%0 Book Section %1 statphys23_0700 %A Einstein, T.L. %A Pimpinelli, A. %B Abstract Book of the XXIII IUPAP International Conference on Statistical Physics %C Genova, Italy %D 2007 %E Pietronero, Luciano %E Loreto, Vittorio %E Zapperi, Stefano %K capture distributions fluctuations interfaces scaling size statphys23 steps surfaces surmise topic-3 wigner zones %T Application of the Generalized Wigner Surmise to Non-equilibrium Problems at Surfaces: Relaxation, Growth, and Capture-Zone Scaling %U http://st23.statphys23.org/webservices/abstract/preview_pop.php?ID_PAPER=700 %X After reviewing applications of the GWS $P_\beta(s)= a_s^\exp(-b_s^2)$, the Wigner surmise from random matrix theory generalized to allow arbitrary positive exponent $\beta$ to equilibrium distributions of terrace widths (TWD) on a stepped surface Appl.\ Phys.\ A 87 (2007) 375 cond-mat/0612311 and references therein, we describe three new applications to non-equilibrium problems in surface/inter\rm- face physics. 1) We develop a Fokker-Planck formalism to describe how such steps on a vicinal surface relax to equilibrium (given by the GWS) from an arbitrary initial configuration Phys.\ Rev.\ Lett.\ 95 (2005) 246101 and submitted. 2) We show how growth narrows the TWD of a vicinal surface, leading to a larger effective value of $\beta$ Ajmi Bhadj-Hamouda, Ph.D.\ thesis, UBP, and in preparation. 3) The distribution of growing island has long been studied numerically but has eluded analytic formulation. Using published kinematic Monte Carlo data, we find the GWS describes well the distribution of the areas of Voronoi polygons (proximity cells) around nucleation centers, i.e. the capture zones. Furthermore, $= i + d/2$, where $i$ is the size of the critical nucleus and $d$ is the spatial dimensionality of the substrate. We demonstrate excellent fits of numerical data for both $d=1$ and $d=2$ and compare with experimental measurements. To clarify the underlying physics, we present a phenomenological derivation by constructing a Langevin equation similar to that used in deriving the Fokker-Planck equation for relaxation of TWDs cond-mat/0612471 and submitted. Work at U. of Maryland supported by the MRSEC, NSF Grant DMR 05-20471, and partially by DOE CMSN grant DEFG0205ER46227. AP's visits to Maryland by supported by a CNRS Travel Grant.

@incollection{statphys23_0700, abstract = {After reviewing applications of the GWS [$P_\beta(s)= a_\beta s^\beta \exp({\rm -}b_\beta s^2)$, the Wigner surmise from random matrix theory generalized to allow arbitrary positive exponent $\beta$] to equilibrium distributions of terrace widths (TWD) on a stepped surface [Appl.\ Phys.\ A 87 (2007) 375 [cond-mat/0612311] and references therein], we describe three new applications to non-equilibrium problems in surface/inter{\rm-} face physics. 1) We develop a Fokker-Planck formalism to describe how such steps on a vicinal surface relax to equilibrium (given by the GWS) from an arbitrary initial configuration [Phys.\ Rev.\ Lett.\ 95 (2005) 246101 and submitted]. 2) We show how growth narrows the TWD of a vicinal surface, leading to a larger effective value of $\beta$ [Ajmi Bhadj-Hamouda, Ph.D.\ thesis, UBP, and in preparation]. 3) The distribution of growing island has long been studied numerically but has eluded analytic formulation. Using published kinematic Monte Carlo data, we find the GWS describes well the distribution of the areas of Voronoi polygons (proximity cells) around nucleation centers, i.e. the capture zones. Furthermore, $\beta = i + d/2$, where $i$ is the size of the critical nucleus and $d$ is the spatial dimensionality of the substrate. We demonstrate excellent fits of numerical data for both $d=1$ and $d=2$ and compare with experimental measurements. To clarify the underlying physics, we present a phenomenological derivation by constructing a Langevin equation similar to that used in deriving the Fokker-Planck equation for relaxation of TWDs [cond-mat/0612471 and submitted]. Work at U. of Maryland supported by the MRSEC, NSF Grant DMR 05-20471, and partially by DOE CMSN grant DEFG0205ER46227. AP's visits to Maryland by supported by a CNRS Travel Grant.}, added-at = {2007-06-20T10:16:09.000+0200}, address = {Genova, Italy}, author = {Einstein, T.L. and Pimpinelli, A.}, biburl = {https://www.bibsonomy.org/bibtex/2b1d29835445014b40e3cbb160bf42cb6/statphys23}, booktitle = {Abstract Book of the XXIII IUPAP International Conference on Statistical Physics}, editor = {Pietronero, Luciano and Loreto, Vittorio and Zapperi, Stefano}, interhash = {34389a9d284716f8144c84c54543f5a1}, intrahash = {b1d29835445014b40e3cbb160bf42cb6}, keywords = {capture distributions fluctuations interfaces scaling size statphys23 steps surfaces surmise topic-3 wigner zones}, month = {9-13 July}, timestamp = {2007-06-20T10:16:27.000+0200}, title = {Application of the Generalized Wigner Surmise to Non-equilibrium Problems at Surfaces: Relaxation, Growth, and Capture-Zone Scaling}, url = {http://st23.statphys23.org/webservices/abstract/preview_pop.php?ID_PAPER=700}, year = 2007 }