H-Quantum and an Integral Lorentz Transformation

Mori, K.; Nakamura, Hiroshi

doi:10.1143/ptp.41.1378

Cited by 60 publications

(77 citation statements)

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“…The power spectra in the intermittency are characterized by an enhancement of 1/f -type low frequency noise 7 and the spectral power law f Ϫ␦ . 8,9 Figure 7 shows the loglog plots of the power spectra obtained from the time series shown in Fig. 4.…”

Section: Resultsmentioning

confidence: 99%

“…In order to get rid of the effect of the noise, we perform the mathematical analysis of the idealized signals following the simplified theory. 7,9 When each value of the data points is smaller ͑or larger͒ than ͉I͉, the data points are converted into a train of zero ͑or size unity͒. Here, ͉I͉ is the average amplitude of signals in the case of absence of the bursts.…”

Section: Resultsmentioning

confidence: 99%

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Observation of type-1 intermittency caused by current-driven ion acoustic instability

et al. 1998

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Intermittent chaotic phenomena caused by the current-driven ion acoustic instability are experimentally observed using a Double Plasma device, in which two mesh grids are installed to excite the instability. When a dc potential is applied to one of the two mesh grids and exceeds a certain threshold, the system suddenly transits from a periodic state to a chaotic state. At the same time, the signals picked up as perturbation components of a current exhibit intermittent turbulent bursts. The calculations of the correlation dimension and the Lyapunov exponent indicate that the system reaches a chaotic state. Furthermore, it is found that the results of mathematical and statistical analysis of observed signals agree with the theoretical properties of the type-1 intermittency: the occurrence of 1/f-type low-frequency noise and the probability distribution of the duration between two bursts. Therefore, it is concluded that the present system reaches a chaotic state via the type-1 intermittency.

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Section: Resultsmentioning

confidence: 99%

Section: Resultsmentioning

confidence: 99%

Observation of type-1 intermittency caused by current-driven ion acoustic instability

et al. 1998

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“…In the case of vector linear Langevin equation, the fluctuationdissipation theorem 29,30 ͑FDT͒ can be utilized to infer the system parameters even when noise sources are mutually correlated. In spite of the vector linear Langevin equation, the general theory of FDT for vector nonlinear Langevin equations is not known.…”

Section: Introductionmentioning

confidence: 99%

Maximum likelihood estimators for generalized Cauchy processes

Konno

Watanabe

2007

Journal of Mathematical Physics

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Maximum likelihood estimator ͑MLE͒ for a generalized Cauchy process ͑GCP͒ is studied with the aid of the method of information geometry in statistics. Our GCP is described by the Langevin equation with multiplicative and additive noises. The exact expressions of MLEs are given for the two cases that the two types of noises are uncorrelated and mutually correlated. It is shown that the MLEs for these two GCPs are free from divergence even in the parameter region wherein the ordinary moments diverge. The MLE relations can be regarded as a generalized fluctuationdissipation theorem for the present Langevin equation. Availability of them and of some other higher order statistics is demonstrated theoretically and numerically.

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“…There is a second postulated relation between Lyapunov exponents and dimension due to Mori (1980). 10.3.29) where m 0 and m + are the number of zero and positive exponents respectively, and λ ± is the mean value of the positive or negative exponents (depending upon the superscript).…”

Section: Lyapunov Dimensionmentioning

confidence: 99%

Conservation Equations

2015

Analytical Fluid Dynamics, Third Edition

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H-Quantum and an Integral Lorentz Transformation

Cited by 60 publications

References 0 publications

Observation of type-1 intermittency caused by current-driven ion acoustic instability

Observation of type-1 intermittency caused by current-driven ion acoustic instability

Maximum likelihood estimators for generalized Cauchy processes

Conservation Equations

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