Search results for "boundary"

showing 10 items of 1626 documents

Positive solutions for a discrete two point nonlinear boundary value problem with p-Laplacian

2017

Abstract In the framework of variational methods, we use a two non-zero critical points theorem to obtain the existence of two positive solutions to Dirichlet boundary value problems for difference equations involving the discrete p -Laplacian operator.

Difference equationDiscrete boundary value problemTwo solution01 natural sciencesElliptic boundary value problemDirichlet distributionCritical point theory; Difference equations; Discrete boundary value problems; p-Laplacian; Positive solutions; Two solutions; Analysis; Applied MathematicsPositive solutionsymbols.namesakePoint (geometry)Boundary value problem0101 mathematicsMathematicsApplied Mathematics010102 general mathematicsMathematical analysisp-LaplacianAnalysiMixed boundary condition010101 applied mathematicssymbolsp-LaplacianCritical point theoryNonlinear boundary value problemLaplace operatorAnalysis
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A hierarchy of simplified constitutive models within isotropic strain gradient elasticity

2017

Abstract Simplified isotropic models of strain gradient elasticity are presented, based on the mutual relationship between the inherent (dual) gradient directions (i.e. the gradient direction of any strain gradient source and the lever arm direction of the promoted double stress). A class of gradient-symmetric materials featured by gradient directions obeying a reciprocity relation and by 4 independent h.o. (higher order) coefficients is envisioned, along with the sub-classes of hemi-collinear materials (3 h.o. coefficients, gradient directions in part coincident), collinear materials (2 h.o. coefficients, equal gradient directions) and micro-affine materials (1 h.o. coefficient, behavioral…

Differential equationMechanical EngineeringMathematical analysisIsotropyGeneral Physics and AstronomyGeometry02 engineering and technology021001 nanoscience & nanotechnology020303 mechanical engineering & transports0203 mechanical engineeringPositive definitenessMechanics of MaterialsCoincidentReciprocity (electromagnetism)TorqueGeneral Materials ScienceBoundary value problemElasticity (economics)0210 nano-technologyMathematicsEuropean Journal of Mechanics - A/Solids
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High-Pressure High-Temperature Stability and Thermal Equation of State of Zircon-Type Erbium Vanadate.

2018

Inorganic chemistry 57(21), 14005 - 14012 (2018). doi:10.1021/acs.inorgchem.8b01808

DiffractionDYNAMICSEquation of statePhase boundaryThermodynamics02 engineering and technologyzircon010402 general chemistry01 natural sciencesThermal expansionInorganic Chemistrychemistry.chemical_compoundX-RAY-DIFFRACTIONPhase (matter)Physical and Theoretical ChemistryChemistryX-RAY-DIFFRACTION; DYNAMICS021001 nanoscience & nanotechnology5400104 chemical scienceshigh pressureScheeliteX-ray crystallographyddc:5400210 nano-technologyZirconInorganic chemistry
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Equation of state and high-pressure/high-temperature phase diagram of magnesium

2014

The phase diagram of magnesium has been investigated to 211 GPa at 300 K, and to 105 GPa at 4500 K, by using a combination of x-ray diffraction and resistive and laser heating. The ambient pressure hcp structure is found to start transforming to the bcc structure at ∼45 GPa, with a large region of phase-coexistence that becomes smaller at higher temperatures. The bcc phase is stable to the highest pressures reached. The hcp-bcc phase boundary has been studied on both compression and decompression, and its slope is found to be negative and steeper than calculations have previously predicted. The laser-heating studies extend the melting curve of magnesium to 105 GPa and suggest that, at the h…

DiffractionPhase boundaryEquation of stateMaterials scienceCondensed matter physicsMagnesiumThermodynamicschemistry.chemical_elementCondensed Matter PhysicsElectronic Optical and Magnetic MaterialschemistryPhase (matter)X-ray crystallographyPhase diagramAmbient pressure
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Melting curve and phase diagram of vanadium under high-pressure and high-temperature conditions

2019

Melting curve and phase diagram of vanadium under high-pressure and high-temperature conditions We report a combined experimental and theoretical study of the melting curve and the structural behavior of vanadium under extreme pressure and temperature. We performed powder x-ray-diffraction experiments up to 120 GPa and 4000 K, determining the phase boundary of the body-centered cubic-to-rhombohedral transition and melting temperatures at different pressures. Melting temperatures have also been established from the observation of temperature plateaus during laser heating, and the results from the density-functional theory calculations. Results obtained from our experiments and calculations a…

DiffractionPhase boundaryEquation of stateMaterials scienceThermodynamicsVanadiumchemistry.chemical_element02 engineering and technology01 natural sciencesMelting curve analysisCrystalCondensed Matter::Materials ScienceX-RAY-DIFFRACTIONNACLCondensed Matter::Superconductivity0103 physical sciencesELEMENTSCELL010306 general physicsTANTALUMPhase diagramCRYSTALIRON021001 nanoscience & nanotechnologyEQUATION-OF-STATEchemistryX-ray crystallographyCondensed Matter::Strongly Correlated Electrons0210 nano-technologySYSTEM
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Detection of morphotropic phase boundary in A-site/Ca-substituted Na0.5Bi0.5TiO3 complex oxides ferroelectric system

2020

Abstract Vibrational and structural properties of lead-free piezoelectric (1-x)Na0.5Bi0.5TiO3–xCaTiO3 (0 ≤ x ≤ 1.00) solid solutions have been investigated using Raman spectroscopy and X-ray diffraction. Different anomalies were detected and analyzed taking into consideration the phase transition from rhombohedral to orthorhombic phase at room temperature. All Raman bands were interpreted through the variation in the peak positions (frequency) and the corresponding half-widths at half maximum (HWHM) as a function of x. XRD used as a complementary technique to Raman spectroscopy, showed that the rhombohedral – orthorhombic phase transition went gradually through an intermediate phase consist…

DiffractionPhase boundaryPhase transitionMaterials scienceMechanical EngineeringMetals and AlloysAnalytical chemistry02 engineering and technology010402 general chemistry021001 nanoscience & nanotechnology01 natural sciencesFerroelectricity0104 chemical sciencessymbols.namesakeMechanics of MaterialsPhase (matter)Materials Chemistrysymbols[CHIM]Chemical SciencesOrthorhombic crystal system0210 nano-technologyRaman spectroscopySolid solution
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Structure and Dielectric Properties of Na1/2Bi1/2TiO3-BaTiO3Solid Solutions

2013

Dielectric properties, polarization and x-ray diffraction are studied for (1-x)Na1/2Bi1/2TiO3-xBaTiO3 solid solutions in a concentration range above the morphotropic phase boundary. It is showed that all the studied compositions have tetragonal structure with maximal tetragonality slightly above the morphotropic phase boundary. Ferroelectric relaxor behavior is observed in a wide concentration range of BaTiO3. Stability of the relaxor state decreases with increasing BaTiO3 concentration, but only for compositions with low Na1/2Bi1/2TiO3 content the normal ferroelectric-paraelectric phase transition, which is characteristic to pure BaTiO3, occurs. Mechanisms, which influence the change of th…

DiffractionPhase transitionPhase boundaryTetragonal crystal systemMaterials scienceNuclear magnetic resonanceThermodynamicsDielectricCondensed Matter PhysicsPolarization (electrochemistry)Electronic Optical and Magnetic MaterialsPhase diagramSolid solutionFerroelectrics
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An Analysis of the Broadening Induced by Beam Damage in Transmission Electron Diffraction Spots from an Oriented Aliphatic Monolayer

1991

We have analysed the progressive changes in diffraction spot shape during prolonged transmission electron diffraction observation of a soap monolayer supported on a thin polymer film. The material used to form the monolayer was cadmium eicosanoate (arachidate). The observed changes cannot be explained at all in terms of the chemical crosslinking which is known to occur as a result of beam damage, nor completely in terms of the strain fields caused by unbound dislocation defects of the crystalline lattice. The most plausible explanation involves the formation of linear dislocation aggregates which resemble grain boundaries but yet which are not linked into a continuous network. The evolution…

Diffractionchemistry.chemical_compoundCrystallographyElectron diffractionChemistryMonolayerGrain boundaryCrystal structureDislocationSilicon monoxideMolecular physicsBeam (structure)
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Textures and c-axis orientations of deformed quartz crystals from porphyric dikes of the Alpine »Root Zone« (Western Alps)

1986

Deformation textures and c-axis preferred orientations of quartz phenocrysts from porphyric dikes of the Alpine »Root Zone« have been formed under conditions of greenschist to low amphibolite facies. It is shown that the deformation textures as shear planes and kink bands, boudins, grain boundary sutures, subgrains, coarse and fine recrystallized grains, deformation lamellae and fractures are developed in a chronological sequence during first increasing and later decreasing temperatures. The c-axis orientations are chiefly influenced by kinking during the early stage of metamorphism and later by recrystallization but not by the initial orientations of the c-axes. The shape of crossed-girdle…

Dikegeographygeography.geographical_feature_categoryGreenschistGeochemistryMineralogyMetamorphismShear (geology)General Earth and Planetary SciencesPhenocrystGrain boundaryQuartzGeologyMetamorphic faciesGeologische Rundschau
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<title>Thermostimulated electronic and ionic processes in irradiated sapphire</title>

2003

Electronic and ionic thermostimulated (TS) relaxation (TSR) processes in nominally pure sapphire (α-Al2O3 grown with oxygen deficiency) have been investigated at 290 - 650 K by means of the TS current (TSC), ionic depolarization current (TSDC) and electron emission (TSEE) techniques. After thermal (ionic) polarization of the reduced sapphire wide (approximately 75 K) and asymmetric ionic dipolar TSDC peak at 590 K (disorientation of the anion vacancy-related dipoles) was detected. Above 450 - 500 K the anion vacancy hopping (migration) starts and their interaction with defects take place. This can lead to lattice dynamic disordering and anion vacancy diffusion-controlled processes in sapphi…

DipoleCrystallographyMaterials scienceImpurityElectric fieldVacancy defectAnalytical chemistrySapphireIonic bondingGrain boundaryIonSPIE Proceedings
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