Mesogranulation and small-scale dynamo action in the quiet Sun

Regions of quiet Sun generally exhibit a complex distribution of small-scale magnetic field structures, which interact with the near-surface turbulent convective motions. Furthermore, it is probable that some of these magnetic fields are generated locally by a convective dynamo mechanism. In addition to the well-known granular and supergranular convective scales, various observations have indicated that there is an intermediate scale of convection, known as mesogranulation, with vertical magnetic flux concentrations accumulating preferentially at mesogranular boundaries. Our aim is to investigate the small-scale dynamo properties of a convective flow that exhibits both granulation and mesogranulation, comparing our findings with solar observations. Adopting an idealised model for a localised region of quiet Sun, we use numerical simulations of compressible magnetohydrodynamics, in a 3D Cartesian domain, to investigate the parametric dependence of this system (focusing particularly upon the effects of varying the aspect ratio and the Reynolds number). In purely hydrodynamic convection, we find that mesogranulation is a robust feature of this system provided that the domain is wide enough to accommodate these large-scale motions. The mesogranular peak in the kinetic energy spectrum is more pronounced in the higher Reynolds number simulations. We investigate the dynamo properties of this system in both the kinematic and the nonlinear regimes and we find that the dynamo is always more efficient in larger domains, when mesogranulation is present. Furthermore, we use a filtering technique in Fourier space to demonstrate that it is indeed the larger scales of motion that are primarily responsible for driving the dynamo. In the nonlinear regime, the magnetic field distribution compares very favourably to observations, both in terms of the spatial distribution and the measured field strengths.Comment: 12 pages, 11 figures, accepted for publication in Astronomy & Astrophysic

Rayleigh-B\'enard convection with a melting boundary

We study the evolution of a melting front between the solid and liquid phases of a pure incompressible material where fluid motions are driven by unstable temperature gradients. In a plane layer geometry, this can be seen as classical Rayleigh-B\'enard convection where the upper solid boundary is allowed to melt due to the heat flux brought by the fluid underneath. This free-boundary problem is studied numerically in two dimensions using a phase-field approach, classically used to study the melting and solidification of alloys, which we dynamically couple with the Navier-Stokes equations in the Boussinesq approximation. The advantage of this approach is that it requires only moderate modifications of classical numerical methods. We focus on the case where the solid is initially nearly isothermal, so that the evolution of the topography is related to the inhomogeneous heat flux from thermal convection, and does not depend on the conduction problem in the solid. From a very thin stable layer of fluid, convection cells appears as the depth -- and therefore the effective Rayleigh number of the layer increases. The continuous melting of the solid leads to dynamical transitions between different convection cell sizes and topography amplitudes. The Nusselt number can be larger than its value for a planar upper boundary, due to the feedback of the topography on the flow, which can stabilize large-scale laminar convection cells.Comment: 36 pages, 16 figure

Modeling the deformation textures and microstructural evolutions of a Fe–Mn–C TWIP steel during tensile and shear testing

The high manganese austenitic steels with low stacking fault energy (SFE) present outstanding mechanical properties due to the occurrence of two strain mechanisms: dislocation glide and twinning. Both mechanisms are anisotropic. In this paper, we analyzed the effect of monotonous loading path on the texture, the deformation twinning and the stress–strain response of polycrystalline high Mn TWIP steel. Experimental data were compared to predicted results obtained by two polycrystalline models. These two models are based on the same single crystal constitutive equations but differ from the homogenization scheme. The good agreement between experiments and calculations suggest that the texture plays a key role in twinning activity and kinetics with regard to the intergranular stress heterogeneities. Rolling direction simple shear induces single twinning while rolling and transverse direction uniaxial tensions induce multi-twinning leading to lower twin volume fractions due to twin–twin interactions

Directional solidification of Al2-Cu-Al and Al3-Ni-Al eutectics during TEXUS rocket flight

One lamellar eutectic sample and one fiber-like eutectic sample were solidified directionally during the TEXUS-6 rocket flight. The microstructures and the results of the thermal analysis, obtained from the temperatures recorded on the cartridge skin, are compared. No appreciable modifications of the regularity of the eutectic structures were observed by passing from 1 g to 0.0001 g in these experiments. No steady state growth conditions were achieved in these experiments

Overview of Constrained PARAFAC Models

In this paper, we present an overview of constrained PARAFAC models where the constraints model linear dependencies among columns of the factor matrices of the tensor decomposition, or alternatively, the pattern of interactions between different modes of the tensor which are captured by the equivalent core tensor. Some tensor prerequisites with a particular emphasis on mode combination using Kronecker products of canonical vectors that makes easier matricization operations, are first introduced. This Kronecker product based approach is also formulated in terms of the index notation, which provides an original and concise formalism for both matricizing tensors and writing tensor models. Then, after a brief reminder of PARAFAC and Tucker models, two families of constrained tensor models, the co-called PARALIND/CONFAC and PARATUCK models, are described in a unified framework, for $N^{th}$ order tensors. New tensor models, called nested Tucker models and block PARALIND/CONFAC models, are also introduced. A link between PARATUCK models and constrained PARAFAC models is then established. Finally, new uniqueness properties of PARATUCK models are deduced from sufficient conditions for essential uniqueness of their associated constrained PARAFAC models

Investigation of delamination mechanisms during a laser drilling on a cobalt-base superalloy

Temperatures in the high pressure chamber of aircraft engines are continuously increasing to improve the engine efficiency. As a result, constitutive materials such as cobalt and nickel-base superalloys need to be thermally protected. The first protection is a ceramic thermal barrier coating (TBC) cast on all the hot gas-exposed structure. The second protection is provided by a cool air layer realized by the use of a thousand of drills on the parts where a cool air is flowing through. The laser drilling process is used to realize these holes at acute angles. It has been shown on coated single crystal nickel-base superalloy that the laser drilling process causes an interfacial cracking (also called delamination), detected by a cross section observation. The present work aims at characterizing interfacial cracking induced by laser drilling on coated cobalt-base super alloy. On the one hand, this work attempted to quantify the crack by several microscopic observations with regards to the most significant process parameters related as the angle beam. On the other hand, we studied the difference of the laser/ceramic and the laser/substrate interaction with real time observation by using a fast movie camera

Parametric instability and wave turbulence driven by tidal excitation of internal waves

We investigate the stability of stratified fluid layers undergoing homogeneous and periodic tidal deformation. We first introduce a local model which allows to study velocity and buoyancy fluctuations in a Lagrangian domain periodically stretched and sheared by the tidal base flow. While keeping the key physical ingredients only, such a model is efficient to simulate planetary regimes where tidal amplitudes and dissipation are small. With this model, we prove that tidal flows are able to drive parametric subharmonic resonances of internal waves, in a way reminiscent of the elliptical instability in rotating fluids. The growth rates computed via Direct Numerical Simulations (DNS) are in very good agreement with WKB analysis and Floquet theory. We also investigate the turbulence driven by this instability mechanism. With spatio-temporal analysis, we show that it is a weak internal wave turbulence occurring at small Froude and buoyancy Reynolds numbers. When the gap between the excitation and the Brunt-V\"ais\"al\"a frequencies is increased, the frequency spectrum of this wave turbulence displays a -2 power law reminiscent of the high-frequency branch of the Garett and Munk spectrum (Garrett & Munk 1979) which has been measured in the oceans. In addition, we find that the mixing efficiency is altered compared to what is computed in the context of DNS of stratified turbulence excited at small Froude and large buoyancy Reynolds numbers and is consistent with a superposition of waves.Comment: Accepted for publication in Journal of Fluid Mechanics, 27 pages, 21 figure

On the effect of rotation on magnetohydrodynamic turbulence at high magnetic Reynolds number

This article is focused on the dynamics of a rotating electrically conducting fluid in a turbulent state. As inside the Earth's core or in various industrial processes, a flow is altered by the presence of both background rotation and a large scale magnetic field. In this context, we present a set of 3D direct numerical simulations of incompressible decaying turbulence. We focus on parameters similar to the ones encountered in geophysical and astrophysical flows, so that the Rossby number is small, the interaction parameter is large, but the Elsasser number, defining the ratio between Coriolis and Lorentz forces, is about unity. These simulations allow to quantify the effect of rotation and thus inertial waves on the growth of magnetic fluctuations due to Alfv\'en waves. Rotation prevents the occurrence of equipartition between kinetic and magnetic energies, with a reduction of magnetic energy at decreasing Elsasser number {\Lambda}. It also causes a decrease of energy transfer mediated by cubic correlations. In terms of flow structure, a decrease of {\Lambda} corresponds to an increase in the misalignment of velocity and magnetic field.Comment: 18 pages, 12 figure

Generalized analytic model for rotational and anisotropic metasolids

An analytical approach is presented to model a metasolid accounting for anisotropic effects and rotational mode. The metasolid is made of either cylindrical or spherical hard inclusions embedded in a stiff matrix via soft claddings, and the analytical approach to study the composite material is a generalization of the method introduced by Liu \textit{et al.} [Phys. Rev. B, 71, 014103 (2005)]. It is shown that such a metasolid exhibits negative mass densities near the translational-mode resonances, and negative density of moment of inertia near the rotational resonances. The results obtained by this analytical and continuum approach are compared with those from discrete mass-spring model, and the validity of the later is discussed. Based on derived analytical expressions, we study how different resonance frequencies associated with different modes vary and are placed with respect to each other, in function of the mechanical properties of the coating layer. We demonstrate that the resonances associated with additional modes taken into account, that is, axial translation for cylinders, and rotations for both cylindrical and spherical systems, can occur at lower frequencies compared to the previously studied plane-translational modes.Comment: 30 pages, 10 figure