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Analysis and characterization of surface topographies with the theory of Markov processes
Author(s) -
Waechter Matthias,
Peinke Joachim
Publication year - 2005
Publication title -
pamm
Language(s) - English
Resource type - Journals
ISSN - 1617-7061
DOI - 10.1002/pamm.200510326
Subject(s) - characterization (materials science) , statistical physics , surface (topology) , langevin equation , stochastic process , markov process , markov chain , fokker–planck equation , surface roughness , mathematics , computer science , physics , mathematical analysis , statistics , thermodynamics , optics , geometry , partial differential equation
Abstract For the characterization of surface height profiles we present a new stochastic approach which is based on the theory of Markov processes. With this analysis we achieve a characterization of the complexity of the surface roughness by means of a Fokker‐Planck or Langevin equation, providing the complete stochastic information of multiscale joint probabilities. Furthermore, this approach allows the reconstruction of topographies with given stochastic properties. Estimations for the parameters of the Fokker‐Planck equation are based on pure, parameter free data analysis. (© 2005 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim)