On the fractal dimension of self-affine profiles

Moreira, Jacqueline de Oliveira; Silva, J. Kamphorst Leal da; Kamphorst, Sylvie Oliffson

doi:10.1088/0305-4470/27/24/018

Cited by 85 publications

(63 citation statements)

References 8 publications

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“…3(a) and 3(b)), the root-mean square (rms) roughness (over 3Â3 lm The roughness exponent of the two samples [0.62(1) -low rate-and 0.70(1) -high rate-] further confirms the rougher character of the low rate films. 19,20 This implies that in the low-rate sample the islands are more isolated and consequently the tip can penetrate deeper in between the islands. The high-rate film is more prone to form a continuous film due to the higher kinetic energy and mobility of the sputtered atoms.…”

Section: Resultsmentioning

confidence: 99%

Nanostructured MnGa films on Si/SiO2 with 20.5 kOe room temperature coercivity

Zha¹,

Dumas²,

Lau³

et al. 2011

Journal of Applied Physics

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Enhanced ferroelectric, magnetoelectric, and magnetic properties in Pr and Cr co-doped BiFeO3 nanotubes fabricated by template assisted route J. Appl. Phys. 111, 104115 (2012) Sol-gel NiFe2O4 nanoparticles: Effect of the silica coating J. Appl. Phys. 111, 103911 (2012) Screen-printing of ferrite magnetic nanoparticles produced by carbon combustion synthesis of oxides J. Appl. Phys. 111, 094311 (2012) Texture-induced magnetic interactions in ferrofluids J. Appl. Phys. 111, 093910 (2012) Additional information on J. Appl. Phys.

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Section: Resultsmentioning

confidence: 99%

Nanostructured MnGa films on Si/SiO2 with 20.5 kOe room temperature coercivity

Zha¹,

Dumas²,

Lau³

et al. 2011

Journal of Applied Physics

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“…F 2 FA is the variance of the fluctuations (residuals) from local trends fitted in each subsample. These local trends are defined as local linear or polynomial regressions in DFA (a three-order polynomial is used in this study) [10,[59][60][61]. It should be noted that LRD diagnostics are commonly affected by the presence of seasonal/cyclic patterns [6,[62][63][64][65][66]; therefore, the deseasonalization procedure in Equation (1) provides a simple but effective way to handle this aspect.…”

Section: Methodsmentioning

confidence: 99%

Understanding Persistence to Avoid Underestimation of Collective Flood Risk

Serinaldi

Kilsby

2016

Water

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Abstract:The assessment of collective risk for flood risk management requires a better understanding of the space-time characteristics of flood magnitude and occurrence. In particular, classic formulation of collective risk implies hypotheses concerning the independence of intensity and number of events over fixed time windows that are unlikely to be tenable in real-world hydroclimatic processes exhibiting persistence. In this study, we investigate the links between the serial correlation properties of 473 daily stream flow time series across the major river basins in Europe, and the characteristics of over-threshold events which are used as proxies for the estimation of collective risk. The aim is to understand if some key features of the daily stream flow data can be used to infer properties of extreme events making a more efficient and effective use of the available data. Using benchmark theoretical processes such as Hurst-Kolmogorov (HK), generalized HK (gHK), autoregressive fractionally integrated moving average (ARFIMA) models, and Fourier surrogate data preserving second order linear moments, our findings confirm and expand some results previously reported in the literature, namely: (1) the interplay between short range dependence (SRD) and long range dependence (LRD) can explain the majority of the serial dependence structure of deseasonalized data, but losing information on nonlinear dynamics; (2) the standardized return intervals between over-threshold values exhibit a sub-exponential Weibull-like distribution, implying a higher frequency of return intervals longer than expected under independence, and expected return intervals depending on the previous return intervals; this results in a tendency to observe short (long) inter-arrival times after short (long) inter-arrival times; (3) as the average intensity and the number of events over one-year time windows are not independent, years with larger events are also the more active in terms of number of events; and (4) persistence influences the distribution of the collective risk producing a spike of probability at zero, which describes the probability of years with no events, and a heavier upper tail, suggesting a probability of more extreme annual losses higher than expected under independence. These results provide new insights into the clustering of stream flow extremes, paving the way for more reliable simulation procedures of flood event sets to be used in flood risk management strategies.

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“…We analyzed each snapshot measuring its Hurst exponent H, using detrended fluctuation analysis (DFA) [13,11], and taking the average of several snapshots to obtain H(t). We consider the roughness as the fluctuation of the heights in the function h(x,t) obtained after the image analysis,…”

Section: Methodsmentioning

confidence: 99%

Pattern formation during capillary rising of a fluid front into a granular media

Atman¹,

Combe²,

Ferreira³

et al. 2013

AIP Conference Proceedings

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Abstract. We report results concerning the pattern formation during the capillary rising of a fluid front into a dense dry granular media. The system consists in a modified Hele-Shaw cell filled with grains of different gradings and confined in a narrow gap between the glass plates. This assembly is vertically installed over a water reservoir to allow an ascending front of liquid to percolate into the granular media. We acquire digital images of the liquid/air front which are treated by means of imaging analysis techniques. Thus, we are able to assess the temporal evolution of the air/liquid boundary profiles. We measure the roughness of the profiles, using a detrended fluctuation analysis technique, to obtain their fractal dimension. We compare our results with similar experiments reported in literature considering fluid displacement into heterogeneous media and directed percolation theory. However, the range of values for the Hurst exponent obtained from our experiments are odd to the measured/predicted values in experiments or theory.

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On the fractal dimension of self-affine profiles

Cited by 85 publications

References 8 publications

Nanostructured MnGa films on Si/SiO2 with 20.5 kOe room temperature coercivity

Nanostructured MnGa films on Si/SiO2 with 20.5 kOe room temperature coercivity

Understanding Persistence to Avoid Underestimation of Collective Flood Risk

Pattern formation during capillary rising of a fluid front into a granular media

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