Groove instabilities in surface growth with diffusion

Amar, Jacques G.; Lam, Pui-Man; Family, Fereydoon

doi:10.1103/physreve.47.3242

Cited by 99 publications

(61 citation statements)

References 8 publications

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“…for surfaces with a global roughness exponent X > 1, the usual assumption of the equivalence between the global and local descriptions of the surface is not valid. In these systems [8,9] While it is currently clearly understood that super-roughening always leads to anomalous scaling, in a recent paper [13] two of us have demonstrated that growth models in which X < 1 may also exhibit an unconventional scaling behavior with similar scaling relations between exponents. In that reference, for an analytically solvable growth model with tunable values of X, we identified anomalous dynamic scaling with the lack of self-affinity.…”

Section: W(lt) = \ \ (H(xt) -Het)) X'mentioning

confidence: 99%

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Power spectrum scaling in anomalous kinetic roughening of surfaces

López

Rodríguez

Cuerno

1997

Physica A: Statistical Mechanics and its Applications

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In this paper we study kinetically rough surfaces which display anomalous scaling in their local properties such as roughness, or height-height correlation function, By studying the power spectrum of the surface and its relation to the height-height correlation, we distinguish two independent causes for anomalous scaling, One is super-roughening (global roughness exponent larger than or equal to one), even if the spectrum behaves nonanomalously, Another cause is what we term an intrinsically anomalous spectrum, in whose scaling an independent exponent exists, which induces different scaling properties for small and large length scales (that is, the surface is not self-affine), In this case, the surface does not need to be super-rough in order to display anomalous scaling, In both cases, we show how to extract the independent exponents and scaling relations from the correlation functions, and we illustrate our analysis with two exactly solvable examples. One is the simplest linear equation for molecular beam epitaxy, well known to display anomalous scaling due to super-roughening. The second example is a random diffusion equation, which features anomalous scaling independent of the value of the global roughness exponent below or above one.

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Section: W(lt) = \ \ (H(xt) -Het)) X'mentioning

confidence: 99%

“…Let us start studying the simplest equation relevant for MBE growth [8,9,21]. For a one-dimensional interface, it reads ah a 4 h -;:;--= -K;;--4 + f/(x,t),…”

Section: Linear M Be Equation: Super-rougheningmentioning

confidence: 99%

Power spectrum scaling in anomalous kinetic roughening of surfaces

López

Rodríguez

Cuerno

1997

Physica A: Statistical Mechanics and its Applications

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“…and the system will develop a "groove" instability of the type discussed in [13]. The case d = 2 is marginal with w(L) ∼ L. The σ∂ x φ term suppresses the growth of fluctuations in the x−direction.…”

Section: Effective Model For Sliding Cdwsmentioning

confidence: 99%

Dynamical transition in sliding charge-density waves with quenched disorder

Chen

Fisher

1996

Phys. Rev. B

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We have studied numerically the dynamics of sliding charge-density waves (CDWs) in the presence of impurities in d=1,2. The model considered exhibits a first order dynamical transition at a critical driving force Fc between "rough" (disorder dominated) (F < Fc) and "flat" (F > Fc) sliding phases where disorder is washed out by the external drive. The effective model for the sliding CDWs in the presence of impurities can be mapped onto that of a magnetic flux line pinned by columnar defects and tilted by an applied field. The dynamical transition of sliding CDWs corresponds to the transverse Meissner effect of the tilted flux line.

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“…The standard self-affine Family-Vicsek scaling [2] is then recovered when α = α loc . This singular phenomenon was first noticed in numerical simulations of both continuous and discrete models of ideal molecular beam epitaxial growth [3,4,5,6,7,8,9,10,11]. Anomalous roughening has later on been reported to occur in growth models in the presence of disorder [12,13] Nowadays it has become clear [3,23] that anomalous kinetic roughening is related to a non-trivial dynamics of the average surface gradient (local slope), so that (∇h) 2 ∼ t 2κ .…”

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

2005

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We argue that symmetries and conservation laws greatly restrict the form of the terms entering the long wavelength description of growth models exhibiting anomalous roughening. This is exploited to show by dynamic renormalization group arguments that intrinsic anomalous roughening cannot occur in local growth models. However some conserved dynamics may display super-roughening if a given type of terms are present. PACS numbers: 81.15.Aa,64.60.Ht,05.70.Ln Recent theoretical and experimental studies of self-affine kinetic roughening have uncovered a rich variety of novel features [1]. In particular, the existence of anomalous roughening has received much attention. Anomalous roughening refers to the observation that local and global surface fluctuations may have distinctly different scaling exponents. This leads to the existence of an independent local roughness exponent α loc that characterizes the local interface fluctuations and differs from the global roughness exponent α. More precisely, global fluctuations are measured by the global interface width, which for a system of total lateral size L scales according to the Family-Vicsek ansatz [2] aswhere the scaling function f (u) behaves asThe roughness exponent α and the dynamic exponent z characterize the universality class of the model under study. The ratio β = α/z is the time exponent. In contrast, local surface fluctuations are given by either the height-height correlation function,, where the average is calculated over all x (overline) and noise (brackets), or the local width,where · · · l denotes an average over x in windows of size l. For growth processes in which an anomalous roughening takes place these functions scale as w(l, t) ∼ G(l, t) = t β f A (l/t 1/z ), with an anomalous scaling function [3,4] given byinstead of Eq.(2). The standard self-affine Family-Vicsek scaling [2] is then recovered when α = α loc . This singular phenomenon was first noticed in numerical simulations of both continuous and discrete models of ideal molecular beam epitaxial growth [3,4,5,6,7,8,9,10,11]. Anomalous roughening has later on been reported to occur in growth models in the presence of disorder [12,13] Nowadays it has become clear [3,23] that anomalous kinetic roughening is related to a non-trivial dynamics of the average surface gradient (local slope), so that (∇h) 2 ∼ t 2κ . Anomalous scaling occurs whenever κ > 0, which leads to the existence of a local roughness scaling with exponent α loc = α − zκ [23]. 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 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). T...

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Groove instabilities in surface growth with diffusion

Cited by 99 publications

References 8 publications

Power spectrum scaling in anomalous kinetic roughening of surfaces

Power spectrum scaling in anomalous kinetic roughening of surfaces

Dynamical transition in sliding charge-density waves with quenched disorder

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

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