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Cavity sequences in continuously cast billets: Part II. Stochastic models

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Abstract

A stream of voids is often encountered in the core of continuously cast steel billets. This article presents mathematical simulations of the cavity process. Parameters of the models are deduced from the data described in Part I of this article. A Markov simulation represents the chain as a binary sequence; an autoregressive (AR[2]) model and two other related simulations produce series of interval lengths and void fractions. A bridge model uses two independent random numbers to simulate cavity events. The performance of the models is checked against empirical findings. Dynamics of the cavity process are, finally, discussed.

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References

  1. K.-H. Tacke: Metall. Mater. Trans. B, 1999, vol. 30B, pp. 751–61.

    CAS  Google Scholar 

  2. G.E.P. Box and G.M. Jenkins: Time Series Analysis, Hoden-Day, Oakland, CA, 1976.

    Google Scholar 

  3. M.B. Priestley: Spectral Analysis and Time Series, Volume 1, Academic Press, London, 1981.

    Google Scholar 

  4. R. Goodman: Introduction to Stochastic Models, Benjamin Cummings Publishing, Menlo Park, CA, 1988.

    Google Scholar 

  5. H. Tong: Non-Linear Time Series, Clarendon Press, Oxford, United Kingdom, 1990.

    Google Scholar 

  6. R. Kluiving, H.W. Cappel, and R.A. Pasmanter: Physica A, 1992, vol. 183, pp. 67–95.

    Article  Google Scholar 

  7. P. Grassberger: Int. J. Theor. Phys., 1986, vol. 25 (9), pp. 907–38.

    Article  Google Scholar 

  8. D. Senk: Ph.D. Thesis, Technical University of Clausthal, Clausthal, Germany, 1985.

    Google Scholar 

  9. D. Ameling, H. Litterscheidt, K. Schwerdtfeger, and D. Senk: Proc. 69th Steelmaking Conf. AIME-ISS, Warrendale, PA, 1986, pp. 387–95.

    Google Scholar 

  10. K. Wunnenberg, H. Jacobi, and H.-E. Wiemer: METEC Congr. 94, 2nd Eur. Continuous Casting Conf. Proc., Verein Deutscher Eisenhuttenleute, Dusseldorf, 1994, vol. 1, pp. 305–15.

    Google Scholar 

  11. H.-E. Wiemer, H. Jacobi, and K. Wunnenberg: Stahl Eisen., 1995, vol. 115 (9), pp. 67–76.

    CAS  Google Scholar 

  12. I. Prigogine: From Being to Becoming, W.H. Freeman, San Francisco, CA, 1980.

    Google Scholar 

  13. H. Haken: Synergetics, Springer-Verlag, Berlin, 1983.

    Google Scholar 

  14. M.C. Cross and P.C. Hohenberg: Rev. Mod. Phys., 1993, vol. 65 (3), pp. 851–1112.

    Article  CAS  Google Scholar 

  15. S. Chandrasekhar: Hydrodynamic and Hydromagnetic Stability, Dover Publications, New York, NY, 1981.

    Google Scholar 

  16. W. Kurz and D.J. Fisher: Fundamentals of Solidification, Trans Tech Publications, Aedermannsdorf, Switzerland, 1984.

    Google Scholar 

  17. J.S. Langer: Rev. Mod. Phys., 1980, vol. 52 (1), pp. 1–28.

    Article  CAS  Google Scholar 

  18. R. Shaw: The Dripping Faucet as a Model Chaotic System, Aerial Press, Santa Cruz, CA, 1984.

    Google Scholar 

  19. P. Martien, S.C. Pope, P.L. Scott, and R.S. Shaw: Phys. Lett. A, 1985, vol. 110, pp. 399–404.

    Article  Google Scholar 

  20. X. Wu and Z.A. Schelly: Physica D, 1989, vol. 40, pp. 433–43.

    Article  Google Scholar 

  21. H.G. Schuster: Deterministic Chaos, VCH Verlagsgesellschaft, Weinheim, 1988.

    Google Scholar 

  22. S.N. Rasband: Chaotic Dynamics of Nonlinear Systems, John Wiley & Sons, New York, NY, 1990.

    Google Scholar 

  23. R. Shaw: Z. Naturforsch., 1981, vol. 36a, pp. 80–112.

    Google Scholar 

  24. J.D. Farmer: Physica, 1982, vol. 4D, pp. 4D.

  25. J.D. Farmer, E. Ott, and J.A. Yorke: Physica, 1983, vol. 7D, pp. 153–80.

    Google Scholar 

  26. K.-H. Tacke: in Free Boundary Problems: Theory and Applications, Vol. II, Pitman Research Notes in Mathematics, K.-H. Hoffman and J. Sprekels, ed., Longman, Birmingham, AL, 1990, pp. 636–43.

    Google Scholar 

  27. K.-H. Tacke and A. Harnisch: in Computational Modelling of Free and Moving Boundary Problems, Vol. 2: Heat Transfer, L.C. Wrobel and C.A. Brebbia, eds., Wessex Institute of Technology, Computational Mechanics Publications, Southampton, Boston-de Gruyter, Behin, NY, 1991, pp. 165–75.

    Google Scholar 

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Tacke, KH. Cavity sequences in continuously cast billets: Part II. Stochastic models. Metall Mater Trans B 30, 763–772 (1999). https://doi.org/10.1007/s11663-999-0038-1

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