Non-linear Mean-Field Galactic Dynamos

We use the recently developed Kinetic Field Theory (KFT) for cosmic structure formation to show how non-linear power spectra for cosmic density fluctuations can be calculated in a mean-field approximation to the particle interactions. Our main result is a simple, closed and analytic, approximate expression for this power spectrum. This expression has two parameters characterising non-linear structure growth which can be calibrated within KFT itself. Using this self-calibration, the non-linear power spectrum agrees with results obtained from numerical simulations to within typically \lesssim10\,\%≲10% up to wave numbers k\lesssim10\,h\,\mathrm{Mpc}^{-1}k≲10hMpc−1 at redshift z = 0z=0. Adjusting the two parameters to optimise agreement with numerical simulations, the relative difference to numerical results shrinks to typically \lesssim 5\,\%≲5%. As part of the derivation of our mean-field approximation, we show that the effective interaction potential between dark-matter particles relative to Zel’dovich trajectories is sourced by non-linear cosmic density fluctuations only, and is approximately of Yukawa rather than Newtonian shape.

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Derivation and precision of mean field electrodynamics with mesoscale fluctuations

Journal of Plasma Physics ◽

10.1017/s0022377818000375 ◽

2018 ◽

Vol 84 (3) ◽

Cited By ~ 4

Author(s):

Hongzhe Zhou ◽

Eric G. Blackman ◽

Luke Chamandy

Keyword(s):

Large Scale ◽

Mean Field ◽

Scale Separation ◽

Precision Error ◽

Theoretical Predictions ◽

Wide Scale ◽

The Mean ◽

Scale Properties ◽

Galactic Dynamos ◽

Correction Terms

Mean field electrodynamics (MFE) facilitates practical modelling of secular, large scale properties of astrophysical or laboratory systems with fluctuations. Practitioners commonly assume wide scale separation between mean and fluctuating quantities, to justify equality of ensemble and spatial or temporal averages. Often however, real systems do not exhibit such scale separation. This raises two questions: (I) What are the appropriate generalized equations of MFE in the presence of mesoscale fluctuations? (II) How precise are theoretical predictions from MFE? We address both by first deriving the equations of MFE for different types of averaging, along with mesoscale correction terms that depend on the ratio of averaging scale to variation scale of the mean. We then show that even if these terms are small, predictions of MFE can still have a significant precision error. This error has an intrinsic contribution from the dynamo input parameters and a filtering contribution from differences in the way observations and theory are projected through the measurement kernel. Minimizing the sum of these contributions can produce an optimal scale of averaging that makes the theory maximally precise. The precision error is important to quantify when comparing to observations because it quantifies the resolution of predictive power. We exemplify these principles for galactic dynamos, comment on broader implications, and identify possibilities for further work.

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Schrödinger approach to Mean Field Games with negative coordination

SciPost Physics ◽

10.21468/scipostphys.9.4.059 ◽

2020 ◽

Vol 9 (4) ◽

Author(s):

Thibault Bonnemain ◽

Thierry Gobron ◽

Denis Ullmo

Keyword(s):

Mean Field ◽

Time Limit ◽

External Potential ◽

Mean Field Games ◽

Relative Importance ◽

Mean Field Game ◽

Non Linear ◽

The Mean ◽

The Way

Mean Field Games provide a powerful framework to analyze the dynamics of a large number of controlled agents in interaction. Here we consider such systems when the interactions between agents result in a negative coordination and analyze the behavior of the associated system of coupled PDEs using the now well established correspondence with the non linear Schrödinger equation. We focus on the long optimization time limit and on configurations such that the game we consider goes through different regimes in which the relative importance of disorder, interactions between agents and external potential vary, which makes possible to get insights on the role of the forward-backward structure of the Mean Field Game equations in relation with the way these various regimes are connected.

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