Theoretical analysis of photoinduced H-atom elimination in thiophenol

The photoinduced hydrogen elimination reaction in thiophenol via the conical intersections of the dissociative (1)pi sigma* excited state with the bound (1)pi pi* excited state and the electronic ground state has been investigated with ab initio electronic-structure calculations and time-dependent quantum wave-packet calculations. A screening of the coupling constants of the symmetry-allowed coupling modes at the (1)pi pi*-(1)pi sigma* and (1)pi sigma*-S-0 conical intersection shows that the SH torsional mode is by far the most important coupling mode at both conical intersections. A model including three intersecting potential-energy surfaces (S-0, (1)pi pi*, (1)pi sigma*) and two nuclear degrees of freedom (SH stretch and SH torsion) has been constructed on the basis of ab initio complete-active-space self-consistent field and multireference second-order perturbation theory calculations. The nonadiabatic quantum wave-packet dynamics initiated by optical excitation of the (1)pi pi* and (1)pi sigma* states has been explored for this three-state two-coordinate model. The photodissociation dynamics is characterized in terms of snapshots of time-dependent wave packets, time-dependent electronic population probabilities, and the branching ratio of the (2)sigma/(2)pi electronic states of the thiophenoxyl radical. The dependence of the timescale of the photodissociation process and the branching ratio on the initial excitation of the SH stretching and SH torsional vibrations has been analyzed. It is shown that the node structure, which is imposed on the nuclear wave packets by the initial vibrational preparation as well as by the transitions through the conical intersections, has a profound effect on the photodissociation dynamics. The effect of additional weak coupling modes of CC twist (nu(16a)) and ring-distortion (nu(16b)) character has been investigated with three-dimensional and four-dimensional time-dependent wave-packet calculations, and has been found to be minor. (C) 2012 American Institute of Physics. http://dx.doi.org/10.1063/1.4709608]

Fourth order accurate compact scheme with group velocity control (GVC)

For solving complex flow field with multi-scale structure higher order accurate schemes are preferred. Among high order schemes the compact schemes have higher resolving efficiency. When the compact and upwind compact schemes are used to solve aerodynamic problems there are numerical oscillations near the shocks. The reason of oscillation production is because of non-uniform group velocity of wave packets in numerical solutions. For improvement of resolution of the shock a parameter function is introduced in compact scheme to control the group velocity. The newly developed method is simple. It has higher accuracy and less stencil of grid points.

Subdiffusion of nonlinear waves in quasiperiodic potentials

19 p.

Tools for the study of dynamical spacetimes

This thesis covers a range of topics in numerical and analytical relativity, centered around introducing tools and methodologies for the study of dynamical spacetimes. The scope of the studies is limited to classical (as opposed to quantum) vacuum spacetimes described by Einstein's general theory of relativity. The numerical works presented here are carried out within the Spectral Einstein Code (SpEC) infrastructure, while analytical calculations extensively utilize Wolfram's Mathematica program.

We begin by examining highly dynamical spacetimes such as binary black hole mergers, which can be investigated using numerical simulations. However, there are difficulties in interpreting the output of such simulations. One difficulty stems from the lack of a canonical coordinate system (henceforth referred to as gauge freedom) and tetrad, against which quantities such as Newman-Penrose Psi_4 (usually interpreted as the gravitational wave part of curvature) should be measured. We tackle this problem in Chapter 2 by introducing a set of geometrically motivated coordinates that are independent of the simulation gauge choice, as well as a quasi-Kinnersley tetrad, also invariant under gauge changes in addition to being optimally suited to the task of gravitational wave extraction.

Another difficulty arises from the need to condense the overwhelming amount of data generated by the numerical simulations. In order to extract physical information in a succinct and transparent manner, one may define a version of gravitational field lines and field strength using spatial projections of the Weyl curvature tensor. Introduction, investigation and utilization of these quantities will constitute the main content in Chapters 3 through 6.

For the last two chapters, we turn to the analytical study of a simpler dynamical spacetime, namely a perturbed Kerr black hole. We will introduce in Chapter 7 a new analytical approximation to the quasi-normal mode (QNM) frequencies, and relate various properties of these modes to wave packets traveling on unstable photon orbits around the black hole. In Chapter 8, we study a bifurcation in the QNM spectrum as the spin of the black hole a approaches extremality.

Magnetohydrodynamic turbulence

We simulate incompressible, MHD turbulence using a pseudo-spectral code. Our major conclusions are as follows.

1) MHD turbulence is most conveniently described in terms of counter propagating shear Alfvén and slow waves. Shear Alfvén waves control the cascade dynamics. Slow waves play a passive role and adopt the spectrum set by the shear Alfvén waves. Cascades composed entirely of shear Alfvén waves do not generate a significant measure of slow waves.

2) MHD turbulence is anisotropic with energy cascading more rapidly along k_⊥ than along k_∥, where k_⊥ and k_∥ refer to wavevector components perpendicular and parallel to the local magnetic field. Anisotropy increases with increasing k_⊥ such that excited modes are confined inside a cone bounded by k_∥ ∝ k^γ_⊥ where γ less than 1. The opening angle of the cone, θ(k_⊥) ∝ k^-(1-γ)_⊥, defines the scale dependent anisotropy.

3) MHD turbulence is generically strong in the sense that the waves which comprise it suffer order unity distortions on timescales comparable to their periods. Nevertheless, turbulent fluctuations are small deep inside the inertial range. Their energy density is less than that of the background field by a factor θ² (k_⊥)≪1.

4) MHD cascades are best understood geometrically. Wave packets suffer distortions as they move along magnetic field lines perturbed by counter propagating waves. Field lines perturbed by unidirectional waves map planes perpendicular to the local field into each other. Shear Alfvén waves are responsible for the mapping's shear and slow waves for its dilatation. The amplitude of the former exceeds that of the latter by 1/θ(k_⊥) which accounts for dominance of the shear Alfvén waves in controlling the cascade dynamics.

5) Passive scalars mixed by MHD turbulence adopt the same power spectrum as the velocity and magnetic field perturbations.

6) Decaying MHD turbulence is unstable to an increase of the imbalance between the flux of waves propagating in opposite directions along the magnetic field. Forced MHD turbulence displays order unity fluctuations with respect to the balanced state if excited at low k by δ(t) correlated forcing. It appears to be statistically stable to the unlimited growth of imbalance.

7) Gradients of the dynamic variables are focused into sheets aligned with the magnetic field whose thickness is comparable to the dissipation scale. Sheets formed by oppositely directed waves are uncorrelated. We suspect that these are vortex sheets which the mean magnetic field prevents from rolling up.

8) Items (1)-(5) lend support to the model of strong MHD turbulence put forth by Goldreich and Sridhar (1995, 1997). Results from our simulations are also consistent with the GS prediction γ = 2/3. The sole not able discrepancy is that the 1D power law spectra, E(k_⊥) ∝ k^-∝_⊥, determined from our simulations exhibit ∝ ≈ 3/2, whereas the GS model predicts ∝ = 5/3.

Stability of Hypervelocity Boundary Layers

The early stage of laminar-turbulent transition in a hypervelocity boundary layer is studied using a combination of modal linear stability analysis, transient growth analysis, and direct numerical simulation. Modal stability analysis is used to clarify the behavior of first and second mode instabilities on flat plates and sharp cones for a wide range of high enthalpy flow conditions relevant to experiments in impulse facilities. Vibrational nonequilibrium is included in this analysis, its influence on the stability properties is investigated, and simple models for predicting when it is important are described.

Transient growth analysis is used to determine the optimal initial conditions that lead to the largest possible energy amplification within the flow. Such analysis is performed for both spatially and temporally evolving disturbances. The analysis again targets flows that have large stagnation enthalpy, such as those found in shock tunnels, expansion tubes, and atmospheric flight at high Mach numbers, and clarifies the effects of Mach number and wall temperature on the amplification achieved. Direct comparisons between modal and non-modal growth are made to determine the relative importance of these mechanisms under different flow regimes.

Conventional stability analysis employs the assumption that disturbances evolve with either a fixed frequency (spatial analysis) or a fixed wavenumber (temporal analysis). Direct numerical simulations are employed to relax these assumptions and investigate the downstream propagation of wave packets that are localized in space and time, and hence contain a distribution of frequencies and wavenumbers. Such wave packets are commonly observed in experiments and hence their amplification is highly relevant to boundary layer transition prediction. It is demonstrated that such localized wave packets experience much less growth than is predicted by spatial stability analysis, and therefore it is essential that the bandwidth of localized noise sources that excite the instability be taken into account in making transition estimates. A simple model based on linear stability theory is also developed which yields comparable results with an enormous reduction in computational expense. This enables the amplification of finite-width wave packets to be taken into account in transition prediction.

The evolution of a stratified turbulent cloud

Localized regions of turbulence, or turbulent clouds, in a stratified fluid are the subject of this study, which focuses on the edge dynamics occurring between the turbulence and the surrounding quiescent region. Through laboratory experiments and numerical simulations of stratified turbulent clouds, we confirm that the edge dynamics can be subdivided into materially driven intrusions and horizontally travelling internal wave-packets. Three-dimensional visualizations show that the internal gravity wave-packets are in fact large-scale pancake structures that grow out of the turbulent cloud into the adjacent quiescent region. The wave-packets were tracked in time, and it is found that their speed obeys the group speed relation for linear internal gravity waves. The energetics of the propagating waves, which include waveforms that are inclined with respect to the horizontal, are also considered and it is found that, after a period of two eddy turnover times, the internal gravity waves carry up to 16 % of the cloud kinetic energy into the initially quiescent region. Turbulent events in nature are often in the form of decaying turbulent clouds, and it is therefore suggested that internal gravity waves radiated from an initial cloud could play a significant role in the reorganization of energy and momentum in the atmosphere and oceans.©2013 Cambridge University Press.

Effect of phase relaxation on quantum superpositions in complex collisions

We study the effect of phase relaxation on coherent superpositions of rotating clockwise and anticlockwise wave packets in the regime of strongly overlapping resonances of the intermediate complex. Such highly excited deformed complexes may be created in binary collisions of heavy ions, molecules, and atomic clusters. It is shown that phase relaxation leads to a reduction of the interference fringes, thus mimicking the effect of decoherence. This reduction is crucial for the determination of the phase-relaxation width from the data on the excitation function oscillations in heavy-ion collisions and bimolecular chemical reactions. The difference between the effects of phase relaxation and decoherence is discussed.

A study of internal solitary waves observed on the continental shelf in the northwestern South China Sea

Based on in-situ time series data from the acoustic Doppler current profiler (ADCP) and thermistor chain in Wenchang area, a sequence of internal solitary wave (ISW) packets was observed in September 2005, propagating northwest on the continental shelf of the northwestern South China Sea (SCS). Corresponding to different stratification of the water column and tidal condition, both elevation and depression ISWs were observed at the same mooring location with amplitude of 35 m and 25 m respectively in different days. Regular arrival of the remarkable ISW packets at approximately the diurnal tidal period and the dominance of diurnal internal waves in the study area, strongly suggest that the main energy source of the waves is the diurnal tide. Notice that the wave packets were all riding on the troughs and shoulders of the internal tides, they were probably generated locally from the shelf break by the evolution of the internal tides due to nonlinear and dispersive effects.

中高层大气对低层大气声重波响应的分析

Acoustic Gravity waves (AGW) play an important role in balancing the atmospheric energy and momentum budget. Propagation of gravity wave in the atmosphere is one of the important factors of changing middle and upper atmosphere and ionosphere. The purpose of this dissertation is to study the propagation of gravity wave in a compression atmosphere whit means of numerical simulation and to analyze the response of middle and upper atmosphere to pulse disturbance from lower atmosphere. This work begins with the establishment of 2-D fully nonlinear compressible atmospheric dynamic model in polar coordinate, which is used ton numerically study gravity wave propagation. Then the propagation characteristics of acoustic gravity wave packets are investigated and discussed. We also simulate the response of middle and upper atmosphere to pulse disturbance of lower atmosphere in background winds or without background winds by using this model and analyze the data we obtained by using Fourier Transform (FT), Short-time Fourier Transform (STFT) and Empirical Mode Decomposition (EMD) method which is an important part of Hilbert-Huang Transform (HHT). The research content is summarized in the following: 1. By using a two-dimensional full-implicit-continuous-Eulerian (FICE) scheme and taking the atmospheric basic motion equations as the governing equations, a numerical model for nonlinear propagation of acoustic gravity wave disturbance in two-dimensional polar coordinates is solved. 2. Then the propagation characteristics of acoustic gravity wave packets are investigated and discussed. Results of numerical simulation show that the acoustic gravity wave packets propagate steadily upward and keep its shape well after several periods. 3. We simulate the response of middle and upper atmosphere to pulse disturbance of lower atmosphere in background winds or without background winds by using this model, and obtain the distribution of a certain physical quantity in time and space from earth’s surface to 300km above. The results reveal that the response of ionosphere occurs at a large horizontal distance from the source and the disturbance becomes greater with increasing of height. The situation when the direction of the background wind is opposite to or the same as the direction of disturbed velocity of gravity-wave is studied. The results show that gravity wave propagating against winds is easier than those propagating along winds and the background wind can accelerate gravity wave propagation. Just upon the source, an acoustic wave component with period of 6 min can be found. These images of simulation are similar to observations of the total electron content (TEC) disturbances caused by the great Sumatra-Andaman earthquake on December 26 in 2004. 4. Using the EMD method the disturbed velocity data of a certain physical quantity in time and space can be decomposed into a series of intrinsic mode function (IMF) and a trend mode respectively. The results of EMD reveal impact of the gravity wave frequency under the background winds.

Pump-dump control and the related transient absorption spectroscopies

We combine theories of optimal pump-dump control and the related transient probe absorption spectroscopy in order to elucidate the relation between these two optical processes and the possibility of experimental realization. In the weak response regime, we identify the globally optimal pair of pump-dump control fields, and further propose a second-order difference detection scheme to monitor the wave packets dynamics that is jointly controlled by both the pump and dump fields. The globally optimal solution serves also as the initial input for the iterative search for the optimal control fields in the strong response regime. We use a model I-2 molecule to demonstrate numerically the pump-dump control and the detection of a highly vibrationally excited wave packet focusing dynamics on the ground X surface in both the weak and strong response regimes. The I2B surface serves as the intermediate to assist the pump-dump control and the optical detection processes. Demonstrated in the strong response regime are the optimal pair of pump-dump molecular-pi pulses that invert nearly total population onto the predefined target region within a half period of vibration motion. (C) 1999 American Institute of Physics. [S0021-9606(99)00115-4].

Waveguide QED: Many-body bound-state effects in coherent and Fock-state scattering from a two-level system

Strong coupling between a two-level system (TLS) and bosonic modes produces dramatic quantum optics effects. We consider a one-dimensional continuum of bosons coupled to a single localized TLS, a system which may be realized in a variety of plasmonic, photonic, or electronic contexts. We present the exact many-body scattering eigenstate obtained by imposing open boundary conditions. Multiphoton bound states appear in the scattering of two or more photons due to the coupling between the photons and the TLS. Such bound states are shown to have a large effect on scattering of both Fock- and coherent-state wave packets, especially in the intermediate coupling-strength regime. We compare the statistics of the transmitted light with a coherent state having the same mean photon number: as the interaction strength increases, the one-photon probability is suppressed rapidly, and the two- and three-photon probabilities are greatly enhanced due to the many-body bound states. This results in non-Poissonian light. © 2010 The American Physical Society.

Observational Evidence for Mode Coupling in the Chromospheric Network

Oscillations in network bright points (NBPs) are studied at a variety of chromospheric heights. In particular, the three-dimensional variation of NBP oscillations is studied using image segmentation and cross-correlation analysis between images taken in light of Ca II K3, Ha core, Mg I b2, and Mg I b1-0.4 Å. Wavelet analysis is used to isolate wave packets in time and to search for height-dependent time delays that result from upward- or downward-directed traveling waves. In each NBP studied, we find evidence for kink-mode waves (1.3, 1.9 mHz), traveling up through the chromosphere and coupling with sausage-mode waves (2.6, 3.8 mHz). This provides a means for depositing energy in the upper chromosphere. We also find evidence for other upward- and downward-propagating waves in the 1.3-4.6 mHz range. Some oscillations do not correspond to traveling waves, and we attribute these to waves generated in neighboring regions.

Wavelet phase coherence analysis: Application to a quiet-sun magnetic element

A new application of wavelet analysis is presented that utilizes the inherent phase information residing within the complex Morlet transform. The technique is applied to a weak solar magnetic network region, and the temporal variation of phase difference between TRACE 1700 Angstrom and SOHO/SUMER C II 1037 Angstrom intensities is shown. We present, for the first time in an astrophysical setting, the application of wavelet phase coherence, including a comparison between two methods of testing real wavelet phase coherence against that of noise. The example highlights the advantage of wavelet analysis over more classical techniques, such as Fourier analysis, and the effectiveness of the former to identify wave packets of similar frequencies but with differing phase relations is emphasized. Using cotemporal, ground-based Advanced Stokes Polarimeter measurements, changes in the observed phase differences are shown to result from alterations in the magnetic topology.

Propagating waves and magnetohydrodynamic mode coupling in the quiet-sun network

High-cadence multiwavelength optical observations were taken with the Dunn Solar Telescope at the National Solar Observatory, Sacramento Peak, accompanied by Advanced Stokes Polarimeter vector magnetograms. A total of 11 network bright points (NBPs) have been studied at different atmospheric heights using images taken in wave bands centered on Mg I b(1) - 0.4 Angstrom, Halpha, and Ca II K-3. Wavelet analysis was used to study wave packets and identify traveling magnetohydrodynamic waves. Wave speeds were estimated through the temporal cross-correlation of signals, in selected frequency bands of wavelet power, in each wavelength. Four mode-coupling cases were identified, one in each of four of the NBPs, and the variation of the associated Fourier power with height was studied. Three of the detected mode-coupling, transverse-mode frequencies were observed in the 1.2-1.6 mHz range (mean NBP apparent flux density magnitudes over 99-111 Mx cm(-2)), with the final case showing 2.0-2.2 mHz (with 142 Mx cm(-2)). Following this, longitudinal-mode frequencies were detected in the range 2.6-3.2 mHz for three of our cases, with 3.9-4.1 mHz for the remaining case. After mode coupling, two cases displayed a decrease in longitudinal-mode Fourier power in the higher chromosphere.