaviour”, Solid State Ionics, vol. 60, 319-333, 1993.
[115] G.E. Pike, and C.H. Seager, “Percolation and conuctivity: A computer study I”, Phys. Rev. B, vol. 10, No. 4, 1421-1434, Aug. 1974.
[116] J.P. Fitzpatrick, R.B. Malt, F. Spaepen, Percolation theory and the conductivity of random close packed mixtures of hard spheres, Physics Letters A, Vol. 47, No 3, 207–208 March 1974.
[117] I. Webman and J. Jortner, “Numerical simulation of electrical conductivity in microscopically inhomogeneous materials”, Phys. Rev. B, vol. 11, No. 8, 2885-2892, April 1975.
[118] R. B. Stinchcombe, “The branching model for percolation theory and electrical conductivity”, J. Phys. C: Solid State Phys., vol. 6, L1-L5, 1973.
[119] D. S. McLachlan, M. Blaszkiewicz, R. E. Newnham, “Electrical Resistivity of Composites”, Journal of the American Ceramic Society, Vol. 73, No 8, 2187–2203, Aug. 1990
[120] J.P. Clerca, G. Girauda, J.M. Laugierab and J.M. Luckc “The electrical conductivity of binary disordered systems, percolation clusters, fractals
and related models”, Advances in Physics, Vol. 39, No 3, 191-309, 1990.
[121] I.J. Youngs, “Exploring the universal nature of electrical percolation exponents by genetic algorithms fitting with general effective medium theory”, J. Phys. D: Appl. Phys., vol. 35, 3127-3137, 2002.
[122] J. R. Macdonald, “Impedance spectroscopy”, Annals of Biomedical Engineering, Vol 20, 289-305, 1992. [123] Kress R, Kühn L and Potthast R 2002 “Reconstruction of a current distribution from its magnetic fields”, Inverse Problems vol. 18 1127–46. [124] N. Lowery, R. Potthast, M. Vahdati and W. Holderbaum, “On discrimination algorithms for ill-posed problems with an application to magnetic tomography”, Inverse Problems, vol. 28, 065010, 2012. [125] J. H. Van Vleck and V. F. Weisskopf, “On the shape of collision broadened lines”, Rev. Mod. Phys., vol. 17, pp. 227–236, 1945. [126] R. Diaz, W. Merrill and N. Alexopoulos, “Analytic framework for the modeling of effective media”, J. Appl. Phys., vol. 84, pp. 6815–6826, 1998. [127] K. Kärkkäinen, A. Sihvola and K. Nikoskinen, “Analysis of a three dimensional dielectric mixture with finite difference method”, IEEE Trans. Geosci. Remote Sens., vol. 39, pp. 1013-1018, 2001. [128] G. Kristensson, S. Rikte, and A. Sihvola, “Mixing formulas in time domain”, J. Opt. Soc. Am. A, vol. 15, pp. 1411–1422, 1998. [129] J. Qi and A. Sihvola, Dispersion of the Dielectric Fröhlich Model and Mixtures IEEE Trans. Dielectr. Electr. Insul., vol. 18, No. 1; February 2011 pp.149-154. [130] J. R. Jameson and W. Harrison, “Double-well model of dielectric relaxation current”, Appl. Phys. Lett., vol. 84, 3489,3491, 2004. [131] H. Kliem, “Kohlrausch relaxation: new aspects about the everlasting story”, IEEE Trans. Dielectr. Electr. Insul., vol. 12, pp. 709-718,2005. [132] M. Kühn and H. Kliem, “Modelling non-exponential polarization relaxations in interacting dipole systems”, Phys. Stat. Sol. (b), vol. 243, pp. 2913-2928, 2006. University Staff: Request a correction | Centaur Editors: Update this record |