Material Equations

  • Peter Hertel
Part of the Graduate Texts in Physics book series (GTP)


In the preceding chapter of this book on Continuum Physics we have discussed the notion of material points. They are infinitely small from a macroscopic point of view and infinitely large from a microscopic point of view. Just think of the temperature field T = T(t, x). The material point at location x at time t is large enough for obeying the rules of infinitely large systems, such as the ideal gas law, for example. On the other hand, it is small enough so that it approaches thermodynamic equilibrium practically immediately. The state of the material point is always an equilibrium, or Gibbs state which is characterized by parameters such as temperature or chemical potentials.


Internal Energy Charge Transport Material Point Kinetic Coefficient Fluid Medium 
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.


  1. 1.
    Gray, P., Scott, S.K.: Autocatalytic reactions in the isothermal, continuous stirred tank reactor: isolas and other forms of multistability. Chem. Eng. Sci. 38, 29–43 (1983)Google Scholar
  2. 2.
    Gundogdu, M., et al.: Experimental demonstration of negative magnetic permeability in the far infrared frequency region. Appl. Phys. Lett. 89, 084103 (2006)Google Scholar
  3. 3.
    Johnson, P.B., Christy, R.W.: Optical constants of the noble metals. Phys. Rev. B 6(12), 4370–4379 (1972)Google Scholar
  4. 4.
    Kac, M.: Can you hear the shape of a drum? Am. Math. Mon. 73, 1–23 (1966)Google Scholar
  5. 5.
    Kaye, G.W.C., Laby, T.H.: Tables of Physical and Chemical Constants, 16th edn. Longman Group Ltd., London (1995)Google Scholar
  6. 6.
    Landau, L.D., Lifshitz, E.M.: Theory of Elasticity, vol. 7, 3rd edn. Butterworth-Heinemann, Oxford, ISBN 978-0-750-62633-0 (1986)Google Scholar
  7. 7.
    Moin, P., Ki, J.: Tackling turbulence with supercomputers. Sci. Am. 276, 62 (1997)Google Scholar
  8. 8.
    Newburgh, R., Peidle, J., Rueckner, W.: Einstein, Perrin, and the reality of atoms: 1905 revisited. Am. J. Phys. 74, 478 (2006)Google Scholar
  9. 9.
    Pearson, J.E.: Complex patterns in a simple system. Science 261, 189–192 (1993)Google Scholar
  10. 10.
    Rossing, T.D. (ed.): Springer Handbook of Acoustics. Springer, New York, ISBN 978-0-387-30446-5 (2007)Google Scholar
  11. 11.
    Sakoda, K.: Optical properties of photonic crystals. In: Springer Series in Optical Sciences, vol. 80, 2nd edn., ISBN 978-3-540-20682-8 (2005)Google Scholar
  12. 12.
    Solymar, L., Shamonina, E.: Waves in Metamaterials. Oxford University Press, London, ISBN 978-0-19-921533-1 (2009)Google Scholar
  13. 13.
    Turing, A.: The chemical basis of morphogenesis. Phil. Trans. R. Soc. Lond. B 237, 37–72 (1952)Google Scholar
  14. 14.
    Kafesaki, M., et al.: Left-handed metamaterials: detailed numerical studies of the transmission properties. J. Opt. A: Pure Appl. Opt. 7, S12–S22 (2005)Google Scholar

Copyright information

© Springer Berlin Heidelberg 2012

Authors and Affiliations

  • Peter Hertel
    • 1
  1. 1.Fachbereich PhysikUniversität OsnabrückOsnabrückGermany

Personalised recommendations