A Hurwitz-Pair Approach to the Pre-Melting Problem

  • Fray De Landa Castillo Alvarado
  • Gerardo Contreras Puente
  • Julian Ławrynowicz
  • Leszek Wojtczak

Abstract

The pre-melting at the crystal surface is one of the most interesting and recently studied surface phenomena. In this contribution the pre-melting is considered as an example for illustration of the idea of a stochastic space discussed in connection with the Clifford-analytical formulation related to Hurwitz pairs of bidimension (8,5). We confine ourselves to the curved case where only one structural Clifford-algebraic constant is involved. The space fluctuations influence on the melting temperature shifting it to lower values. The conditions for the existence of pre-melting are also changed.

Keywords

Free Energy Phase Transition Temperature Homogeneous Function Landau Free Energy Stochastic Space 
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References

  1. [1]
    Barrio, R.A. and Castillo Alvarado, F.de L. (1993) ‘Model for the vibrational spectra of B2O3xLi 2O’, Phys. Rev. B 47, to appear.Google Scholar
  2. [2]
    Contreras Puente, G., Aguilar Herńandez, J., Cardenas García, M., Gnatenko, Yu.P., and Rutkowski, J.H. (1992) ‘Optical studies of II–VI semiconductor compounds doped with transition metals’, Proceedings of the 1992 March Meeting of the American Physical Society, Bull. Amer. Phys. Soc. 37, no. 1, 292.Google Scholar
  3. [3]
    González de la Cruz, G., Contreras Puente, G., Castillo Alvarado, F. de L., Mejía García, C., and Compaan, A. (1993) ‘Raman scattering by phonons in heavily doped semiconductors’, Solid State Commun. 85, to appear.Google Scholar
  4. [4]
    Ławrynowicz, J., Avendaño López, J., Castillo Alvarado, F. de L., Barrio, R.A., and Urbaniak-Kucharczyk, A. (1993) ‘Clifford analysis, Riemannian geometry and the electromagnetic field’, in A. Lakhtakia (ed.), Essays on the Formal Aspects of Electromagnetic Theory, World Scientific Publ. Co., Singapore, pp. 1–24.Google Scholar
  5. [5]
    Ławrynowicz, J. and Suzuki, O. (1993) ‘The duality theorem for the Hurwitz pairs of bidimension (8,5) and the Penrose theory’, this volume, pp. 195–202.Google Scholar
  6. [6]
    Ławrynowicz, J. and Wojtczak, L. in cooperation with Koshi, S. and Suzuki, O. (1993) ‘Stochastical mechanics of particle systems in Clifford-analytical formulation related to Hurwitz pairs of bidimension (8,5)’, this volume, pp. 203–252.Google Scholar
  7. [7]
    Lipowsky, R. and Speth, W. (1983) ‘Semi-infinite systems with fist-order bulk transitions’, Phys. Rev. B 28, 3983–3993.CrossRefGoogle Scholar
  8. [8]
    Pluis, B. (1990) Surface Induced Melting of Lead, Thesis, Rijksuniversiteit te Leiden, Leiden, Ch.3. Surface-induced melting and freezing: a semi-empirical Landau-type model, pp. 47–89.Google Scholar
  9. [9]
    Ruppeiner, G. (1991) ‘Riemannian geometric theory of critical phenomena’, Phys. Rev. A44, 3583–3595.Google Scholar
  10. [10]
    Surry, C. (1992), private communication.Google Scholar
  11. [11]
    Urbaniak-Kucharczyk, A. (1993) ‘Spin polarization transport in thin magnetic films’, this volume p. 317–330.Google Scholar
  12. [12]
    Wojtczak, L., Mrygoń, B., and Michalak, S. (1983) ‘Local fluctuations and scaling hypothesis, Bull. Soc. Sci. Lettres Łódź 33, no. 3, 24 pp.Google Scholar

Copyright information

© Springer Science+Business Media Dordrecht 1994

Authors and Affiliations

  • Fray De Landa Castillo Alvarado
    • 1
  • Gerardo Contreras Puente
    • 1
  • Julian Ławrynowicz
    • 2
  • Leszek Wojtczak
    • 3
  1. 1.Escuela Superior de Fisica y MatemáticasInstituto Politecnico NationalMéxico, D.F.Mexico
  2. 2.Institute of MathematicsPolish Academy of SciencesŁódźPoland
  3. 3.University of ŁódźŁódźPoland

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