Test-field method for mean-field coefficients with MHD background

2020 ◽

Vol 500 (3) ◽

pp. 3527-3535

Author(s):

Abhijit B Bendre ◽

Detlef Elstner ◽

Oliver Gressel

Keyword(s):

Magnetic Field ◽

Magnetic Fields ◽

Large Scale ◽

Mean Field ◽

Cosmic Ray ◽

Field Method ◽

Dynamo Model ◽

Test Field ◽

Dynamo Action ◽

Magnetohydrodynamic Simulations

ABSTRACT Large-scale coherent magnetic fields observed in the nearby galaxies are thought to originate by a mean-field dynamo. This is governed via the turbulent electromotive force (EMF, $\overline{{\boldsymbol {\cal E}} {}}$) generated by the helical turbulence driven by supernova (SN) explosions in the differentially rotating interstellar medium (ISM). In this paper, we aim to investigate the possibility of dynamo action by the virtue of buoyancy due to a cosmic ray (CR) component injected through the SN explosions. We do this by analysing the magnetohydrodynamic simulations of local shearing box of ISM in which the turbulence is driven via random SN explosions and the energy of the explosion is distributed in the CR and/or thermal energy components. We use the magnetic field aligned diffusion prescription for the propagation of CR. We compare the evolution of magnetic fields in the models with the CR component to our previous models that did not involve the CR. We demonstrate that the inclusion of CR component enhances the growth of dynamo slightly. We further compute the underlying dynamo coefficients using the test-field method and argue that the entire evolution of the large-scale mean magnetic field can be reproduced with an α − Ω dynamo model. We also show that the inclusion of CR component leads to an unbalanced turbulent pumping between magnetic field components and additional dynamo action by the Rädler effect.

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Advances in mean-field dynamo theory and applications to astrophysical turbulence

Journal of Plasma Physics ◽

10.1017/s0022377818000806 ◽

2018 ◽

Vol 84 (4) ◽

Cited By ~ 17

Author(s):

Axel Brandenburg

Keyword(s):

Magnetic Fields ◽

Early Universe ◽

Mean Field Theory ◽

Mean Field ◽

Field Method ◽

Magnetic Helicity ◽

Test Field ◽

Dynamo Theory ◽

Length Scales ◽

Recent Advances

Recent advances in mean-field theory are reviewed and applications to the Sun, late-type stars, accretion disks, galaxies and the early Universe are discussed. We focus particularly on aspects of spatio-temporal non-locality, which provided some of the main new qualitative and quantitative insights that emerged from applying the test-field method to magnetic fields of different length and time scales. We also review the status of nonlinear quenching and the relation to magnetic helicity, which is an important observational diagnostic of modern solar dynamo theory. Both solar and some stellar dynamos seem to operate in an intermediate regime that has not yet been possible to model successfully. This regime is bracketed by antisolar-like differential rotation on one end and stellar activity cycles belonging to the superactive stars on the other. The difficulty in modelling this regime may be related to shortcomings in simulating solar/stellar convection. On galactic and extragalactic length scales, the observational constraints on dynamo theory are still less stringent and more uncertain, but recent advances both in theory and observations suggest that more conclusive comparisons may soon be possible also here. The possibility of inversely cascading magnetic helicity in the early Universe is particularly exciting in explaining the recently observed lower limits of magnetic fields on cosmological length scales. Such magnetic fields may be helical with the same sign of magnetic helicity throughout the entire Universe. This would be a manifestation of parity breaking.

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Turbulent diffusion and galactic magnetism

Proceedings of the International Astronomical Union ◽

10.1017/s1743921310010148 ◽

2009 ◽

Vol 5 (H15) ◽

pp. 432-433 ◽

Cited By ~ 1

Author(s):

Axel Brandenburg ◽

Fabio Del Sordo

Keyword(s):

Turbulent Diffusion ◽

Mean Field ◽

Reynolds Numbers ◽

Field Method ◽

Test Field ◽

Expansion Waves ◽

Magnetic Diffusivity ◽

Spherical Expansion ◽

Mean Field Dynamo

AbstractUsing the test-field method for nearly irrotational turbulence driven by spherical expansion waves it is shown that the turbulent magnetic diffusivity increases with magnetic Reynolds numbers. Its value levels off at several times the rms velocity of the turbulence multiplied by the typical radius of the expansion waves. This result is discussed in the context of the galactic mean-field dynamo.

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Supernova-driven interstellar turbulence and the galactic dynamo

Proceedings of the International Astronomical Union ◽

10.1017/s1743921311007253 ◽

2010 ◽

Vol 6 (S274) ◽

pp. 348-354

Author(s):

Oliver Gressel ◽

Detlef Elstner ◽

Günther Rüdiger

Keyword(s):

Mean Field ◽

Field Method ◽

Test Field ◽

Dynamo Theory ◽

Quasilinear Theory ◽

Interstellar Turbulence ◽

Supernova Explosions ◽

The Mean ◽

Numerical Astrophysics

AbstractThe fractal shape and multi-component nature of the interstellar medium together with its vast range of dynamical scales provides one of the great challenges in theoretical and numerical astrophysics. Here we will review recent progress in the direct modelling of interstellar hydromagnetic turbulence, focusing on the role of energy injection by supernova explosions. The implications for dynamo theory will be discussed in the context of the mean-field approach.Results obtained with the test field-method are confronted with analytical predictions and estimates from quasilinear theory. The simulation results enforce the classical understanding of a turbulent Galactic dynamo and, more importantly, yield new quantitative insights. The derived scaling relations enable confident global mean-field modelling.

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On the spatial and temporal non-locality of dynamo mean-field effects in supersonic interstellar turbulence

Monthly Notices of the Royal Astronomical Society ◽

10.1093/mnras/staa663 ◽

2020 ◽

Vol 494 (1) ◽

pp. 1180-1188

Author(s):

Oliver Gressel ◽

Detlef Elstner

Keyword(s):

Large Scale ◽

Mean Field ◽

Field Method ◽

Relevant Parameter ◽

Test Field ◽

Surprising Result ◽

Closure Relation ◽

Interstellar Turbulence ◽

Field Effects ◽

Magnetohydrodynamic Simulations

ABSTRACT The interstellar medium (ISM) of the Milky Way and nearby disc galaxies harbour large-scale coherent magnetic fields of microgauss strength, that can be explained via the action of a mean-field dynamo. As in our previous work, we aim to quantify dynamo effects that are self-consistently emerging in realistic direct magnetohydrodynamic simulations, but we generalize our approach to the case of a non-local (non-instantaneous) closure relation, described by a convolution integral in space (time). To this end, we leverage our comprehensive simulation framework for the supernova-regulated turbulent multiphase ISM. By introducing spatially (temporally) modulated mean fields, we extend the previously used test-field method to the spectral realm – providing the Fourier representation of the convolution kernels. The resulting spectra of the dynamo mean-field coefficients that we obtain broadly match expectations and allow to rigorously constrain the degree of scale separation in the Galactic dynamo. A surprising result is found for the diamagnetic pumping term, which increases in amplitude when going to smaller scales. Our results amount to the most comprehensive description of dynamo mean-field effects in the Galactic context to date. Surveying the relevant parameter space and quenching behaviour, this will ultimately enable the development of assumption-free subgrid prescriptions for otherwise unresolved global galaxy simulations.

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Structured mean field method for single-microphone speech separation with factorial Hidden Markov Model

2013 IEEE China Summit and International Conference on Signal and Information Processing ◽

10.1109/chinasip.2013.6625311 ◽

2013 ◽

Author(s):

Yu Ting Yeung ◽

Tan Lee

Keyword(s):

Markov Model ◽

Hidden Markov Model ◽

Hidden Markov ◽

Mean Field ◽

Field Method ◽

Speech Separation

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Micromechanics Method to Evaluate Fatigue Life of Ni-Based Superalloys during Morphological Evolution

Key Engineering Materials ◽

10.4028/www.scientific.net/kem.385-387.221 ◽

2008 ◽

Vol 385-387 ◽

pp. 221-224

Author(s):

Wen Ping Wu ◽

Ya Fang Guo ◽

Yue Sheng Wang

Keyword(s):

Fatigue Life ◽

Plastic Strain ◽

Life Prediction ◽

Morphological Evolution ◽

Mean Field ◽

Prediction Method ◽

Field Method ◽

External Stress ◽

Equivalent Inclusion ◽

Evolution Of Precipitates

A quantitative life prediction method has been proposed to evaluate fatigue life during morphological evolution of precipitates in Ni-based superalloys. The method is essentially based on Eshelby’s equivalent inclusion theory and Mori-Tanaka’s mean field method. The shape stability and life prediction are discussed when the external stress and matrix plastic strain are applied. The calculated results show that the fatigue life is closely related with microstructures evolution of precipitates. The magnitude and sign of the external stress and matrix plastic strain have an important effect on fatigue life of Ni-based superalloys during the morphological evolution of precipitates.

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