On modelling physical systems with stochastic models: diffusion versus Lévy processes

Penland, Cécile; Ewald, Brian D.

doi:10.1098/rsta.2008.0051

Cited by 30 publications

(24 citation statements)

References 50 publications

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“…I suggest collaboration with theoretical chemists and statistical physicists to perform molecular dynamics calculations of sample air parcels, now possible for populations of order 10 11 molecules. Penland and Ewald (2008) is an example, although not explicitly molecularly based. If scale invariance can be simulated, there will be a way forward for parametrization by upscaling, guided by the scaling of observations reported above.…”

Section: Discussion and Summarymentioning

confidence: 99%

From molecules to meteorology via turbulent scale invariance

Tuck

2010

Quart J Royal Meteoro Soc

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This review attempts to interpret the generalized scale invariance observed in common atmospheric variables -wind, temperature, humidity, ozone and some trace species -in terms of the computed emergence of ring currents (vortices) in simulations of populations of Maxwellian molecules subject to an anisotropy in the form of a flux. The data are taken from 'horizontal' tracks of research aircraft and from 'vertical' trajectories of research dropsondes. It is argued that any attempt to represent the energy distribution in the atmosphere quantitatively must have a proper basis in molecular physics, a prerequisite to accommodate the observed longtailed velocity probability distributions and the implied effects on radiative transfer, atmospheric chemistry, turbulent structure and the definition of temperature itself. The relationship between fluctuations and dissipation is discussed in a framework of non-equilibrium statistical mechanics, and a link between maximization of entropy production and scale invariance is hypothesized.

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Section: Discussion and Summarymentioning

confidence: 99%

From molecules to meteorology via turbulent scale invariance

Tuck

2010

Quart J Royal Meteoro Soc

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“…The PDF of ambient noise is compared with Gaussian and a-stable Levy distribution 63 as shown in Fig. 3.…”

Section: B Ambient Noise Variabilitymentioning

confidence: 99%

“…This form of variability suggests that ambient noise systems may be represented as stable levy processes 63 or through a stochastically forced nonlinear model with correlated additive and multiplicative noise whose components experience damping at disparate rates 64,65 which can be used to represent skewed and heavy-tailed distributions. In the following sections, a detailed nonlinear dynamical analysis of ambient noise to verify the underlying dynamics is carried out.…”

Section: B Ambient Noise Variabilitymentioning

confidence: 99%

On the dynamics of ocean ambient noise: Two decades later

Siddagangaiah

Guo

et al. 2015

Chaos: An Interdisciplinary Journal of Nonlinear Science

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Two decades ago, it was shown that ambient noise exhibits low dimensional chaotic behavior. Recent new techniques in nonlinear science can effectively detect the underlying dynamics in noisy time series. In this paper, the presence of low dimensional deterministic dynamics in ambient noise is investigated using diverse nonlinear techniques, including correlation dimension, Lyapunov exponent, nonlinear prediction, and entropy based methods. The consistent interpretation of different methods demonstrates that ambient noise can be best modeled as nonlinear stochastic dynamics, thus rejecting the hypothesis of low dimensional chaotic behavior. The ambient noise data utilized in this study are of duration 60 s measured at South China Sea.

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“…On the other hand, elements such as the redness of the spectra and the deviation from the Gaussian tails for all the variables suggest that other processes, such as stable Levy processes (e.g., Penland and Ewald 2008), might be a possible representation of the system. Further work is required to determine the presence of multifractal structures and the correct statistical representation of the variability.…”

Section: Discussionmentioning

confidence: 99%

A Search for Chaotic Behavior in Northern Hemisphere Stratospheric Variability

Badin

Domeisen

2014

Journal of the Atmospheric Sciences

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Northern Hemisphere stratospheric variability is investigated with respect to chaotic behavior using time series from three different variables extracted from four different reanalysis products and two numerical model runs with different forcing. The time series show red spectra at all frequencies and the probability distribution functions show persistent deviations from a Gaussian distribution. An exception is given by the numerical model forced with perpetual winter conditions-a case that shows more variability and follows a Gaussian distribution, suggesting that the deviation from Gaussianity found in the observations is due to the transition between summer and winter variability. To search for the presence of a chaotic attractor the correlation dimension and entropy, the Lyapunov spectrum, and the associated Kaplan-Yorke dimension are estimated. A finite value of the dimensions can be computed for each variable and data product, with the correlation dimension ranging between 3.0 and 4.0 and the Kaplan-Yorke dimension between 3.3 and 5.5. The correlation entropy varies between 0.6 and 1.1. The model runs show similar values for the correlation and Lyapunov dimensions for both the seasonally forced run and the perpetual-winter run, suggesting that the structure of a possible chaotic attractor is not determined by the seasonality in the forcing, but must be given by other mechanisms.

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On modelling physical systems with stochastic models: diffusion versus Lévy processes

Cited by 30 publications

References 50 publications

From molecules to meteorology via turbulent scale invariance

From molecules to meteorology via turbulent scale invariance

On the dynamics of ocean ambient noise: Two decades later

A Search for Chaotic Behavior in Northern Hemisphere Stratospheric Variability

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