Crystallography of deformation twinning in hexagonal close-packed metals. Revisiting the case of the (56 deg, a) contraction twins in magnesium

Contraction twinning in magnesium alloys leads to new grains that are misoriented from the parent grain by a rotation of 56 deg around the a-axis. The classical theory of deformation twinning does not precise the atomic displacements and does not explain why contractions twinning is less frequent than extension twinning. The paper proposes a new model in the continuity of our previous works on martensitic transformations and extension twinning. A continuous angular distortion matrix that transforms the initial hcp crystal into a final hcp crystal is determined such that the atoms move as hard spheres and reach the final positions expected by the orientation relationship. The calculations prove that the distortion is not a simple shear when it is considered in its continuity. The (01-11) twin plane is untilted and restored, but it is not fully invariant because some interatomic distances in this plane evolve during the distortion process; the unit volume also increases up to 5% before coming back to its initial value when the twinning distortion is complete. Then, the distortion takes the form a simple shear on the twin plane with a shear direction along the direction [18,-5,-5] and a shear amplitude of 0.358. It is the first time that this twinning mode is reported. Experiments are proposed to validate or infirm the new model.Comment: 18 references, 7 figures, 37 equations, no table. The supplementary Materials are not attache

Comment on 'A new nanoscale metastable iron phase in carbon steels'

We show that the selected area diffraction patterns presented in a recent paper (T. Liu et al. Sci. Rep. 2015 5, 15331) do not prove the existence of a new hexagonal phase in martensitic steels. They can be actually simulated by twin effects.Comment: 5 pagesm 3 figure

Spatial smoothness of the stationary solutions of the 3D Navier--Stokes equations

We consider stationary solutions of the three dimensional Navier--Stokes equations (NS3D) with periodic boundary conditions and driven by an external force which might have a deterministic and a random part. The random part of the force is white in time and very smooth in space. We investigate smoothness properties in space of the stationary solutions. Classical technics for studying smoothness of stochastic PDEs do not seem to apply since global existence of strong solutions is not known. We use the Kolmogorov operator and Galerkin approximations. We first assume that the noise has spatial regularity of order $p$ in the $L^2$ based Sobolev spaces, in other words that its paths are in $H^p$. Then we prove that at each fixed time the law of the stationary solutions is supported by $H^{p+1}$. Then, using a totally different technic, we prove that if the noise has Gevrey regularity then at each fixed time, the law of a stationary solution is supported by a Gevrey space. Some informations on the Kolmogorov dissipation scale are deduced

One-dimensional reduction of viscous jets. I. Theory

We build a general formalism to describe thin viscous jets as one-dimensional objects with an internal structure. We present in full generality the steps needed to describe the viscous jets around their central line, and we argue that the Taylor expansion of all fields around that line is conveniently expressed in terms of symmetric trace-free tensors living in the two dimensions of the fiber sections. We recover the standard results of axisymmetric jets and we report the first and second corrections to the lowest order description, also allowing for a rotational component around the axis of symmetry. When applied to generally curved fibers, the lowest order description corresponds to a viscous string model with circular sections. However, when including the first corrections we find that curved jets generically develop elliptic sections. Several subtle effects imply that the first corrections cannot be described by a rod model, since it amounts to selectively discard some corrections. For completeness, we also recover the constitutive relations for forces and torques in rod models and exhibit a missing term in the lowest order expression of viscous torque. Given that our method is based on tensors, the complexity of all computations has been beaten down by using an appropriate tensor algebra package such as {\it xAct}, allowing us to obtain a one-dimensional description of curved viscous jets with all the first order corrections consistently included. Finally, we find a description for straight fibers with elliptic sections as a special case of these results, and recover that ellipticity is dynamically damped by surface tension. An application to toroidal viscous fibers is presented in the companion paper [Pitrou, Phys. Rev. E 97, 043116 (2018)].Comment: 41 pages, 1 figur

Fast & Confident Probabilistic Categorization

We describe NRC's submission to the Anomaly Detection/Text Mining competition organised at the Text Mining Workshop 2007. This submission relies on a straightforward implementation of the probabilistic categoriser described in (Gaussier et al., ECIR'02). This categoriser is adapted to handle multiple labelling and a piecewise-linear confidence estimation layer is added to provide an estimate of the labelling confidence. This technique achieves a score of 1.689 on the test data