Heat Diffusion and Random Media

  • D. Fournier
  • A. C. Boccara
Part of the Topics in Current Physics book series (TCPHY, volume 47)


Nowadays random media are structures of paramount importance for physicists and engineers. More and more disordered structures such as glasses, sintered materials, and concrete belong to our everyday world and it is of importance to be able to describe their specific properties when we compare them to homogeneous materials. The first attempt usually consists in replacing the random media by an effective medium whose properties reflect a specific physical behavior (e.g. the thermal or the electric conductivity of a polycrystalline sample). Although very useful, the previous approach has been found to be limited in its ability to describe most of the dynamical processes, other than those occurring in the “long time” or “low frequency” range where the sample behaves like a homogeneous medium. Indeed, between this and the microscopic scale, dealing with the individual entities of the structure, one can find a full range of anomalous behaviors which are more clearly revealed by studying diffusive transport. Among all the diffusion phenomena, that of heat offers certain specific advantages: the ability to operate with various kinds of materials (insulators or conductors), the possibility of repeating an experiment, and nondestructive and noncontact testing. We intend to illustrate how, by following the heat diffusion temporal behavior, rough surfaces and random media which can be mapped on fractal structures may be characterized.


Fractal Dimension Fractal Structure Fractal Geometry Random Medium Plane Source 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.


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  1. 11.1
    E.R. Eckert, R.M. Drake: Analysis of Heat and Mass Transfer ( MacGraw-Hill, New York 1972 )MATHGoogle Scholar
  2. 11.2
    H.S. Carlsraw, J.C. Jaeger: Conduction of Heat in Solids ( Clarendon, Oxford 1959 )Google Scholar
  3. 11.3
    B. Mandelbrot: The Fractal Geometry of Nature (Freeman, New York 1983 ); Les objets fractals ( Flammarion, Paris 1975 )Google Scholar
  4. 11.4
    R. Zallen: The Physics of Amorphous Materials ( Wiley, New York 1983 )CrossRefGoogle Scholar
  5. 115.
    R. Orbach: Science 231, 814 (1986)ADSCrossRefGoogle Scholar
  6. 11.6
    R. Rammal, G. Toulouse: J. de Phys. Lett. 44, L-13 (1983)CrossRefGoogle Scholar
  7. 11.7
    R. Pynn, A. Skjeltorp: Scaling Phenomena in Disordered Systems, NATO ASI Series ( Plenum, New York 1985 )Google Scholar
  8. 11.8
    H.E. Stanley, N. Ostrowsky: On Growth and Form, NATO ASI Series ( Nijhoff, Amsterdam 1985 )Google Scholar
  9. 11.9
    B.K. Bein, S. Krieger, J. Pelzl: Can. J. Phys. 64, 1208 (1986)ADSCrossRefGoogle Scholar
  10. 11.10
    Int. Cong. on Opt. Sci. Eng., Program on Optical Sensoring and Metrology. Hamburg 19–23 September 1988Google Scholar
  11. 11.11
    P. Cielo: J. Appl. Phys. 56, 230 (1984)ADSCrossRefGoogle Scholar
  12. 11.12
    P. Cielo, R. Lewack, D. Balageas: In Proc. of the Int. Conf. on Thermal Sensing for Diagnostics and Control, Cambridge, MA 1985Google Scholar
  13. 11.13
    S. Alexander, R.Orbach: J. de Phys. Lett. 43, 1–265 (1982)CrossRefGoogle Scholar
  14. 11.14
    B. Sapoval, M. Rosso, J.F. Gouyet: J. Phys. Lett. 46, 149 (1985)CrossRefGoogle Scholar
  15. 11.15
    J.P. Hulin, E. Clément, C. Baudet, J.F. Gouyet, M. Rosso: Phys. Rev. Leu. 61, 333 (1988)ADSCrossRefGoogle Scholar

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© Springer-Verlag Berlin Heidelberg 1989

Authors and Affiliations

  • D. Fournier
  • A. C. Boccara

There are no affiliations available

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