Bose-Einstein condensation (BEC) has been observed in a dilute gas of sodium atoms. A Bose-Einstein condensate consists of a macroscopic population of the ground state of the system, and is a coherent state of matter. In an ideal gas, this phase transition is purely quantum-statistical. The study of BEC in weakly interacting systems which can be controlled and observed with precision holds the promise of revealing new macroscopic quantum phenomena that can be understood from first principles.

Bose-Einstein condensation in a gas of sodium atoms

Annual review of condensed matter physics

A comprehensive review of zonal flow phenomena in plasmas is presented. While the emphasis is on zonal flows in laboratory plasmas, planetary zonal flows are discussed as well. The review presents the status of theory, numerical simulation and experiments relevant to zonal flows. The emphasis is on developing an integrated understanding of the dynamics of drift wave–zonal flow turbulence by combining detailed studies of the generation of zonal flows by drift waves, the back-interaction of zonal flows on the drift waves, and the various feedback loops by which the system regulates and organizes itself. The implications of zonal flow phenomena for confinement in, and the phenomena of fusion devices are discussed. Special attention is given to the comparison of experiment with theory and to identifying directions for progress in future research.

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Zonal flows in plasma—a review

Astrophysical magnetic fields and nonlinear dynamo theory

Advanced Mathematical Methods for Scientists and Engineers

We derive a weak turbulence formalism for incompressible magnetohy- drodynamics. Three-wave interactions lead to a system of kinetic equations for the spectral densities of energy and helicity. The kinetic equations conserve energy in all wavevector planes normal to the applied magnetic eld B0 ^k. Numerically and analytically, we nd energy spectra E k n ? , such that n+ +n = 4, where E are the spectra of the Elsvariables z = v b in the two-dimensional case (kk = 0). The constants of the spectra are computed exactly and found to depend on the amount of correlation between the velocity and the magnetic eld. Comparison with several numerical simulations and models is also made.

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A weak turbulence theory for incompressible magnetohydrodynamics

In this paper we review recent developments in the statistical theory of weakly nonlinear dispersive waves, the subject known as Wave Turbulence (WT) We revise WT theory using a generalisation of the random phase approximation (RPA) This generalisation takes into account that not only the phases but also the amplitudes of the wave Fourier modes are random quantities and it is called the ``Random Phase and Amplitude'' approach This approach allows to systematically derive the kinetic equation for the energy spectrum from the the Peierls-Brout-Prigogine (PBP) equation for the multi-mode probability density function (PDF) The PBP equation was originally derived for the three-wave systems and in the present paper we derive a similar equation for the four-wave case Equation for the multi-mode PDF will be used to validate the statistical assumptions about the phase and the amplitude randomness used for WT closures Further, the multi-mode PDF contains a detailed statistical information, beyond spectra, and it finally allows to study non-Gaussianity and intermittency in WT, as it will be described in the present paper In particular, we will show that intermittency of stochastic nonlinear waves is related to a flux of probability in the space of wave amplitudes

Wave Turbulence

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Wave turbulence and intermittency

Weak turbulence of shear-Alfven waves is considered in the limit of strongly anisotropic pulsations that are elongated along the external magnetic field. The kinetic equation thus derived agrees with the Galtier et al. formulation of the full three-dimensional helical case when taking the proper limit. This new approach allows for significant simplification, and, as a result, the applicability conditions for the weak turbulence theory are now more transparent. It thus provides an attractive theoretical framework for describing anisotropic MHD turbulence in astrophysical contexts where a strong magnetic field is present and for which shear-Alfven waves are important.

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Anisotropic turbulence of shear-Alfven waves

Numerical simulations are used to determine the influence of the nonlocal and local interactions on the intermittency corrections in the scaling properties of three-dimensional turbulence. We show that neglect of local interactions leads to an enhanced small-scale energy spectrum and to a significantly larger number of very intense vortices (“tornadoes”) and stronger intermittency (e.g., wider tails in the probability distribution functions of velocity increments and greater anomalous corrections). On the other hand, neglect of the nonlocal interactions results in even stronger small-scale spectrum but significantly weaker intermittency. Thus, the amount of intermittency is not determined just by the mean intensity of the small scales, but it is nontrivially shaped by the nature of the scale interactions. Namely, the role of the nonlocal interactions is to generate intense vortices responsible for intermittency and the role of the local interactions is to dissipate them. Based on these observations, a new...

Sergey Nazarenko

Papers

A weak turbulence theory for incompressible magnetohydrodynamics

Wave Turbulence

Wave turbulence and intermittency

Anisotropic turbulence of shear-Alfven waves

Nonlocality and intermittency in three-dimensional turbulence