Prediction and Elimination of Multiples Based on Energy Flux Conservation Theorem and Prediction Operator Equation

The received wave field including primaries and all of the multiples can be associated with the reflection coefficients which are only primaries by a prediction operator and two equations： the energy flux conservation equation and the prediction operator equation that is developed from the Levinson recursion and can be easily solved by Li group method under a two-dimensional condition. Given reflection coefficients, the prediction operator can be obtained by solving the prediction operator equation. By the energy flux conservation equation, the reciprocal of the prediction operator times the conjugate of it, the wave field can be predicted, in which both of the surface multiples and the internal multiples are involved. On the other hand, if the wave field is given, based on the energy flux conservation equation solved by the 2D spectral factorization, a fully automated data-driven algorithm is developed to remove the surface multiples as well as the internal multiples.     

Symmetry Reduction, Exact Solutions, and Conservation Laws of （2＋1）-Dimensional Burgers Korteweg-de Vries Equation

Using the classical Lie method of infinitesimals, we first obtain the symmetry of the （2＋1）-dimensional Burgers-Korteweg-de-Vries （3D-BKdV） equation. Then we reduce the 3D-BKdV equation using the symmetry and give some exact solutions of the 3D-BKdV equation. When using the direct method, we restrict a condition and get a relationship between the new solutions and the old ones. Given a solution of the 3D-BKdV equation, we can get a new one from the relationship. The relationship between the symmetry obtained by using the classical Lie method and that obtained by using the direct method is also mentioned. At last, we give the conservation laws of the 3D-BKdV equation.     

Periodicity-suppressing effect of periodic lossy-dielectric-loaded cylindrical waveguide

Periodic dielectric-loaded waveguide is one of the diaphragmatic waveguides.For the excellent mode-selective propagation ability,it is of value for applications in gyrotron-traveling-wave amplifiers(gyro-TWT),accelerators,and other microwave propagation systems.This paper focuses on studying the application of the strong lossy-dielectricloaded periodic waveguide in millimeter-wave gyro-TWT.It is revealed that due to the lossy property of the dielectric,the energy in the dielectric slots is absorbed effectively and the high order Bloch harmonics induced by the periodicity of the structure are suppressed,which changes the discrete spectrum under lossless condition into a continuous one.As a result,the periodicity of the system is severely suppressed and a mode in the hollow region could be approximated by a fast wave mode in an empty waveguide.These results bring specific guidance for the applications of the lossy dielectric-loaded waveguide in gyro-TWTs and other devices.     

Cluster Model for Wave-Like Motions of a 2D Vertically Vibrated Granular System

The fact that trapezoid clusters exist in 2D vertically vibrated granular systems leads us to construct a cluster model, in which wave-like motions are explained as the result of cluster-plate and cluster-cluster collisions. By analyzing the collision of one cluster with the plate in detail, we deduce a basic equation from velocity relationship, which could be separated into two correlative equations： one relates wave-like motion with exciting acceleration, and we call it the excitation condition; the other relates wavelength with exciting frequency, viz., the dispersion relation. The theoretical results are in agreement with the experimental ones, which supports the idea of the cluster model. Moreover, from the cluster model, we also predict a possibility of abnormal dispersion relation of a 213 granular system.     

A New Conservation Law Derived from Mei Symmetry for the System of Generalized Classical Mechanics

A new conservation theorem derived directly from Mei symmetry of the generalized classical mechanical system is presented. First, the differential equations of motion of the system are established, and the definition and criterion of Mei symmetry for the system of generalized classical mechanics are given, which are based upon the invariance of dynamical functions under irdinitesimal transformations. Second, the condition under which a Mei symmetry can lead to a new conservation law is obtained and the form of the conservation law is presented. And finadly, an example is given to illustrate the application of the results.     

Orientation Dependence of Photoelectron Angular Distribution in Nitrogen Molecule Irradiated by XUV Laser Field

We theoretically study the dependence of photoelectron angular distribution on laser polarization direction in nitrogen molecules.The approach is based on the time-dependent density functional theory at the level of local density approximation complemented by self-interaction correction.It is found that photoelectron emission in one photon regime could be considered as a probing tool for the main character of different types of molecular orbitals(a or π).The pattern of emitted photoelectrons strongly depends on the polarized angle of the laser,for a orbital,the number of photoelectron decreases with increasing the polarized angle,while for ir orbital,it has the inverse relation to the polarized angle,which reveals the multi-electron effect in molecules.On the other hand,concerning the total photoelectron emission,one should take into account a few occupied orbitals instead of only the outmost one.     

Conservation Laws of a Class of Combined Equations

In this paper, we investigate conservation laws of a class of partial differential equations, which combines the nonlinear telegraph equations and the nonlinear diffusion-convection equations. Moreover, some special conservation laws of the combined equations are obtained by means of symmetry classifications of wave equations uxx = H （x）utt.     

Reflection and refraction of elastic wave at VTI-TTI media interface

We explore the physical phenomenon of acoustic waves induced at the interface between two different anisotropic rock media.Specifically,one medium is a transversely isotropic medium with a vertical axis of symmetry(VTI medium)and the other one is a transversely isotropic medium with a tilt axis of symmetry(TTI medium).By solving the Kelvin-Christoffel equation,an eighth-order polynomial is established for reflection and refraction angles,which is confirmed from SnelFs law.Three types of analytical expressions of the polarization coefficients of the induced waves are obtained corresponding to different incident angle regions.An effective algorithm has been developed for numerical analysis of the polarization coefficients.Applying characteristic anisotropic parameters reported in the literature,the influencing factors on reflection and refraction coefficients are analyzed,e.g.,the anisotropy,the tilt-angle of rock-layer,and the incident-angle.The calculated reflection and refraction coefficients have been rechecked for energy conservation.     

Stability of Bright Solitons in Bose-Einstein Condensates

We investigate the stability of bright solitons in Bose-Einstein condensates by including a feeding term and a loss one in the Oross-Pitaevskii equation. Based on the direct approach of perturbation theory for the nonlinear Schroedinger equation, we give the explicit dependence of the height and other related quantities of bright solitons on the feeding and loss term. It is found that the three-body recombination loss plays a crucial role in stabilizing bright solitons.     

A New Method to Study Hawking Radiation of Charged Particle from Stationary Axisymmetric Sen Black Hole

Taking the self-gravitation interaction and energy conservation,charge conservation and angular momentum conservation into accpunt, we discuss the tunnelling characteristics of the charged particle from Sen black hole by the Hamilton-Jacobi method. The result shows that the tunnelling probability is related to the change of Bekenstein-Hawking entropy, and the actual radiation spectrum deviates from the pure thermal one, which is consistent with the result of Parikh and Wilczek and gives a new method to correct the Hawking pure thermal spectrum of Sen black hole.     

The Necessary and Sufficient Conditions for a Universal Conservation of a State of a Unitary Quantum Circuit

By A. Peres and A. Stern‘s opinions a computational process evolves along a cyclic logic orbit defined by a computation. A. Stern thought that if we could design such a circuit, its operations can be extended to including nonconservative behavior associated with the external perturbations or internal quantum errors. A. Peres did not discuss how to make φM-1 ＝φo. A. Stern proposed only a necessary condition for a conservation of a state of a quantum circuit.In this paper we present a necessary and sufficient condition for a universal conservation of a state of a quantum circuit.We also find all operators which can allow the conservation.     

Revised Iterative Solution for Groundstate of Schrodinger Equation

A revised iterative method based on Green function defined by quadratures along a single trajectory is proposed to solve the low-lying quantum wave function for Schro^edinger equation. Specially a new expression of the perturbed energy is obtained, which is much simpler than the traditional one. The method is applied to solve the unharmonic oscillator potential. The revised iteration procedure gives exactly the same result as those based on the single trajectory quadrature method. A comparison of the revised iteration method to the old one is made using the example of Stark effect. The obtained results are consistent to each other after making power expansion.     

A novel hierarchy of differential integral equations and their generalized bi-Hamiltonian structures

With the aid of the zero-curvature equation, a novel integrable hierarchy of nonlinear evolution equations associated with a 3 x 3 matrix spectral problem is proposed. By using the trace identity, the bi-Hamiltonian structures of the hierarchy are established with two skew-symmetric operators. Based on two linear spectral problems, we obtain the infinite many conservation laws of the first member in the hierarchy.     

A conservative Fourier pseudospectral algorithm for the nonlinear Schrdinger equation

In this paper, we derive a new method for a nonlinear Schrodinger system by using the square of the first-order Fourier spectral differentiation matrix D1 instead of the traditional second-order Fourier spectral differentiation matrix D2 to approximate the second derivative. We prove that the proposed method preserves the charge and energy conservation laws exactly. A deduction argument is used to prove that the numerical solution is second-order convergent to the exact solutions in ｜｜·｜｜2 norm. Some numerical results are reported to illustrate the efficiency of the new scheme in preserving the charge and energy conservation laws.     

Two expanding forms of a Lie algebra and their application

With the help of a known Lie algebra,two new high order Lie algebras are constructed.It is remarkable that they have different constructing approaches.The first Lie algebra is constructed by the definition of integrable couplings.the second one by an extension of Lie algebra,Then by making use of Tu scheme,a generalized AKNS hierarchy and another new hierarchy are obtained.As a reduction case of the first hierarchy,a kind of coupled KdV equation is presented.As a reduction case of the second one,a new coupled Schroedinger equation is given.     

Observation of two multiwave mixing processes via dual optical pumping channels

Based on double optical pumping channels,we experimentally study the competition between two coexistent six-wave mixing(SWM) processes falling into two electromagnetically induced transparency windows by scanning the frequency of the probe field in two similar five-level atomic systems of 85Rb.By blocking one optical pumping channel unrelated to the four-wave mixing(FWM) process,one SWM process,together with the FWM process,generated by a conjugated small-angle static grating could be observed in the spectrum.Moreover,the other SWM process obtained by blocking the first SWM channel is also observed together with the FWM process in a lower N-type four-level subsystem.These experimental results agree well with theoretical predictions.     

Dynamical chiral symmetry breaking in NJL Model with a strong background magnetic field and Lorentz-violating extension of the Standard Model

The Eigenstate Method has been developed to deduce the fermion propagator with a constant external magnetic field. In general, we find its result is equivalent to other methods and this new method is more convenient,especially when one evaluates the contribution from the infinitesimal imaginary term of the fermion propagator. Using the Eigenstate Method we try to discuss whether the infinitesimal imaginary frequency of the fermion propagator in a strong magnetic field and Lorentz-violating extension of the minimal SU(3)×SU(2)×SU(1) Standard Model could have a significant influence on the dynamical mass. When the imaginary term of the fermion propagator in this model is not trivial(((α-1)eB/3)~(1/2) σ ((α-1)2eB/3)~(1/2)), this model gives a correction to the dynamical mass.When one does not consider the influence from the imaginary term(σ ((α-1)2eB/3)~(1/2)), there is another correction from the conventional term. Under both circumstances, chiral symmetry is broken.     

Generation and control of chaos in a Bose--Einstein condensate

For a Bose--Einstein condensate (BEC) confined in a double lattice consisting of two weak laser standing waves we find the Melnikov chaotic solution and chaotic region of parameter space by using the direct perturbation method. In the chaotic region, spatial evolutions of the chaotic solution and the corresponding distribution of particle number density are bounded but unpredictable between their superior and inferior limits. It is illustrated that when the relation k₁\approx k₂ between the two laser wave vectors is kept, the adjustment from k₂1 to k₂\ge k₁ can transform the chaotic region into regular one or the other way round. This suggests a feasible scheme for generating and controlling chaos, which could lead to an experimental observation in the near future.     

Effects of charge on the structures and spin moments of Nil3 cluster

The structural stability and magnetic properties of the icosahedral Ni13, Ni13^＋1 and Ni13^-1 clusters have been obtained by utilizing all-electron density functional theory with the generalized gradient approximations for the exchange-correlation energy. The calculated results show that the ground states of neutral and charged clusters all favour a D3d structure, a distorted icosahedron, due to the Jahn-Teller effect. The radial distortions caused by doping one electron and by doping one hole are opposite to each other. Doping one electron will result in a 1/2 decrease and doping one hole will result in a 1/2 increase of the total spin. Both increasing interatomic spacing and decreasing coordination will lead to an enhancement of the spin magnetic moments for Nil3 clusters.     

Continuous feedback control of KdV Burgers system

The chaos in the KdV Burgers equation describing a ferroelectric system has been successfully controlled by using a continuous feedback control. This system has two stationary points. In order to know whether the chaos is controlled or not, the instability of control equation has been analysed numerically. The numerical analysis shows that the chaos can be converted to one point by using one control signal, however, it can converted to the other point by using three control signals. The chaotic motion is converted to two desired stationary points and periodic orbits in numerical experiment separately.