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Poly-Gaussian models of a non-Gaussian randomly rough surface

  • Surface, Electron and Ion Emission
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Abstract

Poly-Gaussian models are developed for non-Gaussian random processes, which make it possible to describe and imitate rough surfaces with various densities of roughness height distribution and correlation properties; the algorithms for numerical and analytical calculations of statistical characteristics of non-Gaussian reliefs are also worked out. Examples are given for the application of the integral poly-Gaussian model.

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References

  1. Rough Surfaces, Ed. by N. R. Thomas (Longman Groups, London, 1982).

    Google Scholar 

  2. A. P. Khusu, Yu. R. Vitenberg, and V. A. Pal’mov, Roughness of Surfaces: Theoretical Probabilistic Approach (Nauka, Moscow, 1975) [in Russian].

    Google Scholar 

  3. V. A. Valetov, Optimization of Surface Fine Irregularities of Parts in Instrument Making (LITMO, Leningrad, 1989) [in Russian].

    Google Scholar 

  4. V. I. Malyugin and M. Ya. Litvak, Opt. Spectrosc. 107, 144 (2009).

    Article  ADS  Google Scholar 

  5. M. Ya. Litvak and V. I. Malyugin, Opt. Spectrosc. 109 (2010).

  6. M. Ya. Litvak and V. I. Malyugin, Opt. Spectrosc. 109, 783 (2010).

    Article  ADS  Google Scholar 

  7. A. N. Malakhov, Cumulative Analysis of Non-Gaussian Random Processes and Their Transformations (Sovetskoe Radio, Moscow, 1978) [in Russian].

    Google Scholar 

  8. A. S. Shalygin and Yu. I. Palagin, Applied Methods of Statistical Modelling (Mashinostroenie, Leningrad, 1986) [in Russian].

    MATH  Google Scholar 

  9. V. V. Bykov, Numerical Modeling in Statistical Radio Engineering (Sovetskoe Radio, Moscow, 1971) [in Russian].

    Google Scholar 

  10. A. Urzica and S. Sp. Cretu, Acta Tribol. 18, 126 (2010).

    Google Scholar 

  11. M. M. Sondhi, Bell Syst. Tech. J. 62, 679 (1983).

    MathSciNet  Google Scholar 

  12. V. I. Trofimov and V. A. Osadchenko, Opt. Mekh. Prom-st’, No. 6, 9 (1987).

  13. V. I. Trofimov and V. A. Osadchenko, Opt. Zh., No. 8, 39 (1993).

  14. W. Peng and B. Bhushan, Proc. Inst. Mech. Eng., Part C: J. Mech. Eng. Sci. 214, 459 (2000).

    Article  Google Scholar 

  15. Y.-P. Zhao, G.-C. Wang, and T.-M. Lu, Phys. Rev. B 55, 13938 (1997).

    Article  ADS  Google Scholar 

  16. O. I. Shelukhin and I. V. Belyakov, Non-Gaussian Processes (Politekhnika, St. Petersburg, 1992) [in Russian].

    MATH  Google Scholar 

  17. S. M. Ermakov and G. A. Mikhailov, Statistical Modelling (Nauka, Moscow, 1982) [in Russian].

    Google Scholar 

  18. C. A. Guerin, Waves Random Media 12, 293 (2002).

    Article  ADS  MATH  Google Scholar 

  19. Y. Cocheril, R. Vauzelle, and L. Aveneau, in Proceeding of the 64th IEEE Vehicular Technology Conference (VTC 2006 Fall), Montreal, 2006, pp. 1–5.

  20. W. Feller, An Introduction to Probability Theory and Its Applications, 3rd ed. (Wiley, New York, 1967; Mir, Moscow, 1984).

    Google Scholar 

  21. V. M. Kruglov, Vestn. Mosk. Univ., Ser. 15: Vychislit. Mat. Kibernet., No. 2, 3 (1991).

  22. D. V. Kizevetter, M. Ya. Litvak, and V. I. Malyugin, Opt. Mekh. Prom-st’, No. 6, 33 (1989).

  23. I. A. Koltunov and A. P. Monastyrev, Stat. Probl. Upr., No. 78, 83 (1987).

  24. G. Ya. Volozhin, I. A. Burlakov, and S. T. Kosenkova, Vestn. Dal’nevost. Otd. Akad. Nauk SSSR, No. 4, 100 (1990).

  25. A. A. Dorodnov, Information Receipt and Processing in Complex Systems (Kazansk. Univ., Kazan’, 1972), No. 3, pp. 139–143.

    Google Scholar 

  26. A. A. Dorodnov and Sh. M. Chabdarov, Radiotekhnika 30, 127 (1975).

    Google Scholar 

  27. Sh. M. Chabdarov and A. T. Trofimov, Radiotekh. Elektron. (Moscow) 20, 734 (1975).

    MathSciNet  Google Scholar 

  28. V. I. Tatarskii and V. V. Tatarskii, Prog. Electromagn. Res. 25, 259 (1999).

    Google Scholar 

  29. V. I. Tatarskii and V. V. Tatarskii, Prog. Electromagn. Res. 25, 293 (1999).

    Google Scholar 

  30. Sh. M. Chabdarov, N. Z. Safiullin, and A. Yu. Feoktistov, Fundamentals of Statistical Theory in Radio Communications, Polygaussian Models and Methods (KAI, Kazan’, 1983) [in Russian].

    Google Scholar 

  31. I. M. Sobol’, Monte Carlo Numerical Methods (Nauka, Moscow, 1973) [in Russian].

    Google Scholar 

  32. P. Beckmann, IEEE Trans. Antennas Propag. 21, 169 (1973).

    Article  ADS  Google Scholar 

  33. V. I. Krylov and L.T. Shul’gina, Handbook on Numerical Integration (Nauka, Moscow, 1966) [in Russian].

    Google Scholar 

  34. B. D. Bunday, Basic Optimization Methods (Edward Arnold, London, 1984; Radio i Svyaz’, Moscow, 1988).

    Google Scholar 

  35. I. A. Abroyan, V. Ya. Velichko, M. Ya. Litvak, V. I. Malyugin, O. A. Merkulova, and A. B. Fadeev, Izv. Ross. Akad. Nauk, Ser. Fiz. 58, 116 (1994).

    Google Scholar 

  36. M. Ya. Litvak, V. I. Malyugin, and O. A. Merkulova, Tech. Phys. Lett. 22, 523 (1996).

    ADS  Google Scholar 

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Authors and Affiliations

  1. St. Petersburg State Polytechnical University, Politekhnicheskaya ul. 29, St. Petersburg, 195251, Russia

    M. Ya. Litvak & V. I. Malyugin

Authors
  1. M. Ya. Litvak
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  2. V. I. Malyugin
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Correspondence to V. I. Malyugin.

Additional information

Original Russian Text © M.Ya. Litvak, V.I. Malyugin, 2012, published in Zhurnal Tekhnicheskoi Fiziki, 2012, Vol. 82, No. 4, pp. 105–113.

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Litvak, M.Y., Malyugin, V.I. Poly-Gaussian models of a non-Gaussian randomly rough surface. Tech. Phys. 57, 524–533 (2012). https://doi.org/10.1134/S1063784212040172

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