Advertisement

Lorentz models revisited what one can learn from ants in a labyrinth

  • M.H. Ernst
Lectures
Part of the Lecture Notes in Physics book series (LNP, volume 253)

Keywords

Master Equation Kinetic Theory Percolation Threshold Jump Rate Uniform Lattice 
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.

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References

  1. [ 1]
    E.H. Hauge, in Transport Phenomena, Eds. G. Kirczenow and J. Marro, Lecture Notes in Physics 31 (Springer Verlag, Berlin 1974) p. 338.Google Scholar
  2. [ 2]
    P.G. De Gennes, La Recherche 7 (1976) 919.Google Scholar
  3. [ 3]
    A.B. Harris and S. Kirkpatrick, Phys. Rev. B16 (1977) 542.Google Scholar
  4. [ 4]
    B.P. Watson and P.J. Leath, Phys. Rev. B 9 (1974) 4893; B12 (1975) 498(E).Google Scholar
  5. [ 5]
    Th.M. Nieuwenhuizen, P.F.J. van Velthoven and M.H. Ernst, to be published.Google Scholar
  6. [ 6]
    B.J. Alder and T.E. Wainwright, Phys. Rev. A1 (1970) 18.Google Scholar
  7. [ 7]
    J.R. Dorfman and E.G.D. Cohen, Phys. Rev. A6 (1972) 776; A12 (1975) 292.Google Scholar
  8. [ 8]
    M.H. Ernst, E.H. Hauge and J.M.J. van Leeuwen, Phys. Rev. A4 (1971) 2055; J. Stat. Phys. 15 (1976) 7.Google Scholar
  9. [ 9]
    M.H. Ernst and A. Weyland, Phys. Lett. 34A (1971) 39.Google Scholar
  10. [10]
    E.G.D. Cohen, Colloques Internationaux CNRS No. 236-Theories cinetique classiques et relativistes; H. van Beijeren, Rev. Mod. Phys. 54 (1982) 195; P. Grassberaer, Physica 103A (1980) 558.Google Scholar
  11. [11]
    M.H. Ernst, J. Machta, J.R. Dorfman and H. van Beijeren, J. Stat. Phys. 34 (1984) 477; 35 (1984) 413.Google Scholar
  12. [12]
    P.B. Visscher, Phys. Rev. B29 (1984) 5462; 5472.Google Scholar
  13. [13]
    I.M. de Schepper, H. van Beijeren and M.H. Ernst, Physica 75 (1974) 1.Google Scholar
  14. [14]
    M.H. Ernst and H. van Beijeren, J. Stat. Phys. 26 (1981) 1.Google Scholar
  15. [15]
    B.J. Alder and W.E. Alley, Physics Today, January 1984, p. 56.Google Scholar
  16. [16]
    J.R. Dorfman, in: Fundamental Problems in Statistical Mechanics III, ed. E.G.D. Cohen (North Holland Publ. Comp., Amsterdam, 1975); E.C.D. Cohen, Physics Today, January 1984, p. 64Google Scholar
  17. [17]
    W.W. Wood, in: Fundamental Problems in Statistical Mechanics III, ed. E.G.D. Cohen (North Holland Publ. Comp., Amsterdam, 1975); T.T. Erpenbeck and W.W. Wood, Phys. Rev. A32 (1985) 23.Google Scholar
  18. [18]
    C. Bruin, Phys. Rev. Lett. 29 (1972) 1670; Physica 72 (1974) 261.Google Scholar
  19. [19]
    J.C. Lewis and J.A. Tjon, Phys. Lett. 66A (1978) 349.Google Scholar
  20. [20]
    B.J. Alder and W.E. Alley, J. Stat. Phys. 19 (1978) 341; Physica 121A (1983) 523.Google Scholar
  21. [21]
    S. Alexander, J. Bernasconi, W.R. Schneider and R. Orback, Rev. Mod. Phys. 53 (1981) 175.Google Scholar
  22. [22]
    S. Kirkpatrick, Rev. Mod. Phys. 45 (1973) 574.Google Scholar
  23. [23]
    S. Kirkpatrick, in: Ill-condensed-matter, eds. R. Balian, K. Maynard, G. Toulouse, Les Houches 1978, Session XXXI (North Holland Publ. Comp., Amsterdam, 1979).Google Scholar
  24. [24]
    T. Odagaki, M. Lax and A. Puri, Phys. Rev. B28 (1983) 2755.Google Scholar
  25. [25]
    J.M.J. van Leeuwen and A. Weyland, Physica 36 (1967) 457, 38 (1968) 35.Google Scholar
  26. [26]
    N.G. Van Kampen, Stochastic Processes in Physics and Chemistry (North Holland Publ. Comp., Amsterdam, 1981).Google Scholar
  27. [27]
    J.W. Haus, K. Kehr and K. Kitahara, Phys. Rev. B25 (1982) 4918; I. Webman and J. Klafter, Phys. Rev. B26 (1982) 5950.Google Scholar
  28. [28]
    Y. Gefen, A. Aharony and S. Alexander, Phys. Rev. Lett. 50 (1982) 77; J.P. Straley, J. Phys. C. Solid State 15 (1982) 2333; 14 (1981) 909; T. Keyes, Phys. Rev. A28 (1983x2584; B.I. Halperin, S. Feng and P.N. Sen, Phys. Rev. Lett. 54 (1985) 2391; J. Machta and S.M. Moore, preprint, Aug 1985.Google Scholar
  29. [29]
    J.P. Straley, J. Phys. C, Solid State Phys. 9 (1976) 783.Google Scholar
  30. [30]
    P. Li and W. Strieder, J. Phys. C, Solid State Phys. 15 (1982) 6591.Google Scholar
  31. [31]
    R.B. Pandey, D. Stauffer, A. Margolina and J.G. Zabolitzky, J. Stat. Phys 34 (1984) 427.Google Scholar
  32. [32]
    W. Götze, E. Leutheusser and S. Yip, Phys. Rev. A25 (1982) 533; E. Leutheusser, Phys. Rev. A28 (1983) 1762.Google Scholar
  33. [33]
    A. Masters and T. Keyes, Phys. Rev. A25 (1982) 1010; A26 (1982) 2129.Google Scholar
  34. [34]
    T. Keyes and J.W. Lyklema, J. Stat. Phys. 27 (1982) 487.Google Scholar
  35. [35]
    P.J.H. Denteneer and M.H. Ernst, Phys. Rev B29 (1984) 1755.Google Scholar
  36. [36]
    T. Morita and T. Horiguchi, J. Math. Phys. 12 (1971) 981, 986.Google Scholar
  37. [37]
    P.J.H. Denteneer and M.H. Ernst, J. Phys. C, Solid State Phys. 16 (1983) L961.Google Scholar
  38. [38]
    H. van Beijeren and M.H. Ernst, Physica 68 (1973) 437; 70 (1973) 225.Google Scholar
  39. [39]
    S.W. Hahn and R. Zwanzig, J. Phys. A, Math. Gen. 10 (1977) 1547; J. Chem. Phys. 68 (1978) 1879.Google Scholar
  40. [40]
    Y. Izyumov, Proc. Phys. Soc. London 87 (1966) 505.Google Scholar
  41. [41]
    J.W. Haus, K.W. Kehr and J. Lyklema, Phys. Rev. B25 (1982) 2905.Google Scholar
  42. [42]
    Th.M. Nieuwenhuizen and M.H. Ernst, J. Stat. Phys., December 1985.Google Scholar
  43. [43]
    D. Frenkel, to be published.Google Scholar
  44. [44]
    B. Derrida, J. Stat. Phys. 31 (1983) 31, B. Derrida and J.M. Luck, Phys. Rev. B28 (1983) 7183; J.B.T.M. Roerdink and K.E. Shuler, preprint 1985.Google Scholar
  45. [45]
    F.J. Dyson, Phys. Rev. 92 (1983) 1331; H. Schmidt, Phys. Rev. 105 (1957) 425; Th.M. Nieuwenhuizen, Physica (Utrecht) 125A (1984) 127.Google Scholar
  46. [46]
    N. J. Stephen and R. Kariotis, Phys. Rev. B26 (1982) 2917.Google Scholar
  47. [47]
    V.D. Ozrin, Teor. Mat. Fiz. 60 (1984) 93 (Engl. Transl. p. 694); A.K. Harrison and R.M. Zwanzig, preprint August 1985.Google Scholar

Copyright information

© Springer-Verlag 1986

Authors and Affiliations

  • M.H. Ernst
    • 1
  1. 1.Institute for Theoretical PhysicsUniversity of UtrechtThe Netherlands

Personalised recommendations