Generic Dynamic Scaling in Kinetic Roughening

Abstract

We study the dynamic scaling hypothesis in invariant surface growth. We show that the existence of power-law scaling of the correlation functions (scale invariance) does not determine a unique dynamic scaling form of the correlation functions, which leads to the different anomalous forms of scaling recently observed in growth models. We derive all the existing forms of anomalous dynamic scaling from a new generic scaling ansatz. The different scaling forms are subclasses of this generic scaling ansatz associated with bounds on the roughness exponent values. The existence of a new class of anomalous dynamic scaling is predicted and compared with simulations.

Nanoscale studies of ferroelectric domain walls as pinned elastic interfaces

“…In addition, these studies suggest superroughening of the interface, with ζ > 1 at depinning [169], although with nonetheless apparently mono-affine scaling. Experimentally, such anomalous scaling, previously reported in fracture surfaces [170,171], has also been extracted for ferromagnetic domain walls in ultrathin films [172]. Investiga- • C. The vertical (magenta) bar corresponds to 7 µm.…”

New dynamic scaling in increasing systems

“…These fluctuations can be characterized by means of different functions: power spectrum, S(q, t), global width function W (L, t), height-height correlation function, G(l, t) and local width function, w(l, t), where L is the system size and l is a local length. From these functions behavior we can obtain a set of critical exponents: global, local and spectral roughness exponents, α, α l and α s , respectively, growth exponent, β, and dynamical exponent, z [10]. A scaling law links α, β, and z as, z = α/β.…”

Scaling of Local Slopes, Conservation Laws, and Anomalous Roughening in Surface Growth

“…Also, it has recently been shown that the existence of power-law scaling of the correlation functions (i.e. scale invariance) does not determine a unique dynamic scaling form of the correlation functions [24]. On the one hand, there are super-rough processes, α > 1, for which α loc = 1 always.…”

“…On the one hand, there are super-rough processes, α > 1, for which α loc = 1 always. On the other hand, there are intrinsically anomalous roughened surfaces, for which the local roughness α loc < 1 is actually an independent exponent and α may take values larger or smaller than one depending on the universality class (see [4,24] and references therein). The existence of intrinsically anomalous roughened surfaces is a most intriguing observation and leads to the still open question concerning the basic physical features (symmetries, form of the nonlinearities, conservation laws, non-locality, etc) required for anomalous roughening to occur in surface growth.…”