We derive some new generating function formulae of the two-variable Hermite polynomials, such as , , and . We employ the operator Hermite polynomial method and the technique of integration within an ordered product of operators to solve these problems, which will be useful in constructing new optical field states.

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 ∑=C_ps and △ =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 case ∑ =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.

Solid helium bubbles were directly observed in the helium ion implanted tungsten (W), by different transmission electron microscopy (TEM) techniques at room temperature. The diameters of these solid helium bubbles range from 1 nm to 8 nm in diameter with the mean bubble size about 3 nm. The selected area electron diffraction (SAED) and fast Fourier transform (FFT) images revealed that solid helium bubbles possess body-centered cubic (bcc) structure with a lattice constant of 0.447 nm. High-angle annular dark-field scanning transmission electron microscopy (HAADF-STEM) images further confirmed the existence of helium bubble in tungsten. The present findings provide an atomic level view of the microstructure evolution of helium in the materials, and revealed the existence of solid helium bubbles in materials.

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.

We theoretically analyze the steady state emission spectrum and transient temporal dynamics in a coupled biexciton quantum dot (QD)–cavity system. For steady state, a phonon-assisted biexciton–exciton cascade model under continuous wave (CW) excitation is presented to explain the asymmetric QD–cavity emission spectrum intensities (intensities of cavity, exciton, and biexciton emission peak) in off-resonance condition. Results demonstrate that the electron–phonon process is crucial to the asymmetry of emission spectrum intensity. Moreover the transient characteristics of the biexciton–exciton cascade system under pulse excitation show abundant nonlinear temporal dynamic behaviors, including complicated oscillations which are caused by the four-level structure of QD model. We also reveal that under off-resonance condition the cavity outputs are slightly reduced due to the electron–phonon interaction.

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 mHz within an hour.

By using semiclassical theory combined with multiple-scale method, we analytically study the linear absorption and the nonlinear dynamical properties in a lifetime broadened Λ -type three-level self-assembled quantum dots. It is found that this system can exhibit the transparency, and the width of the transparency window becomes wider with the increase of control light field. Interestingly, a weak probe light beam can form spatial weak-light dark solitons. When it propagates along the axial direction, the soliton will transform into a steady spatial weak-light ring dark soltion. In addition, the stability of two-dimensional spatial optical solitons is testified numerically.

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 ModHV models.

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.

The Noether symmetry and the conserved quantity of a fractional Birkhoffian system are studied within the Riemann–Liouville fractional derivatives. Firstly, the fractional Birkhoff's equations and the corresponding transversality conditions are given. Secondly, from special to general forms, Noether's theorems of a standard Birhoffian system are given, which provide an approach and theoretical basis for the further research on the Noether symmetry of the fractional Birkhoffian system. Thirdly, the invariances of the fractional Pfaffian action under a special one-parameter group of infinitesimal transformations without transforming the time and a general one-parameter group of infinitesimal transformations with transforming the time are studied, respectively, and the corresponding Noether's theorems are established. Finally, an example is given to illustrate the application of the results.

Crystal orientation influences the morphological stability of solid–liquid interface during directional solidification of alloy, resulting in the variation of solidified microstructure. In this paper, the morphological evolution near grain boundary grooves (GBGs) with different crystal orientations in a dilute succinonitrile alloy under low temperature gradient and interface velocity is observed in situ. Under experimental conditions, the macroscopic solid–liquid interface is planar and keeps stable, while in GBGs there emerge protrusion and undulation. It is found that the morphological stability of GBG is dependent on crystal orientation. Specifically, for succinonitrile with a body-centered cubic crystal structure, GBGs around the <100> crystal orientation keep stable, while those apart from the <100> crystal orientation become unstable under the same conditions. So it is concluded that <100> crystal orientation favors the morphological stability of GBG.

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 (D_e) 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= 5×10⁴, where Re= U_eD_e/ν with U_e 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phenomenon 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.

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 non-conserved 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.

A novel lateral double-diffused metal–oxide semiconductor (LDMOS) with a high breakdown voltage (BV) and low specific on-resistance (R_on.sp) is proposed and investigated by simulation. It features a junction field plate (JFP) over the drift region and a partial N-buried layer (PNB) in the P-substrate. The JFP not only smoothes the surface electric field (E-field), but also brings in charge compensation between the JFP and the N-drift region, which increases the doping concentration of the N-drift region. The PNB reshapes the equipotential contours, and thus reduces the E-field peak on the drain side and increases that on the source side. Moreover, the PNB extends the depletion width in the substrate by introducing an additional vertical diode, resulting in a significant improvement on the vertical BV. Compared with the conventional LDMOS with the same dimensional parameters, the novel LDMOS has an increase in BV value by 67.4%, and a reduction in R_on.sp by 45.7% simultaneously.

The transition from vortex glass to a liquid phase is studied in BaNi_0.1Fe_1.9As₂ single crystal with T_c=19.4 K by magneto-resistance measurements. The resistivity curves are measured in magnetic fields in a range of 0 T–13 T for H‖c and H⊥c. Good scalings for all values of resistivity ρ(H,T) and the effective pinning potential U₀(H,T) are obtained with the modified vortex glass theory by using the critical exponents s and H₀. Phase diagrams for H‖c and H⊥c are determined based on the obtained vortex glass temperature T_g, the vortex dimensionality crossover temperature T^*, and the upper critical magnetic field H_c2. Our results suggest that both below and above 5 T, single vortex pinning co-exists with collective creep, and collective creep is dominant. There is a narrower vortex liquid region for H⊥c than for H‖c in the vortex phase diagram, which may originate from a stronger pinning force.

We synthesize the perovskite compound SmCr_0.9Fe_0.1O₃ by the sol–gel method and investigate its exchange bias properties through thermomagnetic and isothermal magnetization measurements. The sign reversals of the exchange bias field are observed at the magnetization compensation temperatures 29.6 K and 96.2 K. It is demonstrated that the occurrence of the exchange bias originates from the antiferromagnetic coupling between the Cr-rich and Fe–Cr regions, of which the net magnetization is temperature-dependent. These results imply that there are potential applications in single systems with sign reversals of both magnetization and exchange bias.

Highly c-axis oriented un-doped zinc oxide (ZnO) 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 ZnO films are oxygen vacancies. Photoluminescence (PL) and magnetic property measurements indicate that the room-temperature ferromagnetism in the un-doped ZnO 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 ZnO films are also discussed.

A simplified quasi-static computational model for self-sensing applications of magnetostrictive actuators based on terfenol-D rods is presented. Paths and angle changes in the magnetic moments rotation of Tb_0.3Dy_0.7Fe₂ alloy are studied as functions of compressive stress and magnetic field, and then used to determine the magnetization in its actuation. Then sensing of magnetic induction picked from a driving coil in an actuator is derived. The model is quick and efficient to solve moments rotation and its magnetization. Sensing results of compressive stress and magnetostriction calculated by the model are in good agreement with experiments and will be helpful in the design and control of self-sensing applications in actuators.

The temperature dependence of the photoluminescence (PL) from MnS/ZnS core–shell quantum dots is investigated in a temperature range of 8 K–300 K. The orange emission from the ⁴T₁ → ⁶A₁ transition of Mn²⁺ ions and the blue emission related to the trapped surface state are observed in the MnS/ZnS core–shell quantum dots. As the temperature increases, the orange emission is shifted toward a shorter wavelength while the blue emission is shifted towards the longer wavelength. Both the orange and blue emissions reduce their intensities with the increase of temperature but the blue emission is quenched faster. The temperature-dependent luminescence intensities of the two emissions are well explained by the thermal quenching theory.

A multi-band circular polarizer using a twisted triple split-ring resonator (TSRR) is presented and studied numerically and experimentally. At four distinct resonant frequencies, the incident linearly polarized wave can be transformed into left/right-handed circularly polarized waves. Numerical simulation results show that a y-polarized wave can be converted into a right-handed circularly polarized wave at 5.738 GHz and 9.218 GHz, while a left-handed circularly polarized wave is produced at 7.292 GHz and 10.118 GHz. The experimental results are in agreement with the numerical results. The surface current distributions are investigated to illustrate the polarization transformation mechanism. Furthermore, the influences of the structure parameters of the circular polarizer on transmission spectra are discussed as well.

High-performance AlGaN/GaN high electron mobility transistors (HEMTs) grown on silicon substrates by metal–organic chemical-vapor deposition (MOCVD) with a selective non-planar n-type GaN source/drain (S/D) regrowth are reported. A device exhibited a non-alloyed Ohmic contact resistance of 0.209 Ω·mm and a comprehensive transconductance (g_m) of 247 mS/mm. The current gain cutoff frequency f_T and maximum oscillation frequency f_MAX of 100-nm HEMT with S/D regrowth were measured to be 65 GHz and 69 GHz. Compared with those of the standard GaN HEMT on silicon substrate, the f_T and f_MAX is 50% and 52% higher, respectively.

We report a facile method of synthesizing graphene quantum dots (GQDs) with tunable emission. The as-prepared GQDs each with a uniform lateral dimension of ca. 6 nm have fine solubility and high stability. The photoluminescence mechanism is further investigated based on the surfacestructure and the photoluminescence behaviors. Based on our discussion, the green fluorescence emission can be attributed to the oxygen functional groups, which could possess broad emission bands within the π–π^* gap. This work is helpful to explain the vague fluorescent mechanism of GQDs, and the reported synthetic method is useful to prepare GQDs with controllable fluorescent colors.

Spectrum sensing is an essential component to realize the cognitive radio, and the requirement for real-time spectrum sensing in the case of lacking prior information, fading channel, and noise uncertainty, indeed poses a major challenge to the classical spectrum sensing algorithms. Based on the stochastic properties of scalar transformation of power spectral density (PSD), a novel spectrum sensing algorithm, referred to as the power spectral density split cancellation method (PSC), is proposed in this paper. The PSC makes use of a scalar value as a test statistic, which is the ratio of each subband power to the full band power. Besides, by exploiting the asymptotic normality and independence of Fourier transform, the distribution of the ratio and the mathematical expressions for the probabilities of false alarm and detection in different channel models are derived. Further, the exact closed-form expression of decision threshold is calculated in accordance with Neyman–Pearson criterion. Analytical and simulation results show that the PSC is invulnerable to noise uncertainty, and can achive excellent detection performance without prior knowledge in additive white Gaussian noise and flat slow fading channels. In addition, the PSC benefits from a low computational cost, which can be completed in microseconds.

We investigate the impact of financial factors on daily volume recurrent time intervals in the developing Chinese stock markets. The tails of probability distribution functions (PDFs) of volume recurrent intervals behave as a power-law, and the scaling exponent decreases with the increase of stock lifetime, which are similar to those in the US stock markets, and they are typical representatives of developed markets. The difference is that the power-law exponent values remain almost the same with the changes of market capitalization, mean volume, and mean trading value, respectively. These findings enrich the results for event statistics for financial markets.