A Reilly formula and eigenvalue estimates for differential forms

We derive a Reilly-type formula for differential p-forms on a compact manifold with boundary and apply it to give a sharp lower bound of the spectrum of the Hodge Laplacian acting on differential forms of an embedded hypersurface of a Riemannian manifold. The equality case of our inequality gives rise to a number of rigidity results, when the geometry of the boundary has special properties and the domain is non-negatively curved. Finally we also obtain, as a by-product of our calculations, an upper bound of the first eigenvalue of the Hodge Laplacian when the ambient manifold supports non-trivial parallel forms.Comment: 22 page

On a spin conformal invariant on manifolds with boundary

On a n-dimensional connected compact manifold with non-empty boundary equipped with a Riemannian metric, a spin structure and a chirality operator, we study some properties of a spin conformal invariant defined from the first eigenvalue of the Dirac operator under the chiral bag boundary condition. More precisely, we show that we can derive a spinorial analogue of Aubin's inequality.Comment: 26 page

The Dirac operator on untrapped surfaces

We establish a sharp extrinsic lower bound for the first eigenvalue of the Dirac operator of an untrapped surface in initial data sets without apparent horizon in terms of the norm of its mean curvature vector. The equality case leads to rigidity results for the constraint equations with spherical boundary as well as uniqueness results for constant mean curvature surfaces in Minkowski space.Comment: 16 page

Elastic and vibrational properties of alpha and beta-PbO

The structure, electronic and dynamic properties of the two layered alpha (litharge) and beta (massicot) phases of PbO have been studied by density functional methods. The role of London dispersion interactions as leading component of the total interaction energy between layers has been addressed by using the Grimme's approach, in which new parameters for Pb and O atoms have been developed. Both gradient corrected and hybrid functionals have been adopted using Gaussian-type basis sets of polarized triple zeta quality for O atoms and small core pseudo-potential for the Pb atoms. Basis set superposition error (BSSE) has been accounted for by the Boys-Bernardi correction to compute the interlayer separation. Cross check with calculations adopting plane waves that are BSSE free have also been performed for both structures and vibrational frequencies. With the new set of proposed Grimme's type parameters structures and dynamical parameters for both PbO phases are in good agreement with experimental data.Comment: 8 pages, 5 figure

Defect formation energy and magnetic properties of off-stoichiometric Ni-Mn-In alloys by first-principles calculations

International audienceNi-Mn-In is a novel type of magnetic shape memory alloy; it actualizes the shape memory effect through reverse martensitic transformation induced by magnetic field. But martensitic transformation cannot occur in the stoichiometric Ni2MnIn. Therefore, the composition adjustment must be carried out around stoichiometric Ni2MnIn in order to get the appropriate martensitic transformation temperature and Curie temperature. A variety of point defects would be generated during the process of composition adjustment. In this paper, the defect formation energies and the magnetic properties of the defect-introduced off-stoichiometric Ni-Mn-In alloys are systematically investigated. The results are particularly useful in guiding composition design

Magnetic-field-enhanced carbon solution in proeutectoid ferrite

International audienceModification of phase solubility of Fe-C system by magnetic field has been recognized by thermodynamic calculations and indirectly by microstructural examinations. However, there has been no direct experimental verification and the underlying physical mechanism is not fully uncovered. In this work, the enhanced carbon content in proeutectoid ferrite under a 12 T magnetic field is evidenced through wavelength-dispersive spectroscopy using a Shimadzu 1610 electron probe microanalyser measurements. The magnetic-field-enhanced carbon solution reduces the demagnetization energy of the system and makes it energetically more stable

Composition dependent phase stability of Ni-Mn-Ga alloys studied by ab initio calculations

International audienceComposition dependent phase stability of Ni-Mn-Ga magnetic shape memory alloys was studied by first-principles density-functional calculations. It is demonstrated that the three kinds of doping (Ni substitution for Mn, Ni for Ga, and Mn for Ga) destabilize all the three structures. However, Ni-doping relatively stabilizes the non-modulated martensite (NM) with simple tetragonal crystal structure, whereas proper Mn-doping relatively stabilizes the monoclinic seven-layered modulated (7M) martensite with monoclinic structure. Comparing the energy difference between the parent and the product phases, we found that martensitic transformation experiences much larger driving force than that of the intermar-tensitic transformation. Chemical bonds between Ni and Mn are observed not only with the stoichiometric Mn, but also with the excess ones. Bonds between Ni and Mn in modulated martensite is stronger than that of the non-modulated martensite, which is beneficial to the stability of the modulated martensite. The present result provides useful information for further development of magnetic shape memory alloys that is difficult to be obtained from experiments

Artificial intelligence applied to atomistic kinetic Monte Carlo simulations in Fe–Cu alloys

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