Analysis of Large Scale Interacting Systems by Mean Field Method

2008 ◽  
Author(s):  
Andrea Bobbio ◽  
Marco Gribaudo ◽  
Miklós Telek
Keyword(s):  
Large Scale ◽  
Mean Field ◽  
Field Method ◽  
Interacting Systems

scholarly journals On the combined role of cosmic rays and supernova-driven turbulence for galactic dynamos

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.

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

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.

scholarly journals On the Throughput Optimization in Large-Scale Batch-Processing Systems

2021 ◽  
Vol 48 (3) ◽  
pp. 128-129
Author(s):  
Sounak Kar ◽  
Robin Rehrmann ◽  
Arpan Mukhopadhyay ◽  
Bastian Alt ◽  
Florin Ciucu ◽  
...  
Keyword(s):  
Large Scale ◽  
Mean Field ◽  
Queueing Network ◽  
Processing System ◽  
Batch Size ◽  
System Throughput ◽  
Throughput Optimization ◽  
Mean Field Model ◽  
Optimal Batch Size ◽  
Globally Attractive

We analyze a data-processing system with n clients producing jobs which are processed in batches by m parallel servers; the system throughput critically depends on the batch size and a corresponding sub-additive speedup function that arises due to overhead amortization. In practice, throughput optimization relies on numerical searches for the optimal batch size which is computationally cumbersome. In this paper, we model this system in terms of a closed queueing network assuming certain forms of service speedup; a standard Markovian analysis yields the optimal throughput in w n4 time. Our main contribution is a mean-field model that has a unique, globally attractive stationary point, derivable in closed form. This point characterizes the asymptotic throughput as a function of the batch size that can be calculated in O(1) time. Numerical settings from a large commercial system reveal that this asymptotic optimum is accurate in practical finite regimes.

scholarly journals Mean-Field Models for EEG/MEG: From Oscillations to Waves

2021 ◽  
Author(s):  
Áine Byrne ◽  
James Ross ◽  
Rachel Nicks ◽  
Stephen Coombes
Keyword(s):  
Gap Junction ◽  
Large Scale ◽  
Mean Field ◽  
Coarse Grained ◽  
Neural Mass Model ◽  
Neuron Network ◽  
Mass Model ◽  
Mean Field Model ◽  
Neural Mass ◽  
The Rich

AbstractNeural mass models have been used since the 1970s to model the coarse-grained activity of large populations of neurons. They have proven especially fruitful for understanding brain rhythms. However, although motivated by neurobiological considerations they are phenomenological in nature, and cannot hope to recreate some of the rich repertoire of responses seen in real neuronal tissue. Here we consider a simple spiking neuron network model that has recently been shown to admit an exact mean-field description for both synaptic and gap-junction interactions. The mean-field model takes a similar form to a standard neural mass model, with an additional dynamical equation to describe the evolution of within-population synchrony. As well as reviewing the origins of this next generation mass model we discuss its extension to describe an idealised spatially extended planar cortex. To emphasise the usefulness of this model for EEG/MEG modelling we show how it can be used to uncover the role of local gap-junction coupling in shaping large scale synaptic waves.

scholarly journals On the dynamical interaction between overshooting convection and an underlying dipole magnetic field – I. The non-dynamo regime

2021 ◽  
Vol 503 (1) ◽  
pp. 362-375
Author(s):  
L Korre ◽  
NH Brummell ◽  
P Garaud ◽  
C Guervilly
Keyword(s):  
Magnetic Field ◽  
Turbulent Diffusion ◽  
Large Scale ◽  
Molecular Diffusion ◽  
Mean Field ◽  
Stable Region ◽  
Turbulent Regime ◽  
Poloidal Magnetic Field ◽  
Dynamical Interaction ◽  
Large Scale Field

ABSTRACT Motivated by the dynamics in the deep interiors of many stars, we study the interaction between overshooting convection and the large-scale poloidal fields residing in radiative zones. We have run a suite of 3D Boussinesq numerical calculations in a spherical shell that consists of a convection zone with an underlying stable region that initially compactly contains a dipole field. By varying the strength of the convective driving, we find that, in the less turbulent regime, convection acts as turbulent diffusion that removes the field faster than solely molecular diffusion would do. However, in the more turbulent regime, turbulent pumping becomes more efficient and partially counteracts turbulent diffusion, leading to a local accumulation of the field below the overshoot region. These simulations suggest that dipole fields might be confined in underlying stable regions by highly turbulent convective motions at stellar parameters. The confinement is of large-scale field in an average sense and we show that it is reasonably modelled by mean-field ideas. Our findings are particularly interesting for certain models of the Sun, which require a large-scale, poloidal magnetic field to be confined in the solar radiative zone in order to explain simultaneously the uniform rotation of the latter and the thinness of the solar tachocline.

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

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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