The effect of finish rolling temperature (FRT) on the austenite- () to-bainite () phase transformation is quantitatively investigated in high-strength C-Mn steels. In particular, the present study aims to clarify the respective contributions of the c
onditioning during the hot rolling and the variant selection (VS) during the phase transformation to the inherited texture. To this end, an alternative crystallographic reconstruction procedure, which can be directly applied to experimental electron backscatter diffraction (EBSD) mappings, is developed by combining the best features of the existing models: the orientation relationship (OR) refinement, the local pixel-by-pixel analysis and the nuclei identification and spreading strategy. The applicability of this method is demonstrated on both quenching and partitioning (Q&P) and as-quenched lath-martensite steels. The results obtained on the C-Mn steels confirm that the sample finish rolled at the lowest temperature (829{deg}C) exhibits the sharpest transformation texture. It is shown that this sharp texture is exclusively due to a strong VS from parent brass {110}<1-12>, S {213}<-3-64> and Goss {110}<001> grains, whereas the VS from the copper {112}<-1-11> grains is insensitive to the FRT. In addition, a statistical VS analysis proves that the habit planes of the selected variants do not systematically correspond to the predicted active slip planes using the Taylor model. In contrast, a correlation between the Bain group to which the selected variants belong and the FRT is clearly revealed, regardless of the parent orientation. These results are discussed in terms of polygranular accommodation mechanisms, especially in view of the observed development in the hot-rolled samples of high-angle grain boundaries with misorientation axes between <111> and <110> .
The neutron-rich $^{11}$Li halo nucleus is unique among nuclei with known separation energies by its ability to emit a proton and a neutron in a $beta$ decay process. The branching ratio towards this rare decay mode is evaluated within a three-body m
odel for the initial bound state and with Coulomb three-body final scattering states. The branching ratio should be comprised between two extreme cases, i.e. a lower bound $6 times 10^{-12}$ obtained with a pure Coulomb wave and an upper bound $5 times 10^{-10}$ obtained with a plane wave. A simple model with modified Coulomb waves provides plausible values between between $0.8 times 10^{-10}$ and $2.2 times 10^{-10}$ with most probable total energies of the proton and neutron between 0.15 and 0.3 MeV.
Some one-neutron halo nuclei can emit a proton in a beta decay of the halo neutron. The branching ratio towards this rare decay mode is calculated within a two-body potential model of the initial core+neutron bound state and final core+proton scatter
ing states. The decay probability per second is evaluated for the $^{11}$Be, $^{19}$C and $^{31}$Ne one-neutron halo nuclei. It is very sensitive to the neutron separation energy.
We show that there is no positive loop inside the component of a fiber in the space of Legendrian embeddings in the contact manifold $ST^*M$, provided that the universal cover of $M$ is $RM^n$. We consider some related results in the space of one-jet
s of functions on a compact manifold. We give an application to the positive isotopies in homogeneous neighborhoods of surfaces in a tight contact 3-manifold.
We consider the electrostatic field of a point charge coupled to Horava-Lifshitz gravity and find an exact solution describing the space with a surplus (or deficit) solid angle. Although, theoretically in general relativity, a surplus angle is hardly
to be obtained in the presence of ordinary matter with positive energy distribution, it seems natural in Horava-Lifshitz gravity. We present the sudden disappearance and reappearance of a star image as an astrophysical effect of a surplus angle. We also consider matter configurations of all possible power law behaviors coupled to Horava-Lifshitz gravity and obtain a series of exact solutions.
M1 transitions from the $^6$Li($0^+;T=1$) state at 3.563 MeV to the $^6$Li($1^+$) ground state and to the $alpha+d$ continuum are studied in a three-body model. The bound states are described as an $alpha+n+p$ system in hyperspherical coordinates on
a Lagrange mesh. The ground-state magnetic moment and the gamma width of the $^6$Li(0$^+$) resonance are well reproduced. The halo-like structure of the $^6$Li$(0^+)$ resonance is confirmed and is probed by the M1 transition probability to the $alpha+d$ continuum. The spectrum is sensitive to the description of the $alpha+d$ phase shifts. The corresponding gamma width is around 1.0 meV, with optimal potentials. Charge symmetry is analyzed through a comparison with the $beta$-delayed deuteron spectrum of $^6$He. In $^6$He, a nearly perfect cancellation effect between short-range and halo contributions was found. A similar analysis for the $^6$Li($0^+;T=1$) $gamma$ decay is performed; it shows that charge-symmetry breaking at large distances, due to the different binding energies and to different charges, reduces this effect. The present branching ratio $Gamma_{gamma}(0^+to alpha+d)/Gamma_{gamma}(0^+to1^+)approx 1.3times 10^{-4}$ should be observable with current experimental facilities.
Let $X$ be a locally compact Hadamard space and $G$ be a totally disconnected group acting continuously, properly and cocompactly on $X$. We show that a closed subgroup of $G$ is amenable if and only if it is (topologically locally finite)-by-(virtua
lly abelian). We are led to consider a set $bdfine X$ which is a refinement of the visual boundary $bd X$. For each $x in bdfine X$, the stabilizer $G_x$ is amenable.
