We elucidate the role of zonal flows in transient phenomena observed during $L\mathrm{\text{−}}H$ transition by studying a simple $L\mathrm{\text{−}}H$ transition model which contains the evolution of zonal flows, mean $\mathbf{E}\times \mathbf{B}$ flows, and the ion pressure gradient. Zonal flows are shown to trigger the $L\mathrm{\text{−}}H$ transition and cause time-transient behavior through the self-regulation of turbulence before a mean shearing, due to a steep pressure profile, secures a quiescent $H$ mode. Surprisingly, this self-regulation lowers the power threshold for the ultimate transition to a quiescent $H$-mode state.

We study the generation and evolution of density perturbations and peculiar velocities due to primordial magnetic fields. We assume that a random magnetic field was present before recombination and follow the field's effect on the baryon fluid starting at recombination. We find that magnetic fields generate growing density perturbations on length scales larger than the magnetic Jeans length, $\lambda_B$, and damped oscillations for scales smaller than $\lambda_B$. For small wavenumbers $k$ (large length scales), we find the magnetic field-induced density power spectrum generally scales as $k^4$. We derive the magnetic Jeans length explicitly by including the back--reaction of the velocity field onto the magnetic field by decomposing the magnetic field into a force-free background field and perturbations about it. Depending on the strength of the magnetic field and the ultraviolet cutoff of its spectrum, structure can be generated on small or intermediate scales early in the history of the universe. For a present {\it rms} magnetic field of $10^{-10}$ G on intergalactic scales, we find that perturbations on galactic scales could have gone non--linear at $z \simeq 6$. Finally, we discuss how primordial magnetic fields affect scenarios of structure formation with non--baryonic dark matter.Comment: Final version to appear ApJ, August 1996. Significant changes in the formal approach but similar conclusions. 47 pages, plain TeX, 3 figures available from olinto@fnalv.fnal.go

Significance: Cancer progression, as an evolutionary process, should accelerate if higher cellular variability is present. However, the sources of nongenetic variability in metastatic progression are largely unknown. To address this question, we characterized a transcriptional regulatory network for the metastasis suppressor Raf kinase inhibitory protein (RKIP). We previously showed that the transcription factor BACH1 is negatively regulated by RKIP and promotes breast cancer metastasis. Here we reveal a network architecture between the metastasis suppressor RKIP and the metastasis promoter BACH1 that enables single cells to generate a stable subpopulation of prometastatic cells without any genetic changes.

A simplified nonlinear dynamo model is constructed that allows the transition from the kinematic to the dynamic regime to be studied in detail. We apply this construction to a chaotic flow recently studied in the context of fast dynamo action. It is found that the structure of the magnetic field in the two regimes is markedly different. Furthermore, the saturation of the exponential growth of the magnetic field is achieved by a drastic suppression of the chaotic properties of the flow.

Generalized Kelvin–Helmholtz (GKH) instability is examined as a mechanism for the saturation of zonal flows in the collisionless regime. By focusing on strong turbulence regimes, GKH instability is analyzed in the presence of a background of finite-amplitude drift waves. A detailed study of a simple model with cold ions shows that nonlinear excitation of GKH modes via modulational instability can be comparable to their linear generation. Furthermore, it is demonstrated that zonal flows are likely to grow faster than GKH mode near marginality, with insignificant turbulent viscous damping by linear GKH. The effect of finite ion temperature fluctuations is incorporated in a simple toroidal ion temperature gradient model, within which both zonal flow and temperature are generated by modulational instability. The phase between the two is calculated self-consistently and shown to be positive. Furthermore, the correction to nonlinear generation of GKH modes appears to be small, being of order ${\mathrm{O(\rho }}_i^2{k}^2\mathrm{).}$ Thus, the role of linear GKH instability in the saturation of collisionless zonal flows, in general, seems dubious.

The dynamics of and an interplay among structures (mean shear flows, zonal flows, and generalized Kelvin–Helmholtz modes) are studied in drift wave turbulence. Mean shear flows are found to inhibit the nonlinear generation of zonal flows by weakening the coherent modulation response of the drift wave spectrum. Based on this result, a minimal model for the $\mathrm{L}\to \mathrm{H}$ (low- to high-confinement) transition is proposed, which involves the amplitude of drift waves, zonal flows, and the density gradient. A transition to quiescent H-mode sets in as the profile becomes sufficiently steep to completely damp out drift waves, following an oscillatory transition phase where zonal flows regulate drift wave turbulence. The different roles of mean flows and zonal flows are elucidated. Finally, the effect of poloidally nonaxisymmetric structures (generalized Kelvin–Helmholtz mode) on anomalous transport is investigated, especially in reference to damping of collisionless zonal flows. Results indicate that nonlinear excitation of this structure can be potentially important in enhancing anomalous transport as well as in damping zonal flows.