Tao, CG and Cullen, WG and Williams, ED and Dasgupta, C
(2007)
*Generalized survival in step fluctuations.*
In: Physical Review E - Statistical, Nonlinear and Soft Matter Physics, 76
(2).

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## Abstract

The properties of the generalized survival probability, that is, the probability of not crossing an arbitrary location R during relaxation, have been investigated experimentally (via scanning tunneling microscope observations) and numerically. The results confirm that the generalized survival probability decays exponentially with a time constant tau(s)(R). The distance dependence of the time constant is shown to be tau(s)(R)=tau(s0)exp[-R/w(T)], where w(2)(T) is the material-dependent mean-squared width of the step fluctuations. The result reveals the dependence on the physical parameters of the system inherent in the prior prediction of the time constant scaling with R/L-alpha, with L the system size and alpha the roughness exponent. The survival behavior is also analyzed using a contrasting concept, the generalized inside survival S-in(t,R), which involves fluctuations to an arbitrary location R further from the average. Numerical simulations of the inside survival probability also show an exponential time dependence, and the extracted time constant empirically shows (R/w)(lambda) behavior, with lambda varying over 0.6 to 0.8 as the sampling conditions are changed. The experimental data show similar behavior, and can be well fit with lambda=1.0 for T=300 K, and 0.5 <lambda < 1 for T=460 K. Over this temperature range, the ratio of the fixed sampling time to the underlying physical time constant, and thus the true correlation time, increases by a factor of similar to 10(3). Preliminary analysis indicates that the scaling effect due to the true correlation time is relevant in the parameter space of the experimental observations.

Item Type: | Journal Article |
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Additional Information: | Copyright of this article belongs to The American Physical Society. |

Department/Centre: | Division of Physical & Mathematical Sciences > Physics |

Date Deposited: | 10 Jun 2010 10:41 |

Last Modified: | 19 Sep 2010 05:57 |

URI: | http://eprints.iisc.ernet.in/id/eprint/26319 |

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