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When orthogonal detrending matters in roughness scaling.

Thiago A de Assis1

  • 1Universidade Federal Fluminense, Instituto de Física, Avenida Litorânea s/n, 24210-340 Niterói, Rio de Janeiro, Brazil.

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Summary

Optimal Detrended Fluctuation Analysis (ODFA) accurately determines surface roughness exponents in complex growth models. This study provides the analytical framework explaining how ODFA overcomes transient effects for reliable measurements.

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Area of Science:

  • Surface growth dynamics
  • Statistical physics
  • Non-equilibrium systems

Background:

  • Determining local roughness exponents (α_{l}) in nonequilibrium surface growth is difficult due to transient morphologies obscuring asymptotic regimes.
  • Villain-Lai-Das Sarma (VLDS) models exhibit long crossover times, complicating accurate roughness exponent measurements.
  • Previous numerical simulations showed Optimal Detrended Fluctuation Analysis (ODFA) yields accurate α_{l} values even in transient regimes.

Purpose of the Study:

  • To develop a quantitative analytical framework explaining why ODFA accurately determines roughness exponents in VLDS models.
  • To elucidate the mechanism by which ODFA suppresses geometric corrections from local slope and curvature.

Main Methods:

  • Derivation of an analytical framework for ODFA's suppression of geometric corrections.
  • Analysis of orthogonal projection of height fluctuations onto local polynomial trends.
  • Numerical simulations of Clarke-Vvedensky and Das Sarma-Tamborenea lattice models with noise reduction.

Main Results:

  • The theoretical framework demonstrates ODFA suppresses slope and curvature corrections via orthogonal projection.
  • Slope-induced corrections decay slower than curvature-induced ones, dominating intermediate-scale biases.
  • Numerical simulations corroborate theoretical predictions, confirming correction exponents and the hierarchy of suppression.

Conclusions:

  • The derived analytical framework explains ODFA's effectiveness in determining roughness exponents in complex surface growth models.
  • ODFA successfully mitigates biases from local geometric features, providing accurate measurements even in transient regimes.
  • This work establishes a robust theoretical foundation for applying ODFA in nonequilibrium surface growth studies.