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A Method of Trigonometric Modelling of Seasonal Variation Demonstrated with Multiple Sclerosis Relapse Data
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Sampling-time effects for persistence and survival in step structural fluctuations.

D B Dougherty1, C Tao, O Bondarchuk

  • 1Department of Physics, University of Maryland, College Park, Maryland 20742-4111, USA.

Physical Review. E, Statistical, Nonlinear, and Soft Matter Physics
|March 24, 2005
PubMed
Summary

Sampling rate and measurement time significantly impact first-passage properties of step fluctuations. Persistence probability scales with sampling interval, while survival probability shows complex scaling, independent of temperature for large systems.

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Area of Science:

  • Surface Science
  • Materials Science
  • Physical Chemistry

Background:

  • Step fluctuations are crucial for understanding surface dynamics and growth.
  • First-passage properties offer insights into the kinetics of these fluctuations.
  • Previous studies have not fully elucidated the influence of experimental parameters on these properties.

Purpose of the Study:

  • To determine the effects of sampling rate and total measurement time on single-point measurements of step fluctuations.
  • To investigate the temperature dependence of step fluctuation properties.
  • To compare experimental observations with theoretical predictions.

Main Methods:

  • Time-dependent scanning tunneling microscopy (STM) was employed.
  • Measurements were conducted on Ag(111) films, Pb crystallites, and Al-terminated Si(111).
  • Temperatures ranged from 300 K to 970 K, depending on the material.

Main Results:

  • Persistence amplitude showed no dependence on temperature.
  • Persistence probability scaled directly with the ratio of total measurement time to sampling interval (t/Δt).
  • Survival probabilities exhibited a more complex scaling, dependent on both sampling interval and total measurement time, but independent of temperature for large systems.

Conclusions:

  • Experimental parameters like sampling rate and measurement time are critical for accurately characterizing step fluctuations.
  • The observed scaling behavior aligns with theoretical predictions, suggesting a universal behavior for large systems.
  • Surface dynamics, as reflected in step fluctuations, can be understood through first-passage properties, with minimal temperature influence under specific measurement conditions.