Search results for " critical points"

showing 10 items of 21 documents

On the existence and multiplicity of solutions for Dirichlet's problem for fractional differential equations

2016

In this paper, by using variational methods and critical point theorems, we prove the existence and multiplicity of solutions for boundary value problem for fractional order differential equations where Riemann-Liouville fractional derivatives and Caputo fractional derivatives are used. Our results extend the second order boundary value problem to the non integer case. Moreover, some conditions to determinate nonnegative solutions are presented and examples are given to illustrate our results.

Applied Mathematics010102 general mathematicsMathematical analysisMultiplicity (mathematics)01 natural sciencesDirichlet distribution010101 applied mathematicssymbols.namesakeSettore MAT/05 - Analisi MatematicasymbolsApplied mathematics0101 mathematicsFractional differentialAnalysisfractional differential equations critical points theorem variational methods multiple solutionsMathematics
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Characterization of the pressure induced Ringwoodite toMg-perovskite and Mg-wüstite phase transition by Catastrophe Theory

2010

Bader’s topological analysis Catastrophe Theory ab initio critical points
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The pressure-induced ringwoodite to Mg-perovskite and periclase post-spinel phase transition: a Bader’s topological analysis of the ab initio electro…

2011

In order to characterize the pressure-induced decomposition of ringwoodite (c-Mg2SiO4), the topological analysis of the electron density q(r), based upon the theory of atoms in molecules (AIM) developed by Bader in the framework of the catastrophe theory, has been performed. Calculations have been carried out by means of the ab initio CRYSTAL09 code at the HF/DFT level, using Hamiltonians based on the Becke- LYP scheme containing hybrid Hartree– Fock/density functional exchange–correlation terms. The equation of state at 0 K has been constructed for the three phases involved in the post-spinel phase transition (ringwoodite -> Mg-perovskite + periclase) occurring at the transition zone–lower…

Bader’s topological analysisElectron densityEquation of statePhase transitionRingwoodite Post-spinel phase transition Bader’s topological analysis Ab initio Catastrophe theory Critical pointsChemistryCatastrophe theoryAtoms in moleculesRingwooditeAb initioCritical pointsHartreeengineering.materialTopologyRingwoodite; Post-spinel phase transition; Bader’s topological analysis; Ab initio; Catastrophe theory; Critical pointsPost-spinel phase transitionRingwooditeGeochemistry and PetrologyBader’s topological analysiAb initioengineeringGeneral Materials SciencePerovskite (structure)
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Oscillatory integrals and fractal dimension

2021

Theory of singularities has been closely related with the study of oscillatory integrals. More precisely, the study of critical points is closely related to the study of asymptotic of oscillatory integrals. In our work we investigate the fractal properties of a geometrical representation of oscillatory integrals. We are motivated by a geometrical representation of Fresnel integrals by a spiral called the clothoid, and the idea to produce a classification of singularities using fractal dimension. Fresnel integrals are a well known class of oscillatory integrals. We consider oscillatory integral $$ I(\tau)=\int_{; ; \mathbb{; ; R}; ; ^n}; ; e^{; ; i\tau f(x)}; ; \phi(x) dx, $$ for large value…

Box dimensionGeneral Mathematics010102 general mathematicsMathematical analysisPhase (waves)Resolution of singularitiesOscillatory integral ; Box dimension ; Minkowski content ; Critical points ; Newton diagramCritical points01 natural sciencesFractal dimensionCritical point (mathematics)Oscillatory integralAmplitudeDimension (vector space)Mathematics - Classical Analysis and ODEsMinkowski contentClassical Analysis and ODEs (math.CA)FOS: Mathematics0101 mathematicsMinkowski contentOscillatory integralNewton diagram[MATH]Mathematics [math]fractal dimension; box dimension; oscillatory integrals; theory of singularitiesMathematics
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Calibrations and isoperimetric profiles

2007

We equip many noncompact nonsimply connected surfaces with smooth Riemannian metrics whose isoperimetric profile is smooth, a highly nongeneric property. The computation of the profile is based on a calibration argument, a rearrangement argument, the Bol-Fiala curvature dependent inequality, together with new results on the profile of surfaces of revolution and some hardware know-how.

Calibration Riemann manifold Critical points Surfaces of revolution Radius of curvature Mathematical surfaces Mathematical constants DuetsSettore MAT/03 - Geometria
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Multiple solutions for a discrete boundary value problem involving the p-Laplacian.

2008

Multiple solutions for a discrete boundary value problem involving the p-Laplacian are established. Our approach is based on critical point theory.

Computational MathematicsComputational Theory and MathematicsSettore MAT/05 - Analisi MatematicaModeling and SimulationMathematical analysisFree boundary problemp-LaplacianBoundary value problemMixed boundary conditionElliptic boundary value problemCritical point (mathematics)Discrete boundary value problem multiple solutions p-Laplacian critical points theoryMathematics
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Existence of non-zero solutions for a Dirichlet problem driven by (p(x),q(x)-Laplacian

2021

The paper focuses on a Dirichlet problem driven by the (Formula presented.) -Laplacian. The existence of at least two non-zero solutions under suitable conditions on the nonlinear term is established. The approach is based on variational methods.

Dirichlet problemPure mathematicsmultiple solutionscritical pointsApplied Mathematics010102 general mathematicsZero (complex analysis)q(x))-LaplacianMathematics::Spectral Theory-Laplacian01 natural sciences(p(x)q(x))-Laplacian critical points multiple solutions Dirichlet problemTerm (time)010101 applied mathematicsNonlinear systemSettore MAT/05 - Analisi Matematica0101 mathematics(p(x)Laplace operatorAnalysisDirichlet problemMathematicsApplicable Analysis
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Electron-density critical points analysis and catastrophe theory to forecast structure instability in periodic solids

2018

The critical points analysis of electron density,i.e. ρ(x), fromab initiocalculations is used in combination with the catastrophe theory to show a correlation between ρ(x) topology and the appearance of instability that may lead to transformations of crystal structures, as a function of pressure/temperature. In particular, this study focuses on the evolution of coalescing non-degenerate critical points,i.e. such that ∇ρ(xc) = 0 and λ1, λ2, λ3≠ 0 [λ being the eigenvalues of the Hessian of ρ(x) atxc], towards degenerate critical points,i.e. ∇ρ(xc) = 0 and at least one λ equal to zero. The catastrophe theory formalism provides a mathematical tool to model ρ(x) in the neighbourhood ofxcand allo…

Hessian matrixElectron densitycatastrophe theory010504 meteorology & atmospheric sciencesCondensed Matter Physic010502 geochemistry & geophysics01 natural sciencesBiochemistryInstabilityInorganic Chemistrysymbols.namesakeStructural BiologyAb initio quantum chemistry methodsGeneral Materials Sciencephase/state transitions in crystalPhysical and Theoretical Chemistryphase/state transitions in crystalsEigenvalues and eigenvectors0105 earth and related environmental sciencesPhysicsab initio calculationelectron-density critical pointCondensed matter physicsab initio calculationsDegenerate energy levelsCondensed Matter PhysicsGibbs free energyelectron-density critical points catastrophe theory phase/state transitions in crystals ab initio calculations.symbolsMaterials Science (all)Catastrophe theoryelectron-density critical points
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Raman study of self-assembled InAs/InP quantum wire stacks with varying spacer thickness

2008

http://link.aip.org/link/?JAPIAU/104/033523/1

III-V semiconductorsMaterials sciencePhononAnnealing (metallurgy)General Physics and AstronomyCritical pointsDielectricAnnealingCondensed Matter::Materials Sciencesymbols.namesake:FÍSICA [UNESCO]Indium compoundsCondensed matter physicsQuantum wireUNESCO::FÍSICAAnnealing ; Critical points ; III-V semiconductors ; Indium compounds ; Phonons ; Raman spectra ; Self-assembly ; Semiconductor quantum wiresSelf-assemblyCondensed Matter::Mesoscopic Systems and Quantum Hall EffectMolecular vibrationSemiconductor quantum wiressymbolsPhononsRaman spectraRaman spectroscopyExcitationRaman scatteringJournal of Applied Physics
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Pressure stability field of Mg-perovskite under deep mantle conditions: A topological approach based on Bader's analysis coupled with catastrophe the…

2019

Abstract The pressure stability field of the Mg-perovskite phase was investigated by characterizing the evolution of the electron arrangement in the crystal. Ab initio calculations of the perovskite structures in the range 0–185 GPa were performed at the HF/DFT (Hartree-Fock/Density Functional Theory) exchange–correlation terms level. The electron densities, calculated throughout the ab-initio wave functions, were analysed by means of the Bader's theory, coupled with Thom's catastrophe theory. To the best of our knowledge the approach is used for the first time. The topological results show the occurrence of two topological anomalies at P~20 GPa and P~110 GPa which delineate the pressure ra…

Materials Chemistry2506 Metals and AlloysMaterials scienceBader analysisAb initioSurfaces Coatings and FilmCritical pointsCeramics and Composite02 engineering and technologyElectronD’’ regionPerovskiteTopology01 natural sciencesCritical pointPhysics::GeophysicsFock spaceCoatings and FilmsCondensed Matter::Materials ScienceAb initio quantum chemistry methods0103 physical sciencesElectronicMaterials ChemistryOptical and Magnetic MaterialsAb initio; Bader analysis; Catastrophe theory; Critical points; Deep mantle; D’’ region; HF/DFT; High pressure; Perovskite; Topological analysis; Electronic Optical and Magnetic Materials; Ceramics and Composites; Process Chemistry and Technology; Surfaces Coatings and Films; Materials Chemistry2506 Metals and AlloysWave function010302 applied physicsCatastrophe theoryElectronic Optical and Magnetic MaterialProcess Chemistry and TechnologyHartree021001 nanoscience & nanotechnologyHF/DFTSurfaces Coatings and FilmsElectronic Optical and Magnetic MaterialsSurfacesTopological analysiHigh pressureAb initioCeramics and CompositesDensity functional theoryDeep mantleCatastrophe theory0210 nano-technologyTopological analysisBader analysiCeramics International
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