We present a numerical study of the magnetic field generated by the Taylor-Green vortex. We show that periodic boundary conditions can be used to mimic realistic boundary conditions by prescribing the symmetries of the velocity and magnetic fields. This gives insight into some problems of central interest for dynamos: the possible effect of velocity fluctuations on the dynamo threshold, and the role of boundary conditions on the threshold and on the geometry of the magnetic field generated by dynamo action. In particular, we show that an axial dipolar dynamo similar to the one observed in a recent experiment can be obtained with an appropriate choice of the symmetries of the magnetic field. The nonlinear saturation is studied and a simple model explaining the magnetic Prandtl number dependence of the super- and subcritical nature of the dynamo transition is given.

International audienceGrowth of ferroelectric nanotori is reported and first-principles-based effective Hamiltonian simulations were performed on these new objects. They could reproduce the nonpolar (phase I) and homogeneously toroidized (phase II) states of an isolated nanotorus. Computation of an axial hypertoroidal moment leads to numerical observation of two new phases: (i) a homogeneously hypertoroidized one (phase III) that can be switched by a homogeneous electric field and (ii) another one with striking newpolarization patterns (phase IV) due to azimuthal variations of the hypertoroidal moment. In both phases, hypertoroidization coexists with a homogeneous axial toroidal moment

A rich variety of single crystalline BaTiO3 (BT) nanostructures have been synthesized by two different routes using titanate nanorods and nanotubes as precursors. Free standing, mixed or agglomerated nanotori, solid or hollow nanospheres and nanocubes were obtained. A careful analysis of the shape evolution of the resulting BT nano-objects obtained with both types of precursors and different parameters (precursor composition and shape, temperature, Ba/Ti molar ratio) allowed an improved understanding of the nanostructure formation. The morphogenesis models at play such as Ostwald ripening and the Kirkendall effect have been identified. Other mechanisms hereafter called the self and merging rebuilding processes and a tentative Turing-reaction-diffusion-model are proposed to explain the formation of these obtained nanoparticles.