Nonlinear theory of a “shear-current” effect and mean-field magnetic dynamos

2004 ◽  
Vol 70 (4) ◽  
Author(s):  
Igor Rogachevskii ◽  
Nathan Kleeorin
Keyword(s):  
Nonlinear Theory ◽  
Mean Field ◽  
Current Effect ◽  
Shear Current

scholarly journals On the shear-current effect: Toward understanding why theories and simulations have mutually and separately conflicted

2021 ◽  
Author(s):  
Hongzhe Zhou ◽  
Eric G Blackman
Keyword(s):  
Spectral Index ◽  
Theoretical Calculations ◽  
Strong Dependence ◽  
Mean Field ◽  
Reynolds Numbers ◽  
Test Field ◽  
Current Effect ◽  
Dynamo Theory ◽  
Shear Current ◽  
O 10

Abstract The shear-current effect (SCE) of mean-field dynamo theory refers to the combination of a shear flow and a turbulent coefficient β21 with a favorable negative sign for exponential mean-field growth, rather than positive for diffusion. There have been long standing disagreements among theoretical calculations and comparisons of theory with numerical experiments as to the sign of kinetic ($\beta ^u_{21}$) and magnetic ($\beta ^b_{21}$) contributions. To resolve these discrepancies, we combine an analytical approach with simulations, and show that unlike $\beta ^b_{21}$, the kinetic SCE $\beta ^u_{21}$ has a strong dependence on the kinetic energy spectral index and can transit from positive to negative values at $\mathcal {O}(10)$ Reynolds numbers if the spectrum is not too steep. Conversely, $\beta ^b_{21}$ is always negative regardless of the spectral index and Reynolds numbers. For very steep energy spectra, the positive $\beta ^u_{21}$ can dominate even at energy equipartition urms ≃ brms, resulting in a positive total β21 even though $\beta ^b_{21}<0$. Our findings bridge the gap between the seemingly contradictory results from the second-order-correlation approximation (SOCA) versus the spectral-τ closure (STC), for which opposite signs for $\beta ^u_{21}$ have been reported, with the same sign for $\beta ^b_{21}<0$. The results also offer an explanation for the simulations that find $\beta ^u_{21}>0$ and an inconclusive overall sign of β21 for $\mathcal {O}(10)$ Reynolds numbers. The transient behaviour of $\beta ^u_{21}$ is demonstrated using the kinematic test-field method. We compute dynamo growth rates for cases with or without rotation, and discuss opportunities for further work.

scholarly journals The magnetic shear-current effect: generation of large-scale magnetic fields by the small-scale dynamo

2016 ◽  
Vol 82 (2) ◽  
Author(s):  
J. Squire ◽  
A. Bhattacharjee
Keyword(s):  
Shear Flow ◽  
Large Scale ◽  
Mean Field ◽  
Future Research ◽  
Small Scale ◽  
Magnetic Fluctuations ◽  
Current Effect ◽  
Magnetic Shear ◽  
Shear Current ◽  
High Reynolds

A novel large-scale dynamo mechanism, the magnetic shear-current effect, is discussed and explored. The effect relies on the interaction of magnetic fluctuations with a mean shear flow, meaning the saturated state of the small-scale dynamo can drive a large-scale dynamo – in some sense the inverse of dynamo quenching. The dynamo is non-helical, with the mean field ${\it\alpha}$ coefficient zero, and is caused by the interaction between an off-diagonal component of the turbulent resistivity and the stretching of the large-scale field by shear flow. Following up on previous numerical and analytic work, this paper presents further details of the numerical evidence for the effect, as well as an heuristic description of how magnetic fluctuations can interact with shear flow to produce the required electromotive force. The pressure response of the fluid is fundamental to this mechanism, which helps explain why the magnetic effect is stronger than its kinematic cousin, and the basic idea is related to the well-known lack of turbulent resistivity quenching by magnetic fluctuations. As well as being interesting for its applications to general high Reynolds number astrophysical turbulence, where strong small-scale magnetic fluctuations are expected to be prevalent, the magnetic shear-current effect is a likely candidate for large-scale dynamo in the unstratified regions of ionized accretion disks. Evidence for this is discussed, as well as future research directions and the challenges involved with understanding details of the effect in astrophysically relevant regimes.

Rem Study of Current Effect on the Structure of Clean Si(111) Surface

1990 ◽  
Vol 48 (1) ◽  
pp. 306-307
Author(s):  
A. Yamanaka ◽  
H. Ohse ◽  
K. Yagi
Keyword(s):  
The Other ◽  
Current Direction ◽  
Clean Surface ◽  
Current Effect ◽  
Atomic Steps ◽  
Step Bunching ◽  
Terrace Width ◽  
Step Down ◽  
A Current

Recently current effects on clean and metal adsorbate surfaces have attracted much attention not only because of interesting phenomena but also because of practically importance in treatingclean and metal adsorbate surfaces [1-6]. In the former case, metals deposited migrate on the deposit depending on the current direction and a patch of the deposit expands on the clean surface [1]. The migration is closely related to the adsorbate structures and substrate structures including their anisotropy [2,7]. In the latter case, configurations of surface atomic steps depends on the current direction. In the case of Si(001) surface equally spaced array of monatom high steps along the [110] direction produces the 2x1 and 1x2 terraces. However, a relative terrace width of the two domain depends on the current direction; a step-up current widen terraces on which dimers are parallel to the current, while a step-down current widen the other terraces [3]. On (111) surface, a step-down current produces step bunching at temperatures between 1250-1350°C, while a step-up current produces step bunching at temperatures between 1050-1250°C [5].In the present paper, our REM observations on a current induced step bunching, started independently, are described.Our results are summarized as follows.(1) Above around 1000°C a step-up current induces step bunching. The phenomenon reverses around 1200 C; a step-down current induces step bunching. The observations agree with the previous reports [5].

On closed-loop equilibrium strategies for mean-field stochastic linear quadratic problems

2020 ◽  
Vol 26 ◽  
pp. 41
Author(s):  
Tianxiao Wang
Keyword(s):  
Optimal Control ◽  
Closed Loop ◽  
Optimal Control Problems ◽  
Mean Field ◽  
Open Loop ◽  
Time Inconsistency ◽  
Control Problems ◽  
Linear Quadratic ◽  
Linear Quadratic Optimal Control ◽  
Equilibrium Strategies

This article is concerned with linear quadratic optimal control problems of mean-field stochastic differential equations (MF-SDE) with deterministic coefficients. To treat the time inconsistency of the optimal control problems, linear closed-loop equilibrium strategies are introduced and characterized by variational approach. Our developed methodology drops the delicate convergence procedures in Yong [Trans. Amer. Math. Soc. 369 (2017) 5467–5523]. When the MF-SDE reduces to SDE, our Riccati system coincides with the analogue in Yong [Trans. Amer. Math. Soc. 369 (2017) 5467–5523]. However, these two systems are in general different from each other due to the conditional mean-field terms in the MF-SDE. Eventually, the comparisons with pre-committed optimal strategies, open-loop equilibrium strategies are given in details.

Mean field theory of n-layer unbinding

1993 ◽  
Vol 3 (3) ◽  
pp. 385-393 ◽  
Author(s):  
W. Helfrich
Keyword(s):  
Field Theory ◽  
Mean Field Theory ◽  
Mean Field
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