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Aims: The test-field method for computing turbulent transport coefficients from simulations of hydromagnetic flows is extended to the regime with a magnetohydrodynamic (MHD) background. Methods: A generalized set of test equations is derived using both the induction equation and a modified momentum equation. By employing an additional set of auxiliary equations, we derive linear equations describing the response of the system to a set of prescribed test fields. Purely magnetic and MHD backgrounds are emulated by applying an electromotive force in the induction equation analogously to the ponderomotive force in the momentum equation. Both forces are chosen to have Roberts flow-like geometry. Results: Examples with an MHD background are studied where the previously used quasi-kinematic test-field method breaks down. In cases with homogeneous mean fields it is shown that the generalized test-field method produces the same results as the imposed-field method, where the field-aligned component of the actual electromotive force from the simulation is used. Furthermore, results for the turbulent diffusivity tensor are given, which are inaccessible to the imposed-field method. For MHD backgrounds, new mean-field effects are found that depend on the occurrence of cross-correlations between magnetic and velocity fluctuations. For strong imposed fields, $alpha$ is found to be quenched proportional to the fourth power of the field strength, regardless of the type of background studied.
We show that in a spontaneously broken effective gauge field theory, quantized in a general background $R_xi$-gauge, also the background fields undergo a non-linear (albeit background-gauge invariant) field redefinition induced by radiative correctio
We present a reformulation of the background field method for Yang-Mills type theories, based on using a superalgebra of generators of BRST and background field transformations. The new approach enables one to implement and consistently use non-linea
Direct numerical simulations of isotropically forced homogeneous stationary turbulence with an imposed passive scalar concentration gradient are compared with an analytical closure model which provides evolution equations for the mean passive scalar
We give a short introduction to the subject and review advances in understanding the basic ingredients of the mean-field dynamo theory. The discussion includes the recent analytic and numerical work in developments for the mean electromotive force of
We present a new method to compute the electronic structure of correlated materials combining the hybrid functional method with the dynamical mean-field theory. As a test example of the method we study cerium sesquioxide, a strongly correlated Mott-b