Sampling-time effects for persistence and survival in step structural fluctuations

Dougherty, DB and Tao, C and Bondarchuk, O and Cullen, WG and Williams, ED and Constantin, M and Dasgupta, C and Sarma, Das S (2005) Sampling-time effects for persistence and survival in step structural fluctuations. In: Physical Review E, 71 (2). 021602-1.

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Abstract

The effects of sampling rate and total measurement time have been determined for single-point measurements of step fluctuations within the context of first-passage properties. Time dependent scanning tunneling microscopy has been used to evaluate step fluctuations on Ag(111) films grown on mica as a function of temperature (300-410 K), on screw dislocations on the facets of Pb crystallites at 320 K, and on Al-terminated Si(111) over the temperature range 770-970 K. Although the fundamental time constant for step fluctuations on Ag and Al/Si varies by orders of magnitude over the temperature ranges of measurement, no dependence of the persistence amplitude on temperature is observed. Instead, the persistence probability is found to scale directly with t/Delta t where Delta t is the time interval used for sampling. Survival probabilities show a more complex scaling dependence, which includes both the sampling interval and the total measurement time t(m). Scaling with t/Delta t occurs only when Delta t/t(m) is a constant. We show that this observation is equivalent to theoretical predictions that the survival probability will scale as Delta t/L-z, where L is the effective length of a step. This implies that the survival probability for large systems, when measured with fixed values of t(m) or Delta t, should also show little or no temperature dependence.

Item Type:	Journal Article
Publication:	Physical Review E
Publisher:	The American Physical Society
Additional Information:	Copyright of this article belongs to The American Physical Society.
Department/Centre:	Division of Physical & Mathematical Sciences > Physics
Date Deposited:	10 Feb 2010 07:33
Last Modified:	19 Sep 2010 04:56
URI:	http://eprints.iisc.ac.in/id/eprint/17318

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