The PDF file you selected should load here if your Web browser has a PDF reader plug-in installed (for example, a recent version of Adobe Acrobat Reader).

Alternatively, you can also download the PDF file directly to your computer, from where it can be opened using a PDF reader. To download the PDF, click the Download link below.

If you would like more information about how to print, save, and work with PDFs, Highwire Press provides a helpful Frequently Asked Questions about PDFs.

Download this PDF file Fullscreen Fullscreen Off

References

  1. M. Aizenman, G. Grimmett, Strict monotonicity for critical points in percolation and ferromagnetic models, J. Stat. Phys. 63 (1991), 817--835. Math. Review 92i:82060
  2. R. M. Bradley, A Comment on ``Ring Dynamics and percolation in an excitable medium,'' J. Chem. Phys. 86 (1987), 7245--7246. Math. Review number not available.
  3. R. Durrett, D. Griffeath, Asymptotic behavior of excitable cellular automata, Experimental Math. 2 (1993), 184--208. Math. Review 95e:58095
  4. R. Durrett, C. Neuhauser, Epidemic with recovery in d=2, Ann. Appl. Prob. 1 (1991), 189--206. Math. Review 92k:60222
  5. R. Durrett, J. E. Steif, Some rigorous results for the Greenberg-Hastings model, J. Theor. Prob. 4 (1991), 669--690. Math. Review 93h:60162
  6. R. Durrett, Multicolor particle systems with large threshold and range, J. Theor. Prob. 5 (1992), 127--152. Math. Review 93b:60227
  7. R. Fisch, J. Gravner, D. Griffeath, Threshold-range scaling of excitable cellular automata, Statistic and Computing 1 (1991), 23--39. Math. Review number not available.
  8. R. Fisch, J. Gravner, D. Griffeath, Metastability in the Greenberg--Hastings model, Ann. Appl. Prob. 3 (1993), 935--967. Math. Review 95f:60120
  9. S. Fraser, R. Kapral, Ring dynamics and percolation in an excitable medium, J. Chem. Phys. 85 (1986), 5682--5688. Math. Review 87k:82085
  10. J. M. Greenberg, S. P. Hastings, Spatial patterns for discrete models of diffusion in exitable media, SIAM J. Appl. Math. 34 (1978), 515--523. Math. Review 58#4408
  11. J. Gravner, Mathematical aspects of excitable media, Ph. D. Thesis, University of Wisconsin, 1991. Math. Review number not available.
  12. J. Gravner, The boundary of iterates in Euclidean growth models, Trans. Amer. Math. Soc., to appear. Math. Review 1 370 643
  13. J. Gravner, Recurrent ring dynamics in two--dimensional excitable cellular automata, submitted. Math. Review number not available.
  14. J. Gravner, D. Griffeath, First passage times for threshold growth dynamics on Z^2 Ann. Prob., to appear. Math. Review number not available.
  15. G. Grimmett, ``Percolation,'' Springer-Verlag, 1989. Math. Review 90j:60109
  16. W.A. Johnson and R.F. Mehl, Reaction kinetics in processes of nucleation and growth, Trans. A.I.M.M.E. 135 (1939), 416--458. Math. Review number not available.
  17. R. Kapral, M. Weinberg, Phase transformation kinetics in finite inhomogenuosly nucleated systems, J. Chem. Phys. 11 (1989), 7146--7152. Math. Review number not available.
  18. R. Kapral, Discrete models for chemically reacting systems, J. Math. Chem. 6 (1991), 113--163. Math. Review 1 101 758
  19. H. Kesten, ``Percolation Theory for Mathematicians,'' Birkhauser, 1982. Math. Review 84i:60145
  20. M. D. Penrose, Single linkage clustering and continuum percolation, J. of Multivariate Analysis 53(1995), 90--104. Math. Review 96e:62099
  21. R. Roy, The Russo--Seymour--Welsh theorem and the equality of critical densities and the ``dual'' critical densities for continuum percolation on R^2, Ann. Prob. 18 (1990), 1563--1575. Math. Review 92a:60209
  22. J. M. Smith, A. L. Ritzenberg, R. J. Cohen, Percolation theory and cardiac conduction, Computers in Cardiology (1984), 175--178. Math. Review number not available.
  23. J. Steif, Two applications of percolation to cellular automata, J. Stat. Phys. 78 (1995), 1325--1335. Math. Review 96f:82027
  24. S. J. Willson, On convergence of configurations, Discrete Mathematics 23 (1978), 279--300. Math. Review 80g:68074
  25. N. Wiener, A. Rosenbluth, The mathematical formulation of the problem of conduction of impulses in a network of connected excitable elements, specifically in cardiac muscle, Arch. Inst. Cardiol. Mexico 16 (1946), 205--265. Math. Review 9,604a
  26. J. R. Weimar, J. J. Tyson, L. T. Watson, Third generation cellular automaton for modeling excitable media, Physica D 55 (1992), 328--339. Math. Review 93b:65200
  27. S. A. Zuev, A. T. Sidorenko, Continuous models of percolation theory I, II, Theoretical and Mathematical Physics 62 (1985), 51--58, 171--177. Math. Review 86j:82044a Math. Review 86j:82044b


Creative Commons License
This work is licensed under a Creative Commons Attribution 3.0 License.