The fluctuation theorem. (Shot effect)

Campbell, Norman R.

doi:10.1017/s0305004100020818

Cited by 4 publications

(4 citation statements)

References 6 publications

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“…For large values of n, n ≫ 1, that is when a large number of shots occur during each decay timescale, one can make use of the asymptotic formulation known as Campbell's Theorem (Campbell 1909a(Campbell , 1909b). Campbell's Theorem states that for n ≫ 1 the distribution asymptotically approaches that of a Gaussian or normal distribution with mean…”

Section: Appendix A: Application Of Shot Noise To Accretion Onto Whitmentioning

confidence: 99%

Stochastic accretion of planetesimals on to white dwarfs: constraints on the mass distribution of accreted material from atmospheric pollution

Wyatt¹,

Farihi²,

Pringle³

et al. 2014

Monthly Notices of the Royal Astronomical Society

134

172

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This paper explores how the stochastic accretion of planetesimals onto white dwarfs would be manifested in observations of their atmospheric pollution. Archival observations of pollution levels for unbiased samples of DA and non-DA white dwarfs are used to derive the distribution of inferred accretion rates, confirming that rates become systematically lower as sinking time (assumed here to be dominated by gravitational settling) is decreased, with no discernable dependence on cooling age. The accretion rates expected from planetesimals that are all the same mass (i.e., a mono-mass distribution) are explored both analytically and using a Monte Carlo model, quantifying how measured accretion rates inevitably depend on sinking time, since different sinking times probe different times since the last accretion event. However, that dependence is so dramatic that a mono-mass distribution can be excluded within the context of this model. Consideration of accretion from a broad distribution of planetesimal masses uncovers an important conceptual difference: accretion is continuous (rather than stochastic) for planetesimals below a certain mass, and the accretion of such planetesimals determines the rate typically inferred from observations; smaller planetesimals dominate the rates for shorter sinking times. A reasonable fit to the observationally inferred accretion rate distributions is found with model parameters consistent with a collisionally evolved mass distribution up to Pluto-mass, and an underlying accretion rate distribution consistent with that expected from descendants of debris discs of main sequence A stars. With these parameters, while both DA and non-DA white dwarfs accrete from the same broad planetesimal distribution, this model predicts that the pollution seen in DAs is dominated by the continuous accretion of < 35 km objects, and that in non-DAs by > 35 km objects (though the dominant size varies between stars by around an order of magnitude from this reference value). Further observations that characterise the dependence of inferred accretion rates on sinking time and cooling age (including a consideration of the effect of thermohaline convection on models used to derive those rates), and the decadal variability of DA accretion signatures, will improve constraints on the mass distribution of accreted material and the lifetime of the disc through which it is accreted.

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Section: Appendix A: Application Of Shot Noise To Accretion Onto Whitmentioning

confidence: 99%

Stochastic accretion of planetesimals on to white dwarfs: constraints on the mass distribution of accreted material from atmospheric pollution

Wyatt¹,

Farihi²,

Pringle³

et al. 2014

Monthly Notices of the Royal Astronomical Society

134

172

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show abstract

“…The number of pulses or structures in any given record can not exceed N , m  t º D and it can not be argued that a limiting case exists with , m  ¥ resulting in a Gaussian probability density. In the process proposed by, for instance, Campbell [40,41], structures are allowed to overlap and a Gaussian process results by the central limit theorem [38,39] when the number of overlapping structures increases on average as . m  ¥ The Gaussian limit is not reached for large structure densities with models like ours where structures do not overlap.…”

Section: Simple Model Based On Coherent Structuresmentioning

confidence: 99%

“…Here we will refer to the Rice model [39,49,50] that has been used often. Elements of these ideas were presented before [40,41,51].…”

Section: Appendix Analytical Models For Synthetic Datamentioning

confidence: 99%

Models for the probability densities of the turbulent plasma flux in magnetized plasmas

et al. 2015

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Observations of turbulent transport in magnetized plasmas indicate that plasma losses can be due to coherent structures or bursts of plasma rather than a classical random walk or diffusion process. A model for synthetic data based on coherent plasma flux events is proposed, where all basic properties can be obtained analytically in terms of a few control parameters. One basic parameter in the present case is the density of burst events in a long time-record, together with parameters in a model of the individual pulse shapes and the statistical distribution of these parameters. The model and its extensions give the probability density of the plasma flux. An interesting property of the model is a prediction of a near-parabolic relation between skewness and kurtosis of the statistical flux distribution for a wide range of parameters. The model is generalized by allowing for an additive random noise component. When this noise dominates the signal we can find a transition to standard results for Gaussian random noise. Applications of the model are illustrated by data from the toroidal Blaamann plasma.

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“…Consider a stochastic process given by the super-position of a random sequence of K pulses in a time interval of duration T , [13][14][15][16][17][18][19][20]…”

mentioning

confidence: 99%

Power law spectra and intermittent fluctuations due to uncorrelated Lorentzian pulses

Garcia

Theodorsen

2017

Physics of Plasmas

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A stochastic model for intermittent fluctuations due to a super-position of uncorrelated Lorentzian pulses is presented. For constant pulse duration, this is shown to result in an exponential power spectral density for the stationary process. A random distribution of pulse durations modifies the frequency spectrum and several examples are shown to result in power law spectra. The distribution of pulse durations does not influence the characteristic function and thus neither the moments nor the probability density function for the random variable. It is demonstrated that the fluctuations are intrinsically intermittent through a large excess kurtosis moment in the limit of weak pulse overlap. These results allow to estimate the basic properties of fluctuations from measurement data and describe the diversity of frequency spectra reported from measurements in magnetized plasmas.

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The fluctuation theorem. (Shot effect)

Cited by 4 publications

References 6 publications

Stochastic accretion of planetesimals on to white dwarfs: constraints on the mass distribution of accreted material from atmospheric pollution

Stochastic accretion of planetesimals on to white dwarfs: constraints on the mass distribution of accreted material from atmospheric pollution

Models for the probability densities of the turbulent plasma flux in magnetized plasmas

Power law spectra and intermittent fluctuations due to uncorrelated Lorentzian pulses

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