Calculation and analysis of the number of return photons from sodium laser beacon excited by the long pulse laser with circular polarization

The number of return photons from sodium laser beacon（SLB） greatly suffers down-pumping, recoil, and geomagnetic field when the long pulse laser with circular polarization interacts with sodium atoms in the mesosphere. Considering recoil and down-pumping effects on the number of return photons from SLB, the spontaneous radiation rates are obtained by numerical computations and fittings. Furthermore, combining with the geomagnetic field effects, a new expression is achieved for calculating the number of return photons. By using this expression and considering the stochastic distribution of laser intensity in the mesosphere under different turbulence models for atmosphere, the number of return photons excited by the narrow-band single mode laser and that by the narrow-band three-mode laser are respectively calculated. The results show that the narrow-band three-mode laser with a specific spectrum structure has a higher spontaneous radiation rate and more return photons than a narrow-band single mode laser. Of note, the effect of the atmospheric turbulence on the number of return photons is remarkable. Calculation results indicate that the number of return photons under the HV5/7 model for atmospheric turbulence is much higher than that under the Greenwood and Mod HV models.     

Effect of electromagnetic disturbance on the practical QKD system in the smart grid

To improve the security of the smart grid, quantum key distribution（QKD） is an excellent choice. The rapid fluctuations on the power aerial optical cable and electromagnetic disturbance in substations are two main challenges for implementation of QKD. Due to insensitivity to birefringence of the channel, the stable phase-coding Faraday–Michelson QKD system is very practical in the smart grid. However, the electromagnetic disturbance in substations on this practical QKD system should be considered. The disturbance might change the rotation angle of the Faraday mirror, and would introduce an additional quantum bit error rate（QBER）. We derive the new fringe visibility of the system and the additional QBER from the electromagnetic disturbance. In the worst case, the average additional QBER only increases about 0.17% due to the disturbance, which is relatively small to normal QBER values. We also find the way to degrade the electromagnetic disturbance on the QKD system.     

Relativistic effect of pseudospin symmetry and tensor coupling on the Mie-type potential via Laplace transformation method

A relativistic Mie-type potential for spin-1/2 particles is studied. The Dirac Hamiltonian contains a scalar S（r） and a vector V（r） Mie-type potential in the radial coordinates, as well as a tensor potential U（r） in the form of Coulomb potential. In the pseudospin（p-spin） symmetry setting Σ = Cps and Δ = V（r）, an analytical solution for exact bound states of the corresponding Dirac equation is found. The eigenenergies and normalized wave functions are presented and particular cases are discussed with any arbitrary spin–orbit coupling number κ. Special attention is devoted to the caseΣ = 0 for which p-spin symmetry is exact. The Laplace transform approach（LTA） is used in our calculations. Some numerical results are obtained and compared with those of other methods.     

Phase field modeling of the ring-banded spherulites of crystalline polymers: The role of thermal diffusion

The ring-banded spherulite is a special morphology of polymer crystals and has attracted considerable attention over recent decades. In this study, a new phase field model with polymer characteristics is established to investigate the emergence and formation mechanism of the ring-banded spherulites of crystalline polymers. The model consists of a nonconserved phase field representing the phase transition and a temperature field describing the diffusion of the released latent heat. The corresponding model parameters can be obtained from experimentally accessible material parameters.Two-dimensional calculations are carried out for the ring-banded spherulitic growth of polyethylene film under a series of crystallization temperatures. The results of these calculations demonstrate that the formation of ring-banded spherulites can be triggered by the self-generated thermal field. Moreover, some temperature-dependent characteristics of the ring-banded spherulites observed in experiments are reproduced by simulations, which may help to study the effects of crystallization temperature on the ring-banded structures.     

The effect of cellular aging on the dynamics of spiral waves

Cellular aging can result in deterioration of electrical coupling, the extension of the action potential duration, and lower excitability of the cell. Those factors are introduced into the Greenberg–Hastings cellular automaton model and the effects of the cellular aging on the dynamics of spiral waves are studied. The numerical results show that a 50% reduction of the coupling strength of aging cells has a little influence on spiral waves. If the coupling strength of aging cells equals zero, the ability for the medium to maintain spiral waves will be reduced by approximately 50% when the aging cell ratio increases from 0 to 0.5, where the reduction of cell excitability plays a major role in inducing disappearance of spiral waves. When the relevant parameters are properly chosen, the cellular aging can lead to the meandering of spiral waves,the emergence of the binary spiral waves, and even the disappearance of spiral waves via the stopping rotation or shrinkage of wave. Physical mechanisms of the above phenomena are analyzed briefly.     

Effects of N doping on photoelectric properties of along different directions of ZnO bulk and nanotube

The electronic structures and optical properties of N-doped Zn O bulks and nanotubes are investigated using the firstprinciples density functional method. The calculated results show that the main optical parameters of Zn O bulks are isotropic（especially in the high frequency region）, while Zn O nanotubes exhibit anisotropic optical properties. N doping results show that Zn O bulks and nanotubes present more obvious anisotropies in the low-frequency region. Thereinto, the optical parameters of N-doped Zn O bulks along the [100] direction are greater than those along the [001] direction, while for N-doped nanotubes, the variable quantities of optical parameters along the [100] direction are less than those along the[001] direction. In addition, refractive indexes, electrical conductivities, dielectric constants, and absorption coefficients of Zn O bulks and nanotubes each contain an obvious spectral band in the deep ultraviolet（UV）（100 nm～ 300 nm）. For each of N-doped Zn O bulks and nanotubes, a spectral peak appears in the UV and visible light region, showing that N doping can broaden the application scope of the optical properties of Zn O.     

Superwide-angle acoustic propagations above the critical angles of the Snell law in liquid solid superlattice

In this paper, superwide-angle acoustic propagations above the critical angles of the Snell law in liquid–solid superlattice are investigated. Incident waves above the critical angles of the Snell law usually inevitably induce total reflection.However, incident waves with big oblique angles through the liquid–solid superlattice will produce a superwide angle transmission in a certain frequency range so that total reflection does not occur. Together with the simulation by finite element analysis, theoretical analysis by using transfer matrix method suggests the Bragg scattering of the Lamb waves as the physical mechanism of acoustic wave super-propagation far beyond the critical angle. Incident angle, filling fraction,and material thickness have significant influences on propagation. Superwide-angle propagation phenomenon may have potential applications in nondestructive evaluation of layered structures and controlling of energy flux.     

Species separation of binary colloidal mixtures in the multi-Gauss potential: Effect of depletion

For the asymmetrical colloidal mixture subject to a confining potential and an external multi-Gauss potential, the separation of species is studied based on the classical density functional theory of simple fluids. The multi-Gauss potential consists of several Gauss barriers, which are distributed along the axial direction with uniform distance. The barrier width,barrier distance, and barrier height are individually adjusted to investigate their effects on the species separation. From the numerical results, it is concluded that in each condition, the competition between the external potential and the depletion potential determines the phase equilibrium and the separation. Species separation appears only in the region where the depletion is dominant. On the contrary, both species are absent in the regions where the external potential takes the absolute advantage.     

A spherical higher-order finite-difference time-domain algorithm with perfectly matched layer

A higher-order finite-difference time-domain（HO-FDTD） in the spherical coordinate is presented in this paper. The stability and dispersion properties of the proposed scheme are investigated and an air-filled spherical resonator is modeled in order to demonstrate the advantage of this scheme over the finite-difference time-domain（FDTD） and the multiresolution time-domain（MRTD） schemes with respect to memory requirements and CPU time. Moreover, the Berenger＇s perfectly matched layer（PML） is derived for the spherical HO-FDTD grids, and the numerical results validate the efficiency of the PML.     

Exact Solutions and Invariant Sets to General Reaction-Diffusion Equation

In this paper, we introduce new invariant sets, and the invariant sets and exact solutions to general reactiondiffusion equation are discussed. It is shown that there exist a class of exact solutions to the equations that belong to the invariant sets.     

A New Type of Conserved Quantity Deduced from Mei Symmetry for Relativistic Mechanical System in Phase Space

In this paper, a new type of conserved quantity indirectly deduced from the Mei symmetry for relativistic mechanical system in phase space is studied. The definition and the criterion of the Mei symmetry for the system are given. The condition for existence and the form of the new conserved quantity are obtained. Finally, an example is given to illustrate the application of the results.     

Some new generating function formulae of the two-variable Hermite polynomials and their application in quantum optics

We explore the theoretical possibility of extending the usual squeezed state to those produced by nonlinear singlemode squeezing operators. We derive the wave functions of exp[-（ig/2）（（1-X2）1/2P ＋ P（1-X2）1/2）]｜0 in the coordinate representation. A new operator＇s disentangling formula is derived as a by-product.     

Dynamical behaviors of a system with switches between the Rssler oscillator and Chua circuits

The behaviors of a system that alternates between the R¨ossler oscillator and Chua＇s circuit is investigated to explore the influence of the switches on the dynamical evolution.Switches related to the state variables are introduced,upon which a typical switching dynamical model is established.Bifurcation sets of the subsystems are derived via analysis of the related equilibrium points,which divide the parameters into several regions corresponding to different types of attractors.The dynamics behave typically in period orbits with the variation of the parameters.The focus/cycle periodic switching phenomenon is explored in detail to present the mechanism of the movement.The period-doubling bifurcation to chaos can be observed via the doubling increase of the turning points related to the switches.Furthermore,period-decreasing sequences have been obtained,which can be explained by the variation of the eigenvalues associated with the equilibrium points of the subsystems.     

Pump-induced carrier envelope offset frequency dynamics and stabilization of an Yb-doped fiber frequency comb

In this paper, we demonstrate a carrier envelope phase-stabilized Yb-doped fiber frequency comb seeding by a nonlinear-polarization-evolution（NPE） mode-locked laser at a repetition rate of 60 MHz with a pulse duration of 191 fs.The pump-induced carrier envelope offset frequency（ f0） nonlinear tuning is discussed and further explained by the spectrum shift of the laser pulse. Through the environmental noise suppression, the drift of the free-running f0 is reduced down to less than 3 MHz within an hour. By feedback control on the pump power with a self-made phase-lock loop（PLL）electronics the carrier envelope offset frequency is well phase-locked with a frequency jitter of 85 m Hz within an hour.     

Modified 2CLJDQP model and the second virial coefficients for linear molecules

A modified form of 2CLJDQP potential model is proposed to calculate the second virial coefficients of two-center Lennard-Jones molecules. In the presented potential model, the potential parameters σ and ε are considered as the temperature-dependent parameters in the form of hyperbolical temperature function based on the theory of temperaturedependent potential parameters. With this modified model, the second virial coefficients of some homonuclear molecules（such as O2, Cl2, CH3CH3, and CF3CF3） and heteronuclear molecules（such as CO, NO, CH3 F, CH3 Cl, CH3CF3,CH3CHF2, and CF3CH2F） are calculated. Then the Lorentz–Berthelot mixing rule is modified with a temperaturedependent expression, and the second virial coefficients of the heteronuclear molecules（such as CH3 F, CH3 Cl, and CH3CF3） are calculated. Moreover, CO2 and N2O are also studied with the modified 3CLJDQP model. The calculated results from the modified 2CLJDQP model accord better with the experimental data than those from the original model.It is shown that the presented model improves the positive deviation in low temperature range and negative deviation in high temperature range. So the modified 2CLJDQP potential model with the temperature-dependent parameters can be employed satisfactorily in large temperature range.     

Radio-frequency compressed electron pulse-width characterization by cross-correlation between electron bunches and laser-induced plasma

A method is proposed to determine the temporal width of high-brightness radio-frequency compressed electron pulses based on cross-correlation technique involving electron bunches and laser-induced plasma. The temporal evolution of 2-dimensional transverse profile of ultrafast electron bunches repelled by the formed transient electric field of laser-induced plasma on a silver needle is investigated, and the pulse-width can be obtained by analyzing these time-dependent images.This approach can characterize radio-frequency compressed ultrafast electron bunches with picosecond or sub-picosecond timescale and up to 105 electron numbers.     

Defect characterization and magnetic properties in un-doped ZnO thin film annealed in a strong magnetic field

Highly c-axis oriented un-doped zinc oxide（Zn O） thin films, each with a thickness of ～ 100 nm, are deposited on Si（001） substrates by pulsed electron beam deposition at a temperature of ～ 320℃, followed by annealing at 650℃ in argon in a strong magnetic field. X-ray photoelectron spectroscopy（XPS）, positron annihilation analysis（PAS）, and electron paramagnetic resonance（EPR） characterizations suggest that the major defects generated in these Zn O films are oxygen vacancies. Photoluminescence（PL） and magnetic property measurements indicate that the room-temperature ferromagnetism in the un-doped Zn O film originates from the singly ionized oxygen vacancies whose number depends on the strength of the magnetic field applied in the thermal annealing process. The effects of the magnetic field on the defect generation in the Zn O films are also discussed.     

Gate-modulated generation–recombination current in n-type metal–oxide–semiconductor field-effect transistor

Gate-modulated generation–recombination（GMGR） current IGMGRinduced by the interface traps in an n-type metal–oxide–semiconductor field-effect transistor（n MOSFET） is investigated. The generation current is found to expand rightwards with increasing the reversed drain PN junction bias, and the recombination current is enhanced as the forward drain bias increases. The variations of IGMGRcurves are ascribed to the changes of the electron density and hole density at the interface, NSand PS, under the different drain bias voltages. Based on an analysis of the physical mechanism, the IGMGR model is set up by introducing two coefficients（m and t）. The coefficients m and t can modulate the curves widths and peak values. The simulated results under reverse mode and forward mode are obviously in agreement with the experimental results. This proves that this model can be applicable for generation current and recombination current and that the theory behind the model is reasonable. The details of the relevant mechanism are given in the paper.     

Effect of noncircular orifice plates on the near flow field of turbulent free jets

In this paper, we experimentally investigate the near-field flow characteristics of turbulent free jets respectively issued from circular, triangular, diamond, rectangular, and notched-rectangular orifice plates into air surroundings. All the orifice plates have identical opening areas or equivalent diameters（De） and their aspect ratios（AR） range from 1 to 6.5. Planar particle image velocimetry（PIV） is used to measure the velocity field at the same Reynolds number of Re = 5 × 10^4,where Re = Ue De/ν with Ue being the exit bulk velocity and ν the kinematic viscosity of fluid. The mean and turbulent velocity fields of all the five jets are compared in detail. Results show that the noncircular jets can enhance the entrainment rate, reflected by the higher acceleration rates of mean velocity decay and spread, shorten the length of the unmixed core,expedite the increase of turbulent intensity compared with the circular counterpart shortened unmixed core, and increase turbulent intensity comparing to the circular counterpart. Among the five jets, the rectangular jet（AR = 6.5） produces the greatest decay rate of the near-field mean velocity, postpones the position at which the 鈥榓xis-switching鈥檖henomenon occurs. This supports that axis switching phenomenon strongly depends on jet initial conditions. In addition, the hump in the centerline variation of the turbulence intensity is observed in the rectangular and triangular jets, but not in the circular jet, nor in diamond jet nor in notched-rectangular jet.     

Perturbation to Mei Symmetry and Noether Adiabatic Invariants for Birkhoffian Systems

Based on the concept of adiabatic invariant, the perturbation to Mei symmetry and Noether adiabatic invariants for Birkhoffian systems are studied. The exact invariants of Mei symmetry for the system without perturbation are given. The perturbation to Mei symmetry is discussed and the Noether adiabatic invariants induced from the perturbation to Mei symmetry of the system are obtained.