%0 Book Section %1 statphys23_0542 %A Szendro, I.G. %A López, J.M. %A Rodr\'ıguez, M.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 critical dynamic film fluctuation growth models noise patterns phenomena processes random statphys23 theory topic-3 %T Localization in disordered media, anomalous roughening and coarsening dynamics of faceted surfaces %U http://st23.statphys23.org/webservices/abstract/preview_pop.php?ID_PAPER=542 %X We study a surface growth model related to the Kardar-Parisi-Zhang equation for nonequilibrium kinetic roughening, but where the thermal noise is replaced by a static columnar disorder $\eta(x)$, equation \partial_t h = \nabla^2 h + (h)^2 + \eta(x). kpz_eq equation This model is one of the many representations of the problem of particle diffusion in trapping/amplifying disordered media, equation \partial_t = \nabla^2 + \eta(x) \phi(x,t), mult_eq equation where the random field $\eta(x)$ is Gaussian with zero mean and delta correlated equation \eta(x) \eta(x') = 2D \delta^d(x-x'). equation after the the nonlinear Hopf-Cole transformation $\phi(x,t) = \exp\, h(x,t)/\nu$. We find that probability localization in the diffusion problem translates into facet formation in the equivalent surface growth problem. Coarsening of the pattern can therefore be identified with the diffusion of the localization center. The faceted pattern leads to nontrivial scaling properties, including anomalous scaling. This is in excellent agreement with and earlier conjecture of Ramasco et. al. for kinetic roughening of faceted surfaces. Moreover, we have found that the surface can be decomposed in two different contributions. The global pattern, which dominates the surface scaling at long wavelengths, and a local fluctuation component, which spatial properties are characterized by a roughness exponent $= \alpha_KPZ$. An adiabatic approximation allowed us to relate the spatial scaling of the local noisy component to KPZ critical behavior. However, the dynamic exponent is dominated by the global pattern and we found $z=1.35 0.05$ and $z = 1.10 0.05$ in $d=1$ and $d=2$, respectively In a wider context, our study sheds light onto the scaling properties in other systems displaying this kind of patterned surfaces. We believe that similar mechanisms might be at work in other growth systems that produce kinetically rough faceted surfaces. In particular, our study suggests that the spectral roughness exponent that was conjectured by Ramasco et. al. can play a role in the description of the scaling properties in other systems displaying this kind of patterned surfaces.

@incollection{statphys23_0542, abstract = {We study a surface growth model related to the Kardar-Parisi-Zhang equation for nonequilibrium kinetic roughening, but where the thermal noise is replaced by a static columnar disorder $\eta(\mathbf{x})$, \begin{equation} \partial_t h = \nu \nabla^2 h + \lambda (\nabla h)^2 + \eta({\bf x}). \label{kpz_eq} \end{equation} This model is one of the many representations of the problem of particle diffusion in trapping/amplifying disordered media, \begin{equation} \partial_t \phi = \gamma \nabla^2 \phi + \eta(\mathbf{x}) \phi(\mathbf{x},t), \label{mult_eq} \end{equation} where the random field $\eta(\mathbf{x})$ is Gaussian with zero mean and delta correlated \begin{equation} \langle \eta(\mathbf{x}) \eta(\mathbf{x}') \rangle = 2D \delta^{d}(\mathbf{x}-\mathbf{x}'). \end{equation} after the the nonlinear Hopf-Cole transformation $\phi(\mathbf{x},t) = \exp[\lambda \, h(\mathbf{x},t)/\nu]$. We find that probability localization in the diffusion problem translates into facet formation in the equivalent surface growth problem. Coarsening of the pattern can therefore be identified with the diffusion of the localization center. The faceted pattern leads to nontrivial scaling properties, including anomalous scaling. This is in excellent agreement with and earlier conjecture of Ramasco {\it et. al.} for kinetic roughening of faceted surfaces. Moreover, we have found that the surface can be decomposed in two different contributions. The global pattern, which dominates the surface scaling at long wavelengths, and a local fluctuation component, which spatial properties are characterized by a roughness exponent $\alpha = \alpha_\mathrm{KPZ}$. An adiabatic approximation allowed us to relate the spatial scaling of the local noisy component to KPZ critical behavior. However, the dynamic exponent is dominated by the global pattern and we found $z=1.35 \pm 0.05$ and $z = 1.10 \pm 0.05$ in $d=1$ and $d=2$, respectively In a wider context, our study sheds light onto the scaling properties in other systems displaying this kind of patterned surfaces. We believe that similar mechanisms might be at work in other growth systems that produce kinetically rough faceted surfaces. In particular, our study suggests that the spectral roughness exponent that was conjectured by Ramasco {\it et. al.} can play a role in the description of the scaling properties in other systems displaying this kind of patterned surfaces.}, added-at = {2007-06-20T10:16:09.000+0200}, address = {Genova, Italy}, author = {Szendro, I.G. and L\'opez, J.M. and Rodr{\'\i}guez, M.A.}, biburl = {https://www.bibsonomy.org/bibtex/25701298b8ae39a92b7c3f81e165d6050/statphys23}, booktitle = {Abstract Book of the XXIII IUPAP International Conference on Statistical Physics}, editor = {Pietronero, Luciano and Loreto, Vittorio and Zapperi, Stefano}, interhash = {c1027577d8ea0918b730fd678cf02b87}, intrahash = {5701298b8ae39a92b7c3f81e165d6050}, keywords = {critical dynamic film fluctuation growth models noise patterns phenomena processes random statphys23 theory topic-3}, month = {9-13 July}, timestamp = {2007-06-20T10:16:23.000+0200}, title = {Localization in disordered media, anomalous roughening and coarsening dynamics of faceted surfaces}, url = {http://st23.statphys23.org/webservices/abstract/preview_pop.php?ID_PAPER=542}, year = 2007 }