Earth's Inner Core dynamics induced by the Lorentz force

Seismic studies indicate that the Earth's inner core has a complex structure and exhibits a strong elastic anisotropy with a cylindrical symmetry. Among the various models which have been proposed to explain this anisotropy, one class of models considers the effect of the Lorentz force associated with the magnetic field diffused within the inner core. In this paper we extend previous studies and use analytical calculations and numerical simulations to predict the geometry and strength of the flow induced by the poloidal component of the Lorentz force in a neutrally or stably stratified growing inner core, exploring also the effect of different types of boundary conditions at the inner core boundary (ICB). Unlike previous studies, we show that the boundary condition that is most likely to produce a significant deformation and seismic anisotropy is impermeable, with negligible radial flow through the boundary. Exact analytical solutions are found in the case of a negligible effect of buoyancy forces in the inner core (neutral stratification), while numerical simulations are used to investigate the case of stable stratification. In this situation, the flow induced by the Lorentz force is found to be localized in a shear layer below the ICB, which thickness depends on the strength of the stratification, but not on the magnetic field strength. We obtain scaling laws for the thickness of this layer, as well as for the flow velocity and strain rate in this shear layer as a function of the control parameters, which include the magnitude of the magnetic field, the strength of the density stratification, the viscosity of the inner core, and the growth rate of the inner core. We find that the resulting strain rate is probably too small to produce significant texturing unless the inner core viscosity is smaller than about $10^{12}$ Pa.s.Comment: submitted to Geophysical Journal Internationa

Is inner core seismic anisotropy a marker for plastic flow of cubic iron?

International audienceThis paper investigates whether observations of seismic anisotropy are compatible with a cubic structure of the inner core Fe alloy.We assume that anisotropy is the result of plastic deformation within a large scale flow induced by preferred growth at the inner core equator. Based on elastic moduli from the literature, bcc- or fcc-Fe produce seismic anisotropy well below seismic observations ($<0.4\%$). A Monte-Carlo approach allows us to generalize this result to any form of elastic anisotropy in a cubic system. Within our model, inner core global anisotropy is not compatible with a cubic structure of Fe alloy.Hence, if the inner core material is indeed cubic, large scale coherent anisotropic structures, incompatible with plastic deformation induced by large scale flow, must be present

What is responsible for thermal coupling in layered convection ?

Laboratory experiments have been conducted on convection in a layered system. The system consists in two liquid layers of equal thickness. The liquids are immiscible : the upper one is silicon oil, and the lower one is glycerol. The structure of convection has been analysed, and data obtained both on the temperature field and the velocity field. It is shown that the coupling between the two convecting systems in « thermal », i.e. convection cells are superposed with uprising currents above uprisings. This result is surprising because it contradicts numerical experiments recently obtained for layered convection. These find « mechanical » coupling (cells are superposed but turn in opposite senses) to be the stable mode for the conditions we tried to reproduce in the laboratory. Several tests have been conducted in order to isolate the phenomenon which is responsible for the discrepancy between the two types of analyses. A tentative mechanism is proposed : it involves an equivalent interfacial longitudinal viscosity, whose origin is not yet clearly understood

Simultaneous mesoscopic and two-photon imaging of neuronal activity in cortical circuits.

Spontaneous and sensory-evoked activity propagates across varying spatial scales in the mammalian cortex, but technical challenges have limited conceptual links between the function of local neuronal circuits and brain-wide network dynamics. We present a method for simultaneous cellular-resolution two-photon calcium imaging of a local microcircuit and mesoscopic widefield calcium imaging of the entire cortical mantle in awake mice. Our multi-scale approach involves a microscope with an orthogonal axis design where the mesoscopic objective is oriented above the brain and the two-photon objective is oriented horizontally, with imaging performed through a microprism. We also introduce a viral transduction method for robust and widespread gene delivery in the mouse brain. These approaches allow us to identify the behavioral state-dependent functional connectivity of pyramidal neurons and vasoactive intestinal peptide-expressing interneurons with long-range cortical networks. Our imaging system provides a powerful strategy for investigating cortical architecture across a wide range of spatial scales

Introduzione soft alla matematica per l'economia e la finanza: il concetto di funzione come elemento base della modellizzazione

Quaderni di didattica. Dipartimento di Matematica Applicata. Università Ca'Foscari di Venezia