Search results for "Convergence of numerical method"

showing 3 items of 3 documents

Vacuum induced berry phase: Theory and experimental proposal

2003

We investigate quantum effects in geometric phases arising when a two-level system is interacting with a quantized electromagnetic field. When the system is adiabatically driven along a closed loop in the parameter space, signatures of the field quantization are observable in the geometric phase. We propose a feasible experiment to measure these effects in cavity QED and also analyse the semi-classical limit, recovering the usual Berry phase results.

Electromagnetic fieldPhysicsJaynes–Cummings modelVacuumGround stateMathematical transformationObservableParameter spaceComputational geometryAtomic and Molecular Physics and OpticsClosed loop control systemQuantization (physics)Mathematical operatorGeometric phaseConvergence of numerical methodQuantum electrodynamicsQuantum mechanicsElectromagnetic fieldBerry connection and curvatureFunctionClosed loopLight polarizationJournal of Modern Optics
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Size-intensive decomposition of orbital energy denominators

2000

We introduce an alternative to Almlöf and Häser’s Laplace transform decomposition of orbital energy denominators used in obtaining reduced scaling algorithms in perturbation theory based methods. The new decomposition is based on the Cholesky decomposition of positive semidefinite matrices. We show that orbital denominators have a particular short and size-intensive Cholesky decomposition. The main advantage in using the Cholesky decomposition, besides the shorter expansion, is the systematic improvement of the results without the penalties encountered in the Laplace transform decomposition when changing the number of integration points in order to control the convergence. Applications will…

Laplace transformIntegrationGeneral Physics and AstronomyMinimum degree algorithmOrbital calculations ; Perturbation theory ; Convergence of numerical methods ; Integration ; Coupled cluster calculationsPositive-definite matrixPerturbation theoryUNESCO::FÍSICA::Química físicaOrbital calculationsSpecific orbital energyPhysics and Astronomy (all)Coupled cluster calculationsComputational chemistryConvergence (routing)Decomposition (computer science)Convergence of numerical methodsApplied mathematicsPhysical and Theoretical ChemistryPerturbation theory:FÍSICA::Química física [UNESCO]Cholesky decompositionMathematics
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Modeling Atmospheric Turbulence via Rapid Distortion Theory: Spectral Tensor of Velocity and Buoyancy

2017

Abstract A spectral tensor model is presented for turbulent fluctuations of wind velocity components and temperature, assuming uniform vertical gradients in mean temperature and mean wind speed. The model is built upon rapid distortion theory (RDT) following studies by Mann and by Hanazaki and Hunt, using the eddy lifetime parameterization of Mann to make the model stationary. The buoyant spectral tensor model is driven via five parameters: the viscous dissipation rate ε, length scale of energy-containing eddies L, a turbulence anisotropy parameter , gradient Richardson number (Ri) representing the local atmospheric stability, and the rate of destruction of temperature variance . Model outp…

Length scaleAtmospheric Science010504 meteorology & atmospheric sciencesK-epsilon turbulence modelFLOWVelocityTensorsWind01 natural sciencesWind speedAtmospheric temperature010305 fluids & plasmasPhysics::Fluid DynamicsEnergy-containing eddiesConvergence of numerical methodsMonin-Obukhov similarity theorySCALEPhysicsTurbulenceAtmospheric turbulenceMechanicsBuoyancySURFACE-LAYER TURBULENCEClassical mechanicsFluxesStratified turbulenceSIMILARITYSIMULATIONBoundary layersStabilityBuoyancyMETEOROLOGYengineering.materialPROFILEAtmospheric thermodynamics0103 physical sciencesAtmospheric instabilityWind shearsSTABLY STRATIFIED TURBULENCETensorRapid distortion theory0105 earth and related environmental sciencesWind shearBoundary layer flowRichardson numberAtmospheric observationsViscous dissipation rateHorizontal array turbulence study field programsTurbulenceBoundary layerengineeringJournal of the Atmospheric Sciences
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