基于哈密顿动力系统新变分原理的保辛算法之二：算法保辛性质证明

文献[1]给出了哈密顿系统的一个新的变分原理,并基于此变分原理,通过选择一个时间步长两端不同广义位移或广义动量为独立变量,给出了四种不同类型的求解哈密顿动力系统的数值方法。本文将分别证明这四类数值方法都是保辛的数值方法。     

Three-dimensional stretched flow of Jeffrey fluid with variable thermal conductivity and thermal radiation

This article addresses the three-dimensional stretched flow of the Jeffrey fluid with thermal radiation. The thermal conductivity of the fluid varies linearly with respect to temperature. Computations are performed for the velocity and temperature fields. Graphs for the velocity and temperature are plotted to examine the behaviors with different parameters. Numerical values of the local Nusselt number are presented and discussed. The present results are compared with the existing limiting solutions, showing good agreement with each other.     

Binary nonlinearization of the super classical-Boussinesq hierarchy

The symmetry constraint and binary nonlinearization of Lax pairs for the super classical-Boussinesq hierarchy is obtained.Under the obtained symmetry constraint,the n-th flow of the super classical-Boussinesq hierarchy is decomposed into two super finite-dimensional integrable Hamiltonian systems,defined over the super-symmetry manifold with the corresponding dynamical variables x and t n.The integrals of motion required for Liouville integrability are explicitly given.     

Modeling Photo-dissociation Dynamics of HBr+ by Vibrational Wave-packet Formalism

Photo dissociation dynamics of diatomic molecular ion HBr⁺ interacting with ultra fast laser pulses of different envelop function has been presented both in zero and non zero temperature environment. The calculations pertain primarily to the ground electronic state of the molecular ion HBr+. The used potential of HBr⁺ is calibrated with the help of the ab initio theoretical calculation at the CCSD/6-311++G(3df, 2pd) level and then fitted with appropriate Morse parameters. The numerical bound states vibrational eigenvalues obtained by the time independent Fourier Grid Hamiltonian method have been compared with analytical values of the fitted Morse potential. The effect of temperature, pulse envelops function, and light intensity on the dissociation process has been explored.     

Adaptive H∞ synchronization of chaotic systems via linear and nonlinear feedback control

Adaptive H∞ synchronization of chaotic systems via linear and nonlinear feedback control is investigated.The chaotic systems are redesigned by using the generalized Hamiltonian systems and observer approach.Based on Lyapunov’s stability theory,linear and nonlinear feedback control of adaptive H∞ synchronization is established in order to not only guarantee stable synchronization of both master and slave systems but also reduce the effect of external disturbance on an H∞-norm constraint.Adaptive H∞ synchronization of chaotic systems via three kinds of control is investigated with applications to Lorenz and Chen systems.Numerical simulations are also given to identify theeffectiveness of the theoretical analysis.     

Noether conserved quantities and Lie point symmetries for difference nonholonomic Hamiltonian systems in irregular lattices

The Noether conserved quantities and the Lie point symmetries for difference nonholonomic Hamiltonian systems in irregular lattices are studied. The generalized Hamiltonian equations of the systems are given on the basis of the transformation operators in the space of discrete Hamiltonians. The Lie transformations acting on the lattice, as well as the equations and the determining equations of the Lie symmetries are obtained for the nonholonomic Hamiltonian systems. The discrete analogue of the Noether conserved quantity is constructed by using the Lie point symmetries. An example is discussed to illustrate the results.     

Bargmann Symmetry Constraint for a Family of Liouville Integrable Differential-Difference Equations

A family of integrable differential-difference equations is derived from a new matrix spectral problem. The Hamiltonian forms of obtained differential-difference equations are constructed. The Liouville integrability for the obtained integrable family is proved. Then, Bargmann symmetry constraint of the obtained integrable family is presented by binary nonliearization method of Lax pairs and adjoint Lax pairs. Under this Bargmann symmetry constraints, an integrable symplectic map and a sequences of completely integrable finite-dimensional Hamiltonian systems in Liouville sense are worked out, and every integrable differential-difference equations in the obtained family is factored by the integrable symplectic map and a completely integrable finite-dimensional Hamiltonian system.     

High sensitivity CW-cavity ring down spectroscopy of N2O near 1.5 μm (III)

We present the third part of the investigation of the high sensitivity absorption spectrum of nitrous oxide by CW-Cavity Ring Down Spectroscopy near 1.5 μm. In the two first contributions (A. Liu, et al., J. Mol. Spectrosc. 244 (2007) 33-47 and A. Liu, et al., J. Mol. Spectrosc. 244 (2007) 48-62) devoted to the 5905-6833 cm⁻¹ region, more than 9000 line positions of five isotopologues (¹⁴N₂¹⁶O, ¹⁵N¹⁴N¹⁶O, ¹⁴N¹⁵N¹⁶O, ¹⁴N₂¹⁷O and ¹⁴N₂¹⁸O), were rovibrationally assigned to a total of 115 bands, most of them being newly detected. The achieved sensitivity (α_min∼3 × 10⁻¹⁰ cm⁻¹) allowed for the detection of lines with intensity weaker than 2 × 10⁻²⁹ cm/molecule. In this contribution, the investigated region was extended up to 7066 cm⁻¹. The analysis based on the predictions of the effective Hamiltonian model has allowed assigning about 1500 transitions to 17, 1, 2 and 1 bands of the ¹⁴N₂¹⁶O, ¹⁴N¹⁵N¹⁶O, ¹⁵N¹⁴N¹⁶O and ¹⁴N₂¹⁸O isotopologues, respectively. Eleven of these 21 bands are newly reported, while the observations of the transitions are extended to higher J values for most of the others. The band by band analysis has allowed reproducing the measured line positions within the experimental uncertainty (about 1 × 10⁻³ cm⁻¹) and determining the corresponding spectroscopic parameters. A detailed analysis of the rovibrational perturbations affecting three bands of ¹⁴N₂¹⁶O is presented.     

New Analysis of the ν3 fundamental band of HDCO: Positions and intensities

Using high-resolution Fourier transform spectra of mono deuterated formaldehyde (HDCO) recorded in the 5.8-μm spectral range at Giessen (Germany), we carried out an extensive analysis of the strong ν₃ fundamental band (carbonyl stretching mode) at 1724.2676 cm⁻¹, starting from results of a previous analysis [J.W.C. Johns, A.R.W. McKellar, J. Mol. Spectrosc. 64 (1977) 327-339]. For this hybrid band (with both A- and B-type transitions) the analysis was pursued up to high rotational quantum numbers. In this way, it was possible to evidence a resonance which perturbs the ν₃ lines for high K_a values which is due to the existence of the 2ν₅ and ν₅ + ν₆ dark bands in the same spectral region. In addition a local resonance is perturbing the 3¹ levels in  = 8 which is due to a crossing with the 4¹ energy levels in K_a = 11. The model used to calculate the energy levels accounts for the observed A- type, B- type C-type Coriolis (and/or) Fermi resonances which couple the 3¹ and the 5¹6¹, 5², and 4¹ energy levels. However the 4¹ state is also involved in strong vibration-rotation interactions coupling the {5¹,6¹,4¹} system of resonation states of HDCO [A. Perrin, J.M. Flaud, L. Margulès, J. Demaison, H. Mäder, S. Wörmke, J. Mol. Spectrosc. 216 (2002) 214-224]. Therefore the final energy levels calculation was performed for the {5¹,6¹,4¹,3¹,5²,5¹6¹} resonating states and in this way it was possible to reproduce the observed line positions, within their experimental uncertainties. The present work also led to the determination of the intensity ratio of the B- to A-type components of the ν₃ band I_A/I_B ∼24 band from spectral fittings performed in several parts of the observed spectrum. Finally, using the 5.8 μm band intensity available in the literature we generated, for the first time, a list of line parameters (positions and intensities) for the 5.8 μm region of HDCO.     

Effective correlation-free reduced Hamiltonian for the νt(E), νn(A1) Coriolis-interacting states of C3v symmetric-top molecules

The effective correlation-free vibrational-rotational Hamiltonian for the Coriolis-interacting ν_t(E) and ν_n(A₁) states in C_3v molecules has been derived. The Hamiltonian includes the terms describing the x-y Coriolis interaction up to the fourth-order, and several useful reduction schemes for the Hamiltonian are suggested.