255 research outputs found
Continuous Time Random Walks in periodic systems: fluid limit and fractional differential equations on the circle
In this article, the continuous time random walk on the circle is studied. We
derive the corresponding generalized master equation and discuss the effects of
topology, especially important when Levy flights are allowed. Then, we work out
the fluid limit equation, formulated in terms of the periodic version of the
fractional Riemann-Liouville operators, for which we provide explicit
expressions. Finally, we compute the propagator in some simple cases. The
analysis presented herein should be relevant when investigating anomalous
transport phenomena in systems with periodic dimensions.Comment: 14 pages, 1 figure. References added. Published versio
Spatiotemporal and Wavenumber Resolved Bicoherence at the Low to High Confinement Transition in the TJ-II Stellarator
Plasma turbulence is studied using Doppler reflectometry at the TJ-II
stellarator. By scanning the tilt angle of the probing beam, different values
of the perpendicular wave numbers are probed at the reflection layer. In this
way, the interaction between zonal flows and turbulence is reported with (a)
spatial, (b) temporal, and (c) wavenumber resolution for the first time in any
magnetic confinement fusion device.
We report measurements of the bicoherence across the Low to High (L--H)
confinement transition at TJ-II. We examine both fast transitions and slow
transitions characterized by an intermediate (I) phase. The bicoherence,
understood to reflect the non-linear coupling between the perpendicular
velocity (zonal flow) and turbulence amplitude, is significantly enhanced in a
time window of several tens of ms around the time of the L--H transition. It is
found to peak at a specific radial position (slightly inward from the radial
electric field shear layer in H mode), and is associated with a specific
perpendicular wave number ( cm, ). In all cases, the bicoherence is due to the interaction between
high frequencies ( MHz) and a rather low frequency (
kHz), as expected for a zonal flow.Comment: 11 pages, 3 figure
Causality detection and turbulence in fusion plasmas
This work explores the potential of an information-theoretical causality
detection method for unraveling the relation between fluctuating variables in
complex nonlinear systems. The method is tested on some simple though nonlinear
models, and guidelines for the choice of analysis parameters are established.
Then, measurements from magnetically confined fusion plasmas are analyzed. The
selected data bear relevance to the all-important spontaneous confinement
transitions often observed in fusion plasmas, fundamental for the design of an
economically attractive fusion reactor. It is shown how the present method is
capable of clarifying the interaction between fluctuating quantities such as
the turbulence amplitude, turbulent flux, and Zonal Flow amplitude, and
uncovers several interactions that were missed by traditional methods.Comment: 26 pages, 14 figure
Fractional generalization of Fick's law: a microscopic approach
In the study of transport in inhomogeneous systems it is common to construct
transport equations invoking the inhomogeneous Fick law. The validity of this
approach requires that at least two ingredients be present in the system.
First, finite characteristic length and time scales associated to the dominant
transport process must exist. Secondly, the transport mechanism must satisfy a
microscopic symmetry: global reversibility. Global reversibility is often
satisfied in nature. However, many complex systems exhibit a lack of finite
characteristic scales. In this Letter we show how to construct a generalization
of the inhomogeneous Fick law that does not require the existence of
characteristic scales while still satisfying global reversibility.Comment: 4 pages. Published versio
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