scholarly journals Mode Fluctuations as Fingerprints of Chaotic and Non-Chaotic Systems

1997 ◽  
Vol 11 (07) ◽  
pp. 805-849 ◽  
Author(s):  
R. Aurich ◽  
A. Bäcker ◽  
F. Steiner
Keyword(s):  
Gaussian Distribution ◽  
Integrable Systems ◽  
Chaotic Systems ◽  
Energy Levels ◽  
Numerical Results ◽  
Rigorous Results ◽  
Non Gaussian

The mode-fluctuation distribution P(W) is studied for chaotic as well as for non-chaotic quantum billiards. This statistic is discussed in the broader framework of the E(k,L) functions being the probability of finding k energy levels in a randomly chosen interval of length L, and the distribution of n(L), where n(L) is the number of levels in such an interval, and their cumulants ck(L). It is demonstrated that the cumulants provide a possible measure for the distinction between chaotic and non-chaotic systems. The vanishing of the normalized cumulants Ck, k ≥ 3, implies a Gaussian behaviour of P(W), which is realized in the case of chaotic systems, whereas non-chaotic systems display non-vanishing values for these cumulants leading to a non-Gaussian behaviour of P(W). For some integrable systems there exist rigorous proofs of the non-Gaussian behaviour which are also discussed. Our numerical results and the rigorous results for integrable systems suggest that a clear fingerprint of chaotic systems is provided by a Gaussian distribution of the mode-fluctuation distribution P(W).

scholarly journals Level III Reliability Design of an Armor Block of Rubble Mound Breakwater Using Probabilistic Model of Wave Height Optimized for the Korean Sea Wave Conditions and Non-Gaussian Wave Slope Distribution

2021 ◽  
Vol 9 (2) ◽  
pp. 223
Author(s):  
Yong Jun Cho
Keyword(s):  
Wave Height ◽  
Gaussian Distribution ◽  
Wave Interaction ◽  
Numerical Results ◽  
Controversial Issues ◽  
Reliability Design ◽  
Resonant Wave ◽  
Wave Slope ◽  
Rubble Mound ◽  
Non Gaussian

In this study, a Level III reliability design of an armor block of rubble mound breakwater was developed using the optimized probabilistic wave height model for the Korean marine environment and Van der Meer equation. To demonstrate what distinguishes this study from the others, numerical simulation was first carried out, assuming that wave slope follows Gaussian distribution recommended by PIANC. Numerical results showed that Gaussian wave slope distribution overpredicted the failure probability of armor block, longer and shorter waves, and on the contrary, underpredicted waves of the medium period. After noting the limitations of Gaussian distribution, some efforts were made to develop an alternative for Gaussian distribution. As a result, non-Gaussian wave slope distribution was analytically derived from the joint distribution of wave amplitude and period by Longuet–Higgins using the random variables transformation technique. Numerical results showed that non-Gaussian distribution could effectively address the limitations of Gaussian distribution due to its capability to account for the nonlinear resonant wave–wave interaction and its effects on the wave slope distribution that significantly influences the armor block’s stability. Therefore, the non-Gaussian wave slope distribution presented in this study could play an indispensable role in addressing controversial issues such as whether or not enormous armor blocks like a Tetrapod of 100 t frequently mentioned in developing countermeasures against rough seas due to climate change is too conservatively designed.

scholarly journals Timing of Pubertal Onset in Girls: Evidence for Non-Gaussian Distribution

2008 ◽  
Vol 93 (11) ◽  
pp. 4422-4425 ◽  
Author(s):  
Anastasios Papadimitriou ◽  
Soula Pantsiotou ◽  
Konstandinos Douros ◽  
Dimitrios T. Papadimitriou ◽  
Polyxeni Nicolaidou ◽  
...  
Keyword(s):  
Gaussian Distribution ◽  
Pubertal Onset ◽  
Non Gaussian

scholarly journals Fatigue Life Analysis of Aluminum Alloy Notched Specimens under Non-Gaussian Excitation based on Fatigue Damage Spectrum

2021 ◽  
Vol 2021 ◽  
pp. 1-14
Author(s):  
Kuanyu Chen ◽  
Guangwu Yang ◽  
Jianjun Zhang ◽  
Shoune Xiao ◽  
Yang Xu
Keyword(s):  
Aluminum Alloy ◽  
Fatigue Life ◽  
Fatigue Damage ◽  
Relative Error ◽  
Gaussian Distribution ◽  
Calculation Method ◽  
Shaking Table ◽  
Notched Specimens ◽  
Acceleration Method ◽  
Non Gaussian

In this study, a non-Gaussian excitation acceleration method is proposed, using aluminum alloy notched specimens as a research object and measured acceleration signal of a certain airborne bracket, during aircraft flight as input excitations, based on the fatigue damage spectrum (FDS) theory. The kurtosis and skewness of the input signal are calculated and the non-Gaussian characteristics and amplitude distribution are evaluated. Five task segments obey a non-Gaussian distribution, while one task segment obeys a Gaussian distribution. The fatigue damage spectrum calculation method of non-Gaussian excitation is derived. The appropriate FDS calculation method is selected for each task segment and the acceleration parameters are set to construct the acceleration power spectral density, which is equivalent to the pseudo-acceleration damage. A finite-element model is established, the notch stress concentration factor of the specimen is calculated, the large mass point method is used to simulate the shaking table excitation, and a random vibration analysis is carried out to calculate the accelerated fatigue life. The simulation results show that the relative error between the original cumulative damage and test original fatigue life is 15.7%. The shaking table test results show that the relative error of fatigue life before and after acceleration is less than 16.95%, and the relative error of test and simulation is 24.27%. The failure time of the specimen is accelerated from approximately 12 h to 1 h, the acceleration ratio reaches 12, and the average acceleration ideal factor is 1.125, which verifies the effectiveness of the acceleration method. It provides a reference for the compilation of the load spectrum and vibration endurance acceleration test of other airborne aircraft equipment.

scholarly journals The Spectral Power Density and Shadowing Function of a Glacial Microrelief at the Decimetre Scale

1979 ◽  
Vol 23 (89) ◽  
pp. 57-66 ◽  
Author(s):  
J.-P. Benoist
Keyword(s):  
Power Density ◽  
Gaussian Distribution ◽  
Spectral Power ◽  
Spectral Power Density ◽  
Total Length ◽  
Theoretical Function ◽  
Significant Difference ◽  
Longitudinal Profiles ◽  
Non Gaussian

Abstract Longitudinal profiles of roches moutonnées have been measured once every centimetre over a total length of more than 100 m. Only wavelengths in the range 3.6 cm < λ < 40 cm have been kept and analysed. Levels and their slopes have a symmetrical, non-Gaussian distribution. The spectral power density varies roughly as γ 0 ν–n (ν ═ wavenumber ═ 1/λ); n being the same for all the profiles (n ═ 2.36) and γ 0 being dependent on the studied area. No significant difference has been found for the shadowing function of the different studied areas. It differs consistently from Smith’s theoretical function.

Study on the mutual influence of surface roughness and texture features of rough-textured surfaces on the tribological properties

2020 ◽  
pp. 135065012094021
Author(s):  
Chunxing Gu ◽  
Xianghui Meng ◽  
Shuwen Wang ◽  
Xiaohong Ding
Keyword(s):  
Surface Roughness ◽  
Tribological Properties ◽  
Gaussian Distribution ◽  
Mutual Influence ◽  
Surface Texturing ◽  
Texture Features ◽  
Tribological Performance ◽  
Mixed Lubrication ◽  
Non Gaussian ◽  
Skewness And Kurtosis

In recent years, the efforts to better control friction and wear have focused on surface topography modification through surface texturing. To study the mutual influence of surface roughness and texture features, this paper developed one comprehensive mathematical model of mixed lubrication to study the tribological performance of the rough-textured conjunction. The typical ring-liner conjunction was chosen as the research object. In particular, the effects of skewness and kurtosis were considered based on the non-Gaussian distribution of asperity height. In this way, the influences of non-Gaussian distribution properties and surface texturing on the tribological performance were analyzed. The results show that the influences of skewness and kurtosis on the tribological performance are nontrivial and should not be neglected in the mixed lubrication. Compared to the Gaussian distribution, considering the non-Gaussian distribution can represent the physical rough surfaces more accurately. Surfaces with negative skewness were found to generally result in better tribological properties. Moreover, the tribological performance improved by surface texturing can also be improved or reduced by the effect of skewness and kurtosis. As a result, the optimization of surface texturing should take the effects of roughness parameters into account.

scholarly journals One-loop non-planar anomalous dimensions in super Yang-Mills theory

2020 ◽  
Vol 2020 (10) ◽  
Author(s):  
Tristan McLoughlin ◽  
Raul Pereira ◽  
Anne Spiering
Keyword(s):  
Perturbation Theory ◽  
Integrable Systems ◽  
Chaotic Systems ◽  
Quantum Mechanical ◽  
Matrix Elements ◽  
Mechanical Perturbation ◽  
Yang Mills ◽  
Anomalous Dimensions ◽  
Dilatation Operator ◽  
Scalar Products

Abstract We consider non-planar one-loop anomalous dimensions in maximally supersymmetric Yang-Mills theory and its marginally deformed analogues. Using the basis of Bethe states, we compute matrix elements of the dilatation operator and find compact expressions in terms of off-shell scalar products and hexagon-like functions. We then use non-degenerate quantum-mechanical perturbation theory to compute the leading 1/N2 corrections to operator dimensions and as an example compute the large R-charge limit for two-excitation states through subleading order in the R-charge. Finally, we numerically study the distribution of level spacings for these theories and show that they transition from the Poisson distribution for integrable systems at infinite N to the GOE Wigner-Dyson distribution for quantum chaotic systems at finite N.

Parameterizations and Parameters Relations of Stable Distribution

2014 ◽  
Vol 543-547 ◽  
pp. 1721-1727 ◽  
Author(s):  
Chun Li Liu ◽  
Hai Long Chen ◽  
Lei Shao ◽  
Jun Ting Wang ◽  
Cheng Ji You
Keyword(s):  
Numerical Calculation ◽  
Gaussian Distribution ◽  
Stable Distribution ◽  
Alpha Stable Distribution ◽  
Non Gaussian

For the problem of various non-Gaussian signals and noises have distinct spiky and impulsive characteristics in practice, which cannot be solved by Gaussian distribution, we focus on the Alpha stable distribution. This paper firstly sets forth the representation of standard parameterization, and gives some properties in this parameterization. Secondly, define a representation of the parameterization for the purpose of being suitable for numerical calculation and modeling, clears the meaning of each parameter, finds relations between parameters in these representations. Finally, analyze and prove the properties equally apply in this parameterization.

ENHANCEMENT OF INTRINSIC SPIKING COHERENCE BY EXTERNAL NON-GAUSSIAN NOISE IN A STOCHASTIC HODGKIN–HUXLEY NEURON

2011 ◽  
Vol 10 (04) ◽  
pp. 359-369 ◽  
Author(s):  
LI WANG ◽  
YUBING GONG ◽  
XIU LIN
Keyword(s):  
Information Processing ◽  
Gaussian Distribution ◽  
Gaussian Noise ◽  
Correlation Time ◽  
Temporal Coherence ◽  
Channel Noise ◽  
Coherence Resonance ◽  
Non Gaussian ◽  
Proper Values ◽  
Membrane Patch

In this paper, we study the effect of external non-Gaussian noise on the temporal coherence of the intrinsic spiking induced by the channel noise in a stochastic Hodgkin–Huxley neuron. It is found that, for a sufficiently large membrane patch, the intrinsic spiking coherence can be enhanced by the proper values of non-Gaussian noise's strength, correlation time, or deviation from Gaussian distribution. And that the intrinsic spiking can exhibit coherence resonance when the noise's strength is optimal. This implies that the channel noise-induced intrinsic spiking may become more or the most ordered in time with the assistance of the external non-Gaussian noise. These results show that the external non-Gaussian noise can play a constructive role for improving the time precision of information processing in stochastic neurons.

scholarly journals A Non-Gaussian Distribution Quantifies Distances Measured with Fluorescence Localization Techniques

2006 ◽  
Vol 90 (2) ◽  
pp. 668-671 ◽  
Author(s):  
L. Stirling Churchman ◽  
Henrik Flyvbjerg ◽  
James A. Spudich
Keyword(s):  
Gaussian Distribution ◽  
Non Gaussian
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