Passive Sliders on Growing Surfaces and (anti-)Advection in Burger's Flows

We study the fluctuations of particles sliding on a stochastically growing surface. This problem can be mapped to motion of passive scalars in a randomly stirred Burger's flow. Renormalization group studies, simulations, and scaling arguments in one dimension, suggest a rich set of phenomena: If particles slide with the avalanche of growth sites (advection with the fluid), they tend to cluster and follow the surface dynamics. However, for particles sliding against the avalanche (anti-advection), we find slower diffusion dynamics, and density fluctuations with no simple relation to the underlying fluid, possibly with continuously varying exponents.Comment: 4 pages revtex

Facet Formation in the Negative Quenched Kardar-Parisi-Zhang Equation

The quenched Kardar-Parisi-Zhang (QKPZ) equation with negative non-linear term shows a first order pinning-depinning (PD) transition as the driving force $F$ is varied. We study the substrate-tilt dependence of the dynamic transition properties in 1+1 dimensions. At the PD transition, the pinned surfaces form a facet with a characteristic slope $s_c$ as long as the substrate-tilt $m$ is less than $s_c$. When $m<s_c$, the transition is discontinuous and the critical value of the driving force $F_c(m)$ is independent of $m$, while the transition is continuous and $F_c(m)$ increases with $m$ when $m>s_c$. We explain these features from a pinning mechanism involving a localized pinning center and the self-organized facet formation.Comment: 4 pages, source TeX file and 7 PS figures are tarred and compressed via uufile

Self similar Barkhausen noise in magnetic domain wall motion

A model for domain wall motion in ferromagnets is analyzed. Long-range magnetic dipolar interactions are shown to give rise to self-similar dynamics when the external magnetic field is increased adiabatically. The power spectrum of the resultant Barkhausen noise is of the form $1/\omega^\alpha$, where $\alpha\approx 1.5$ can be estimated from the critical exponents for interface depinning in random media.Comment: 7 pages, RevTex. To appear in Phys. Rev. Let

Roughness of Interfacial Crack Front: Correlated Percolation in the Damage Zone

We show that the roughness exponent zeta of an in-plane crack front slowly propagating along a heterogeneous interface embeded in a elastic body, is in full agreement with a correlated percolation problem in a linear gradient. We obtain zeta=nu/(1+nu) where nu is the correlation length critical exponent. We develop an elastic brittle model based on both the 3D Green function in an elastic half-space and a discrete interface of brittle fibers and find numerically that nu=1.5, We conjecture it to be 3/2. This yields zeta=3/5. We also obtain by direct numerical simulations zeta=0.6 in excellent agreement with our prediction. This modelling is for the first time in close agreement with experimental observations.Comment: 4 pages RevTeX

Evaluation of Probabilistic Streamflow Forecasts Based on EPS for a Mountainous Basin in Turkey

AbstractWhen designing water structures or managing a watershed it is a challenging task to determine the response of a basin to storm and/or snowmelt. In this study, the Upper Euphrates Basin (10,275 km2 area and elevation range of 1125-3500 m) located at the headwater of Euphrates River, one of Turkey's most important rivers, is selected as the application area. In this region, snowmelt runoff constitutes approximately 2/3 in volume of the total yearly runoff, therefore, runoff modeling and forecasting during spring and early summer is important in terms of energy and water resources management. The aim of the study is to make a forward-oriented, medium-range flow forecasting using Ensemble Prediction System (EPS) which is a pioneer study for Turkey. Conceptual hydrological model HBV, which has a common usage in the literature, is chosen to predict streamflows. According to the results, Nash-Sutcliffe model efficiencies are 0.85 for calibration (2001-2008) and 0.71 for validation (2009-2014) respectively. After calibrating/validating the hydrologic model, EPS data including 51 different combinations produced by ECMWF is used as probability based weather forecasts. Melting period during March-June of 2011 is chosen as the forecast period. The probabilistic skill of EPS based hydrological model results are analyzed to verify the ensemble forecasts

Melting of Flux Lines in an Alternating Parallel Current

We use a Langevin equation to examine the dynamics and fluctuations of a flux line (FL) in the presence of an {\it alternating longitudinal current} $J_{\parallel}(\omega)$. The magnus and dissipative forces are equated to those resulting from line tension, confinement in a harmonic cage by neighboring FLs, parallel current, and noise. The resulting mean-square FL fluctuations are calculated {\it exactly}, and a Lindemann criterion is then used to obtain a nonequilibrium `phase diagram' as a function of the magnitude and frequency of $J_{\parallel}(\omega)$. For zero frequency, the melting temperature of the mixed phase (a lattice, or the putative "Bose" or "Bragg Glass") vanishes at a limiting current. However, for any finite frequency, there is a non-zero melting temperature.Comment: 5 pages, 1 figur

Phase ordering and roughening on growing films

We study the interplay between surface roughening and phase separation during the growth of binary films. Already in 1+1 dimension, we find a variety of different scaling behaviors depending on how the two phenomena are coupled. In the most interesting case, related to the advection of a passive scalar in a velocity field, nontrivial scaling exponents are obtained in simulations.Comment: 4 pages latex, 6 figure

Non-Linear Stochastic Equations with Calculable Steady States

We consider generalizations of the Kardar--Parisi--Zhang equation that accomodate spatial anisotropies and the coupled evolution of several fields, and focus on their symmetries and non-perturbative properties. In particular, we derive generalized fluctuation--dissipation conditions on the form of the (non-linear) equations for the realization of a Gaussian probability density of the fields in the steady state. For the amorphous growth of a single height field in one dimension we give a general class of equations with exactly calculable (Gaussian and more complicated) steady states. In two dimensions, we show that any anisotropic system evolves on long time and length scales either to the usual isotropic strong coupling regime or to a linear-like fixed point associated with a hidden symmetry. Similar results are derived for textural growth equations that couple the height field with additional order parameters which fluctuate on the growing surface. In this context, we propose phenomenological equations for the growth of a crystalline material, where the height field interacts with lattice distortions, and identify two special cases that obtain Gaussian steady states. In the first case compression modes influence growth and are advected by height fluctuations, while in the second case it is the density of dislocations that couples with the height.Comment: 9 pages, revtex

Anomalous Height Fluctuation Width in Crossover from Random to Coherent Surface Growths

We study an anomalous behavior of the height fluctuation width in the crossover from random to coherent growths of surface for a stochastic model. In the model, random numbers are assigned on perimeter sites of surface, representing pinning strengths of disordered media. At each time, surface is advanced at the site having minimum pinning strength in a random subset of system rather than having global minimum. The subset is composed of a randomly selected site and its $(\ell-1)$ neighbors. The height fluctuation width $W^2(L;\ell)$ exhibits the non-monotonic behavior with $\ell$ and it has a minimum at $\ell^*$. It is found numerically that $\ell^*$ scales as $\ell^*\sim L^{0.59}$, and the height fluctuation width at that minimum, $W^2(L;\ell^*)$, scales as $\sim L^{0.85}$ in 1+1 dimensions. It is found that the subset-size $\ell^*(L)$ is the characteristic size of the crossover from the random surface growth in the KPZ universality, to the coherent surface growth in the directed percolation universality.Comment: 13 postscript file