Stochastic analysis of different rough surfaces

European Physical Journal B

Volumn 41, Issue 2, 2004, Pages 259-277

  Waechter, M ^a   Riess, F ^a   Schimmel, Th ^b   Wendt, U ^c   Peinke, J ^a  

^a UNIVERSITY OF OLDENBURG   (Germany)

^b UNIVERSITY OF KARLSRUHE   (Germany)

^c OTTO VON GUERICKE UNIVERSITY   (Germany)

Author keywords

[No Author keywords available]

Indexed keywords

DATA REDUCTION; MARKOV PROCESSES; MATHEMATICAL MODELS; PROBABILITY DENSITY FUNCTION; RANDOM PROCESSES; STATISTICAL METHODS; SURFACE STRUCTURE;

SCALING; STOCHASTIC ANALYSIS; SURFACE WIDTH; TOPOGRAPHIC STRUCTURES;

SURFACE ROUGHNESS;

EID: 10044236819     PISSN: 14346028     EISSN: None     Source Type: Journal    
DOI: 10.1140/epjb/e2004-00317-4     Document Type: Article

References (40)

1. R.S. Sayles, T.R. Thomas, Nature 271, 431-434 (1978)
2. T. Viosek, Fractal Growth Phenomena, 2nd edn. (World Scientific, Singapore, 1992)
3. A.-L. Barabasi, H. Eugene Stanley, Fractal concepts in surface growth (Cambridge University Press, Cambridge, 1995)
4. S. Davies, P. Hall, J. Royal Statistical Society B 61, 3-37 (1999)
5. U. Wendt, K. Stiebe-Lange, M. Smid, J. Microscopy 207, 169-179 (2002)
6. C.V. Dharmadhikari, R.B. Kshirsagar, S.V. Ghaisae, Europhys. Lett. 45, 215-221 (1999)
7. M. Saitou, M. Hokama, W. Oshikawa, Appl. Surf. Sci. 185, 79-83 (2001)
8. U. Sydow, M. Buhlert, P. J. Plath, Characterization of dectropolished metal surfaces, Discrete Dynamics in Nature and Society (to be published)
9. J. Feder, Fractals (Plenum Press, New York, London, 1988)
10. Dynamics of fractal surfaces, edited by F. Family, T. Vicsek (World Scientific, Singapore, 1991)
11. R. Friedrich, T. Galla, A. Naert, J. Peinke, Th. Schimmel, Disordered structures analysed by the theory of Markov processes in A Perspective Look at Nonlinear Media, Vol. 503 of Lecture Notes in Physics, edited by Jürgen Parisi, St. C. Müller, W. Zimmermann (Springer Verlag, Berlin, 1998), pp. 313-326
12. M. Waechter, F. Riess, H. Kantz, J. Peinke, Europhys. Lett. 64, 579-585 (2003), see also preprints arxiv:physics/0203068 and arziv:physics/0310159
13. G.R. Jafari, S.M. Fazeli, F. Ghasemi, S.M. Vaez Allaei, M. Reza Rahimi Tabar, A. Iraji Zad, G. Kavei, Phys. Rev. Lett. 91, 226101 (2003)
14. C. Renner, J. Peinke, R. Friedrich, J. Fluid Median. 433, 383-7409 (2001)
15. S. Lueck, J. Peinke, R. Friedrich, Phys. Rev. Lett. 83, 5495-5498 (1999)
16. R. Friedrich, J. Peinke, C. Renner, Phys. Rev. Lett. 84, 5224-5227 (2000)
17. M. Ausloos, K. Ivanova, Phys. Rev. E 68, 046122 (2003)
18. F. Ghasemi, A. Bahraminasab, S. Rahvar, M. Reza Rahimi Tabar, Stochastic nature of cosmic microwave background radiation, preprint arxiv:astro-phy/0312227, 2003
19. r(x) = h(x + r) - h(x). Here we use the symmetrical increment in order to avoid the introduction of spurious correlations between scales [40]
20. M. Haase, Private communication (2003)
21. C. Renner, Markovanalysen stochastisch fluktuierender Zeitserien. Ph.D. thesis, Carl-von-Ossietzky University, Oldenburg, Germany, 2001 http://docserver.bis.uni-oldenburg.de/ publikationen/disBertation/2002/renmar02/ renmar02.html
22. H. Risken, The Fokker-Planck equation (Springer, Berlin, 1984)
23. (k) change only slightly, preserving both the form and behaviour of the Fokker-Planck equation. The logarithmic variable p was used in order to preserve consistency, see [11,14,16].
24. A.N. Kolmogorov, Mathematische Annalen 104, 415-458 (1931)
25. M. Waechter, F. Riess, N. Zacharias, Vehicle System Dynamics 37, 3-28 (2002)
26. R. Benzi, S. Ciliberto, R. Tripiccione, C. Baudet, F. Massaioli, S. Succi, Phys. Rev. E 48, 29 (1993)
27. M. Alber, J. Peinke, Phys. Rev. E 57, 5489 (1998)
28. R. Friedrich, J. Zeller, J. Peinke, Europhys. Lett. 41, 153 (1998)
29. I.N. Bronstein, K.A. Semendjajew, Taschenbuch der Mathematik (Teubner, Stuttgart, 1991)
30. R. Friedrich, J. Peinke, Physica D 102, 147 (1997)
31. R. Friedrich, J. Peinke, Phys. Rev. Lett. 78, 863 (1997)
32. M. Ragwitz, H. Kantz, Phys. Rev. Lett. 87, 254501 (2001)
33. M. Siefert, A. Kittel, R. Friedrich, J. Peinke, Europhys. Lett. 81, 466 (2003)
34. P. Marcq, A. Naert, Phys. Fluids 13, 2590-2595 (2001)
35. R. Friedrich, S. Siegert, J. Peinke, S. Lück, M. Siefert, M. Lindemann, J. Raethjen, G. Deuschl, G. Pfister, Phys. Lett. A 271, 217-222 (2000)
36. R. Friedrich, C. Renner, M. Siefert, J. Peinke, Phys. Rev. Lett. 89, 149401 (2002)
37. P. Sura, J. Barsugli, Phys. Lett. A 305, 304-311 (2002)
38. C. Renner, J. Peinke, R. Friedrich, Physica A 298, 499-520 (2001)
39. J. Honerkamp, Stochastische dynamische Systeme (VCH, Weinheim, 1990)
40. M. Waechter, A. Kouzmitchev, J. Peinke, A note on increment definitions for scale dependent analysis of stochstic data, preprint arxiv:physics/0404021, 2004