Random media

P. Meakin, Multiple Scattering of Waves in Random Media and Random Rough Surfaces, The Pennsylvania State University Press, State College, PA, 1985. 

Y. Rouault. Living polymers in random media a 2D Monte Carlo investigation. Europ Phys J B 2 483-487, 1998. 

I. Gerroff, A. Milchev, W. Paul, K. Binder. A new off-lattice Monte Carlo model for polymers A comparison of static and dynamic properties with the bond fluctuation model and application to random media. J Chem Phys 95 6526-6539, 1993. 

M. Kardar, Y. C. Zhang. Scaling of directed polymers in random media. Phys Rev Lett 55 2087-2090, 1987. 

M. Muthukumar. Localization of a polymer manifold in quenched random media. J Chem Phys 90 4594—4603, 1989. 

J. D. Honeycutt, D. Thirumalai. Influence of optimal cavity shapes on the size of polymer molecules in random media. J Chem Phys 92 6851-6858, 1990. 

Andrews, L.C., Phillips, R.L., Laser beam propagation through random media, SPIE, Bellingham, 1998... 

Rikvold, PA Stell, G, Porosity and Specific Surface for Interpenetrable-Sphere Models of Two-Phase Random Media, Journal of Chemical Physics 82, 1014, 1985. 

Lattice Monte Carlo Model for Polymers A Comparison of Static and Dynamic Properties with the Bond-Fluctuation Model and Application to Random Media. 

A rigid microporous morphology, which does not reorganize upon water uptake, corresponds to a simple linear relation x w) = yw. In this limiting case, the model resembles the archetypal problem of percolation in bicontin-uous random media. Due to deviations of swelling from fhis law, universal percolation exponents in relations between conductivity and water content are not warranted. 

S.M. Rytov, Yu. A. Kravtsov, and V.I. Tatarskii, Principles of Statistical Radiophysics. Vol. 4 Wave Propagation Through Random Media (Springer, Berlin 1989) Yu.A. Kravtsov, Reports Prog. Phys. 55, 39 (1992). 

Sznitman, Alain-Sol Brownian Motion, Obstacles, and Random Media, Springer-Verlag. Inc., New York, NY, 1998. 

Ishimaru A. Wave Propagation and Scattering in Random Media. Academic Press, New York, 1978. 

More generally, the dynamic behavior of domain walls in random media under the influence of a periodic external field gives rise to hysteresis cycles of different shape depending on various external parameters. According to a recent theory of Nattermann et al. [54] on disordered ferroic (ferromagnetic or fe) materials, the polarization, P, is expected to display a number of different features as a function of T, frequency, / = iv/2tt, and probing ac field amplitude, E0. They are described by a series of dynamical phase transitions, whose order parameter Q = uj/2h) Pdt reflects the shape of the P vs. E loop. When increasing the ac... 

V. M. Shalaev, Nonlinear Optics of Random Media, Springer Tracts in Modern Physics, Vol. 158, Springer, Berlin, 2000. 

See, for instance, M. Lax, in Multiple Scattering and Waves in Random Media, P. L. Chow, W. E. Kohler, and G. C. Papanicolaou, Eds., North Holland, 1981, and references therein J. Klafter and M. S. Schlesinger, Proc. Nat. Acad. Sci. U.S.A. 83, 848 (February 1986), and references therein R. Brown, Thesis, University of Bordeaux 1,1987 R. Brown et al. J. Phys. C20, L649 (1987) 21 (1988) in press. (This last work thoroughly discusses the applicability of fractal theory to isotopically mixed crystals as disordered system. Serious criticism is presented both of the analysis of the experimental data and of the fundementals of their description in the present theory of fractals. For this reason we omit all works treated there. 

Carasso AS, Sanderson JG, Hyman JM (1978) Digital removal of random media image degradations by solving the diffusion equation backwards in time. SIAM J Numer Anal 15 344-367... 

In the latter case, the dimensions of the unit cell must be such that the unit cell is statistically representative of the entire medium. For spatially periodic regular media, the unit cell will coincide with one lattice unit. For random media, let Lm — max,( L,) be the maximum characteristic length-scale of all the phases forming the medium, where Lt is defined by Eq. (4) below. The unit cell dimensions (Lx, Ly, L ) should be much larger than the maximum characteristic length-scale Lm for transport properties calculated on the unit cell to become cell size-independent, and thus, representative of the entire medium (Adler, 1992). 

Another frequently used characteristic of random media is the two-point autocorrelation function (Adler, 1992, 1994 Thovert et al., 1993)... 

Sipe JE, Boyd RW (2002) Nanocomposite materials for nonlinear optics based on local field effects, in optical properties of nanostructured random media, 82nd edn. Springer, Berlin, pp 1-19... 

Das, B.B., Liu, R, and Alfano, R.R. (1997) Time-resolved fluorescence and photon migration studies in biomedical and model random media. Reports on Progress in Physics, 60, 227-292. 

Gerroff, A. Milchev, K. Binder, and W. Paul, /. Chem. Phys., 98, 6526 (1993). A New Off-Lattice Monte Carlo Model for Polymers A Comparison of Static and Dynamic Properties with the Bond-Fluctuation Model and Application to Random Media. 

C. Sibilia et al.. Linear and Nonlinear Optical Properties of Quasi-Periodic One-Dimensional Structures, in Optical Properties of Nanostructured Random Media (Springer, Berlin-Heidelberg, 2002). 

Giona, M., and Roman, H.E. 1992. Fractional diffusion equation for transport phenomena in random media. PhysicaA 185, 87-97. 

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