Stochastic analysis of different rough surfaces

Abstract

This paper shows in detail the application of a new stochastic approach for the characterization of surface height profiles, which is based on the theory of Markov processes. With this analysis we achieve a characterization of the scale dependent complexity of surface roughness by means of a Fokker-Planck or Langevin equation, providing the complete stochastic information of multiscale joint probabilities. The method is applied to several surfaces with different properties, for the purpose of showing the utility of this method in more details. In particular we show the evidence of Markov properties, and we estimate the parameters of the Fokker-Planck equation by pure, parameter-free data analysis. The resulting Fokker-Planck equations are verified by numerical reconstruction of conditional probability density functions. The results are compared with those from the analysis of multi-affine and extended multi-affine scaling properties which is often used for surface topographies. The different surface structures analysed here show in details advantages and disadvantages of these methods.

Minor text changes to be identical with the published version

References in corpus (9)

• How to quantify deterministic and random influences on the statistics of the foreign exchange market
• Dynamical model and nonextensive statistical mechanics of a market index on large time windows
• Stochastic Analysis and Regeneration of Rough Surfaces
• On a quantitative method to analyse dynamical and measurement noise
• Comment on "Indispensable Finite Time Correlations for Fokker-Planck Equations from Time Series Data"
• Markov properties of high frequency exchange rate data
• Stochastic analysis of surface roughness
• Increment definitions for scale dependent analysis of stochastic data
• Stochastic analysis of road surface roughness

Cited by in corpus (10)

• On the proper reconstruction of complex dynamical systems spoilt by strong measurement noise
• The Fokker-Planck Approach to Complex Spatio-Temporal Disordered Systems
• Controlling surface statistical properties using bias voltage: Atomic force microscopy and stochastic analysis
• Etched Glass Surfaces, Atomic Force Microscopy and Stochastic Analysis
• Stochastic analysis of ocean wave states with and without rogue waves
• Markov properties in presence of measurement noise
• Memory Effects in Quantum Processes
• The Markov Memory for Generating Rare Events
• Markov Properties of Electrical Discharge Current Fluctuations in Plasma
• Effects of coating rate on morphology of copper surfaces