65
Views
0
CrossRef citations to date
0
Altmetric
Articles

Effective coefficients of quasi-steady Maxwell’s equations with multiscale isotropic log-stable conductivity

, &
Pages 850-866 | Received 26 Dec 2016, Accepted 05 Apr 2017, Published online: 25 Apr 2017

References

  • Sahimi M. Flow phenomena in rocks: from continuum models, to fractals, percolation, cellular automata, and simulated annealing. Rev Mod Phys. 1993;65:1393–1534.
  • Mastryukov AF, Mikhilenko BG. Numerical solution of Maxwell’s equations for anisotropic media using the Laguerre transform. Russ Geol Geophys. 2008;49:621–627.
  • Epov MI, Shurina EP, Nechaev OV. 3D forward modeling of vector field for induction logging. Russ Geol Geophys. 2007;48:770–774.
  • Willis JR. Effective constitutive relations for waves in composites and metamaterials. Proc R Soc A: Math Phys Eng Sci. 2011;467:1865–1879.
  • Allaire G. Homogenization and two-scale convergence. SIAM J Math Anal. 1992;23:1482–1518.
  • Wellander N, Kristensson G. Homogenization of the Maxwell equations at fixed frequency. SIAM J Appl Math. 2003;64(1):170–195.
  • Shelukhin VV, Terentev SA. Frequency dispertion of dialectric permitivity and electric conductivity of rocks via two-scale homogenization of the Maxwell equations. Prog Electromagnet Res B. 2009;14:175–202.
  • Kanaun SK, Levin V. Self-consistent methods for composites. Berlin: Springer; 2008.
  • Tennekoon L, Boufadel MC, Nyquist JE. Multifractal characterization of airborne geophysical data at the Oak Ridge facility. Stoch Environ Res Risk Assess. 2005;19:227–239.
  • Bouffadel MC, Lu S, Fred J, et al. Multifractal scaling of the intrinsic permeability. Phys Earth Plan Inter. 2000;36:3211–3222.
  • Caniego FJ, Espejo R, Martin MA, et al. Multifractal scaling of soil spatial variability. Ecol Model. 2005;182:291–303.
  • Kurochkina EP, Soboleva ON. Effective coefficients of quasi-steady Maxwell’s equations with multiscale isotropic random conductivity. Physica A. 2011;390:231–244.
  • Mandelbrot BB. Intermittent turbulence in self-similar cascades: divergence of high moments and dimension of the carrier. J Fluid Mech. 1974;62:331–358.
  • Molchan GM. Turbulent cascades: Limitations and a statistical test of the lognormal hypothesis. Phys Fluids. 1997;9(8):2387–2396.
  • Molchan GM. Scaling exponents and multifractal dimensions for independent random cascades. Commun Math Phys. 1996;179:681–702.
  • Kolmogorov AN. A refinement of previous hypotheses concerning the local structure of turbulence in a viscous incompressible fluid at high Reynolds number. J Fluid Mech. 1962;13:82–85.
  • Landau LD, Lifshitz EM. Electrodynamics of continuous media. New York (NY): Pergamon Press; 1984.
  • Kuz’min GA, Soboleva ON. Subgrid modeling of filtration in porous self-similar media. J Appl Mech Tech Phys. 2002;43:583–592.
  • Gnedenko BV, Kolmogorov AN. Limit distributions for sums of independent random variables. Cambridge: Addison-Wesley; 1954; (English trans. Chung K.L.).
  • Zolotarev VM. One-dimensional stable distributions. Providence (RI): American Mathematical Society; 1986.
  • Samorodnitsky G, Taqqu MS. Stable non-gaussian random processes. New York (NY): Chapman-Hill; 1994.
  • Koshljakov NS, Smirnov MM, Gliner EB. Differential equations of mathematical physics. Moscow: Fizmatgiz; 1962.
  • Rytov SM, Kravtsov YuA, Tatarskii VI. Principles of statistical radiophysics. Vols. 3,4, Berlin: Springer-Verlag; 1987.
  • Chambers JM, Mallows C, Stuck BW. A method for simulating stable random variables. J Am Stat Assoc. 1976;71:340–344.
  • Lebedev VI. Difference analogies of orthogonal decompositions of basic differential operators and some boundary value problems, I. J Comput Math Math Phys (in Russia). 1964;3:449–465.
  • Davydycheva S, Drushkin V, Habashy T. An efficient finite-difference scheme for electromalnetic logging in 3D anisotropic inhomogeneous media. Geophysics. 2003;68:1525–1536.
  • Sleijpen G, Van der Vorst H, Modersitzki J. Differences in the effects of rounding errors in Krylov solvers for symmetric indefinite linear systems. Matrix Anal Appl. 2000;22:726–751.
  • Yeltsov IN, Nesterova GV, Kashevarov AA. Petrophysical interpretation of time-lapse electromagnetic sounding in wells. Russ Geol Geophys. 2011;52:668–675.

Reprints and Corporate Permissions

Please note: Selecting permissions does not provide access to the full text of the article, please see our help page How do I view content?

To request a reprint or corporate permissions for this article, please click on the relevant link below:

Academic Permissions

Please note: Selecting permissions does not provide access to the full text of the article, please see our help page How do I view content?

Obtain permissions instantly via Rightslink by clicking on the button below:

If you are unable to obtain permissions via Rightslink, please complete and submit this Permissions form. For more information, please visit our Permissions help page.