Search results for "Action"
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Constant sign and nodal solutions for nonlinear robin equations with locally defined source term
2020
We consider a parametric Robin problem driven by a nonlinear, nonhomogeneous differential operator which includes as special cases the p-Laplacian and the (p,q)-Laplacian. The source term is parametric and only locally defined (that is, in a neighborhood of zero). Using suitable cut-off techniques together with variational tools and comparison principles, we show that for all big values of the parameter, the problem has at least three nontrivial smooth solutions, all with sign information (positive, negative and nodal).
Multiple Solutions for Fractional Boundary Value Problems
2018
Variational methods and critical point theorems are used to discuss existence and multiplicity of solutions for fractional boundary value problem where Riemann–Liouville fractional derivatives and Caputo fractional derivatives are used. Some conditions to determinate nonnegative solutions are presented. An example is given to illustrate our results.
Vertical versus horizontal Sobolev spaces
2020
Let $\alpha \geq 0$, $1 < p < \infty$, and let $\mathbb{H}^{n}$ be the Heisenberg group. Folland in 1975 showed that if $f \colon \mathbb{H}^{n} \to \mathbb{R}$ is a function in the horizontal Sobolev space $S^{p}_{2\alpha}(\mathbb{H}^{n})$, then $\varphi f$ belongs to the Euclidean Sobolev space $S^{p}_{\alpha}(\mathbb{R}^{2n + 1})$ for any test function $\varphi$. In short, $S^{p}_{2\alpha}(\mathbb{H}^{n}) \subset S^{p}_{\alpha,\mathrm{loc}}(\mathbb{R}^{2n + 1})$. We show that the localisation can be omitted if one only cares for Sobolev regularity in the vertical direction: the horizontal Sobolev space $S_{2\alpha}^{p}(\mathbb{H}^{n})$ is continuously contained in the vertical Sobolev sp…
Pressure-induced instability of the fergusonite phase of EuNbO4 studied by in situ Raman spectroscopy, x-ray diffraction, and photoluminescence spect…
2020
In this article, we present high-pressure experimental investigations on EuNbO4, an interesting technologically important material, using synchrotron based x-ray powder diffraction, Raman spectroscopy, and europium photoluminescence measurements up to 39.2, 31.6, and 32.4 GPa, respectively. All three techniques show the stability of the ambient monoclinic phase until 20 GPa. Beyond that, a pressure-induced structural phase transition takes place with the coexistence of two phases over a wide pressure range. The structure of the high-pressure phase has been determined as orthorhombic (space group: Imma) with a volume discontinuity of nearly 9% at the transition indicating the nature of trans…
Experimental Equipment for Studying the Residual Stresses Developed During High Temperature Reactions by X-Ray Diffraction
1996
This paper describes a device dedicated to studyng, by X-ray diffraction the residual stresses developed on surface samples as a function of temperature and atmosphere conditions. The setup consists of : a.) an horizontal axis goniometer which allows the programmed positionning of the sealed X-ray source and of the linear detector. b.) a high temperature controlled atmosphere chamber Particular attention has been paid to the thermal stability up to 1200°C and the accurate position on the sample.
X-ray diffraction and Raman spectroscopy studies in Na1/2Bi1/2TiO3-SrTiO3-PbTiO3 solid solutions
2016
The long and short range orders in 0.4Na1/2Bi1/2TiO3-(0.6-x)SrTiO3-xPbTiO3 solid solutions were studied by x-ray diffraction and Raman spectroscopy. X-ray diffraction patterns for these composition...
High quality epitaxial Mn 2 Au (001) thin films grown by molecular beam epitaxy
2020
The recently discovered phenomenon of Neel spin–orbit torque in antiferromagnetic Mn2Au [Bodnar et al., Nat. Commun. 9, 348 (2018); Meinert et al., Phys. Rev. Appl. 9, 064040 (2018); Bodnar et al., Phys. Rev. B 99, 140409(R) (2019)] has generated huge interest in this material for spintronics applications. In this paper, we report the preparation and characterization of high quality Mn2Au thin films by molecular beam epitaxy and compare them with magnetron sputtered samples. The films were characterized for their structural and morphological properties using reflective high-energy electron diffraction, x-ray diffraction, x-ray reflectometry, atomic force microscopy, and temperature dependen…
Structure and dielectric properties of Na0.5Bi0.5TiO3-CaTiO3 solid solutions
2016
Despite wide studies of Na0.5Bi0.5TiO3, structure of this material and its connection with the observed physical properties still raise numerous questions due to mutually contradicting results obtained. Here, structure and dielectric properties of poled and unpoled Na0.5Bi0.5TiO3-CaTiO3 solid solutions are studied, projecting the obtained concentration dependence of structure and dielectric properties on pure Na0.5Bi0.5TiO3 as the end member of this material group. X-ray diffraction patterns for Na0.5Bi0.5TiO3-CaTiO3 solid solutions reveal dominating of an orthorhombic Pnma phase, even for the compositions approaching the end composition (Na0.5Bi0.5TiO3), whereas structure of pure Na0.5Bi0.…
Simultaneous Synthesis and Consolidation of Nanostructured MoSi2
2002
A new process combining electric field activation and the imposition of pressure from mechanically activated powder mixtures is demonstrated as a means to simultaneously synthesize and densify nano-MoSi2 in one step. Nanophase reactants (Mo + 2Si) produced by mechanical activation are reacted by field activation with the simultaneous application of a uniaxial pressure. Mo + 2Si powders were comilled in a specially designed planetary mill to obtain nanometric reactants but to avoid formation of any product phases. These were then subjected to high alternating currents (1600 A) and pressures of 106 MPa. Under these conditions, a reaction is initiated and completed within a short period of tim…
Correlative study of structural and optical properties of ZnSe under severe plastic deformation
2019
The effect of plastic deformation on the optical and structural properties of ZnSe crystals has been investigated. The optical properties have been monitored by cathodoluminescence measurements as a function of the deformation degree. Remarkable differences in the defect-related emissions from the most severely deformed areas have been encountered. Deformation of the crystal lattice of ZnSe, associated with slip phenomena, has been studied by means of Electron Backscattered Diffraction and micro-Raman spectroscopy. The relation between the deformation and the optical properties of the ZnSe crystals has been described.