Convective dynamos: Symmetries and modulation

International audienc

Dipolar dynamos in stratified systems

Observations of low-mass stars reveal a variety of magnetic field topologies ranging from large-scale, axial dipoles to more complex magnetic fields. At the same time, three-dimensional spherical simulations of convectively driven dynamos reproduce a similar diversity, which is commonly obtained either with Boussinesq models or with more realistic models based on the anelastic approximation, which take into account the variation of the density with depth throughout the convection zone. Nevertheless, a conclusion from different anelastic studies is that dipolar solutions seem more difficult to obtain as soon as substantial stratifications are considered. In this paper, we aim at clarifying this point by investigating in more detail the influence of the density stratification on dipolar dynamos. To that end, we rely on a systematic parameter study that allows us to clearly follow the evolution of the stability domain of the dipolar branch as the density stratification is increased. The impact of the density stratification both on the dynamo onset and the dipole collapse is discussed and compared to previous Boussinesq results. Furthermore, our study indicates that the loss of the dipolar branch does not ensue from a specific modification of the dynamo mechanisms related to the background stratification, but could instead result from a bias as our observations naturally favour a certain domain in the parameter space characterized by moderate values of the Ekman number, owing to current computational limitations. Moreover, we also show that the critical magnetic Reynolds number of the dipolar branch is scarcely modified by the increase of the density stratification, which provides an important insight into the global understanding of the impact of the density stratification on the stability domain of the dipolar dynamo branch

Topology and field strength in spherical, anelastic dynamo simulations

Numerical modelling of convection driven dynamos in the Boussinesq approximation revealed fundamental characteristics of the dynamo-generated magnetic fields and the fluid flow. Because these results were obtained for an incompressible fluid, their validity for gas planets and stars remains to be assessed. A common approach is to take some density stratification into account with the so-called anelastic approximation. The validity of previous results obtained in the Boussinesq approximation is tested for anelastic models. We point out and explain specific differences between both types of models, in particular with respect to the field geometry and the field strength, but we also compare scaling laws for the velocity amplitude, the magnetic dissipation time, and the convective heat flux. Our investigation is based on a systematic parameter study of spherical dynamo models in the anelastic approximation. We make use of a recently developed numerical solver and provide results for the test cases of the anelastic dynamo benchmark. The dichotomy of dipolar and multipolar dynamos identified in Boussinesq simulations is also present in our sample of anelastic models. Dipolar models require that the typical length scale of convection is an order of magnitude larger than the Rossby radius. However, the distinction between both classes of models is somewhat less explicit than in previous studies. This is mainly due to two reasons: we found a number of models with a considerable equatorial dipole contribution and an intermediate overall dipole field strength. Furthermore, a large density stratification may hamper the generation of dipole dominated magnetic fields. Previously proposed scaling laws, such as those for the field strength, are similarly applicable to anelastic models. It is not clear, however, if this consistency necessarily implies similar dynamo processes in both settings.Comment: 14 pages, 11 figure

An empirical parameterization of subsurface entrainment temperature for improved SST anomaly simulations in an intermediate ocean model

An empirical model for the temperature of subsurface water entrained into the ocean mixed layer (Te) is presented and evaluated to improve sea surface temperature anomaly (SSTA) simulations in an intermediate ocean model (IOM) of the tropical Pacific. An inverse modeling approach is adopted to estimate Te from an SSTA equation using observed SST and simulated upper-ocean currents. A relationship between Te and sea surface height (SSH) anomalies is then obtained by utilizing a singular value decomposition (SVD) of their covariance. This empirical scheme is able to better parameterize Te anomalies than other local schemes and quite realistically depicts interannual variability of Te, including a nonlocal phase lag relation of Te variations relative to SSH anomalies over the central equatorial Pacific. An improved Te parameterization naturally leads to better depiction of the subsurface effect on SST variability by the mean upwelling of subsurface temperature anomalies. As a result, SSTA simulations are significantly improved in the equatorial Pacific; a comparison with other schemes indicates that systematic errors of the simulated SSTAs are significantly small apparently due to the optimized empirical Te parameterization. Cross validation and comparisons with other model simulations are made to illustrate the robustness and effectiveness of the scheme. In particular it is demonstrated that the empirical Te model constructed from one historical period can be successfully used to improve SSTA simulations in anothe

A Phase I/II Study of a 72-h Continuous Infusion of Etoposide in Advanced Soft Tissue Sarcoma

Purpose. The study was performed to assess the antitumour activity and toxicity of a 72-h continuous infusion of single-agent etoposide as second-line treatment for patients with locally advanced or metastatic soft tissue sarcoma (STS), following reports of substantial activity using this schedule of etoposide administration as first-line treatment in combination with ifosfamide

Relative Riemann-Zariski spaces

In this paper we study relative Riemann-Zariski spaces attached to a morphism of schemes and generalizing the classical Riemann-Zariski space of a field. We prove that similarly to the classical RZ spaces, the relative ones can be described either as projective limits of schemes in the category of locally ringed spaces or as certain spaces of valuations. We apply these spaces to prove the following two new results: a strong version of stable modification theorem for relative curves; a decomposition theorem which asserts that any separated morphism between quasi-compact and quasi-separated schemes factors as a composition of an affine morphism and a proper morphism. (In particular, we obtain a new proof of Nagata's compactification theorem.)Comment: 30 pages, the final version, to appear in Israel J. of Mat

Hypercontractivity on the qq-Araki-Woods algebras

Extending a work of Carlen and Lieb, Biane has obtained the optimal hypercontractivity of the $q$-Ornstein-Uhlenbeck semigroup on the $q$-deformation of the free group algebra. In this note, we look for an extension of this result to the type III situation, that is for the $q$-Araki-Woods algebras. We show that hypercontractivity from $L^p$ to $L^2$ can occur if and only if the generator of the deformation is bounded.Comment: 17 page