Search results for "Fourth order"

showing 10 items of 16 documents

Multiplicity results for fourth order two-point boundary value problems with asymmetric nonlinearities

1998

Point boundaryFourth orderApplied MathematicsMultiplicity resultsConjugate pointsMathematical analysisMultiplicity (mathematics)AnalysisMathematicsNonlinear Analysis: Theory, Methods & Applications
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On the convergence of perturbative coupled cluster triples expansions:Error cancellations in the CCSD(T) model and the importance of amplitude relaxa…

2015

Recently, we proposed a novel Lagrangian-based perturbation series-the CCSD(T-n) series-which systematically corrects the coupled cluster singles and doubles (CCSD) energy in orders of the Møller-Plesset fluctuation potential for effects due to triple excitations. In the present study, we report numerical results for the CCSD(T-n) series up through fourth order which show the predicted convergence trend throughout the series towards the energy of its target, the coupled cluster singles, doubles, and triples (CCSDT) model. Since effects due to the relaxation of the CCSD singles and doubles amplitudes enter the CCSD(T-n) series at fourth order (the CCSD(T-4) model), we are able to separate th…

PhysicsGeneral Physics and AstronomyPerturbation (astronomy)T-modelCoupled clusterFourth orderAmplitudeClassical mechanicsPhysics::Atomic and Molecular ClustersPerturbation theory (quantum mechanics)Physical and Theoretical ChemistryTotal energyTriplet statePhysics::Chemical PhysicsMathematical physics
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Oscillation of fourth-order quasilinear differential equations

2015

We study oscillatory behavior of a class of fourth-order quasilinear differential equations without imposing restrictive conditions on the deviated argument. This allows applications to functional differential equations with delayed and advanced arguments, and not only these. New theorems are based on a thorough analysis of possible behavior of nonoscillatory solutions; they complement and improve a number of results reported in the literature. Three illustrative examples are presented.

Class (set theory)Fourth orderDifferential equationOscillationGeneral MathematicsMathematical analysisArgument (linguistics)MathematicsComplement (set theory)
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Direct perturbation theory in terms of energy derivatives: Fourth-order relativistic corrections at the Hartree–Fock level

2011

In this work, the quantum-chemical treatment of relativistic effects by means of direct perturbation theory is extended from its lowest order, DPT2, to the next higher order, DPT4. The required theory is given in terms of energy derivatives with the DPT4 energy correction defined as the corresponding second derivative with respect to the relativistic perturbation parameter λ(rel) = c(2) and c as the speed of light. To facilitate the implementation in standard quantum-chemical program packages, a general formulation of DPT starting from a nonrelativistic Lagrangian is developed, thereby expanding both wave function and operators in terms of λ(rel). The corresponding expressions, which incorp…

PhysicsHartree–Fock methodGeneral Physics and AstronomyPerturbation (astronomy)symbols.namesakeFourth orderModels ChemicalQuantum electrodynamicssymbolsQuantum TheoryPhysical and Theoretical ChemistryRelativistic quantum chemistryWave functionHyperfine structureSoftwareLagrangianSecond derivativeThe Journal of Chemical Physics
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Some fourth order CY-type operators with non symplectically rigid monodromy

2012

We study tuples of matrices with rigidity index two in $\Sp_4(\mathbb{C})$, which are potentially induced by differential operators of Calabi-Yau type. The constructions of those monodromy tuples via algebraic operations and middle convolutions and the related constructions on the level differential operators lead to previously known and new examples.

Pure mathematicsGeneral Mathematics010102 general mathematics010103 numerical & computational mathematicsDifferential operator01 natural sciencesMathematics - Algebraic GeometryFourth orderMathematics::Algebraic GeometryMonodromyMathematics - Classical Analysis and ODEsAlgebraic operationClassical Analysis and ODEs (math.CA)FOS: MathematicsHadamard product0101 mathematicsTupleMathematics::Symplectic GeometryAlgebraic Geometry (math.AG)Mathematics
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nalysis, Modeling and Simulation of Mechatronic Systems using the Bond Graph Method

2011

The Bond Graph is the proper choice of physical system used for: (i) Modeling which can be applied to systems combining multidisciplinary energy domains, (ii) Analysis to provide a great value proposition for finding the algebraic loops within the system enabling the process of troubleshooting and eliminating the defects by using the proper component(s) to fix the causality conflict even without being acquainted in the proper system, and (iii) Simulation facilitated through derived state space equations from the Bond Graph model is solved using industrial simulation software, such as 20-Sim. The Bond Graph technique is a graphical language of modeling, in which component energy ports are co…

Theoretical computer scienceMomentumComputer sciencePhysical systemDielectric electro active polymers (DEAP)Fourth order electrical systemTroubleshootingTopologycomputer.software_genrelcsh:QA75.5-76.95Modeling and simulationComponent (UML)Bond graphPush actuatorState-space representationProcess (computing)Casual strokeDisplacementEffective strokeComputer Science ApplicationsSimulation software20-Sim toolControl and Systems EngineeringModeling and SimulationEffective forcelcsh:Electronic computers. Computer sciencecomputerBond graphSoftwareModeling, Identification and Control: A Norwegian Research Bulletin
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Electric Field Dependence of the Fluorescence Intensity of Solute Molecules and Fourth Order Effects

1985

Abstract The effect of an external electric field on the total fluorescence of solute molecules is studied up to fourth order theoretically, and is checked experimentally with 4´-N,N-dimethylamino- 4-nitrostilbene in dioxane at room temperature.

Fourth order equationChemistrybusiness.industryGeneral Physics and AstronomyFluorescenceFluorescence intensityOpticsFourth orderElectric fieldExternal fieldMoleculeChemical solutionPhysical and Theoretical ChemistryAtomic physicsbusinessMathematical PhysicsZeitschrift für Naturforschung A
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Fourth-order perturbation theory for the half-filled Hubbard model in infinite dimensions

2003

We calculate the zero-temperature self-energy to fourth-order perturbation theory in the Hubbard interaction $U$ for the half-filled Hubbard model in infinite dimensions. For the Bethe lattice with bare bandwidth $W$, we compare our perturbative results for the self-energy, the single-particle density of states, and the momentum distribution to those from approximate analytical and numerical studies of the model. Results for the density of states from perturbation theory at $U/W=0.4$ agree very well with those from the Dynamical Mean-Field Theory treated with the Fixed-Energy Exact Diagonalization and with the Dynamical Density-Matrix Renormalization Group. In contrast, our results reveal t…

PhysicsStrongly Correlated Electrons (cond-mat.str-el)Hubbard modelBethe latticeFOS: Physical sciencesRenormalization groupCondensed Matter PhysicsElectronic Optical and Magnetic MaterialsCondensed Matter - Strongly Correlated ElectronsFourth orderIterated functionQuasiparticleDensity of statesCondensed Matter::Strongly Correlated ElectronsPerturbation theory (quantum mechanics)Mathematical physicsThe European Physical Journal B - Condensed Matter
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Strain gradient elasticity within the symmetric BEM formulation

2014

The symmetric Galerkin Boundary Element Method is used to address a class of strain gradient elastic materials featured by a free energy function of the (classical) strain and of its (first) gradient. With respect to the classical elasticity, additional response variables intervene, such as the normal derivative of the displacements on the boundary, and the work-coniugate double tractions. The fundamental solutions - featuring a fourth order partial differential equations (PDEs) system - exhibit singularities which in 2D may be of the order 1/ r 4 . New techniques are developed, which allow the elimination of most of the latter singularities. The present paper has to be intended as a resear…

Partial differential equationStrain gradient elasticity Symmetric Galerkin BEM.Mechanical Engineeringlcsh:Mechanical engineering and machineryStrain gradient elasticityMathematical analysislcsh:TA630-695Symmetric Galerkin BEMlcsh:Structural engineering (General)Directional derivativeStrain gradientFourth orderMechanics of MaterialsGravitational singularitylcsh:TJ1-1570Elasticity (economics)Galerkin methodSettore ICAR/08 - Scienza Delle CostruzioniBoundary element methodStrain gradient elasticity; Symmetric Galerkin BEM.MathematicsFrattura ed Integrità Strutturale
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Strong Instability of Ground States to a Fourth Order Schrödinger Equation

2019

Abstract In this note, we prove the instability by blow-up of the ground state solutions for a class of fourth order Schrödinger equations. This extends the first rigorous results on blowing-up solutions for the biharmonic nonlinear Schrödinger due to Boulenger and Lenzmann [8] and confirm numerical conjectures from [1–3, 11].

General Mathematics010102 general mathematicsMathematics::Analysis of PDEs01 natural sciencesInstabilitySchrödinger equationsymbols.namesakeNonlinear systemFourth ordersymbolsBiharmonic equation[MATH.MATH-AP]Mathematics [math]/Analysis of PDEs [math.AP]0101 mathematicsGround stateSchrödinger's catComputingMilieux_MISCELLANEOUSMathematicsMathematical physicsSciences exactes et naturelles
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