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Nonequilibrium Interface and Surface Dynamics 2007
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Morphometric Multi-scale Surface Science
CSIC Building (#406),
Seminar Room 4122.
Directions: home.cscamm.umd.edu/directions
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Morphometric Multi-scale Surface Science
Dr.
Stephen Watson
University of Glasgow
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Abstract:
The characterization of self-assembled faceted
surfaces is a central theoretical challenge in
surface science, since the ensuing morphological
statistics (morphometrics) impact
applications in diverse areas. I'll discuss the
morphometrics emerging from the attachment kinetics
limited coarsening of a thermodynamically unstable
crystalline surface. One commonly used model is a
dissipative ("steepest descent") singularly
perturbed fourth-order partial differential
equation. We first show that its singular limit is
naturally characterized through the asymptotic
expansion of an Onsager-Raleigh-type Principle of
Maximal Dissipation (PMD) [1]. The resulting
limiting faceted surface is then characterized by an
intrinsic dynamical system. The properties of the
resulting Piecewise-Affine Dynamic Surface (PADS)
predict the scaling law L_M t^1/3, for the
growth in time t of a characteristic
morphological length scale L_M. We then introduce a
novel computational geometry tool which directly
simulates the coarsening dynamics of million-facet
PADS. We conclude by presenting data consistent with
the dynamic scaling hypothesis, and report a variety
of associated morphometric scaling-functions.
[1] S.J. Watson & S.A. Norris, Scaling theory
and morphometrics for a coarsening multiscale
surface, via a principle of maximal dissipation,
Physical Review Letters 96 (17), Art. No.
176103 (2006). |
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