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Influence of boundaries on dissipative structures in the Schlögl model

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Zeitschrift für Physik B Condensed Matter

Abstract

The stationary spatial structures arising in the Schlögl model of first order nonequilibrium phase transitions are investigated for a one-dimensionals system of finite length.

The solution manifold and the occurring bifurcations are analysed systematically by varying the type of boundary condition, the boundary valuev R ,the system lengthL and the control parameterg. It is shown by plotting appropriate state diagrams that the bistability range of the infinite system is shifted to larger values ofg for small fixedv R and to smaller values ofg for largev R ,and that the shift depends sensitively uponL.

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References

  1. Schlögl, F.: Z. Phys.253, 147 (1972)

    Google Scholar 

  2. Nitzan, A., Ortoleva, P., Ross, J.: Faraday Symp. Chem. Soc.9, 241 (1974)

    Google Scholar 

  3. Magyari, E.: J. Phys. A15, L 139 (1982)

    Google Scholar 

  4. Schlögl, F., Escher, C., Berry, R.S.: Phys. Rev. A27, 2698 (1983)

    Google Scholar 

  5. For reviews see e.g.: Schlögl, F.: Phys. Rep.62, 267 (1980)

    Google Scholar 

  6. Haken, H.: Synergetics. 3rd Edn. Berlin, Heidelberg, New York: Springer 1983

    Google Scholar 

  7. Albano, A.M., Abraham, N.B., Chyba, D.E., Mortelli, M.: Am. J. Phys.52, 161 (1984)

    Google Scholar 

  8. Hanson, M.: J. Chem. Phys.66, 5551 (1977)

    Google Scholar 

  9. Jetschke, G.: Doctoral Thesis, Jena (1978)

  10. Jetschke, G.: Phys. Lett.72A, 265 (1979)

    Google Scholar 

  11. Ibañez, J., Velarde, M.: Phys. Rev. A18, 750 (1978)

    Google Scholar 

  12. Hemmer, P., Velarde, M.: Z. Phys. B — Condensed Matter31, 111 (1978)

    Google Scholar 

  13. Fairén, V., Velarde, M.G.: Rep. Math. Phys.16, 421 (1979)

    Google Scholar 

  14. Velarde, M.: Stability of Thermodynamics Systems. In: Lecture Notes in Physics. Casas-Vázques, J., Lebon, G. (eds.), Vol. 164, p. 248. Berlin, Heidelberg, New York: Springer 1982

    Google Scholar 

  15. Livshits, M.A., Gurija, G.T., Belintsev, B.N., Volkenstein, M.V.: J. Math. Biol.11, 295 (1981)

    Google Scholar 

  16. Messiah, A.: Quantum mechanics. Vol. I, Chap. III, § 12. Amsterdam: North Holland 1972

    Google Scholar 

  17. Büttiker, M., Thomas, H.: Phys. Rev. A24, 2635 (1981)

    Google Scholar 

  18. Ince, E.L.: Ordinary differential equations. p. 234. New York: Dover 1956

    Google Scholar 

  19. Kramer, L.: Z. Phys. B — Condensed Matter41, 357 (1981)

    Google Scholar 

  20. Schöll, E.: Z. Phys. B — Condensed Matter52, 321 (1983)

    Google Scholar 

  21. Schöll, E.: Proceedings of the 17th International Conference on the Physics of Semiconductors, San Francisco, 1984. Chadi, J.D., Harrison, W.A. (eds.), p. 1353. New York: Springer 1985

    Google Scholar 

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Authors and Affiliations

  1. Institut für Theoretische Physik, Rheinisch-Westfälische, Technische Hochschule Aachen, Templergraben 55, D-5100, Aachen, Federal Republic of Germany

    E. Schöll

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  1. E. Schöll
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Schöll, E. Influence of boundaries on dissipative structures in the Schlögl model. Z. Physik B - Condensed Matter 62, 245–253 (1986). https://doi.org/10.1007/BF01323437

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  • DOI: https://doi.org/10.1007/BF01323437

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