Search results for "Geometry"

showing 10 items of 4487 documents

A double mean field equation related to a curvature prescription problem

2019

We study a double mean field-type PDE related to a prescribed curvature problem on compacts surfaces with boundary. We provide a general blow-up analysis, then a Moser-Trudinger inequality, which gives energy-minimizing solutions for some range of parameters. Finally, we provide existence of min-max solutions for a wider range of parameters, which is dense in the plane if $��$ is not simply connected.

Blow–up analysiPlane (geometry)Applied Mathematics010102 general mathematicsMathematics::Analysis of PDEs35J20 58J32Boundary (topology)Unit normal vectorCurvature01 natural sciencesConformal metric010101 applied mathematicsMathematics - Analysis of PDEsVariational methodsMean field equationSimply connected spaceFOS: Mathematics0101 mathematicsPrescribed curvature problemAnalysisMathematical physicsMathematicsAnalysis of PDEs (math.AP)
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The development of a hybrid technique employing the boundary element method for thermoelastic stress separation

2000

: This paper presents a development of a hybrid technique employing a boundary element method for determining individual stress components in two-dimensional arbitrarily shaped domains from experimental isopachics only. The procedure consists of a numerical solution of two Poisson equations representing equilibrium for two-dimensional plane-stressed solids with zero body forces. An existing technique is employed for smoothing interior thermoelastic data and enhancing boundary information. The algorithm of stress separation has been implemented with the help of commercial codes. The whole procedure has been tested through a complete post-processing example of thermoelastic stress analysis da…

Body forceStress (mechanics)Thermoelastic dampingMechanics of MaterialsMechanical EngineeringNumerical analysisMathematical analysisBoundary (topology)GeometryPoisson's equationBoundary element methodSmoothingMathematics
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Neutron diffraction studies of structural and magnetic properties of niobium doped cobaltites.

2009

Neutron powder diffraction studies of the structural and magnetic properties of the La(1-x)Sr(x)Nb(y)Co(1-y)O(3) solid solutions (x = 0.2, 0.5; y = 0, 0.075, 0.1) have been performed. Substitution of Co(2+) by Nb(5+) prevents the formation of Co(4+) and leads to stabilization of the Co(3+) ions in the high- or intermediate-spin state. This is accompanied by the significant change of the Co-O bond length as well as Co-O-Co bond angle in the CoO(6) octahedron. The obtained data are in agreement with the negative sign of the magnetic exchange interactions Co(3+)-O-Co(3+) in a relatively wide range of the Co-O-Co bond angles. Diamagnetic dilution by the niobium ions prevents long-range magnetic…

Bond lengthCrystallographyMagnetizationMolecular geometryMagnetoresistancechemistryMagnetic momentNeutron diffractionNiobiumchemistry.chemical_elementDiamagnetismGeneral Materials ScienceCondensed Matter PhysicsJournal of physics. Condensed matter : an Institute of Physics journal
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On the geometry of the HO3 radical

2008

Abstract We discuss the equilibrium structure of the hydrogen trioxy radical (HO3). The CCSD(T) geometry at the approximate basis set limit, in conjunction with the geometry obtained using the CCSDT method and a moderate basis set, suggests an equilibrium HO–OO bond length of approximately 1.59 A.

Bond lengthHydrogenchemistryStructure (category theory)General Physics and Astronomychemistry.chemical_elementMoleculeGeometryLimit (mathematics)Physical and Theoretical ChemistryBasis setChemical Physics
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GERMANIUM DICARBIDE: EVIDENCE FOR A T−SHAPED GROUND STATE STRUCTURE

2017

The equilibrium structure of germanium dicarbide GeC2 has been an open question since the late 1950s. Although most high-level quantum calculations predict an L-shaped geometry, a T-shaped or even a linear geometry cannot be ruled out because of the very flat potential energy surface. By recording the rotational spectrum of this dicarbide using sensitive microwave and millimeter techniques, we unambiguously establish that GeC2 adopts a vibrationally averaged T-shaped structure in its ground state. From analysis of 14 isotopologues, a precise r0 structure has been derived, yielding a Ge–C bond length of 1.952(1) A and an apex angle of 38.7(2)°.

Bond lengthMaterials sciencechemistryPotential energy surfacechemistry.chemical_elementMillimeterIsotopologueGermaniumLinear molecular geometryGround stateMolecular physicsMicrowaveNuclear chemistryProceedings of the 72nd International Symposium on Molecular Spectroscopy
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An ab initio study of the tautomeric equilibria of the N-oxides of hydroxypyridines in the vapour phase

1993

Abstract An ab initio self-consistent field molecular orbital study of the N-oxides of hydroxypyridines has been carried out. The optimized structures have been obtained at the 6-31G ∗ level, and the energy values have been computed at the 6-31G ∗ and MP2-6-31G ∗ //6-31G ∗ levels. The tautomerization energies for the three couples of systems in the vapour phase have been evaluated.

Bond lengthMolecular geometryElectronic correlationChemistryAb initio quantum chemistry methodsComputational chemistryPhase (matter)Ab initioMolecular orbitalPhysical and Theoretical ChemistryCondensed Matter PhysicsBiochemistryTautomerJournal of Molecular Structure: THEOCHEM
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Continuum Monte Carlo simulation of phase transitions in rod-like molecules at surfaces

1994

Stiff rod-like chain molecules with harmonic bond length potentials and trigonometric bond angle potentials are used to model Langmuir monolayers at high densities. One end of the rod-like molecules is strongly bound to a flat two-dimensional substrate which represents the air-water interface. A ground-state analysis is performed which suggests phase transitions between phases with and without collective uniform tilt. Large-scale off-lattice Monte Carlo simulations over a wide temperature range show in addition to the tilting transition the presence of a strongly constrained melting transition at high temperatures. The latter transition appears to be related to two-dimensional melting of th…

Bond lengthPhase transitionMolecular geometryMaterials scienceCondensed matter physicsLattice (order)Monte Carlo methodMonolayerGeneral Physics and AstronomyMoleculeAtmospheric temperature rangeIl Nuovo Cimento D
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A theoretical determination of the dissociation energy of the nitric oxide dimer

1994

Multi-reference CI methods have been applied to determine the dissociation energy and structure of thecis-N2O2 molecule. The convergence of the theoretical result has been checked with respect to a systematic expansion of the one-electron basis set and the multi-reference CI wave function. The best calculated value, 13.8 kJ/mol, is in agreement with the experimental value, 12.2 kJ/mol. It has been obtained with an extended ANO-type basis set [6s5p3d2f], including the effect of the basis set superposition error (BSSE) in the geometry optimization, and additional effects, such as the electron correlation of core electrons and relativistic corrections, using the average coupled pair functional…

Bond lengthPhysicsMolecular geometryElectronic correlationCore electronAb initio quantum chemistry methodsThermodynamicsChiropracticsPhysical and Theoretical ChemistryConfiguration interactionBond-dissociation energyBasis setTheoretica Chimica Acta
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AM1 prediction of the equilibrium geometry of Si60

1993

Abstract AM1 calculations have been carried out to determine the equilibrium geometry of Si 60 . The predicted I h geometry shows that bonds may be clearly identified as single (2.297 A) or aromatic (2.092 A). Several analogies and differences between Si 60 and C 60 are pointed out. Especially remarkable is the bigger size of the Si 60 cluster, which is predicted to have a radius 2 A larger than that of the C 60 cluster. Results are compared to other levels of theory.

Bond lengthSiliconChemistryComputational chemistryCluster (physics)General Physics and AstronomyMoleculeThermodynamicschemistry.chemical_elementElectronic structureRadiusPhysical and Theoretical ChemistryEquilibrium geometryChemical Physics Letters
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Experimental and theoretical studies of the molecular and crystal structures of trialkoxy- and chlorodialkoxy-stibanes

2001

The molecular structures of triisopropoxystibane, Sb((OPr)-Pr-i)(3), and chlorodiisopropoxystibane, SbCl((OPr)-Pr-i)(2), were determined in the solid state by single crystal X-ray diffraction. Sb((OPr)-Pr-i)(3) forms discrete centrosymmetric dimers in the solid state via Sb . . .O-Sb interactions, leading to pseudo trigonal bipyramidal configurations of the four co-ordinate Sb atoms, while SbCl((OPr)-Pr-i)(2) forms chains via Sb . . .O-Sb and Sb . . . Cl-Sb bridges, resulting in five-co-ordinate Sb atoms with pseudo octahedral configurations. Comparison of the solid state structures and the density functional optimized molecular structures of Sb(OMe)(3), SbCl(OMe)(2) and their dimers reveal…

Bond lengthTrigonal bipyramidal molecular geometryCrystallographychemistry.chemical_compoundOctahedronChemistryStereochemistryDimerGeneral ChemistryCrystal structureSingle crystalDissociation (chemistry)Natural bond orbital
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