Laser phase effect on asymmetric harmonic distribution in H_2^+

The laser phase effect on the spatial distribution of the molecular high-order harmonic generation（MHHG） spectrum from H_2~＋ is theoretically investigated through solving the Non-Bohn-Oppenheimer（NBO） time-dependent Schrodinger equation（TDSE）.The results are shown as follows,（i） The generated harmonics from the two nuclei each present an asymmetric distribution.Particularly,when the laser phases are chosen from 0.0π to 0.6π and from 1.7π to 2.0π,the contribution from the negative-H plays a main role in harmonic generation.When the laser phases are chosen from 0.7πto 1.6k,the contribution from the positive-H to the harmonic generation is remarkably enhanced and becomes greater than that from the negative-H.The electron localization,the time-frequency analyses of the harmonic spectrum and the time-dependent wave function are shown to explain the asymmetric harmonic distribution in H_2~＋,which provides us with a method to control the electron motion in molecules,（ⅱ） As the pulse duration increases,the asymmetric distributions of the MHHG in two H nuclei decrease,（ⅲ） Isotope investigation shows that the asymmetric harmonic distribution can be reduced by introducing the heavy nucleus（i.e.,D_2~＋）.

Particle swarm optimization algorithm for simultaneous optimal placement and sizing of shunt active power conditioner(APC)and shunt capacitor in harmonic distorted distribution system

Due to development of distribution systems and increase in electricity demand,the use of capacitor banks increases.From the other point of view,nonlinear loads generate and inject considerable harmonic currents into power system.Under this condition if capacitor banks are not properly selected and placed in the power system,they could amplify and propagate these harmonics and deteriorate power quality to unacceptable levels.With attention of disadvantages of passive filters,such as occurring resonance,nowadays the usage of this type of harmonic compensator is restricted.On the other side,one of parallel multi-function compensating devices which are recently used in distribution system to mitigate voltage sag and harmonic distortion,performs power factor correction,and improves the overall power quality as active power conditioner(APC).Therefore,the utilization of APC in harmonic distorted system can affect and change the optimal location and size of shunt capacitor bank under harmonic distortion condition.This paper presents an optimization algorithm for improvement of power quality using simultaneous optimal placement and sizing of APC and shunt capacitor banks in radial distribution networks in the presence of voltage and current harmonics.The algorithm is based on particle swarm optimization(PSO).The objective function includes the cost of power losses,energy losses and those of the capacitor banks and APCs.

ANALYTIC AND HARMONIC CONTINUATIONS AND DISTRIBUTIONS

The present paper gives several theorems concerning analytic and harmonic continuations described by distributional limits. For distributions on spheres, comparatively complete results are given. Generalizing the Direchlet and Neumann problem so that the boundary values are distributions, we obtain the results on existence and uniqueness. For one complex variable, a generalized Riemann's mapping theorem is obtained.

Spectral redshift of high-order harmonics by adding a weak pulse in the falling part of the trapezoidal laser pulse

We investigate the spectral redshift of high-order harmonics of the H_2~＋（D_2~＋） molecule by numerically solving the non-Born–Oppenheimer time-dependent Schr ¨odinger equation（TDSE）. The results show that the spectral redshift of highorder harmonics can be observed by adding a weak pulse in the falling part of the trapezoidal laser pulses. Comparing with the H_2~＋ molecule, the shift of high-order harmonic generation（HHG） spectrum for the D_2~＋ molecule is more obvious.We employ the spatial distribution in HHG and time-frequency analysis to illustrate the physical mechanism of the spectral redshift of high-order harmonics.

Symmetry detection of rotating patterns based on rotational Doppler effect of light

We propose a method for detecting the symmetry of rotating patterns based on the rotational Doppler effect(RDE)of light.The basic mechanisms of the RDE are introduced,and the spiral harmonic distribution of rotating patterns is analyzed.By irradiating the rotating pattern using a superimposed optical vortex and analyzing the amplitude of the RDE signal,the spiral harmonic distribution of the pattern can be measured,and then its symmetry can be detected.We demonstrate this method experimentally by using patterns with different symmetries and shapes.As the method does not need to receive the scattered light completely and accurately,it promises potential application in detecting symmetrical rotating objects at a long distance.