Scaling analysis of the conservation growth equation with temporally correlated noise

2004 ◽  
Vol 338 (3-4) ◽  
pp. 431-436 ◽  
Author(s):  
Li-Ping Zhang ◽  
Gang Tang ◽  
Hui Xia ◽  
Da-Peng Hao ◽  
Hua Chen
Keyword(s):  
Scaling Analysis ◽  
Growth Equation ◽  
Correlated Noise ◽  
Temporally Correlated

SURFACE GROWTH WITH TEMPORALLY CORRELATED NOISE

Fractals ◽  
1993 ◽  
Vol 01 (01) ◽  
pp. 1-9 ◽  
Author(s):  
CHI-HANG LAM ◽  
LEONARD M. SANDER ◽  
DIETRICH E. WOLF
Keyword(s):  
Chaotic Map ◽  
Correlated Noise ◽  
Kpz Equation ◽  
Scaling Exponents ◽  
Spatially Correlated ◽  
Power Law Noise ◽  
Temporally Correlated ◽  
Spatially Correlated Noise ◽  
Anomalous Growth ◽  
Good Agreement

We simulate ballistic deposition with long range temporally correlated noise of bounded amplitude in 1 + 1 dimension. Good agreement with the dynamical renormalization group calculation of Medina et al. is obtained for the scaling exponents when the noise is generated by a version of Mandelbrot's fast fractional Gaussian noise (ffGn) generator. However, using either the original ffGn or a chaotic map generator, other exponents are obtained. We suggest that this difference is due to an extraordinarily slow crossover caused by the existence of an anomalous growth mode incompatible with the KPZ equation. This may have implications on similar model dependent results for recent simulations on growth with power-law noise and spatially correlated noise.

Amplitude Estimation of Multichannel Signal in Spatially and Temporally Correlated Noise

PIERS Online ◽  
2006 ◽  
Vol 2 (4) ◽  
pp. 380-384 ◽  
Author(s):  
Kwang June Sohn ◽  
Hongbin Li ◽  
Braham Himed
Keyword(s):  
Correlated Noise ◽  
Amplitude Estimation ◽  
Temporally Correlated

Residual bootstraps for the uncertainty analysis of tidal models with temporally correlated noise 

2021 ◽  
Author(s):  
Silvia Innocenti ◽  
Pascal Matte ◽  
Vincent Fortin ◽  
Natacha Bernier
Keyword(s):  
Harmonic Analysis ◽  
River Flow ◽  
Analytical Techniques ◽  
Parametric Bootstrap ◽  
Correlated Noise ◽  
Series Length ◽  
Regression Residuals ◽  
Conventional Methods ◽  
Improved Performance ◽  
Temporally Correlated

<div> <div> <div> <p>The accurate characterization of the uncertainty associated with the estimation of tidal constituents is critical to provide accurate water level reconstructions and predictions. However, this represents a challenge in applications since the sparse sampling and finite series length prevent sharply distinguishing between the deterministic tidal signal and the stochastic fluctuations present in the ob- served records. Specifically, the presence of various unresolved sources of vari- ability (e.g., the tide-surge, tide-tide, and tide-river flow interactions, as well as errors and in-homogeneities associated with data measurements) results in sig- nificant broad-spectrum variability of the recorded signals, as well as harmonic analysis parameter modulations from sub-daily to decadal temporal scales. As a result, the residuals obtained after performing regression harmonic analysis are temporally correlated. Conventional methods for assessing the harmonic model uncertainty typically ignore this autocorrelation. A Monte Carlo exper- iment is used to evaluate the effect of neglecting the residual autocorrelation in the estimation of tidal constituent uncertainty. The estimation of regression parameter variability from three commonly used analytical techniques (from the UTide and NS Tide packages, and the IRLS method) and two residual resam- pling (moving-block and semi-parametric bootstrap) are compared. We show that conventional methods (e.g., UTide and the IRLS) may largely underesti- mate the parameter uncertainty when relying on simplified assumptions, such as normality and independence of the regression residuals. This may lead to in- correct assessments about the significance of one or more predictors. We showed improved performance by using the two bootstrap strategies and NS Tide, as a result of a better representation of the autocorrelation structure of residuals. The moving-block bootstrap approach provides a simple alternative that can be easily applied to a large range of (unknown) autocorrelation structures of the observed residuals.</p> </div> </div> </div>

SCALING OF THE NONLOCAL GROWTH EQUATIONS WITH SPATIALLY AND TEMPORALLY CORRELATED NOISE

2001 ◽  
Vol 15 (16) ◽  
pp. 2275-2283 ◽  
Author(s):  
GANG TANG ◽  
BENKUN MA
Keyword(s):  
Strong Coupling ◽  
Long Range ◽  
Scaling Behavior ◽  
Surface Growth ◽  
Correlated Noise ◽  
Scaling Exponents ◽  
Growth Equations ◽  
Temporally Correlated

The Flory-type approach proposed by Hentschel and Family [Phys. Rev. Lett.66, 1982 (1991)] is generalized to analyze the scaling behavior of the nonlocal surface growth equations with long-range spatially and temporally correlated noise. The scaling exponents in both the weak- and strong-coupling regions are obtained. The growth equations studied include the nonlocal Kardar–Parisi–Zhang, nonlocal Sun–Guo–Grant, and nonlocal Lai–Das Sarma–Villain equation.

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