The mean electromotive force generated by elliptic instability

2012 ◽  
Vol 707 ◽  
pp. 111-128 ◽  
Author(s):  
K. A. Mizerski ◽  
K. Bajer ◽  
H. K. Moffatt
Keyword(s):  
Electromotive Force ◽  
Analytical Techniques ◽  
Accretion Discs ◽  
Dynamo Action ◽  
Flow Models ◽  
Euler Flow ◽  
Resonant Instability ◽  
Astrophysical Objects ◽  
The Mean ◽  
Tidal Deformations

AbstractThe mean electromotive force (EMF) associated with exponentially growing perturbations of an Euler flow with elliptic streamlines in a rotating frame of reference is studied. We are motivated by the possibility of dynamo action triggered by tidal deformation of astrophysical objects such as accretion discs, stars or planets. Ellipticity of the flow models such tidal deformations in the simplest way. Using analytical techniques developed by Lebovitz & Zweibel (Astrophys. J., vol. 609, 2004, pp. 301–312) in the limit of small elliptic (tidal) deformations, we find the EMF associated with each resonant instability described by Mizerski & Bajer (J. Fluid Mech., vol. 632, 2009, pp. 401–430), and for arbitrary ellipticity the EMF associated with unstable horizontal modes. Mixed resonance between unstable hydrodynamic and magnetic modes and resonance between unstable and oscillatory horizontal modes both lead to a non-vanishing mean EMF which grows exponentially in time. The essential conclusion is that interactions between unstable eigenmodes with the same wave-vector $\mathbi{k}$ can lead to a non-vanishing mean EMF, without any need for viscous or magnetic dissipation. This applies generally (and not only to the elliptic instabilities considered here).

The magnetoelliptic instability of rotating systems

2009 ◽  
Vol 632 ◽  
pp. 401-430 ◽  
Author(s):  
K. A. MIZERSKI ◽  
K. BAJER
Keyword(s):  
Magnetic Field ◽  
External Magnetic Field ◽  
Gravitational Interaction ◽  
Joint Effect ◽  
Flow Models ◽  
Analytical Technique ◽  
Rotating Systems ◽  
Astrophysical Objects ◽  
Tidal Deformations ◽  
The Magnetic Field

We address the question of stability of the Euler flow with elliptical streamlines in a rotating frame, interacting with uniform external magnetic field perpendicular to the plane of the flow. Our motivation for this study is of astrophysical nature, since many astrophysical objects, such as stars, planets and accretion discs, are tidally deformed through gravitational interaction with other bodies. Therefore, the ellipticity of the flow models the tidal deformations in the simplest way. The joint effect of the magnetic field and the Coriolis force is studied here numerically and analytically in the limit of small elliptical (tidal) deformations (ζ ≪ 1), using the analytical technique developed by Lebovitz & Zweibel (Astrophys. J., vol. 609, 2004, pp. 301–312). We find that the effect of background rotation and external magnetic field is quite complex. Both factors are responsible for new destabilizing resonances as the vortex departs from axial symmetry (ζ ≪ 1); however, just like in the non-rotating case, there are three principal resonances causing instability in the leading order. The presence of the magnetic field is very likely to destabilize the system with respect to perturbations propagating in the direction of the magnetic field if the basic vorticity and the background rotation have opposite signs (i.e. for anticyclonic background rotation). We present the dependence of the growth rates of the modes on various parameters describing the system, such as the strength of the magnetic field (h), the inverse of the Rossby number (ℛv), the ellipticity of the basic flow (ϵ) and the direction of propagation of modes (ϑ). Our analytical predictions agree well with the numerical calculations.

scholarly journals No-z Model for Magnetic Fields of Different Astrophysical Objects and Stability of the Solutions

Data ◽  
2021 ◽  
Vol 6 (1) ◽  
pp. 4
Author(s):  
Evgeny Mikhailov ◽  
Daniela Boneva ◽  
Maria Pashentseva
Keyword(s):  
Magnetic Field ◽  
Magnetic Fields ◽  
Large Scale ◽  
Point Of View ◽  
Accretion Discs ◽  
Wide Range ◽  
Astrophysical Objects ◽  
Alpha Effect ◽  
The Stability ◽  
The Magnetic Field

A wide range of astrophysical objects, such as the Sun, galaxies, stars, planets, accretion discs etc., have large-scale magnetic fields. Their generation is often based on the dynamo mechanism, which is connected with joint action of the alpha-effect and differential rotation. They compete with the turbulent diffusion. If the dynamo is intensive enough, the magnetic field grows, else it decays. The magnetic field evolution is described by Steenbeck—Krause—Raedler equations, which are quite difficult to be solved. So, for different objects, specific two-dimensional models are used. As for thin discs (this shape corresponds to galaxies and accretion discs), usually, no-z approximation is used. Some of the partial derivatives are changed by the algebraic expressions, and the solenoidality condition is taken into account as well. The field generation is restricted by the equipartition value and saturates if the field becomes comparable with it. From the point of view of mathematical physics, they can be characterized as stable points of the equations. The field can come to these values monotonously or have oscillations. It depends on the type of the stability of these points, whether it is a node or focus. Here, we study the stability of such points and give examples for astrophysical applications.

Submicron tip breakage and silanization control improve ion-selective microelectrodes

1985 ◽  
Vol 249 (5) ◽  
pp. C514-C521 ◽  
Author(s):  
S. Tripathi ◽  
N. Morgunov ◽  
E. L. Boulpaep
Keyword(s):  
Electromotive Force ◽  
Contact Angles ◽  
Ambystoma Tigrinum ◽  
Glass Wall ◽  
Solution Interface ◽  
Intracellular Na Activity ◽  
Electrode Resistance ◽  
The Mean ◽  
Liquid Ion Exchanger ◽  
Causes Of Failure

Probable causes of failure of otherwise well-constructed liquid ion-exchanger (LIE) micro-electrodes of average tip size less than 0.15 micron were examined. The problem could be attributed to two major variables, both localized at the tip: partial tip occlusion during fabrication prevents the generation of an electromotive force (small or absent slope and/or selectivity, high resistance); or poor hydrophobicity of the tip permits water to displace the resin from the tip (small or absent slope and/or selectivity and low electrode resistance). Controlled dry tip breakage on paper coated with glassine to final tip sizes well below 0.5 micron (confirmed by scanning electron microscopy) improves the yield of usable electrodes severalfold. Adequate silanization of the tip and consequent retention of resin at the tip can be predicted from the contact angles observed at the glass-LIE-backfilling solution interface. Satisfactory silanization can be achieved despite high ambient humidity. No evidence of shunting of Na+-LIE microelectrodes by the glass wall was seen. In the isolated perfused proximal tubule of Ambystoma tigrinum, the mean intracellular Na+ activity recorded by broken-tip electrodes (13.7 +/- 1.9 meq, n = 4) was similar to that recorded by intact electrodes (15.5 +/- 1.1 meq, n = 31).

scholarly journals Effect of fluctuations on mean-field dynamos

2018 ◽  
Vol 84 (4) ◽  
Author(s):  
A. Alexakis ◽  
S. Fauve ◽  
C. Gissinger ◽  
F. Pétrélis
Keyword(s):  
Turbulent Flows ◽  
Mean Field ◽  
Liquid Sodium ◽  
Mean Flow ◽  
Dynamo Action ◽  
Scale Separation ◽  
Turbulent Fluctuations ◽  
The Mean ◽  
The One ◽  
The Magnetic Field

We discuss the effect of different types of fluctuations on dynamos generated in the limit of scale separation. We first recall that the magnetic field observed in the VKS (von Karman flow of liquid sodium) experiment is not the one that would be generated by the mean flow alone and that smaller scale turbulent fluctuations therefore play an important role. We then consider how velocity fluctuations affect the dynamo threshold in the framework of mean-field magnetohydrodynamics. We show that the detrimental effect of turbulent fluctuations observed with many flows disappears in the case of helical flows with scale separation. We also find that fluctuations of the electrical conductivity of the fluid, for instance related to temperature fluctuations in convective flows, provide an efficient mechanism for dynamo action. Finally, we conclude by describing an experimental configuration that could be used to test the validity of mean-field magnetohydrodynamics in strongly turbulent flows.

scholarly journals Large-scale dynamos in rapidly rotating plane layer convection

2018 ◽  
Vol 612 ◽  
pp. A97 ◽  
Author(s):  
P. J. Bushby ◽  
P. J. Käpylä ◽  
Y. Masada ◽  
A. Brandenburg ◽  
B. Favier ◽  
...  
Keyword(s):  
Magnetic Field ◽  
Large Scale ◽  
Plane Layer ◽  
Cycle Period ◽  
Dynamo Action ◽  
Horizontal Magnetic Field ◽  
Vortex Instability ◽  
Large Scale Vortex ◽  
The Mean ◽  
The Magnetic Field

Context.Convectively driven flows play a crucial role in the dynamo processes that are responsible for producing magnetic activity in stars and planets. It is still not fully understood why many astrophysical magnetic fields have a significant large-scale component.Aims.Our aim is to investigate the dynamo properties of compressible convection in a rapidly rotating Cartesian domain, focusing upon a parameter regime in which the underlying hydrodynamic flow is known to be unstable to a large-scale vortex instability.Methods.The governing equations of three-dimensional non-linear magnetohydrodynamics (MHD) are solved numerically. Different numerical schemes are compared and we propose a possible benchmark case for other similar codes.Results.In keeping with previous related studies, we find that convection in this parameter regime can drive a large-scale dynamo. The components of the mean horizontal magnetic field oscillate, leading to a continuous overall rotation of the mean field. Whilst the large-scale vortex instability dominates the early evolution of the system, the large-scale vortex is suppressed by the magnetic field and makes a negligible contribution to the mean electromotive force that is responsible for driving the large-scale dynamo. The cycle period of the dynamo is comparable to the ohmic decay time, with longer cycles for dynamos in convective systems that are closer to onset. In these particular simulations, large-scale dynamo action is found only when vertical magnetic field boundary conditions are adopted at the upper and lower boundaries. Strongly modulated large-scale dynamos are found at higher Rayleigh numbers, with periods of reduced activity (grand minima-like events) occurring during transient phases in which the large-scale vortex temporarily re-establishes itself, before being suppressed again by the magnetic field.

scholarly journals Molecular Encapsulation of Herbicide Terbuthylazine in Native and Modifiedβ-Cyclodextrin

2017 ◽  
Vol 2017 ◽  
pp. 1-9 ◽  
Author(s):  
E. Manuela Garrido ◽  
Daniela Rodrigues ◽  
Nuno Milhazes ◽  
Fernanda Borges ◽  
Jorge Garrido
Keyword(s):  
Water Solubility ◽  
Analytical Techniques ◽  
Aqueous Solubility ◽  
Mean Values ◽  
H Nmr ◽  
Nmr Data ◽  
Kneading Method ◽  
Other Substances ◽  
The Mean ◽  
The Stability

The herbicide terbuthylazine (TBA) is widely used for preemergence or postemergence control of many grass and broadleaf weeds and has, besides other issues, a poor aqueous solubility profile that results in reduced bioavailability. Cyclodextrins and modified cyclodextrins were considered, among other substances, appropriate agents for improving pesticide water solubility. Therefore, the inclusion complex formation of terbuthylazine withβ-cyclodextrin (β-CD) and hydroxypropyl-β-cyclodextrin (HP-β-CD) was studied to attain its aqueous solubility enhancement. Their characterization was accomplished with different analytical techniques, namely, by UV-Vis, DSC, FTIR, and1H NMR. From the analysis of the complexation performance of the herbicide it was concluded that the interaction of terbuthylazine with CDs leads to the formation of inclusion complexes with a stoichiometry of 1 : 1. The association constants of the TBA/β-CD and TBA/HP-β-CD complexes were determined by UV. The mean values obtained for the stability constants are 460.4 ± 26.5 and 532.1 ± 27.6 to TBA/β-CD and TBA/HP-β-CD, respectively.1H NMR data corroborate the formation of the TBA/β-CD and TBA/HP-β-CD complexes synthesized by the kneading method. A formulation incorporating TBA cyclodextrin complexes might lead to an improvement in terbuthylazine bioavailability. The development of TBA-CD formulations may be interesting since it would enable, through their inclusion into the hydrophobic cavity of CDs, enhancement of solubility, bioavailability, and stability of the herbicide.

ON CLIMBING TRIES

2007 ◽  
Vol 22 (1) ◽  
pp. 133-149 ◽  
Author(s):  
Costas Christophi ◽  
Hosam Mahmoud
Keyword(s):  
Limit Distribution ◽  
Mellin Transform ◽  
Analytical Techniques ◽  
Accurate Calculation ◽  
Random Choice ◽  
The Mean

To sample a typical key in a “trie,” an appropriate climbing might consider generating random edges in the same manner as the data are generated. In the absence of the probability generating the keys, an uninformed random choice among the children still provides an alternative. We are also interested in extremal sampling, achieved by following a leftmost (or a rightmost) path. Each of these climbing strategies always generates a key, but one that might not necessarily be in the database. We investigate the altitude of the position at which climbing is terminated. Analytical techniques, including poissonization and the Mellin transform, are used for the accurate calculation of moments. In all strategies, the mean is always logarithmic. For typical and uninformed climbing, the variance is bounded in unbiased tries but grows logarithmically in biased tries. Consequently, in the biased case, one can find appropriate centering and scaling to produce a limit distribution for these two climbing strategies; the limit is normal. For extremal climbing, the variance is always bounded for both biased and unbiased cases, and no nontrivial limit exists under any scaling.

RANDOM WALKS ON KEBAB LATTICES: LOGARITHMIC DIFFUSION ON ORDERED STRUCTURES

1995 ◽  
Vol 09 (10) ◽  
pp. 601-606 ◽  
Author(s):  
D. CASSI ◽  
S. REGINA
Keyword(s):  
Random Walks ◽  
Linear Chain ◽  
Mean Square Displacement ◽  
Analytical Techniques ◽  
Mean Square ◽  
Ordered Structure ◽  
Ordered Structures ◽  
Asymptotic Expressions ◽  
Long Time ◽  
The Mean

Kebab lattices are ordered lattices obtained matching an infinite two-dimensional lattice to each point of a linear chain. Discrete time random walks on these structures are studied by analytical techniques. The exact asymptotic expressions of the mean square displacement and of the RW Green functions show an unexpected logarithmic behavior that is the first example of such kind of law on an ordered structure. Moreover the probability of returning to the origin shows the fastest long time decay ever found for recursive random walks.

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