The radio telescopes of the European VLBI Network (EVN) and the University of Tasmania (UTAS) conducted an extensive observation campaign of the European Space Agency’s (ESA) Mars Express (MEX) spacecraft between 2013 and 2020. The campaign, carried out under the Planetary Radio Interferometry and Doppler Experiment (PRIDE) framework, aimed to study interplanetary phase scintillation and assess the noise budget in the closed-loop Doppler observations. The average closed-loop Doppler noise was determined to be approximately 10 mHz at a 10-s integration time, reaffirming the technique’s suitability for radio science experiments. We evaluated how different observational parameters such as the solar elongation, antenna size, and elevation angle impact the Doppler noise. A key part of the analysis involved comparing results from co-located telescopes to investigate system noise effects. Co-located telescopes at both Wettzell and Hobart provided highly consistent results, with any deviations serving as diagnostic tools to identify station-dependent issues. Additionally, the use of phase calibration tones during spacecraft tracking showed that the instrumental noise contribution is of the order of 5$\%$ of the total noise. This study provides a detailed noise budget for closed-loop Doppler observations with VLBI telescopes while emphasizing the effectiveness of the co-location method in isolating system-level noise. These findings are important for optimizing future radio science and VLBI tracking missions using stations outside the the Deep Space Network (DSN) and European Space Tracking (ESTRACK) network.

The excitation conditions of the magnetorotational instability (MRI) are studied for axially unbounded Taylor–Couette (TC) flows of various gap widths between the cylinders. The cylinders are considered as made from both perfect-conducting or insulating material and the conducting fluid with a finite but small magnetic Prandtl number rotates with a quasi-Keplerian velocity profile. The solutions are optimized with respect to the wavenumber and the Reynolds number of the rotation of the inner cylinder. For the axisymmetric modes, we find the critical Lundquist number of the applied axial magnetic field: the lower, the wider the gap between the cylinders. A similar result is obtained for the induced cell structure: the wider the gap, the more spherical the cells are. The marginal rotation rate of the inner cylinder – for a fixed size of the outer cylinder – always possesses a minimum for not too wide and not too narrow gap widths. For perfect-conducting walls the minimum lies at $r_{{\rm in}}\simeq 0.4$, where $r_{{\rm in}}$ is the ratio of the radii of the two rotating cylinders. The lowest magnetic field amplitudes to excite the instability are required for TC flows between perfect-conducting cylinders with gaps corresponding to $r_{{\rm in}}\simeq ~0.2$. For even wider and also for very thin gaps the needed magnetic fields and rotation frequencies are shown to become rather huge. Also the non-axisymmetric modes with $|m|=1$ have been considered. Their excitation generally requires stronger magnetic fields and higher magnetic Reynolds numbers in comparison with those for the axisymmetric modes. If TC experiments with too slow rotation for the applied magnetic fields yield unstable modes of any azimuthal symmetry, such as the currently reported Princeton experiment (Wang et al., Phys. Rev. Lett., vol. 129, 115001), then also other players, including axial boundary effects, than the MRI-typical linear combination of current-free fields and differential rotation should be in the game.

Several approaches to judgment and decision making emphasize the effort-reducing properties of heuristics. One prominent example for effort-reduction is the recognition heuristic (RH) which proposes that judgments are made by relying on one single cue (recognition), ignoring other information. Our research aims to shed light on the conditions under which the RH is more useful and thus relied on more often. We propose that intuitive thinking is fast, automatic, and effortless whereas deliberative thinking is slower, stepwise, and more effortful. Because effort-reduction is thus much more important when processing information deliberately, we hypothesize that the RH should be more often relied on in such situations. In two city-size-experiments, we instructed participants to think either intuitively or deliberatively and assessed use of the RH through a formal measurement model. Results revealed that, in both experiments, use of the RH was more likely when judgments were to be made deliberatively, rather than intuitively. As such, we conclude that the potential application of heuristics is not necessarily a consequence of “intuitive” processing. Rather, their effort-reducing features are probably most beneficial when thinking more deliberatively.

In an earlier paper we showed that the combination of azimuthal magnetic fields and super-rotation in Taylor–Couette flows of conducting fluids can be unstable against non-axisymmetric perturbations if the magnetic Prandtl number of the fluid is $\textrm {Pm}\neq 1$. Here we demonstrate that the addition of a weak axial field component allows axisymmetric perturbation patterns for $\textrm {Pm}$ of order unity depending on the boundary conditions. The axisymmetric modes only occur for magnetic Mach numbers (of the azimuthal field) of order unity, while higher values are necessary for the non-axisymmetric modes. The typical growth time of the instability and the characteristic time scale of the axial migration of the axisymmetric mode are long compared with the rotation period, but short compared with the magnetic diffusion time. The modes travel in the positive or negative $z$ direction along the rotation axis depending on the sign of $B_\phi B_z$. We also demonstrate that the azimuthal components of flow and field perturbations travel in phase if $|B_\phi |\gg |B_z|$, independent of the form of the rotation law. Within a short-wave approximation for thin gaps it is also shown (in an appendix) that for ideal fluids the considered helical magnetorotational instability only exists for rotation laws with negative shear.

Consequences of fluctuating microscopic conductivity in mean-field electrodynamics of turbulent fluids are formulated and discussed. If the conductivity fluctuations are assumed to be uncorrelated with the velocity fluctuations then only the turbulence-originated magnetic diffusivity of the fluid is reduced and the decay time of a large-scale magnetic field or the cycle times of oscillating turbulent dynamo models are increased. If, however, the fluctuations of conductivity and flow in a certain well-defined direction are correlated, an additional diamagnetic pumping effect results, transporting the magnetic field in the opposite direction to the diffusivity flux vector $\langle \unicode[STIX]{x1D702}^{\prime }\boldsymbol{u}^{\prime }\rangle$. In the presence of global rotation, even for homogeneous turbulence fields, an alpha effect appears. If the characteristic values of the outer core of the Earth or the solar convection zone are applied, the dynamo number of the new alpha effect does not reach supercritical values to operate as an $\unicode[STIX]{x1D6FC}^{2}$-dynamo but oscillating $\unicode[STIX]{x1D6FC}\unicode[STIX]{x1D6FA}$-dynamos with differential rotation are not excluded.

The stability of conducting Taylor–Couette flows under the presence of toroidal magnetic background fields is considered. For strong enough magnetic amplitudes such magnetohydrodynamic flows are unstable against non-axisymmetric perturbations which may also transport angular momentum. In accordance with the often used diffusion approximation, one expects the angular momentum transport to be vanishing for rigid rotation. In the sense of a non-diffusive $\unicode[STIX]{x1D6EC}$ effect, however, even for rigidly rotating $z$-pinches, an axisymmetric angular momentum flux appears which is directed outward (inward) for large (small) magnetic Mach numbers. The internal rotation in a magnetized rotating tank can thus never be uniform. Those particular rotation laws are used to estimate the value of the instability-induced eddy viscosity for which the non-diffusive $\unicode[STIX]{x1D6EC}$ effect and the diffusive shear-induced transport compensate each other. The results provide the Shakura & Sunyaev viscosity ansatz leading to numerical values linearly growing with the applied magnetic field.

Observations of early-type M stars suggest that there are two characteristic cycle times, one of order one year for fast rotators (Prot < 1 day) and another of order four years for slower rotators. For a sample of fast-rotating stars, the equator-to-pole differences of the rotation rates up to 0.03 rad d−1 are also known from Kepler data. These findings are well-reproduced by mean field models. These models predict amplitudes of the meridional flow, from which the travel time from pole to equator at the base of the convection zone of early-type M stars can be calculated. As these travel times always exceed the observed cycle times, our findings do not support the flux transport dynamo.

It is demonstrated that the azimuthal magnetorotational instability (AMRI) also works with radially increasing rotation rates contrary to the standard magnetorotational instability for axial fields which requires negative shear. The stability against non-axisymmetric perturbations of a conducting Taylor–Couette flow with positive shear under the influence of a toroidal magnetic field is considered if the background field between the cylinders is current free. For small magnetic Prandtl number $Pm\rightarrow 0$ the curves of neutral stability converge in the (Hartmann number,Reynolds number) plane approximating the stability curve obtained in the inductionless limit $Pm=0$. The numerical solutions for $Pm=0$ indicate the existence of a lower limit of the shear rate. For large $Pm$ the curves scale with the magnetic Reynolds number of the outer cylinder but the flow is always stable for magnetic Prandtl number unity as is typical for double-diffusive instabilities. We are particularly interested to know the minimum Hartmann number for neutral stability. For models with resting or almost resting inner cylinder and with perfectly conducting cylinder material the minimum Hartmann number occurs for a radius ratio of $r_{\text{in}}=0.9$. The corresponding critical Reynolds numbers are smaller than $10^{4}$.

We investigate the instability and nonlinear saturation of temperature-stratified Taylor–Couette flows in a finite height cylindrical gap and calculate angular momentum transport in the nonlinear regime. The model is based on an incompressible fluid in Boussinesq approximation with a positive axial temperature gradient applied. While both ingredients, the differential rotation as well as the stratification due to the temperature gradient, are stable themselves, together the system becomes subject of the stratorotational instability and a non-axisymmetric flow pattern evolves. This flow configuration transports angular momentum outwards and will therefore be relevant for astrophysical applications. The belonging coefficient of β viscosity is of the order of unity if the results are adapted to the size of an accretion disk. The strength of the stratification, the fluid's Prandtl number and the boundary conditions applied in the simulations are well suited too for a laboratory experiment using water and a small temperature gradient around 5 K. With such a set-up the stratorotational instability and its angular momentum transport could be measured in an experiment.

The dynamo equation is solved for the solar convection zone withthe given ("observed") rotation law and positive α-effect. If thelatter exists in the entire convection zone the resulting dynamo showsstrong toroidal field belts in the polar region migrating equatorwards. Thesame happens for α concentrated at the bottom of the convection zonebut then we get too many belts with higher amplitude. The cycle period isalways too short. Including meridional circulation which is directed equatorwards at thebottom of the convection zone (where the eddy diffusivity is reduced), the amplitude of the toroidal field grows and the butterfly diagram reacheslow-latitudes. The cycle time approaches the solar value. The dynamo regime is highly sensitive to the interplay between flow anddiffusivity at the bottom of the convection zone. Stationary solutions arenot very seldom. For less active stars a slight increase of the cycle period with the rotation period is observed in agreement with the decrease of the meridional flow for faster rotation.

The turbulent electromotive force as well as the kinetic and current helicities have been computed for a turbulence subject to magnetic buoyancy and global rotation. The dynamo-alpha is found as positive in the northern hemisphere and negative in the southern hemisphere and the kinetic helicity has just the same signs.

In agreement with the observations the current helicity is negative in the northern hemisphere and positive in the southern hemisphere. Our current helicities and alpha-effects are thus always out of phase. The signs of alpha-effect and both helicities exactly correspond to a numerical simulation by Brandenburg & Schmitt (1998).