Coherent structures and wavepackets in subsonic transitional turbulent jets

A large eddy simulation (LES) is performed for two subsonic jets with a Reynolds number of , which have different core temperatures, i.e., the cold and hot jet. The far-field overall sound pressure levels (OASPL) and noise spectra are well validated against previous experimental results. It is found that the OASPL is raised by heating at shallow angles. The most energetic coherent structures are extracted with specified frequencies using the filter based on the frequency domain variant of the snapshot method of proper orthogonal decomposition (POD). The modes have high coherence of near-field pressure for both jets, while the coherence of modes is enhanced greatly by heating. Based on the coherent structures, spatial wavepackets are educed and the characteristics of growth, saturation and decay are analyzed and compared between the two jets in detail. The results show that heating would enhance the linear growth rate for high frequency components, and nonlinear growth rates for low frequency components in general, which are responsible for higher OASPL in the hot jet. The far-field sound generated by wavepackets is computed using the Kirchhoff extrapolation, which matches well with that of LES at shallow angles. This indicates that the wavepackets associated with coherent structures are dominant sound sources in forced transitional turbulent jets. Additionally, the present POD method is proven to be a robust tool to extract the salient features of the wavepackets in turbulent flows.

On Minimum Wavepackets for Generalized Conjugate Space

The forms of minimum wavepackets (MWPs) corresponding to the geueralized momentum space and coordinates spaca are derived by using the generalized Hermitian expression of the momentum operator in curvilinear coordinates. The several MWPs are discussed according to different upper and lower limits of the usual coordinate componets, and the relevant conclusions are drawn in this paper.

Characteristics of nonlinear evolution of wavepackets in boundary layers

The nonlinear evolution of a finite-amplitude disturbance in a 3-D supersonic boundary layer over a cone was investigated recently by Liu et al. using direct numerical simulation （DNS）. It was found that certain small-scale 3-D disturbances amplified rapidly. These disturbances exhibit the characteristics of second modes, and the most amplified components have a well- defined spanwise wavelength, indicating a clear selectivity of the amplification. In the case of a cone, the three-dimensionality of the base flow and the disturbances themselves may be responsible for the rapid amplification. In order to ascertain which of these two effects are essential, in this study we carried out DNS of the nonlinear evolution of a spanwise localized disturbance （wavepacket） in a flat-plate boundary layer. A similar amplification of small-scale disturbances was observed, suggesting that the direct reason for the rapid amplification is the three-dimensionality of the disturbances rather than the three-dimensional nature of the base flow, even though the latter does alter the spanwise distribution of the disturbance. The rapid growth of 3-D waves may be attributed to the secondary instability mechanism. Further simulations were performed for a wavepacket of first modes in a supersonic boundary layer and of Tollmien-Schlichting （T-S） waves in an incompressible boundary layer. The re- suits show that the amplifying components are in the band centered at zero spanwise wavenumber rather than at a finite spanwise wavenumber. It is therefore concluded that the rapid growth of 3-D disturbances in a band centered at a preferred large spanwise wavenumber is the main characteristic of nonlinear evolution of second mode disturbances in supersonic boundary layers.

Theoretical Investigation on Triplet Excitation Energy Transfer in Fluorene Dimer

Triplet-triplet energy transfer in fluorene dimer with electronic structure calculations. The two is investigated by combining rate theories key parameters for the control of energy transfer, electronic coupling and reorganization energy, are calculated based on the diabatic states constructed by the constrained density functional theory. The fluctuation of the electronic coupling is further revealed by molecular dynamics simulation. Succeedingly, the diagonal and off-diagonal fluctuations of the Hamiltonian are mapped from the correlation functions of those parameters, and the rate is then estimated both from the perturbation theory and wavepacket diffusion method. The results manifest that both the static and dynamic fluctuations enhance the rate significantly, but the rate from the dynamic fluctuation is smaller than that from the static fluctuation.

Resonance Raman Spectroscopic and Theoretical Study of Geometry Distortion of Thiourea in 2^1A State

The A-band resonance Raman spectra of thiourea were obtained in water and acetonitrile solution. B3LYP/6-311＋＋G（3df,3pd） and RCIS/6-311＋＋G（3df,3pd） calculations were done to elucidate the ultraviolet electronic transitions, the distorted geometry structure and the saddle point of thiourea in 21A excited state, respectively. The resonance Raman spectra were assigned. The absorption spectrum and resonance Raman intensities were modeled using Heller＇s time-dependent wavepacket approach to resonance Raman scattering. The results indicate that largest change in the displacement takes place with the C--S stretch mode u6 （｜△｜=0.95） and noticeable changes appear in the H5N3H6＋H8N4H7 wag v5 （｜△｜=0.19）, NCN symmetric stretch^-C--S stretch＋N3H6＋H8N4 wag v4 （｜△｜=0.18）, while the moderate intensities of 2-15 and 4-15 are mostly due to the large excited state frequency changes of v15, but not due to its significant change in the normal mode displacement. The mechanism of the appearance of even overtones of the S-CN2 out of plane deformation is explored. The results indicate that a Franck-Condon region saddle point is the driving force for the quadric phonon mechanism within the standard A-term of resonance Raman scattering, which leads to the pyramidalization of the carbon center and the geometry distortion of thiourea molecule in 21A excited state.

Instability waves and low-frequency noise radiation in the subsonic chevron jet

Spatial instability frequency noise radiation at waves associated with low- shallow polar angles in the chevron jet are investigated and are compared to the round counterpart. The Reynolds-averaged Navier-Stokes equations are solved to obtain the mean flow fields, which serve as the baseflow for linear stability analysis. The chevron jet has more complicated instability waves than the round jet, where three types of instability modes are identified in the vicinity of the nozzle, corresponding to radial shear, azimuthal shear, and their integrated effect of the baseflow, respectively. The most unstable frequency of all chevron modes and round modes in both jets decrease as the axial location moves downstream. Besides, the azimuthal shear effect related modes are more unstable than radial shear effect related modes at low frequencies. Compared to a round jet, a chevron jet reduces the growth rate of the most unstable modes at down- stream locations. Moreover, linearized Euler equations are employed to obtain the beam pattern of pressure generated by spatially evolving instability waves at a dominant low frequency St = 0.3, and the acoustic efficiencies of these linear wavepackets are evaluated for both jets. It is found that the acoustic efficiency of linear wavepacket is able to be reduced greatly in the chevron jet, compared to the round jet.

Hermiticity of Hamiltonian Matrix using the Fourier Basis Sets in Bond-Bond-Angle and Radau Coordinates

In quantum calculations a transformed Hamiltonian is often used to avoid singularities in a certain basis set or to reduce computation time. We demonstrate for the Fourier basis set that the Hamiltonian can not be arbitrarily transformed. Otherwise, the Hamiltonian matrix becomes non-hermitian, which may lead to numerical problems. Methods for cor- rectly constructing the Hamiltonian operators are discussed. Specific examples involving the Fourier basis functions for a triatomic molecular Hamiltonian （J=0） in bond-bond angle and Radau coordinates are presented. For illustration, absorption spectra are calculated for the OC10 molecule using the time-dependent wavepacket method. Numerical results indicate that the non-hermiticity of the Hamiltonian matrix may also result from integration errors. The conclusion drawn here is generally useful for quantum calculation using basis expansion method using quadrature scheme.

Laser controlled quantum motion of two Paul trapped ions

We investigate the quantum motion of two ions stored in a Paul trap and interacting with a time-periodic laser field. In the pseudopotential approximation and large detuning condition, we find that the relative motion is independent of the laser field, but the exact centre-of-mass motion is closely related to the laser field. By adjusting the laser intensity and frequency, we can well control the quantum motion of the centre-of-mass. We illustrate some physical properties described by the centre-of-mass states, such as the squeezed coherent property, the widths and heights of the wavepackets of probability density, the classical-quantum correspondence, the resonance ladders of expectation energy and the transition probabilities between time-dependent quantum levels.

Dynamics of electron in a surface quantum well

This paper studies the quantum dynamics of electrons in a surface quantum well in the time domain with auto- correlation of wave packet. The evolution of the wave packet for different manifold eigenstates with finite and infinite lifetimes is investigated analytically. It is found that the quantum coherence and evolution of the surface electronic wave packet can be controlled by the laser central energy and electric field. The results show that the finite lifetime of excited states expedites the dephasing of the coherent electronic wave packet significantly. The correspondence between classical and quantum mechanica is shown explicitly in the system.

An Exact Propagator for Solving the Triatomic Reactive Schrodinger Equation

The exact short time propagator, in a form similar to the Crank-Nicholson method but in the spirit of spectrally transformed Hamiltonian, was proposed to solve the triatomic reactive time-dependent schrodinger equation. This new propagator is exact and unconditionally convergent for calculating reactive scattering processes with large time step sizes. In order to improve the computational efficiency, the spectral difference method was applied. This resulted the Hamiltonian with elements confined in a narrow diagonal band. In contrast to our previous theoretical work, the discrete variable representation was applied and resulted in full Hamiltonian matrix. As examples, the collision energy-dependent probability of the triatomic H＋H2 and O＋O2 reaction are calculated. The numerical results demonstrate that this new propagator is numerically accurate and capable of propagating the wave packet with large time steps. However, the efficiency and accuracy of this new propagator strongly depend on the mathematical method for solving the involved linear equations and the choice of preconditioner.

A Quantum Wavepacket Study of State-to-State Photodissociation Dynamics of HOBr/DOBr

Photodissociation of HOBr is an important step in the reaction network of the depletion of ozone in stratosphere.Here,we report the first three-dimensional potential energy surfaces for the lowest three singlet states for HOBr,based on high level multi reference configuration interaction calculations.Quantum dynamics calculations are performed with a real wavepacket method,yielding not only absorption spectra but also internal state and angular distributions of the photodissociation fragments.Our results agree quantitatively with the measured total absorption cross sections of HOBr in the ultraviolet region and reproduce well the observed vibrationally cold and rotationally hot OH/OD fragments via photodissociation of HOBr/DOBr at 266 nm.In addition,we predict that the recoil anisotropy parameters for OH/OD are close to the limiting value of a parallel transition,suggesting a rapid dissociation process at 266 nm following an in-plane transition from the ground state(1^1A')to the 21A'state.This is consistent with the experimental conclusion derived from the measured rotational alignment.However,spin and electronic angular momenta need to be taken into account in the future to achieve a more quantitative agreement with experiment.Our work is expected to motivate further experimental investigations for this benchmark system.

THE MODULATIONAL THEORY OF NONLINEAR GRAVITY-WAVE IN FLUID WITH VARYING DEPTH AND NONUNIFORM CURRENT

By means of WKB expansions, new fourth order evolution equations are derived for two-dimensional Stokes waves over the bottom with arbitrary depth. The effects of slowly varying depth h= h (ε~2 x) and current U=U(ε~2x, ε~2t, ε~4z) on the evolution of a packet of Stokes waves are considered as well. In addition, numerical simulation is performed for the evolution of single envelope by finite-difference method.

Laser Controlling Wavepacket Trains of a Paul Trapped Ion

We have studied the quantum and classical motions of a single Paul trapped ion interacting with a timeperiodic laser field. By using the test-function method, we construct n exact solutions of quantum dynamics that describe the generalized squeezed coherent states with the expectation orbits being the corresponding classical ones. The spacetime evolutions of the exact probability densities show some wavepacket trains. It is demonstrated analytically that by adjusting the laser intensity and frequency, we can control the center motions of the wavepacket trains. We also discuss the other physical properties such as the expectation value of energy, the widths and heights of the wavepackets, and the resonance loss of stability.

A universal bifurcation mechanism arising from progressive hydroelastic waves

A unidirectional, weakly dispersive nonlinear model is proposed to describe the supercritical bifurcation arising from hydroelastic waves in deep water. This model equation, including quadratic, cubic, and quartic nonlinearities, is an extension of the famous Whitham equation. The coefficients of the nonlinear terms are chosen to match with the key properties of the full Euler equations, precisely, the associated cubic nonlinear Schrödinger equation and the amplitude of the solitary wave at the bifurcation point. It is shown that the supercritical bifurcation, rich with Stokes, solitary, generalized solitary, and dark solitary waves in the vicinity of the phase speed minimum, is a universal bifurcation mechanism. The newly developed model can capture the essential features near the bifurcation point and easily be generalized to other nonlinear wave problems in hydrodynamics.

Unraveling Vibrational Wavepacket Dynamics using Femtosecond Ion Yield Spectroscopy and Photoelectron Imaging

Time-resolved photoionization is a powerful experimental approach to unravel the excited state dynamics in isolated polyatomic molecules. Depending on species of the collected signals, different methods can be performed: time-resolved ion yield spectroscopy (TR-IYS) and time-resolved photoelectron imaging (TR-PEI). In this review, the essential concepts linking photoionization measurement with electronic structure are presented, together with several important breakthroughs in experimentally distinguishing the oscillating wavepacket motion between different geometries. We illustrate how femtosecond TR-IYS and TR-PEI are employed to visualize the evolution of a coherent vibrational wavepacket on the excited state surface.

UV Photolysis of N2O Isotopomers： Isotopic Fractionations and Product Rotational Quantum State Distributions

The time-dependent quantum wave packet method is used to study the dynamics of the pho- todissociation processes for the isotopomers 14N14N16O, 14N15N16O, 15N14N16O, 15N15N16O, 14N14N17O, and 14N14N18O. In general, the computed isotopic fractionation factors derived from the absorption cross sections of five heavy isotopomers are in good agreement with the experimental results. Relative to the 14NI4N16O isotopomer, the N2 rotational state distributions for the isotopically nitrogen substituted N2O are found to be entirely shifted to higher rotational states. Similar to its isotopic fractionation factors, the N2 rotational state distributions for the asymmetric isotopomers 14N15N16O and 15N14N16O are found to be observably different.

State-to-State Quantum Dynamical Study of H+Br_(2)→HBr+Br Reaction

The time-dependent wave packet method has been employed to calculate the state-to-state integral cross sections and differential cross sections(DCSs)for three initial states of the title reaction on the recently constructed neural network potential energy surface.It is found that the product HBr(v′=2,3,4)states have the dominated population in the entire energy region considered here,indicating an inverted HBr vibrational state distribution.More than half of the available energy ends up as product internal motion,and most of which goes into the vibrational motion.Our calculations show that initial rotational excitation of Br2 has little effect on the product ro-vibrational state distributions and DCSs of the reaction.While the initial vibrational excitation has some influences.The initial vibrational excitation to v_(0)=5 obviously enhance the product vibrational excitation in the low energy region.The DCSs for collision energy up to 0.5 eV at the ground and rotationally excited state are peaked in the backward direction,but the width of the angular distribution increases considerably with the increase of collision energy.For the vibrationally excited state,the DCSs are rather complicated with some strong forward scattering peaks for highly vibrationally excited products.

A pseudoclassical theory for the wavepacket dynamics of the kicked rotor model

In this study, we propose a generalized pseudoclassical theory for the kicked rotor model in an attempt to discern the footprints of the classical dynamics in the deep quantum regime. Compared with the previous pseudoclassical theory that applies only in the neighborhoods of the lowest two quantum resonances, the proposed theory is applicable in the neighborhoods of all quantum resonances in principle by considering the quantum effect of the free rotation at a quantum resonance. In particular, it is confirmed by simulations that the quantum wavepacket dynamics can be successfully forecasted based on the generalized pseudoclassical dynamics, offering an intriguing example where it is feasible to bridge the dynamics in the deep quantum regime to the classical dynamics. The application of the generalized pseudoclassical theory to the PT-symmetric kicked rotor is also discussed.

Intensity-independent molecular rotational decoherence lifetimes measured with mean wavelength shifts of femtosecond pulses

We report on an experimental investigation on the dynamic decoherence process of molecular rotational wavepackets during femtosecond laser filamentation based on time-dependent mean wavelength shifts of a weak probe pulse. Details of periodic revival structures of transient alignment can be readily obtained from the measured shifted spectra due to the periodic modulation of the molecular refractive index. Using the method, we measured decoherence lifetimes of molecular rotational wavepackets in N2and O2under different experimental conditions. Our results indicate that decoherence lifetimes of molecular rotational wavepackets are primarily determined by the relative population of rotational states in the wave packet and intermolecular collisions,rather than the focusing intensity.