Non-Gaussian Wave Groups Generated in an Offshore Wave Basin

2012 ◽  
Vol 134 (4) ◽  
Author(s):  
Z. Cherneva ◽  
C. Guedes Soares
Keyword(s):  
Gaussian Process ◽  
Frequency Spectrum ◽  
Local Spectrum ◽  
Wave Groups ◽  
High Wave ◽  
Time Frequency ◽  
Wave Basin ◽  
The Mean ◽  
Non Gaussian ◽  
Experimental Runs

The main goal of the present paper is to study the differences of the descriptors of the wave groups in the nonlinear case in comparison with the same parameters for a Gaussian process. The data analyzed are from a deep water basin of Marintek. They consist of sequence of five identical independent experimental runs of unidirectional waves measured at ten fixed points situated in different distances from the wave maker. Each series contain about 1800 waves. Thus the statistics collected from a given gauge comprise about 9000 waves combined in a number of wave groups. Because the series describe a process significantly different from the Gaussian one, an upper and lower envelopes are introduced as lines which connect the peaks of the crests and the lower points of the troughs respectively. Spline functions are applied to calculate these envelopes. Then, the mean high run and mean group length are estimated for different levels, their ensemble average over five experimental runs is found for every gauge and is compared with the results of the theory of Gaussian process. It is found that the values of the mean time intervals of the groups correlate with coefficient of kurtosis of the process. It is determined also that mean group length is shorter and the mean high run is larger for the nonlinear wave groups in comparison with the Gaussian wave groups. The modification of wave groups in space and time is investigated in the work as well. Wigner time-frequency spectrum with Choi-Williams kernel is applied to describe the process of entire modulation and demodulation of the groups. It is found that before formation of the high wave a wave down-shifting takes place. At this stage the local spectrum is relatively narrow and the group shrinks continuously. Close to the focus the time-frequency spectrum is very wide and the group has a triangle form. Further the high wave breaks and the wave group acquires the form of “three sisters.” The transform of the group continues by its disintegration, the local spectrum stands narrow and an up-shifting is observed.

Non-Gaussian Wave Groups Generated in an Offshore Wave Basin and Their Statistics

2011 ◽  
Author(s):  
Zhivelina Cherneva ◽  
C. Guedes Soares
Keyword(s):  
Wave Groups ◽  
Wave Basin ◽  
Lower Envelopes ◽  
The Mean ◽  
Wave Maker ◽  
Using Data ◽  
Non Gaussian ◽  
Offshore Wave ◽  
The Hilbert Transform ◽  
Theoretical Results

The main goal of this work is to investigate the wave groups using data from a deep water basin. Available data are for unidirectional waves measured at several fixed points situated in different distances from the wave maker. Previous works of many authors show that such series describe a process which differs significantly from the Gaussian one. Omitting the usual envelope definition by the Hilbert transform an upper and lower envelopes are introduced. Then the mean high run, mean group length and their distributions are found and compared with the theoretical results for Gaussian process.

Scalable Gaussian Process Classification With Additive Noise for Non-Gaussian Likelihoods

2021 ◽  
pp. 1-13
Author(s):  
Haitao Liu ◽  
Yew-Soon Ong ◽  
Ziwei Yu ◽  
Jianfei Cai ◽  
Xiaobo Shen
Keyword(s):  
Gaussian Process ◽  
Additive Noise ◽  
Non Gaussian ◽  
Process Classification

scholarly journals Reconstruction of Diffusion Coefficients and Power Exponents from Single Lagrangian Trajectories

Fluids ◽  
2021 ◽  
Vol 6 (3) ◽  
pp. 111
Author(s):  
Leonid M. Ivanov ◽  
Collins A. Collins ◽  
Tetyana Margolina
Keyword(s):  
Black Sea ◽  
Diffusion Coefficients ◽  
Current System ◽  
Mean Square Displacement ◽  
California Current ◽  
The Black Sea ◽  
Mean Square ◽  
California Current System ◽  
The Mean ◽  
Non Gaussian

Using discrete wavelets, a novel technique is developed to estimate turbulent diffusion coefficients and power exponents from single Lagrangian particle trajectories. The technique differs from the classical approach (Davis (1991)’s technique) because averaging over a statistical ensemble of the mean square displacement (<X2>) is replaced by averaging along a single Lagrangian trajectory X(t) = {X(t), Y(t)}. Metzler et al. (2014) have demonstrated that for an ergodic (for example, normal diffusion) flow, the mean square displacement is <X2> = limT→∞τX2(T,s), where τX2 (T, s) = 1/(T − s) ∫0T−s(X(t+Δt) − X(t))2 dt, T and s are observational and lag times but for weak non-ergodic (such as super-diffusion and sub-diffusion) flows <X2> = limT→∞≪τX2(T,s)≫, where ≪…≫ is some additional averaging. Numerical calculations for surface drifters in the Black Sea and isobaric RAFOS floats deployed at mid depths in the California Current system demonstrated that the reconstructed diffusion coefficients were smaller than those calculated by Davis (1991)’s technique. This difference is caused by the choice of the Lagrangian mean. The technique proposed here is applied to the analysis of Lagrangian motions in the Black Sea (horizontal diffusion coefficients varied from 105 to 106 cm2/s) and for the sub-diffusion of two RAFOS floats in the California Current system where power exponents varied from 0.65 to 0.72. RAFOS float motions were found to be strongly non-ergodic and non-Gaussian.

GLOBAL FLUCTUATIONS FOR LINEAR STATISTICS OF β-JACOBI ENSEMBLES

2012 ◽  
Vol 01 (04) ◽  
pp. 1250013 ◽  
Author(s):  
IOANA DUMITRIU ◽  
ELLIOT PAQUETTE
Keyword(s):  
Gaussian Process ◽  
Covariance Matrix ◽  
Law Of Large Numbers ◽  
Test Functions ◽  
Linear Statistics ◽  
Jacobi Ensemble ◽  
Large Numbers ◽  
The Mean ◽  
Shifted Chebyshev Polynomial ◽  
Global Fluctuations

We study the global fluctuations for linear statistics of the form [Formula: see text] as n → ∞, for C1 functions f, and λ1, …, λn being the eigenvalues of a (general) β-Jacobi ensemble. The fluctuation from the mean [Formula: see text] turns out to be given asymptotically by a Gaussian process. We compute the covariance matrix for the process and show that it is diagonalized by a shifted Chebyshev polynomial basis; in addition, we analyze the deviation from the predicted mean for polynomial test functions, and we obtain a law of large numbers.

Optimization of the Ratio of ω-6 Linoleic and ω-3 α-Linolenic Fatty Acids of Hemp Seed Oil with Jackknife and Bootstrap Resampling

2019 ◽  
Vol 15 (1) ◽  
Author(s):  
Vibha Devi ◽  
Shabina Khanam
Keyword(s):  
Fatty Acids ◽  
Standard Deviation ◽  
Flow Rate ◽  
Seed Oil ◽  
Cannabis Sativa ◽  
Bootstrap Resampling ◽  
Hemp Seed ◽  
Solvent Flow Rate ◽  
The Mean ◽  
Experimental Runs

Abstract In the present work, supercritical fluid extraction (SFE) of hemp (Cannabis sativa) seed oil at various ranges of SFE parameters is performed. These parameters and respective ranges are temperature (40–80) °C, pressure (200–350) bar, solvent (CO2) flow rate (5–15) g/min, particle size (0.43–1.02) mm and amount of co-solvent (ethanol) (0–10) % of solvent flow rate. Central composite design (CCD) suggests 32 experimental runs to perform through SFE. The obtained oil is analysed through gas chromatography to identify its fatty acids concentrations. The ratio of ω-6 linoleic and ω-3 α-linolenic fatty acids (ω-6/ω-3) is optimized through CCD to obtain the desired amount of 3:1 as this ratio is highly preferred for various health benefits. Ratio of ω-6/ω-3 is obtained in the range from 2.11 to 3.06:1 for all experimental runs. The effect of SFE parameters on this ratio is investigated. Further, cross-validation is peformed on the experimental data obtained for the concentrations of both fatty acids by jackknife and bootstrap resampling to authenticate the obtained data. Small value of standard deviation (~1), less standard error of the mean (SEM) (<0.8) and less variance coefficient (<0.11) confirms the validity of the obtained data. All the estimators’ values such as standard deviation, variance coefficients and SEM are observed in 95 % of confidence intervals.

scholarly journals Analysis of stimulus-related activity in rat auditory cortex using complex spectral coefficients

2013 ◽  
Vol 110 (3) ◽  
pp. 621-639 ◽  
Author(s):  
Bryan M. Krause ◽  
Matthew I. Banks
Keyword(s):  
Low Frequency ◽  
Phase Changes ◽  
Induced Response ◽  
Top Down ◽  
Time Frequency ◽  
State Dependent ◽  
Spectral Coefficients ◽  
The Mean ◽  
Sensory Responses ◽  
Mean Variance

The neural mechanisms of sensory responses recorded from the scalp or cortical surface remain controversial. Evoked vs. induced response components (i.e., changes in mean vs. variance) are associated with bottom-up vs. top-down processing, but trial-by-trial response variability can confound this interpretation. Phase reset of ongoing oscillations has also been postulated to contribute to sensory responses. In this article, we present evidence that responses under passive listening conditions are dominated by variable evoked response components. We measured the mean, variance, and phase of complex time-frequency coefficients of epidurally recorded responses to acoustic stimuli in rats. During the stimulus, changes in mean, variance, and phase tended to co-occur. After the stimulus, there was a small, low-frequency offset response in the mean and modest, prolonged desynchronization in the alpha band. Simulations showed that trial-by-trial variability in the mean can account for most of the variance and phase changes observed during the stimulus. This variability was state dependent, with smallest variability during periods of greatest arousal. Our data suggest that cortical responses to auditory stimuli reflect variable inputs to the cortical network. These analyses suggest that caution should be exercised when interpreting variance and phase changes in terms of top-down cortical processing.

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