Fractional Lévy motion and its application to network traffic modeling

Laskin, Nick; Lambadatis, I.; Harmantzis, Fotios C.; Devetsikiotis, Michael

doi:10.1016/s1389-1286(02)00300-6

Cited by 69 publications

(44 citation statements)

References 13 publications

(2 reference statements)

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“…Because of this algebraic decay, they have an infinite variance so that the characteristic velocity V c , which still existed for fBm, can no longer be defined. The fLm propagator can also be computed analytically, 38,39 the result being ͑L ␣ ͓x͔ is a symmetric Lévy law of index ␣ and scale factor unity͒…”

Section: -5mentioning

confidence: 99%

On the nature of radial transport across sheared zonal flows in electrostatic ion-temperature-gradient gyrokinetic tokamak plasma turbulence

Sánchez¹,

Newman²,

Leboeuf³

et al. 2009

Physics of Plasmas

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It is argued that the usual understanding of the suppression of radial turbulent transport across a sheared zonal flow based on a reduction in effective transport coefficients is, by itself, incomplete. By means of toroidal gyrokinetic simulations of electrostatic, ion-temperature-gradient turbulence, it is found instead that the character of the radial transport is altered fundamentally by the presence of a sheared zonal flow, changing from diffusive to anticorrelated and subdiffusive. Furthermore, if the flows are self-consistently driven by the turbulence via the Reynolds stresses ͑in contrast to being induced externally͒, radial transport becomes non-Gaussian as well. These results warrant a reevaluation of the traditional description of radial transport across sheared flows in tokamaks via effective transport coefficients, suggesting that such description is oversimplified and poorly captures the underlying dynamics, which may in turn compromise its predictive capabilities.

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Section: -5mentioning

confidence: 99%

On the nature of radial transport across sheared zonal flows in electrostatic ion-temperature-gradient gyrokinetic tokamak plasma turbulence

Sánchez¹,

Newman²,

Leboeuf³

et al. 2009

Physics of Plasmas

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“…But in contrast to it, the successive increments dxðtÞ : ¼ xðt þ dtÞ À xðtÞ are correlated in time so that no finite typical time scale exists if H Þ 1=2. The fBm propagator can be found to be [15]:…”

mentioning

confidence: 99%

“…In contrast, the finite variance of the Gaussian sets a finite typical length scale l 2 / 2 . The fLm propagator is [15] (L ½x is a symmetric Lévy law of index and scale factor unity):…”

mentioning

confidence: 99%

Nature of Transport across Sheared Zonal Flows in Electrostatic Ion-Temperature-Gradient Gyrokinetic Plasma Turbulence

Sánchez

Newman

Leboeuf³

et al. 2008

Phys. Rev. Lett.

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It is shown that the usual picture for the suppression of turbulent transport across a stable sheared flow based on a reduction of diffusive transport coefficients is, by itself, incomplete. By means of toroidal gyrokinetic simulations of electrostatic, collisionless ion-temperature-gradient turbulence, it is found that the nature of the transport is altered fundamentally, changing from diffusive to anticorrelated and subdiffusive. Additionally, whenever the flows are self-consistently driven by turbulence, the transport gains an additional non-Gaussian character. These results suggest that a description of transport across sheared flows using effective diffusivities is oversimplified. It is widely accepted that the rate of the transport (of particles, energy, or any other quantity) carried out by turbulence can be significantly lowered by a perpendicular sheared flow [1]. Since these flows are intrinsically unstable against Kelvin-Helmholz instabilities, their sustainment requires additional stabilizing mechanisms, such as a magnetic field or rotation. These additional mechanisms also introduce waves, which can help drive the flows via the turbulent Reynolds stresses. For instance, drift waves may drive poloidal or toroidal (zonal) sheared flows in tokamak plasmas [2]. These zonal flows are central to the formation of the radial transport barriers characteristic of the enhanced regimes [3] in which the future International Thermonuclear Experimental Reactor tokamak will operate [4]. In atmospheric and oceanic flows, Rossby waves, driven by the change in rotation rate around the local vertical axis with latitude, play an analogous role [5]. The turbulent flux across the flow,À ? ¼ hsṽ ? i (wheres is the advected quantity) can decrease due to a reduction in either the amplitude or the self-coherence of the turbulence [6], or to a shift in the phase between advected and advecting fields [7]. Importantly, the investigation (and modeling) of these various possibilities has traditionally been done by assuming from the start that some effective diffusivity characterizes transport in the absence of the flow, D ? $ l 2 ? = (l ? and being typical transport scales), which is then reduced (via changes in l ? and/or ) by the action of the sheared flow. Note, however, that the nature of transport across the flow must be and remain diffusive for this notion to be applicable. More precisely, this means that the dynamics must be and remain Gaussian and Markovian, so that a finite length l ? and time exist. Otherwise, any description based on these ideas would provide an incomplete, even misleading, explanation. In this Letter we report on the first numerical evidence which suggests that the diffusive assumption is invalid in the presence of sheared zonal flows, driven either self-consistently by turbulence or externally, in magnetically confined toroidal plasmas. In particular, our simulations show that transport across them is subdiffusive for a large range of scales beyond the turbulent decorrelation time. Furthermore, the tr...

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“…And, there has been a recent flood of literature and discussion on the tail behavior of queue-length distribution, motivated by potential applications to the design and control by high-speed telecommunication networks( [1], [2], [3]). …”

Section: Introductionmentioning

confidence: 99%