Search results for "High order"

Three-Dimensional Numerical Model of an H2+ Ion in Intense Laser Fields

2010

The Emergence of Chaos in Quantum Mechanics

2020

Nonlinearity in Quantum Mechanics may have extrinsic or intrinsic origins and is a liable route to a chaotic behaviour that can be of difficult observations. In this paper, we propose two forms of nonlinear Hamiltonian, which explicitly depend upon the phase of the wave function and produce chaotic behaviour. To speed up the slow manifestation of chaotic effects, a resonant laser field assisting the time evolution of the systems causes cumulative effects that might be revealed, at least in principle. The nonlinear Schr&ouml

On the convergent parts of high order spectral moments of stationary structural responses

1986

The paper deals with the evaluation of the convergent parts of the high spectral moments of linear systems subjected to stationary random input. An adequate physical meaning of these quantities in both the time and frequency domains is presented. Recurrence formulas to obtain the high convergent cross spectral moments of any order are given in the case of white noise input.

Some efficient algorithms for the solution of a single nonlinear equation

1981

High order methods for the numerical solution of nonlinear scalar equations are proposed which are more efficient than known procedures, and a unified approach to various methods suggested in literature is given.

Hölder Continuity up to the Boundary of Minimizers for Some Integral Functionals with Degenerate Integrands

2007

We study qualitative properties of minimizers for a class of integral functionals, defined in a weighted space. In particular we obtain Hölder regularity up to the boundary for the minimizers of an integral functional of high order by using an interior local regularity result and a modified Moser method with special test function.

Hybrid equilibrium element with high-order stress fields for accurate elastic dynamic analysis

2021

In the present article the two-dimensional hybrid equilibrium element formulation is initially developed, with quadratic, cubic, and quartic stress fields, for static analysis of compressible and quasi-incompressible elastic solids in the variational framework of the minimum complementary energy principle. Thereafter, the high-order hybrid equilibrium formulation is developed for dynamic analysis of elastic solids in the variational framework of the Toupin principle, which is the complementary form of the Hamilton principle. The Newmark time integration scheme is introduced for discretization of the stress fields in the time domain and dynamic analysis of both the compressible solid and qua…

Subharmonic phase-lock criteria for a class of weakly non-linear high-order oscillators

1985

Subharmonic frequency entrainment of high-order weakly non-linear oscillators is investigated. For the class of circuits considered, equations are first derived which provide the first approximation values for the amplitudes and phases of the two main spectral components of the steady-state waveform. Necessary and sufficient stability criteria are then derived in explicit from. The example worked out (a negative conductance double-tuned oscillator) shows the efficiency and ease of use of the proposed method.

Shock-capturing schemes: high accuracy versus total-variation boundedness

2007

In this reseach work we analyze the total variation growth of some high order accurate reconstruction procedures used for the design of shock capturing schemes. This study allows to measure how oscillatory a high order accurate method is in terms of the basic elementary function chosen to increase the order of accuracy. (© 2008 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim)

Some Theoretical Results About Stability for IMEX Schemes Applied to Hyperbolic Equations with Stiff Reaction Terms

2010

In this work we are concerned with certain numerical difficulties associated to the use of high order Implicit–Explicit Runge–Kutta (IMEX-RK) schemes in a direct discretization of balance laws with stiff source terms. We consider a simple model problem, introduced by LeVeque and Yee in [J. Comput. Phys 86 (1990)], as the basic test case to explore the ability of IMEX-RK schemes to produce and maintain non-oscillatory reaction fronts.

Investigation of the vibrational dynamics of the HCN/CNH isomers through high order canonical perturbation theory

2000

International audience; Molecular vibrations of the molecule HCN/CNH are examined using a combination of a minimum energy path Hamiltonian and high order canonical perturbation theory , as suggested in a recent work [D. Sugny and M. Joyeux, J. Chem. Phys. 112, 31 (2000)]. In addition, the quantum analog of the classical CPT is presented and results obtained therefrom are compared to the classical ones. The MEP Hamiltonian is shown to provide an accurate representation of the original potential energy surface and a convenient starting point for the CPT. The CPT results are subsequently used to elucidate the molecular dynamics: It appears that the isomerization dynamics of HCN/CNH is very tri…