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

An ab-initio study of the rôle of lone pairs in the structure and insulator-metal transition in SnO and PbO

We have performed density functional calculations on tetragonal SnO and PbO (litharge) in the space group P4/nmm with the specific intention of examining the rôle played by Sn 5s and Pb 6s lone pairs in stabilizing the structure, and in giving rise to semi-metallic behavior (of SnO at ambient pressure and of PbO in the γ phase). Use of the electron localization function has permitted real-space visualization of the lone pair in these structures. We also discuss the electronic structure of the orthorhombic PbO (massicot, space group Pbma) which again has localized lone pairs, contrary to some earlier expectation. © 2002 Éditions scientifiques et médicales Elsevier SAS. All rights reserved

Ab initio investigation of the CdTe (001) surface

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Classification of the Critical Resolved Shear Stress in the HCP materials by atomic simulation: Application to alpha-zirconium and alpha- titanium

International audienceThe Embedded Atom Method (EAM) approach has been applied to the study of five principle gliding systems in zirconium and titanium materials. The stacking fault energy maps are obtained and compared to the results of ab initio calculations. A good agreement was observed between the two approaches. Furthermore, the Critical Resolved Shear Stresses (CRSS) have been determined by Molecular Dynamics (MD) simulations based on the EAM potentials. The CRSS in the "a" direction for the basal, prismatic (type 1) and pyramidal (type 2) planes are obtained and compared

Structure and phase stability of NiMnGa ferromagnetic shape memory alloys by experimental and ab-initio techniques

This paper summarizes some of our recent results on crystal structure, microstructure, orientation relationship between martensitic variants and crystallographic features of martensitic transformation in Ni-Mn-Ga FSMAs. It was shown that Ni53Mn25Ga22 has a tetragonal I4/mmm martensitic structure at room temperature. The neighboring martensitic variants in Ni53Mn25Ga22 have a compound twinning relationship with the twinning elements K1={112}, K2={11-2}, &eta;1=&lt;11-1&gt;, &eta;2=&lt;111&gt;, P={1-10} and s=0.379. The ratio of the relative amounts of twins within the same initial austenite grain is ~1.70. The main orientation relationship between austenite and martensite is Kurdjumov-Sachs (K-S) relationship. Based on the crystallographic phenomenological theory, the calculated habit plane is {0.690 -0.102 0.716}A (5.95&deg; from {101}A), and the magnitude, direction and shear angle of the macroscopic transformation shear are 0.121, &lt;-0.709 0.105 0.698&gt;A (6.04&deg; from &lt;-101&gt;A) and 6.88&deg;, respectively.<br /

Composition-dependent structural and magnetic properties of Ni-Mn-Ga alloys studied by ab initio calculations

International audienceWe have revealed the influence of composition doping (Ni2+x Mn1-x Ga, Ni2+x MnGa1-x , and Ni2Mn1+x Ga1-x ) on lattice constants and atomic magnetic moments of austenite, 7 M and NM martensite, by ab initio calculations. It is demonstrated that Ni-doping decreases the volume, whereas Mn-doping increases it. The total magnetic moment of the three series of alloys is mainly dominated by their Mn content with little phase-state dependence. The perturbation of the magnetic moments by atom substitution is mainly dominated by the Mn environment. This study is expected to provide information on composition-related structure and magnetic properties of Ni-Mn-Ga alloys that could not be obtained by experiments