3D simulations of rising magnetic flux tubes in a compressible rotating interior: The effect of magnetic tension

Context: Long-term variability in solar cycles represents a challenging constraint for theoretical models. Mean-field Babcock-Leighton dynamos that consider non-instantaneous rising flux tubes have been shown to exhibit long-term variability in their magnetic cycle. However a relation that parameterizes the rise-time of non-axisymmetric magnetic flux tubes in terms of stellar parameters is still missing. Aims: We aim to find a general parameterization of the rise-time of magnetic flux tubes for solar-like stars. Methods: By considering the influence of magnetic tension on the rise of non-axisymmetric flux tubes, we predict the existence of a control parameter referred as $\Gamma_{\alpha_1}^{\alpha_2}$. This parameter is a measure of the balance between rotational effects and magnetic effects (buoyancy and tension) acting on the magnetic flux tube. We carry out two series of numerical experiments (one for axisymmetric rise and one for non-axisymmetric rise) and demonstrate that $\Gamma_{\alpha_1}^{\alpha_2}$ indeed controls the rise-time of magnetic flux tubes. Results: We find that the rise-time follows a power law of $\Gamma_{\alpha_1}^{\alpha_2}$ with an exponent that depends on the azimuthal wavenumber of the magnetic flux loop. Conclusions: Compressibility does not impact the rise of magnetic flux tubes, while non-axisymmetry does. In the case of non-axisymmetric rise, the tension force modifies the force balance acting on the magnetic flux tube. We identified the three independent parameters required to predict the rise-time of magnetic flux tubes, that is, the stellar rotation rate, the magnetic flux density of the flux tube, and its azimuthal wavenumber. We combined these into one single relation that is valid for any solar-like star. We suggest using this generalized relation to constrain the rise-time of magnetic flux tubes in Babcock-Leighton dynamo models.Comment: 18 pages, 15 figures, 6 tabula

Strong coupling of a qubit to shot noise

We perform a nonperturbative analysis of a charge qubit in a double quantum dot structure coupled to its detector. We show that strong detector-dot interaction tends to slow down and halt coherent oscillations. The transitions to a classical and a low-temperature quantum overdamping (Zeno) regime are studied. In the latter, the physics of the dissipative phase transition competes with the effective shot noise.Comment: 5 pages, 4 figure

A cointegration model for search equilibrium wage formation

In flow models of the labor market, wages are determined by negotiations between workers and employers on the surplus value of a realized match. From this perspective, this paper presents an econometric analysis of the influence of labor market flows on wage formation as an alternative to the traditional specification of wage equations in which unemployment represents Phillips-curve or wage-curve effects. The paper estimates a dynamic wage equation for the Netherlands using a cointegration approach. It finds that labor flows, and notably flows from outside the labor market, are important determinants of both short-run and long-run wage setting.wage curve, labor market flows, cointegration model

Stochastic thermodynamics of chemical reaction networks

For chemical reaction networks described by a master equation, we define energy and entropy on a stochastic trajectory and develop a consistent nonequilibrium thermodynamic description along a single stochastic trajectory of reaction events. A first-law like energy balance relates internal energy, applied (chemical) work and dissipated heat for every single reaction. Entropy production along a single trajectory involves a sum over changes in the entropy of the network itself and the entropy of the medium. The latter is given by the exchanged heat identified through the first law. Total entropy production is constrained by an integral fluctuation theorem for networks arbitrarily driven by time-dependent rates and a detailed fluctuation theorem for networks in the steady state. Further exact relations like a generalized Jarzynski relation and a generalized Clausius inequality are discussed. We illustrate these results for a three-species cyclic reaction network which exhibits nonequilibrium steady states as well as transitions between different steady states.Comment: 14 pages, 2 figures, accepted for publication in J. Chem. Phy

Effective Confinement as Origin of the Equivalence of Kinetic Temperature and Fluctuation-Dissipation Ratio in a Dense Shear Driven Suspension

We study response and velocity autocorrelation functions for a tagged particle in a shear driven suspension governed by underdamped stochastic dynamics. We follow the idea of an effective confinement in dense suspensions and exploit a time-scale separation between particle reorganization and vibrational motion. This allows us to approximately derive the fluctuation-dissipation theorem in a "hybrid" form involving the kinetic temperature as an effective temperature and an additive correction term. We show numerically that even in a moderately dense suspension the latter is negligible. We discuss similarities and differences with a simple toy model, a single trapped particle in shear flow