The Lie symmetry theorem of fractional nonholonomic systems in terms of combined fractional derivatives is established, and the fractional Lagrange equations are obtained by virtue of the d'Alembert-Lagrange principle with fractional derivatives. As the Lie symmetry theorem is based on the invariance of differential equations under infinitesimal transformations, by introducing the differential operator of infinitesimal generators, the determining equations are obtained. Furthermore, the limit equations, the additional restriction equations, the structural equations, and the conserved quantity of Lie symmetry are acquired. An example is presented to illustrate the application of results.

In this paper, third-order nonlinear differential operators are studied. It is shown that they are quadratic forms when they preserve invariant subspaces of maximal dimension. A complete description of third-order quadratic operators with constant coefficients is obtained. One example is given to derive special solutions for evolution equations with third-order quadratic operators.

We obtain the non-local residual symmetry related to truncated Painlevé expansion of Burgers equation. In order to localize the residual symmetry, we introduce new variables to prolong the original Burgers equation into a new system. By using Lie's first theorem, we obtain the finite transformation for the localized residual symmetry. More importantly, we also localize the linear superposition of multiple residual symmetries to find the corresponding finite transformations. It is interesting to find that the n-th Bäcklund transformation for Burgers equation can be expressed by determinants in a compact way.

The finite dissolution model of silicon particles in the aluminum melt is built and calculated by the finite difference method, and the lower dissolution limit of silicon particles in the aluminum melt is proposed and verified by experiments, which could be the origin of microinhomogeneity in aluminum-silicon melts. When the effects of curvature and interface reaction on dissolution are not considered; the dissolution rate first decreases and later increases with time. When the effects of curvature and interface reaction on dissolution are considered, the dissolution rate first decreases and later increases when the interface reaction coefficient (k) is larger than 10^{-1}, and the dissolution rate first decreases and later tends to be constant when k is smaller than 10^{-3}. The dissolution is controlled by both diffusion and interface reaction when k is larger than 10^{-3}, while the dissolution is controlled only by the interface reaction when k is smaller than 10^{-4}.

This paper studies the consensus problems for multi-agent systems with general linear and nonlinear dynamics. The leaderless and leader-following consensus problems are investigated respectively. Contraction theory is employed to generate some sufficient conditions for testing the agents reaching consensus. Under these conditions and certain assumptions, the trajectories of multi-agent systems in directed topology will converge to each other. Finally, two numerical examples are given to illustrate the effectiveness of the proposed results.

Three-dimensional (3D) Fick's diffusion equation and fractional diffusion equation are solved for different reflecting boundaries. We use the continuous time random walk model (CTRW) to investigate the time-averaged mean square displacement (MSD) of a 3D single particle trajectory. Theoretical results show that the ensemble average of the time-averaged MSD can be expressed analytically by a Mittag-Leffler function. Our new expression is in agreement with previous formulas in two limiting cases: <δ^{2}> ～Δ in short lag time and <δ^{2}>～Δ^{1-α} in long lag time. We also simulate the experimental data of mRNA diffusion in living E. coli using a 3D CTRW model under confined and crowded conditions. The simulation results are well consistent with experimental results. The calculations of power spectral density (PSD) further indicate the subdiffsive behavior of an individual trajectory.

Based on the multiquadric trigonometric B-spline quasi-interpolant, this paper proposes a meshless scheme for some partial differential equations whose solutions are periodic with respect to the spatial variable. This scheme takes into account the periodicity of the analytic solution by using derivatives of a periodic quasi-interpolant (multiquadric trigonometric B-spline quasi-interpolant) to approximate the spatial derivatives of the equations. Thus, it overcomes the difficulties of the previous schemes based on quasi-interpolation (requiring some additional boundary conditions and yielding unwanted high-order discontinuous points at the boundaries in the spatial domain). Moreover, the scheme also overcomes the difficulty of the meshless collocation methods (i.e., yielding a notorious ill-conditioned linear system of equations for large collocation points). The numerical examples that are presented at the end of the paper show that the scheme provides excellent approximations to the analytic solutions.

We propose a theorem for the quantum operator that corresponds to the solution of the Helmholtz equation, i.e., ∫∫∫V(x_{1},x_{2},x_{3}|x_{1},x_{2},x_{3}><x_{1},x_{2},x_{3}|d^{3}x = V(X_{1},X_{2},X_{3}) = e^{-λ2/4}:V(X_{1},X_{2},X_{3}):, where IV(x_{1},x_{2},x_{3}) is the solution to the Helmholtz equation ∇^{2}V+λ^{2}V=0, the symbol::denotes normal ordering, and X_{1},X_{2},X_{3} are three-dimensional coordinate operators. This helps to derive the normally ordered expansion of Dirac's radius operator functions. We also discuss the normally ordered expansion of Bessel operator functions.

We present a numerical study of a model of quantum walk in a periodic potential on a line. We take the simple view that different potentials have different affects on the way in which the coin state of the walker is changed. For simplicity and definiteness, we assume that the walker's coin state is unaffected at sites without the potential, and rotated in an unbiased way according to the Hadamard matrix at sites with the potential. This is the simplest and most natural model of a quantum walk in a periodic potential with two coins. Six generic cases of such quantum walks are studied numerically. It is found that, of the six cases, four cases display significant localization effect where the walker is confined in the neighborhood of the origin for a sufficiently long time. Associated with such a localization effect is the recurrence of the probability of the walker returning to the neighborhood of the origin.

Although the multi-level structure of superconducting qubits may result in calculation errors, it can be rationally used to effectively improve the speed of gate operations. Utilizing a current-biased Josephson junction (Λ-type rf-SQUID) as a tunable coupler for superconducting transmission line resonators (TLRs), under the large detuning condition, we demonstrate the controllable generation of entangled coherent states in circuit quantum electrodynamics (circuit QED). The coupling between the TLRs and the qubit can be effectively regulated by an external bias current or coupling capacitor. Further investigations indicate that the maximum entangled state can be obtained through measuring the excited state of the superconducting qubits. Then, the influence of the TLR decay on the prepared entangled states is analyzed.

We study the entanglement trapping of two entangled qubits, each of which is in its own photonic band gap, based on the weak measurement and quantum measurement reversal. An almost maximal entanglement of the two-qubit system can be trapped by using a certain weak measurement strength. Furthermore, we find that the optimal entanglement enhancing is not only dependent on the weak measurement strength but also on the different initial states. The outcomes in our scheme are completely different from that without any measurement on the studied system.

Using the effective non-Markovian measure proposed by Breuer et al. recently, we study the memory effect of a central qubit system coupled to a spin chain environment with Dzyaloshinskii-Moriya interaction in a transverse field. It is discovered that the central qubit system presents different memory effects in different environment phases with the different oscillatory behaviors of the decoherence factor. Moreover, it is revealed that the Dzyaloshinskii-Moriya interaction has a prominent influence on the memory effect of a central qubit system via modifying the amplitude and period of the decoherence factor under certain conditions.

We investigate the characteristics of three kinds of quantum correlations, measured by pairwise quantum discord (QD), geometric measure of quantum discord (GMQD), and measurement-induced disturbance (MID), in the systems of three- and four-dipole arrays. The influence of the temperature on the three quantum correlations and entanglement of the systems is also analyzed numerically. It is found that novel quantum correlation switches called QD, GMQD, and MID respectively can be constructed with the qubits consisting of electric dipoles coupled by the dipole-dipole interaction and oriented along or against the external electric field. Moreover, with the increase of temperature, QD, GMQD, and MID are more robust than entanglement against the thermal environment. It is also found that for each dipole pair of the three- and four-dipole arrangements, the MID is always the largest and the GMQD the smallest.

We analyze the process of a discrete-time quantum walk over 4 steps and 5 positions with linear optics elements. The quantum walk is characterized by a ballistic spread of wavepackets along 4 steps. By employing different initial coin states, we observe non-Gaussian distribution of the walkers' finial position, which characterizes a quadratic enhancement of the spread of photon wavepackets compared to a classical random walk. By introducing controllable decoherence, we observe the quantum-to-classical transmission in a quantum walk architecture.

We investigate a kind of solitons in the two-component Bose-Einstein condensates with axisymmetric configurations in the R^{2}× S^{1} space. The corresponding topological structure is referred to as Hopfion. The spin texture differs from the conventional three-dimensional (3D) skyrmion and knot, which is characterized by two homotopy invariants. The stability of the Hopfion is verified numerically by evolving the Gross-Pitaevskii equations in imaginary time.

A distinct method to show a quantum object behaving both as wave and as particle is proposed and described in some detail. We make a systematic analysis using the elementary methodology of quantum mechanics upon Young's two-slit interferometer and the Mach-Zehnder two-arm interferometer with the focus placed on how to measure the interference pattern (wave nature) and the which-way information (particle nature) of quantum objects. We design several schemes to simultaneously acquire the which-way information for an individual quantum object and the high-contrast interference pattern for an ensemble of these quantum objects by placing two sets of measurement instruments that are well separated in space and whose perturbation of each other is negligibly small within the interferometer at the same time. Yet, improper arrangement and cooperation of these two sets of measurement instruments in the interferometer would lead to failure of simultaneous observation of wave and particle behaviors. The internal freedoms of quantum objects could be harnessed to probe both the which-way information and the interference pattern for the center-of-mass motion. That quantum objects can behave beyond the wave-particle duality and the complementarity principle would stimulate new conceptual examination and exploration of quantum theory at a deeper level.

Event-triggered control has been recently proposed as an effective strategy for the consensus of multi-agent systems. We present an improved distributed event-triggered control scheme that remedies a shortcoming of some previous event-triggered control schemes in the literature. This improved distributed event-triggered method has no need for continuously monitoring each agent' neighbors. Moreover, each agent in the multi-agent systems will not exhibit the Zeno behavior. Numerical simulation results show the effectiveness of the proposed consensus control.

This paper addresses the control law design for synchronization of two different chaotic oscillators with mutually Lipschitz nonlinearities. For analysis of the properties of two different nonlinearities, an advanced mutually Lipschitz condition is proposed. This mutually Lipschitz condition is more general than the traditional Lipschitz condition. Unlike the latter, it can be used for the design of a feedback controller for synchronization of chaotic oscillators of different dynamics. It is shown that any two different Lipschitz nonlinearities always satisfy the mutually Lipschitz condition. Applying the mutually Lipschitz condition, a quadratic Lyapunov function and uniformly ultimately bounded stability, easily designable and implementable robust control strategies utilizing algebraic Riccati equation and linear matrix inequalities, are derived for synchronization of two distinct chaotic oscillators. Furthermore, a novel adaptive control scheme for mutually Lipschitz chaotic systems is established by addressing the issue of adaptive cancellation of unknown mismatch between the dynamics of different chaotic systems. The proposed control technique is numerically tested for synchronization of two different chaotic Chua's circuits and for obtaining identical behavior between the modified Chua's circuit and the Rössler system.

The enhancement of the precision of phase estimation in quantum metrology is investigated by employing weak measurement (WM) and quantum measurement reversal (QMR). We derive the exact expressions of the optimal quantum Fisher information (QFI) and success probability of phase estimation for an exactly solving model consisting of a qubit interacting with a structured reservoir. We show that the QFI can be obviously enhanced by means of the WM and QMR in different regimes. In addition, we also show that the magnitude of the decoherence involved in the WM and QMR can be a general complex number, which extends the applicable scope of the WM and QMR approach.

We analyze the phenomena of phase group synchronization between the different nominal frequency signals and propose a new theory of the equivalent comparison between them. The exact expression of the equivalent comparison is deduced. High resolution frequency measurement and phase comparison can be realized using this theory with the divider. For avoiding the frequency mixing, multiplication and synthesis, the system phase noise is improved and the higher resolution comparison and measurement are achieved between the different nominal frequencies by theory.

A simple and convenient pressure calibration method is developed for a newly designed portable wide-access ‘panoramic’cell. This cell is adapted to angle-dispersive-mode high-pressure in situ neutron diffraction of reactor neutron sources. This pressure calibration method has established a relationship between the cell pressure and the anvil displacement (gasket compression) based on the fixed-point calibration technique. By employing TiZr gasket with a thickness of 3 mm and WC anvil with a culet of 4 mm diameter, the average anvil displacements are 1.31 mm and 2.22 mm for Bi phase transitions (2.55 GPa and 7.7 GPa), and 1.85 mm for Ba phase transitions (5.5 GPa), respectively. In this pressure range, the pressure increases quickly with decreasing gasket thickness, and undergoes a linear increase with the anvil displacement. By extrapolating the calibration curve, the cell pressure will achieve 10 GPa when the anvil displacement is around 2.5 mm.

In this study, the V-I transmission matrix formalism (V-I method) is proposed to analyze the spectrum characteristics of the uniform fiber Bragg grating (FBG)-based acousto-optic modulators (UFBG-AOM). The simulation results demonstrate that both the amplitude of the acoustically induced strain and the frequency of the acoustic wave (AW) have an effect on the spectrum. Additionally, the wavelength spacing between the primary reflectivity peak and the secondary reflectivity peak is proportional to the acoustic frequency with the ratio 0.1425 nm/MHz. Meanwhile, we compare the amount of calculation. For the FBG whose period is M, the calculation of the V-I method is 4×(2M-1) in addition/subtraction, 8×(2M-1) in multiply/division and 2M in exponent arithmetic, which is almost a quarter of the multi-film method and transfer matrix (TM) method. The detailed analysis indicates that, compared with the conventional multi-film method and transfer matrix (TM) method, the V-I method is faster and less complex.

The digital coherent detection technique has been investigated without any frequency-scanning device in the Brillouin optical time domain reflectometry (BOTDR), where the simplex pulse codes are applied in the sensing system. The time domain signal of every code sequence is collected by the data acquisition card (DAQ). A shift-averaging technique is applied in the frequency domain for the reason that the local oscillator (LO) in the coherent detection is fix-frequency deviated from the primary source. With the 31-bit simplex code, the signal-to-noise ratio (SNR) has 3.5-dB enhancement with the same single pulse traces, accordant with the theoretical analysis. The frequency fluctuation for simplex codes is 14.01 MHz less than that for a single pulse as to 4-m spatial resolution. The results are believed to be beneficial for the BOTDR performance improvement.

The effect of Re on stacking fault (SF) nucleation under shear strain in Ni is investigated using the climbing image nudged elastic band method with a Ni-Al-Re embedded-atom-method potential. A parameter (ΔE_{sf}^{b}), the activation energy of SF nucleation under shear strain, is introduced to evaluate the effect of Re on SF nucleation under shear strain. Calculation results show that ΔE_{sf}^{b} decreases with Re addition, which means that SF nucleation under shear strain in Ni may be enhanced by Re. The atomic structure observation shows that the decrease of ΔE_{sf}^{b} may be due to the expansion of local structure around the Re atom when SF goes through the Re atom.

Layered oxides of P2-type Na_{0.68}Cu_{0.34}Mn_{0.66}O_{2}, P2-type Na_{0.68}Cu_{0.34}Mn_{0.50}Ti_{0.16}O_{2}, and O'3-type NaCu_{0.67}Sb_{0.33}O_{2} were synthesized and evaluated as cathode materials for room-temperature sodium-ion batteries. The first two materials can deliver a capacity of around 70 mAh/g. The Cu^{2+} is oxidized to Cu^{3+} during charging, and the Cu^{3+} goes back to Cu^{2+} upon discharging. This is the first demonstration of the highly reversible change of the redox couple of Cu^{2+}/Cu^{3+} with high storage potential in secondary batteries.

The X-ray spectrometer used in high-energy-density plasma experiments generally requires both broad X-ray energy coverage and high temporal, spatial, and spectral resolutions for overcoming the difficulties imposed by the X-ray background, debris, and mechanical shocks. By using an elliptical crystal together with a streak camera, we resolve this issue at the SG-II laser facility. The carefully designed elliptical crystal has a broad spectral coverage with high resolution, strong rejection of the diffuse and/or fluorescent background radiation, and negligible source broadening for extended sources. The spectra that are Bragg reflected (23°<θ<38°) from the crystal are focused onto a streak camera slit 18 mm long and about 80 μm wide, to obtain a time-resolved spectrum. With experimental measurements, we demonstrate that the quartz(1011) elliptical analyzer at the SG-II laser facility has a single-shot spectral range of (4.64-6.45) keV, a typical spectral resolution of E/ΔE=560, and an enhanced focusing power in the spectral dimension. For titanium (Ti) data, the lines of interest show a distribution as a function of time and the temporal variations of the He-α and Li-like Ti satellite lines and their spatial profiles show intensity peak red shifts. The spectrometer sensitivity is illustrated with a temporal resolution of better than 25 ps, which satisfies the near-term requirements of high-energy-density physics experiments.

We calculate the electron impact excitation of Ni-like gold by using the Dirac R-matrix theory, and the corresponding collision strengths and effective collision strengths are obtained. In the calculations of the level energy, (1s^{2}2s^{2}2p^{6})3s^{2}3p^{6}3d^{10}, 3s^{2}3p^{6}3d^{9}4l, 3s^{2}3p^{5}3d^{10}4l, and 3s3p^{6}3d^{10}4l (l=0,1,2,3) configurations are included and 107 fine-structure levels are generated. In the calculations of the collision strengths, only the first 59 levels are included. Comparisons are made with the distorted wave (DW) results of Zeng et al. for both collision strengths and effective collision strengths. For the collision strengths, the two sets of calculations are in excellent agreement for most of the transitions. However, because of the inclusion of the resonances, our effective collision strengths are generally several times larger than those of Zeng et al.. The accuracy of our calculations is assessed.

The (e, 2e) triple differential cross sections (TDCSs) of Ar (3s) are calculated by using distorted-wave Born approximation under coplanar asymmetric geometry. The incident electron energy is 113.5 eV, and the scattering electron angle θ_{1} is -15°. The ejected electron energy is set at 10 eV, 7.5 eV, 5 eV, and 2 eV, respectively. The polarization effects have been discussed and the polarization potential V_{pol} changing from a second-order to a fourth-order term has been analyzed. Our calculated TDCSs have been compared with reported experimental and theoretical results, and the calculated TDCSs of polarization potential up to the fourth order could give a good fit with experimental results in the binary region, but fail to predict the correct recoil-to-binary ratio in most cases.

The electronic structure of nitrogen trifluoride was investigated by combining the high-resolution electron momentum spectroscopy with the high-level calculations. The experimental binding energy spectra and the momentum distributions of each orbital were compared with the results of Hartree-Fock, density functional theory (DFT), and symmetry-adapted-cluster configuration-interaction (SAC-CI) methods. SAC-CI and DFT-B3LYP with the aug-cc-pVTZ basis set can well reproduce the binding energy spectra and the observed momentum distributions of the valence orbitals except 1a_{2} and 4e orbitals. It was found that the calculated momentum distributions using DFT-B3LYP are even better than those using the high-level SAC-CI method.

The dissociative ionization of CO_{2} induced by 5 keV electrons in two-body and three-body dissociative channels of CO_{2}^{2+} and CO_{2}^{3+} is identified by the ion-ion coincidence- method using a momentum imaging spectrometer. The partial ionization cross sections (PICSs) of different ionic fragments are measured and the results generally agree with the calculations made by a semi-empirical approach. Furthermore, the PICSs of the dissociative channels are also obtained by carefully considering the detection efficiency of the micro-channel plates and the total transmission efficiency of the time of flight system.

We theoretically investigate an enhanced electromagnetically induced transparency (EIT) cooling method by introducing a high finesse cavity. We find that the quantum destructive interference that is induced by the EIT effect and the cavity coupling can eliminate all of the heating effects in the cooling process by choosing appropriate parameters. Compared with the EIT cooling scheme, a lower final temperature can be obtained under the same conditions in our scheme.

We systematically investigate the polarization gradient cooling (PGC) process in an optical molasses of ultracold cesium atoms. The SR mode for changing the cooling laser, which means that the cooling laser frequency is stepped to the setting value while its intensity is ramped, is found to be the best for the PGC, compared with other modes studied. We verify that the heating effect of the cold atoms, which appears when the cooling laser intensity is lower than the saturation intensity, arises from insufficient polarization gradient cooling. Finally, an exponential decay function with a statistical explanation is introduced to explain the dependence of the cold atom temperature on the PGC interaction time.

ELECTROMAGNETISM, OPTICS, ACOUSTICS, HEAT TRANSFER, CLASSICAL MECHANICS, AND FLUID DYNAMICS

An efficiently iterative analytical-numerical method is proposed for two-dimensional (2D) electromagnetic scattering from a perfectly electric conducting (PEC) target buried under a dielectric rough surface. The basic idea is to employ the Kirchhoff approximation (KA) to accelerate the boundary integral method (BIM). Below the rough surface, an iterative system is designed between the rough surface and the target. The KA is used to simulate the initial field on the rough surface based on the Fresnel theory, while the target is analyzed by the boundary integral method to obtain a precise result. The fields between the rough surface and the target can be linked by the boundary integral equations below the rough surface. The technique presented here is highly efficient in terms of computational memory, time, and versatility. Numerical simulations of two typical models are carried out to validate the method.

In this study, the bidirectional reflectance distribution function (BRDF) of a one-dimensional conducting rough surface and a dielectric rough surface are calculated with different frequencies and roughness values in the microwave band by using the method of moments, and the relationship between the bistatic scattering coefficient and the BRDF of a rough surface is expressed. From the theory of the parameters of the rough surface BRDF, the parameters of the BRDF are obtained using a genetic algorithm. The BRDF of a rough surface is calculated using the obtained parameter values. Further, the fitting values and theoretical calculations of the BRDF are compared, and the optimization results are in agreement with the theoretical calculation results. Finally, a reference for BRDF modeling of a Gaussian rough surface in the microwave band is provided by the proposed method.

We synthesize Tm^{3+}/Tb^{3+}/Eu^{3+} triply-doped ZrF_{4}-BaF_{2}-LaF_{3}-AlF_{3}-NaF (ZBLAN) transparent glass by using a melt-quenching method. Under excitation of 365 nm, the white emission with Commission internationale deL'Eclairage (CIE) coordinates of (0.33, 0.33) is achieved at the Eu^{3+} concentration of 1.1 mol%. The mechanisms for white emission and the energy transfer process of Tb^{3+}→Eu^{3+} are discussed in terms of the photoluminescence, photoluminescence excitation spectra, and the light emission decay curves. The nature for the Tb^{3+}→Eu^{3+} energy transfer is described with the aid of an energy level diagram.

We study a three-mode double-cavity optomechanical system in which an oscillating membrane of perfect reflection is inserted between two fixed mirrors of partial transmission. We find that electromagnetically induced transparency (EIT) can be realized and controlled in this optomechanical system by adjusting the relative intensity and the relative phase between left-hand and right-hand input (probe and coupling) fields. In particular, one perfect EIT window is seen to occur when the two probe fields are exactly out of phase and the EIT window's width is very sensitive to the relative intensity of two coupling fields. Our numerical findings may be extended to achieve optomechanical storage and switching schemes applicable in quantum information processing.

We present a novel precise angle measurement scheme based on parallel multiplex laser feedback interferometry (PLFI), which outputs two parallel laser beams and thus their displacement difference reflects the angle variation of the target. Due to its ultrahigh sensitivity to the feedback light, PLFI realizes the direct non-contact measurement of non-cooperative targets. Experimental results show that PLFI has an accuracy of 8" within a range of 1400". The yaw of a guide is also measured and the experimental results agree with those of the dual-frequency laser interferometer Agilent 5529A.

This study shows that the photoelectron energy spectrum generated by an intense laser pulse in the presence of a continuous X-ray has interesting and useful statistical properties. The total photoionization production is linearly proportional to the time duration of the laser pulse and the square of the beam size. The spectral double energy-integration is an intrinsic value of the laser-assisted X-ray photoionization, which linearly depends on the laser intensity and which quantitatively reflects the strengths of the laser-field modulation and the quantum interference between photoelectrons. The spectral energy width also linearly depends on the laser intensity. These linear relationships suggest new methods for the in-situ measurement of laser intensity and pulse duration with high precision.

We demonstrate a cost effective, linearly tunable fiber optical parametric oscillator based on a home-made photonic crystal fiber pumped with a mode-locked ytterbium-doped fiber laser, providing linely tuning ranges from 1018 nm to 1038 nm for the idler wavelength and from 1097 nm to 1117 nm for the signal wavelength by tuning the pump wavelength and the cavity length. In order to obtain the desired fiber with a zero dispersion wavelength around 1060 nm, eight samples of photonic crystal fibers with gradually changed structural parameters are fabricated for the reason that it is difficult to accurately customize the structural dimensions during fabrication. We verify the usability of the fabricated fiber experimentally via optical parametric generation and conclude a successful procedure of design, fabirication, and verification. A seed source of home-made all-normal-dispersion mode-locked ytterbium-doped fiber laser with 38.57 ps pulsewidth around the 1064 nm wavelength is used to pump the fiber optical parametric oscillator. The wide picosecond pulse pump laser enables a larger walk-off tolerance between the pump light and the oscillating light as well as a longer photonic crystal fiber of 20 m superior to the femtosecond pulse lasers, resulting in a larger parametric amplification and a lower threshold pump power of 15.8 dBm of the fiber optical parametric oscillator.

A high quality-factor (Q) cavity based on a one-dimensional (1D) photonic crystal with gradated elliptical holes was designed using FDTD simulation. Different gradient profiles of the mirror holes were found to correspond to different Q-values of the cavities. A simple strategy is proposed to construct high-Q cavities by using an S-shaped gradient profile for the elliptical holes' minor axes, such as a cosine function or Gaussian function. Using such a strategy, a Q value exceeding two million is obtained with only ten mirror holes in a cavity.

A novel high-efficiency focusing non-uniform grating coupler is proposed to couple light into or off silicon photonic chips for large-scale silicon photonic integration. This kind of grating coupler decreases the transition length of the linking taper between the grating and the single-mode waveguide by at least 80%. The radian of the grating lines and the size of the taper are optimized to improve the coupling efficiency. An experimental coupling efficiency of ～ 68% at 1556.24 nm is obtained after optimization and the whole size of the grating is 12 μm × 30 μm, with a very short taper transition of ～ 15 μm long.

Using nonequilibrium molecular dynamics simulations, a comprehensive study of the asymmetric heat conduction in the composite system consisting of the Frenkel-Kontorova (FK) model and Fermi-Pasta-Ulam (FPU) model is conducted. The calculated results show that in a larger system, the rectifying direction can be reversed only by adjusting the thermal bias. Moreover, the rectification reversal depends critically on the system size and the properties of the interface. The mechanisms of the two types of asymmetric heat conduction induced by nonlinearity are discussed. Considering the novel asymmetric heat conduction in the system, it may possess possible applications to manage the thermal rectification in situ directionally without re-building the structure.

As is well known, there exists a tradeoff between the breakdown voltage BV_{ CEO} and the cut-off frequency f_{T} for a standard heterojunction bipolar transistor (HBT). In this paper, this tradeoff is alleviated by collector doping engineering in the SiGe HBT by utilizing a novel composite of P^{+} and N^{-} doping layers inside the collector-base (CB) space-charge region (SCR). Compared with the single N-type collector, the introduction of the thin P^{+} layers provides a reverse electric field weakening the electric field near the CB metallurgical junction without changing the field direction, and the thin N^{-} layer further effectively lowers the electric field near the CB metallurgical junction. As a result, the electron temperature near the CB metallurgical junction is lowered, consequently suppressing the impact ionization, thus BV_{CEO} is improved with a slight degradation in f_{T}. The results show that the product of f_{T}× BV_{ CEO} is improved from 309.51 GHz·V to 326.35 GHz·V.

This paper focuses on the Noether symmetries and the conserved quantities for both holonomic and nonholonomic systems based on a new non-conservative dynamical model introduced by El-Nabulsi. First, the El-Nabulsi dynamical model which is based on a fractional integral extended by periodic laws is introduced, and El-Nabulsi-Hamilton's canonical equations for non-conservative Hamilton system with holonomic or nonholonomic constraints are established. Second, the definitions and criteria of El-Nabulsi-Noether symmetrical transformations and quasi-symmetrical transformations are presented in terms of the invariance of El-Nabulsi-Hamilton action under the infinitesimal transformations of the group. Finally, Noether's theorems for the non-conservative Hamilton system under the El-Nabulsi dynamical system are established, which reveal the relationship between the Noether symmetry and the conserved quantity of the system.

Based on cavity resonance and sandwich composite plate theory, this paper presents a universal three-dimensional (3D) theoretical model for frequency dispersion characterization and displacement profile shapes of the film bulk acoustic resonator (FBARs). This model provides results of FBAR excited thickness-extensional and flexure modes, and the result of frequency dispersion is proposed in which the thicknesses and impedance of the electrodes and the piezoelectric material are taken into consideration; its further simplification shows good agreement with the modified Butterworth-Van-Dyke (MBVD) model. The displacement profile reflects the vibration stress distribution of electrode shapes and the lateral resonance effect, which depends on the axis ratio of the electrode shapes a/b. The results are consistent with the 3D finite element method modeling and laser interferometry measurement in general.

This work reports the effects of magnetic field on an electrically conducting fluid with low electrical conductivity flowing in a smooth expanded channel. The governing nonlinear magnetohydrodynamic (MHD) equations in induction-free situations are derived in the framework of MHD approximations and solved numerically using the finite-difference technique. The critical values of Reynolds number (based on upstream mean velocity and channel height) for symmetry breaking bifurcation for a sudden expansion channel (1:4) is about 36, whereas the value in the case of the smooth expansion geometry used in this work is obtained as 298, approximately (non-magnetic case). The flow of an electrically conducting fluid in the presence of an externally applied constant magnetic field perpendicular to the plane of the flow is reduced significantly depending on the magnetic parameter (M). It is found that the critical value of Reynolds number for smooth expansion (1:4) is about 475 for the magnetic parameter M=2. The separating regions developed behind the smooth symmetric expansion are decreased in length for increasing values of the magnetic parameter. The bifurcation diagram is shown for a symmetric smoothly expanding channel. It is noted that the critical values of Reynolds number increase with increasing magnetic field strength.

Experimental studies which focus on flow visualization and the velocity field of a supersonic laminar/turbulent flow over a compression ramp were carried out in a Mach 3.0 wind tunnel. Fine flow structures and velocity field structures were obtained via NPLS (nanoparticle-tracer planar laser scattering) and PIV (particle image velocimetry) techniques, time-averaged flow structures were researched, and spatiotemporal evolutions of transient flow structures were analyzed. The flow visualization results indicated that when the ramp angles were 25°, a typical separation occurred in the laminar flow, some typical flow structures such as shock induced by the boundary layer, separation shock, reversed flow and reattachment shock were visible clearly. While a certain extent separation occurred in turbulent flow, the separation region was much smaller. When the ramp angles were 28°, laminar flow separated further, and the separation region expanded evidently, flow structures in the separation region were complex. While a typical separation occurred in turbulent flow, reversed flow structures were significant, flow structures in the separation region were relatively simple. The experimental results of velocity field were corresponding to flow visualization, and the velocity field structures of both compression ramp flows agreed with the flow structures well. There were three layered structures in the U component velocity, and the V component velocity appeared like an oblique “v”. Some differences between these two compression ramp flows can be observed in the velocity profiles of the shear layer and the shearing intensity.

SPECIAL TOPIC—Non-equilibrium phenomena in soft matters

We study the propulsion matrix of bacterial flagella numerically using slender body theory and the regularized Stokeslet method in a biologically relevant parameter regime. All three independent elements of the matrix are measured by computing propulsive force and torque generated by a rotating flagellum, and the drag force on a translating flagellum. Numerical results are compared with the predictions of resistive force theory, which is often used to interpret micro-organism propulsion. Neglecting hydrodynamic interactions between different parts of a flagellum in resistive force theory leads to both qualitative and quantitative discrepancies between the theoretical prediction of resistive force theory and the numerical results. We improve the original theory by empirically incorporating the effects of hydrodynamic interactions and propose new expressions for propulsive matrix elements that are accurate over the parameter regime explored.

By minimizing a thermodynamic-like potential, we unbiasedly sample the potential energy landscape of soft and frictionless spheres under a constant shear stress. We obtain zero-temperature jammed states under desired shear stresses and investigate their mechanical properties as a function of the shear stress. As a comparison, we also obtain the jammed states from the quasistatic-shear sampling in which the shear stress is not well-controlled. Although the yield stresses determined by both samplings show the same power-law scaling with the compression from the jamming transition point J at zero temperature and shear stress, for finite size systems the quasistatic-shear sampling leads to a lower yield stress and a higher critical volume fraction at point J. The shear modulus of the jammed solids decreases with increasing shear stress. However, the shear modulus does not decay to zero at yielding. This discontinuous change of the shear modulus implies the discontinuous nature of the unjamming transition under nonzero shear stress, which is further verified by the observation of a discontinuous jump in the pressure from the jammed solids to the shear flows. The pressure jump decreases upon decompression and approaches zero at the critical-like point J, in analogy with the well-known phase transitions under an external field. The analysis of the force networks in the jammed solids reveals that the force distribution is more sensitive to the increase of the shear stress near point J. The force network anisotropy increases with increasing shear stress. The weak particle contacts near the average force and under large shear stresses it exhibit an asymmetric angle distribution.

A dual-mode mechanical resonator using an atomic force microscope (AFM) as a force sensor is developed. The resonator consists of a long vertical glass fiber with one end glued onto a rectangular cantilever beam and the other end immersed through a liquid-air interface. By measuring the resonant spectrum of the modified AFM cantilever, one is able to accurately determine the longitudinal friction coefficient ζ_{v} along the fiber axis associated with the vertical oscillation of the hanging fiber and the traversal friction coefficient ζ_{h} perpendicular to the fiber axis associated with the horizontal swing of the fiber around its joint with the cantilever. The technique is tested by measurement of the friction coefficient of a fluctuating (and slipping) contact line between the glass fiber and the liquid interface. The experiment verifies the theory and demonstrates its applications. The dual-mode mechanical resonator provides a powerful tool for the study of the contact line dynamics and the rheological property of anisotropic fluids.

We systematically explore near equilibrium, flow-driven, and flow-activity coupled dynamics of polar active liquid crystals using a continuum model. Firstly, we re-derive the hydrodynamic model to ensure the thermodynamic laws are obeyed and elastic stresses and forces are consistently accounted. We then carry out a linear stability analysis about constant steady states to study near equilibrium dynamics around the steady states, revealing long-wave instability inherent in this model system and how active parameters in the model affect the instability. We then study model predictions for onedimensional (1D) spatial-temporal structures of active liquid crystals in a channel subject to physical boundary conditions. We discuss the model prediction in two selected regimes, one is the viscous stress dominated regime, also known as the flow-driven regime, while the other is the full regime, in which all active mechanisms are included. In the viscous stress dominated regime, the polarity vector is driven by the prescribed flow field. Dynamics depend sensitively on the physical boundary condition and the type of the driven flow field. Bulk-dominated temporal periodic states and spatially homogeneous states are possible under weak anchoring conditions while spatially inhomogeneous states exist under strong anchoring conditions. In the full model, flow-orientation interaction generates a host of planar as well as out-of-plane spatial-temporal structures related to the spontaneous flows due to the molecular self-propelled motion. These results provide contact with the recent literature on active nematic suspensions. In addition, symmetry breaking patterns emerge as the additional active viscous stress due to the polarity vector is included in the force balance. The inertia effect is found to limit the long-time survival of spatial structures to those with small wave numbers, i.e., an asymptotic coarsening to long wave structures. A rich set of mechanisms for generating and limiting the flow structures as well as the spatial-temporal structures predicted by the model are displayed.

PHYSICS OF GASES, PLASMAS, AND ELECTRIC DISCHARGES

By combining the microwave propagation theory and the gas breakdown theory, the microwave propagation with the gas breakdown is analyzed theoretically. Particle-in-cell/Monte Carlo collision (PIC/MCC) simulations are carried out to verify the theoretical results. Based on this theoretical method, the breakdown phenomenon of the pulse microwave is analyzed. The results show that the product values of the initial electron density and the propagation length are the criterion to distinguish the pulse peak decline breakdown and the pulse width reduction breakdown. Furthermore, the energy transmission is also studied, which shows that the total output energy is approximately independent of the input electric field if the electric field is not extremely large.

Castellation of plasma facing components is foreseen as the best solution for ensuring the lifetime of future fusion devices. However, the gaps between the resulting surface elements can increase fuel retention and complicate fuel removal issues. To know how the fuel is retained inside the gaps, the plasma sheath around the gaps needs to be understood first. In this work, a kinetic model is used to study plasma characteristics around the divertor gaps with the focus on the H^{+} penetration depth inside the poloidal gaps, and a rate-theory model is coupled to simulate the hydrogen retention inside the tungsten gaps. By varying the magnetic field strength and plasma temperature, we find that the H^{+} cyclotron radius has a significant effect on the penetration depth. Besides, the increase of magnetic field inclination angle can also increase the penetration depth. It is found in this work that parameters as well as the penetration depth strongly affect fuel retention in tungsten gaps.

The inflexion point of electron density and effective electron temperature curves versus radio-frequency (RF) bias voltage is observed in the H mode of inductively coupled plasmas (ICPs). The electron energy probability function (EEPF) evolves first from a Maxwellian to a Druyvesteyn-like distribution, and then to a Maxwellian distribution again as the RF bias voltage increases. This can be explained by the interaction of two distinct bias-induced mechanisms, that is: bias-induced electron heating and bias-induced ion acceleration loss and the decrease of the effective discharge volume due to the sheath expansion. Furthermore, the trend of electron density is verified by a fluid model combined with a sheath module.

CONDENSED MATTER: STRUCTURAL, MECHANICAL, AND THERMAL PROPERTIES

A detailed theoretical analysis of determining the sum of flexoelectric coefficients in nematic liquid crystals using the capacitance method is given. In the strong anchoring parallel aligned nematic (PAN) and hybrid aligned nematic (HAN) cells, the dependences of the capacitance on the sum of flexoelectric coefficients and the applied voltage are obtained by numerical simulations, and the distributions of the director and the electric potential for different applied voltages and flexoelectric coefficients are also given. Based on this theoretical analysis, we propose an experimental design for measuring the capacitance of a liquid crystal cell using the improved precision LCR meter E4980A (Agilent). Through comparing the experimental data with the simulated results, the sum of flexoeletric coefficients can be determined.

By using high-temperature deep-level transient spectroscopy (HT-DLTS) and other electrical measurement techniques, localized deep levels in n-type Al_{x}Ga_{1-x}N epitaxial films with various Al compositions (x= 0, 0.14, 0.24, 0.33, and 0.43) have been investigated. It is found that there are three distinct deep levels in Al_{x}Ga_{1-x}N films, whose level position with respect to the conduction band increases as Al composition increases. The dominant defect level with the activation energy deeper than 1.0 eV below the conduction band closely follows the Fermi level stabilization energy, indicating that its origin may be related to the defect complex, including the anti-site defects and divacancies in Al_{x}Ga_{1-x}N films.

Tensile-strained Ge/SiGe multiple quantum wells (MQWs) were grown on a Ge-on-Si virtual substrate using ultrahigh vacuum chemical vapor deposition on an n^{+}-Si (001) substrate. Direct-bandgap electroluminescence from the MQWs light emitting diode was observed at room temperature. The quantum confinement effect of the direct-bandgap transitions is in good agreement with the theoretical calculated results. The redshift mechanism of emission wavelength related to the thermal effect is discussed.

The degradations in NPN silicon-germanium (SiGe) heterojunction bipolar transistors (HBTs) were fully studied in this work, by means of 25-MeV Si, 10-MeV Cl, 20-MeV Br, and 10-MeV Br ion irradiation, respectively. Electrical parameters such as the base current (I_{B}), current gain (β), neutral base recombination (NBR), and Early voltage (V_{A}) were investigated and used to evaluate the tolerance to heavy ion irradiation. Experimental results demonstrate that device degradations are indeed radiation-source-dependent, and the larger the ion nuclear energy loss is, the more the displacement damages are, and thereby the more serious the performance degradation is. The maximum degradation was observed in the transistors irradiated by 10-MeV Br. For 20-MeV and 10-MeV Br ion irradiation, an unexpected degradation in I_{C} was observed and Early voltage decreased with increasing ion fluence, and NBR appeared to slow down at high ion fluence. The degradations in SiGe HBTs were mainly attributed to the displacement damages created by heavy ion irradiation in the transistors. The underlying physical mechanisms are analyzed and investigated in detail.

The present paper is concerned with the longitudinal shear elasticity of three-dimensional icosahedral quasicrystals. By virtue of the Dugdale hypothesis along with the method of complex potential theory, it involves two defect problems of the icosahedral quasicrystals. The first one is the calculation of stress intensity factors and the size of the cohesive force zone in a half-infinite crack. Meanwhile, the crack tip tearing displacements can be exactly derived. The other is the demonstration of the generalized stress intensity factors induced by a sharp V-notch as an extension of a crack. The generalized E-integral around the notch tip gives the energy release rate when the V-notch degenerates into a crack. Apart from their own usefulness in carrying out some simplified crack analyses, the results obtained in this work can particularly serve as a basis for fracture mechanics of anti-plane defect problems of icosahedral quasicrystals.

Few-layer graphene grown on Ni thin films has been studied by scanning tunneling microscopy. In most areas on the surfaces, moiré patterns resulted from rotational stacking faults were observed. At a bias lower than 200 mV, only one sublattice shows up in regions without moiré patterns while both sublattices are seen in regions with moiré pattens. This phenomenon can be used to identify AB stacked regions. The scattering characteristics at various types of step edges are different from those of monolayer graphene edges, either armchair or zigzag.

CONDENSED MATTER: ELECTRONIC STRUCTURE, ELECTRICAL, MAGNETIC, AND OPTICAL PROPERTIES

Ferromagnetism in the one-dimensional Hubbard model with the next-nearest-neighbor hopping is explored by using the exact-diagonalization method in a small cluster and the equation-of-motion method in the thermodynamic limit with electron density n=3/2. With these two complementary methods, it is found that an intermediate value of the next-nearest-neighbor hopping amplitude t_{1} tends to stabilize the fully polarized ferromagnetic state under the condition that the on-site coulomb interaction U is sufficiently large in our model. The ground-state phase diagram of the model is presented in the t_{1}-U plane.

We analyze the influences of interstitial atoms on the generalized stacking fault energy (GSFE), strength, and ductility of Ni by first-principles calculations. Surface energies and GSFE curves are calculated for the <112> (111) and <101> (111) systems. Because of the anisotropy of the single crystal, the addition of interstitials tends to promote the strength of Ni by slipping along the <101> direction while facilitating plastic deformation by slipping along the <112> direction. There is a different impact on the mechanical behavior of Ni when the interstitials are located in the slip plane. The evaluation of the Rice criterion reveals that the addition of the interstitials H and O increases the brittleness in Ni and promotes the probability of cleavage fracture, while the addition of S and N tends to increase the ductility. Besides, P, H, and S have a negligible effect on the deformation tendency in Ni, while the tendency of partial dislocation is more prominent with the addition of N and O. The addition of interstitial atoms tends to increase the high-energy barrier γ_{max}, thereby the second partial resulting from the dislocation tends to reside and move on to the next layer.

We investigate the effects of shape and single-atom doping on the structural, optical absorption, Raman, and vibrational properties of Ag_{13}, Ag_{12}Cu_{1}, Cu_{13}, and Cu_{12}Ag_{1} clusters by using the (time-dependent) density functional theory. The results show that the most stable structures are cuboctahedron (COh) for Ag_{13} and icosahedron (Ih) for Cu_{13}, Ag_{12}Cu_{ 1core}, and Cu_{12}Ag_{ 1sur}. In the visible-near infrared optical absorption, the transitions consist of the interband and the intraband transitions. Moreover, red shifts are observed as follows: 1) clusters change from Ag_{12}Cu_{ 1core} to Ag_{13} to Ag_{12}Cu_{ 1sur} with the same motifs, 2) the shapes of pure Ag_{13} and Ag_{12}Cu_{ 1core} clusters change from COh to Ih to decahedron (Dh), 3) the shape of Ag_{12}Cu_{ 1sur} clusters changes from Ih to COh to Dh, and 4) the shapes of pure Cu_{13} and Cu_{12}Ag_{1} clusters change from Ih to Dh to COh. All of the Raman and vibrational spectra exhibit many significant vibrational modes related to the shapes and the compositions of the clusters. The ranges of vibrational spectra of Ag_{13}, Ag_{12}Cu_{1} or Cu_{13}, and Cu_{12}Ag_{1} clusters become narrower and the vibrational intensities increase as the shape of the clusters changes from Ih to Dh to COh.

The inter-relation between zero-field splitting (ZFS) parameters and local lattice structures of the (CrSe_{4})^{6-} clusters in ZnSe semiconductors has been established by using the complete diagonalization (of the energy matrix) method. On the basis of this, the local lattice distortions, the ZFS parameters D, a, F and the optical spectrum for Cr^{2+} ions doped into ZnSe are theoretically investigated, and the contributions of the spin singlets have been taken into account. The calculated ZFS parameters are in good agreement with the experimental values. From our calculations, the tetragonal distortion parameters ΔR = 0.091Å and Δθ = 4.28°of Cr^{2+} in ZnSe are acquired, and the results suggest that there exists a tetragonal expansion distortion for the local lattice structure of (CrSe_{4})^{6-} clusters in ZnSe crystals. The influence of the spin singlets on ZFS parameters is also discussed, indicating that the contributions to ZFS parameters a and F cannot be ignored.

Graphene is a new promising candidate for application in radio-frequency (RF) electronics due to its excellent electronic properties such as ultrahigh carrier mobility, large threshold current density, and high saturation velocity. Recently, much progress has been made in the graphene-based RF field-effect transistors (RF-FETs). Here we present for the first time the high-performance top-gated RF transistors using millimeter-scale single graphene domain on a SiO_{2}/Si substrate through a conventional microfabrication process. A maximum cut-off frequency of 178 GHz and a peak maximum oscillation frequency of 35 GHz are achieved in the graphene-domain-based FET with a gate length of 50 nm and 150 nm, respectively. This work shows that the millimeter-scale single graphene domain has great potential applications in RF devices and circuits.

Bulk n-type Bi_{2}Te_{3} single crystals with optimized chemical composition were successfully prepared by a high temperature-gradient directional solidification method. We investigate the influence of alloy microstructure, chemical composition, and growth orientation on the thermoelectric transport properties. The results show that the composition of single-crystal Bi_{2}Te_{3} alloy, along the c axis direction, could be slightly tuned by changing the growth rate of the crystal. At a rate of 18 mm/h, the formed Bi_{2}Te_{3} crystal exhibits good thermoelectric properties. At 300 K, a maximum Seebeck coefficient of -245 uV/K and an electrical conductivity of 5.6×10^{4} S/m are acquired. The optimal power factor is obtained as 3.3× 10^{-3} W/K^{2}m, with a figure of merit of 0.74. It can be attributed to the increased tellurium allocation in the Bi_{2}Te_{3} alloys, as verified well by the density functional theory calculations.

We numerically investigate the transmission properties of a subwavelength composite hole-pillar array. As the radius of the pillar increases, the transmission properties experience a complex evolution. It is found that the magnetic dipole resonance of the pillar suppresses the surface plasmon polariton resonance (SPPR) at the gold-air interface. There are two strong transmission peaks associated with the magnetic dipole resonance of pillar and SPPR at the gold-silica interface. A peak associated with magnetic quadrupole resonance of the pillar is observed. Moreover, there is a weak peak associated with the coupling between the whispering-gallery plasmon (WGP) mode and magnetic dipole. Our work is helpful for making a dual band optical filter.

Polarization dependence of the coupling of excitation light to surface plasmon polaritons (SPPs) was investigated in a Ag nanoparticle-nanowire waveguide system (a Ag nanoparticle attached to a Ag nanowire). It was found that under the illumination of excitation light on the nanoparticle-nanowire junction, the coupling efficiency of light to SPPs depends on the polarization of the excitation light. Theoretical simulations revealed that it is the local near-field coupling between the nanoparticle and the nanowire that enhances the incident light to excite the nanowire SPPs. Because the shapes of the Ag nanoparticles differ, the local field intensity, and thus the excitement of the nanowire SPPs, vary with the polarization of the excitation light.

The influence of PMOSFET gate length on the parameter degradation relations under negative bias temperature instability (NBTI) stress is studied. The threshold voltage degradation increases with reducing the gate length. By calculating the relations between the threshold voltage and the linear/saturation drain current, we obtain their correlation coefficients. Comparing the test result with the calculated linear/saturation current value, we obtain the ratio factors. The ratio factors decrease differently when the gate length diminishes. When the gate length reduces to some degree, the linear ratio factor decreases from greater than 1 to nearly 1, but the saturation factor decreases from greater than 1 to smaller than 1. This results from the influence of mobility and the velocity saturation effect. Moreover, due to the un-uniform distribution of potential damages along the channel, the descending slopes of the curve are different.

Although hot carriers induced degradation of NMOSFETs has been studied for decades, the role of hot electron in this process is still debated. In this paper, the additional substrate hot electrons have been intentionally injected into the oxide layer to analyze the role of hot electron in hot carrier degradation. The enhanced degradation and the decreased time exponent appear with the injected hot electrons increasing, the degradation increases from 21.80% to 62.00% and the time exponent decreases from 0.59 to 0.27 with V_{b} decreasing from 0 V to -4 V, at the same time, the recovery also becomes remarkable and which strongly depends on the post stress gate bias V_{g}. Based on the experimental results, more unrecovered interface traps are created by the additional injected hot electron from the breaking Si-H bond, but the oxide trapped negative charges do not increase after a rapid recovery.

In this paper, the bipolar resistive switching characteristic is reported in Ti/ZrO_{2}/Pt resistive switching memory devices. The dominant mechanism of resistive switching is the formation and rupture of the conductive filament composed of oxygen vacancies. The conduction mechanisms for low and high resistance states are dominated by the ohmic conduction and the trap-controlled space charge limited current (SCLC) mechanism, respectively. The effect of a set compliance current on the switching parameters is also studied: the low resistance and reset current are linearly dependent on the set compliance current in the log-log scale coordinate; and the set and reset voltage increase slightly with the increase of the set compliance current. A series circuit model is proposed to explain the effect of the set compliance current on the resistive switching behaviors.

In this study, we investigate some main electrical parameters of the gold/poly(3-hexylthiophene):[6,6]-phenyl C61 butyric acid methyl ester:2,3,5,6-tetrafluoro-7,7,8,8-tetracyanoquinodimethane/n-type silicon (Au/P3HT:PCBM:F4-TCNQ/n-Si) metal-polymer-semiconductor (MPS) Schottky barrier diode (SBD) in terms of the effects of F4-TCNQ concentration (0%, 1%, and 2%). F4-TCNQ-doped P3HT:PCBM is fabricated to figure out the p-type doping effect on the device performance. The main electrical parameters, such as ideality factor (n), barrier height (Φ_{B0}), series resistance (R_{s}), shunt resistance (R_{sh}), and density of interface states (N_{ss}) are determined from the forward and reverse bias current-voltage (I-V) characteristics in the dark and at room temperature. The values of n, R_{s}, Φ_{B0}, and N_{ss} are significantly reduced by using the 1% F4-TCNQ doping in P3HT:PCBM:F4-TCNQ organic blend layer, additionally, the carrier mobility and current are increased by the soft (1%) doping. The most ideal values of electrical parameters are obtained for 1% F4-TCNQ used diode. On the other hand, the carrier mobility and current for the hard doping (2%) become far away from the ideal diode values due to the unbalanced generation of holes/electrons and doping-induced disproportion when compared with 1% F4-TCNQ doping. These results show that the electrical properties of MPS SBDs strongly depend on the F4-TCNQ doping and doping concentration of interfacial P3HT:PCBM:F4-TCNQ organic layer. Moreover, the soft F4-TCNQ doping concentration (1%) in P3HT:PCBM:F4-TCNQ organic layer significantly improves the electrical characteristics of the Au/P3HT:PCBM:F4-TCNQ/n-Si (MPS) SBDs which enables the fabricating of high-quality electronic and optoelectronic devices.

Double perovskite manganite Y_{2}MnCrO_{6} ceramic is synthesized and its multiferroic properties are investigated. Novel multiferroic properties are displayed with respect to other multiferroics, such as high ferroelectric phase transition temperature, and the coexistence of ferrimagnetism and ferroelectricity. Moreover, the ferroelectric polarization of Y_{2}MnCrO_{6} below the magnetic phase temperature can be effectively tuned by an external magnetic field, showing a remarkable magnetoelectric effect. These results open an effective avenue to explore magnetic multiferroics with spontaneous magnetization and ferroelectricity, as well as a high ferroelectric transition temperature.

We comparatively investigate the influence of various high-permeability alloys on the hysteretic and remanent resonant magnetoelectric (ME) response in a composite of magnetostrictive nickel (Ni) and piezoelectric Pb(Zr_{1-x}, Ti_{x})O_{3} (PZT). In order to implement this comparative research, Co-based amorphous alloy (CoSiB), Fe-based nanocrystalline alloy (FeCuNbSiB) and Fe-based amorphous alloy (FeSiB) are used according to different magnetostriction (λ_{s}) and saturation magnetization (μ_{0}M_{s}) characteristics. The bending and longitudinal resonant ME voltage coefficients (α_{ME,b} and α_{ME,l}) are observed comparatively for CoSiB/Ni/PZT, FeCuNbSiB/Ni/PZT, and FeSiB/Ni/PZT composites. The experimental data indicate that the FeSiB/Ni/PZT composite has the largest remanent self-biased α_{ME,b} and α_{ME,l} due to the largest magnetic grading of λ_{s} and μ_{0}M_{s} in the FeSiB/Ni layer. When the number of FeSiB foils is four, the maximum remanent α_{ME,b} and α_{ME,l} at zero bias magnetic field are 57.8 V/cm·Oe and 107.6 V/cm·Oe, respectively. It is recommended that the high-permeability alloy is supposed to have larger λ_{s} and μ_{0}M_{s} for obtaining a larger remanent self-biased ME responses in ME composite with high-permeability alloy.

It is found that the core-shell structured grains are easy to produce for fine grain doped BaTiO_{3} ceramics in the sintering process. We study the influence of the core-shell structure on the Curie-Weiss temperature and dielectric properties of BaTiO_{3} ceramics by using effective medium approximation (EMA). Considering the second approximation, the dielectric properties of fine grain doped BaTiO_{3} ceramics are consistent with experimental data.

A theoretical model of flatband voltage (V_{FB}) of metal/high-k/SiO_{2}/Si stack is proposed based on band alignment of entire gate stack, i.e., the V_{FB} is obtained by simultaneously considering band alignments of metal/high-k, high-k/SiO_{2} and SiO_{2}/Si interfaces, and their interactions. Then the V_{FB} of TiN/HfO_{2}/SiO_{2}/Si stack is experimentally obtained and theoretically investigated by this model. The theoretical calculations are in good agreement with the experimental results. Furthermore, both positive V_{FB} shift of TiN/HfO_{2}/SiO_{2}/Si stack and Fermi level pinning are successfully interpreted and attributed to the dielectric contact induced gap states at TiN/HfO_{2} and HfO_{2}/SiO_{2} interfaces.

Bi_{0.9}Ba_{0.1}FeO_{3} (BBFO)/La_{2/3}Sr_{1/3}MnO_{3} (LSMO) heterostructures are fabricated on LaAlO_{3} (100) substrates by pulsed laser deposition. Giant remnant polarization value (～ 85 μC/cm^{2}) and large saturated magnetization value (～ 12.4 emu/cm^{3}) for BBFO/LSMO heterostructures are demonstrated at room temperature. Mixed ferroelectric domain structures and low leakage current are observed and in favor of enhanced ferroelectric properties in the BBFO/LSMO heterostructures. The magnetic field-dependent magnetization measurements reveal the enhancement in the magnetic moment and improved magnetic hysteresis loop originating from the BBFO/LSMO interface. The heterostructure is proved to be effective in enhancing the ferroelectric and ferromagnetic performances in multiferroic BFO films at room temperature.

We have derived a general formula for sensitivity optimization of gravimetric sensors and have used it to design a high sensitivity gravimetric sensor using unidirectional carbon fiber epoxy composite (CFEC) waveguide layer on (1-x)Pb(Zn_{1/3}Nb_{2/3})O_{3}-xPbTiO_{3} (PZN-xPT) single crystal substrate with the carbon fibers parallel to the x_{1} and x_{2} axes, respectively. The normalized maximum sensitivity (|S_{m}^{f}|λ)_{max} exhibits an increasing tendency with the decrease of (h/λ ight)_{opt} and the maximum sensitivity (|S_{m}^{f}|λ)_{max} increases with the elastic constant c_{66}^{E} of the piezoelectric substrate material. For the CFEC/[011]_{c} poled PZN-7%PT single crystal sensor configuration, with the carbon fibers parallel to the x_{1} axis at λ = 24 μm, the maximum sensitivity |S_{m}^{f}|_{max} can reach as high as 1156 cm^{2}/g, which is about three times that of a traditional SiO_{2}/ST quartz structure gravimetric sensor. The better design selection is to have the carbon fibers parallel to the direction of propagation of Love wave in order to obtain the best sensitivity.

Multi-walled carbon nanotube (MWCNT)-Fe composites were prepared via the metal organic chemical vapor deposition by depositing iron pentacarbonyl on the surface of MWCNTs. The structural and morphological analyses demonstrated that Fe nanoparticles were deposited on the surface of the MWCNTs. The electromagnetic properties of the MWCNTs were significantly changed, and the absorbing capacity evidently improved after the Fe deposition on the MWCNT surface. A minimum reflection loss of -29.4 dB was observed at 8.39 GHz, and the less than -10 dB bandwidth was about 10.6 GHz, which covered the whole X band (8.2-12.4 GHz) and the whole Ku band (12.4-18 GHz), indicating that the MWCNT-Fe composites could be used as an effective microwave absorption material.

The symmetric deposition technique is often used to improve the uniformity of sculptured thin film (STF). In this paper, optical properties of STF with the columnar angles ± β are analyzed theoretically, based on the characteristic matrix method for extraordinary waves. Then, the transmittances of uniformity monolayer and bilayer STF in symmetrical style are calculated to show the effect of the bilayer structure on the optical properties of STF. The inhomogeneity of STF is involved in analyzing the differences in transmittance and phase retardation between monolayer and bilayer STF deposited in symmetric style. The results show that optical homogeneity of STF can be improved by depositing in symmetric style at the normal incidence, but it is not the same case as the oblique incidence.

Low temperature photoluminescence (PL) measurements have been performed for a set of GaN/Al_{x}Ga_{1-x}N quantum wells (QWs). The experimental results show that the optical full width at half maximum (FWHM) increases relatively rapidly with increasing Al composition in the Al_{x}Ga_{1-x}N barrier, and increases only slightly with increasing GaN well width. A model considering the interface roughness is used to interpret the experimental results. In the model, the FWHM's broadening caused by the interface roughness is calculated based on the triangle potential well approximation. We find that the calculated results accord with the experimental results well.

A series of Zn-Cu-In-S nanocrystals (ZCIS NCs) are prepared and the optical properties of the ZCIS NCs are tuned by adjusting the reaction time. It is interesting to observe that the temperature-dependent photoluminescence (PL) spectra of the ZCIS NCs show a redshift with decreasing intensity at low temperature (50-280 K) and a blueshift at high temperature (318-403 K). The blueshift can be explained by the thermally active phonon-assisted tunneling from the excited states of the low-energy emission band to the excited states of the high-energy emission band.

SPECIAL TOPIC --- Non-equilibrium phenomena in soft matters

INTERDISCIPLINARY PHYSICS AND RELATED AREAS OF SCIENCE AND TECHNOLOGY

A chiral metasurface is proposed to realize a tri-band polarization angle insensitive cross-polarization converter. The unit cell of the chiral metamaterial is composed by four twisted anisotropic structure pairs in four-fold rotation symmetry. The simulation results show that this device can work at 9.824 GHz, 11.39 GHz, and 13.37 GHz with low loss and a high polarization conversion ratio (PCR) of more than 99%. The proposed design can transmit the co-polarization wave at 14.215 GHz, like a frequency selective surface. The study of the current and electric fields distributions indicates that the cross-polarization transmission is due to electric dipole coupling.

In this paper, we have reported an investigation on the evolution of nitrogen structures in diamond crystals which contain nitrogen donor atoms in the range of 1500 ppm-1600 ppm following an annealing treatment at a high pressure of about 6.5 GPa and high temperatures of 1920 K-2120 K. The annealing treatment was found to completely transform nitrogen atoms originally arranged in a single substitutional form (C-center), into a pair form (A-center), indicated from infrared (IR) spectra. The photoluminescence (PL) spectra revealed that a small fraction of nitrogen atoms remained in C-center form, while some nitrogen atoms in A-center form were further transformed into N3 and H3 center structures. In addition, PL spectra have revealed the existence of two newly observed nitrogen-related structures with zero phonon lines at 611 nm and 711 nm. All these findings above are very helpful in understanding the formation mechanism of natural diamond stones of the Ia-type, which contains nitrogen atoms in an aggregated form.

The transport of water and ions through carbon nanotubes (CNTs) is crucial in nanotechnology and biotechnology. Previous investigation indicated that the ions can hardly pass through (6,6) CNTs due to their hydrated shells. In the present study, utilizing molecular dynamics simulation, it is shown that the energy barrier mainly originating from the hydrated water molecules could be overcome by applying an electric field large enough in the CNT axis direction. Potential of mean force is calculated to show the reduction of energy barrier when the electric field is present for (Na^{+}, K^{+}, Cl^{-}) ions. Consequently, ionic flux through (6,6) CNTs can be found once the electric field becomes larger than a threshold value. The variation of the coordination numbers of ions at different locations from the bulk to the center of the CNT is also explored to elaborate this dynamic process. The thresholds of the electric field are different for Na^{+}, K^{+}, and Cl^{-} due to their characteristics. This consequence might be potentially applied in ion selectivity in the future.

Modeling a memristor is an effective way to explore the memristor properties due to the fact that the memristor devices are still not commercially available for common researchers. In this paper, a physical memristive device is assumed to exist whose ionic drift direction is perpendicular to the direction of the applied voltage, upon which, corresponding to the HP charge-controlled memristor model, a novel threshold flux-controlled memristor model with a window function is proposed. The fingerprints of the proposed model are analyzed. Especially, a practical equivalent circuit of the proposed model is realized, from which the corresponding experimental fingerprints are captured. The equivalent circuit of the threshold memristor model is appropriate for various memristors based breadboard experiments.

The memristor has broad application prospects in many fields, while in many cases, those fields require accurate impedance control. The nonlinear model is of great importance for realizing memristance control accurately, but the implementing complexity caused by iteration has limited the actual application of this model. Considering the approximate linear characteristics at the middle region of the memristance-charge (M-q) curve of the nonlinear model, this paper proposes a memristance controlling approach, which is achieved by linearizing the middle region of the M-q curve of the nonlinear memristor, and establishes the linear relationship between memristances M and input excitations so that it can realize impedance control precisely by only adjusting input signals briefly. First, it analyzes the feasibility for linearizing the middle part of the M-q curve of the memristor with a nonlinear model from the qualitative perspective. Then, the linearization equations of the middle region of the M-q curve is constructed by using the shift method, and under a sinusoidal excitation case, the analytical relation between the memristance M and the charge time t is derived through the Taylor series expansions. At last, the performance of the proposed approach is demonstrated, including the linearizing capability for the middle part of the M-q curve of the nonlinear model memristor, the controlling ability for memristance M, and the influence of input excitation on linearization errors.

We investigate niobium thin film superconducting quantum interference devices (SQUIDs) with different Steward-McCumber parameters β_{c} operated in both current- and voltage-bias modes. We experimentally prove that there is no difference between the two bias modes with respect to the SQUID intrinsic noise and the noise contribution from the preamplifier. Furthermore, the relationships of the SQUID dynamic parameters, (R_{d})_{current bias} ≈ (R_{d})_{voltage bias} and (∂V/∂Φ)_{current bias} ≈ [(∂i/∂Φ)R_{d}]_{voltage bias}, are always satisfied. For a strongly damped SQUID with β_{c} ≈ 0.25, additional positive feedback (APF) and noise cancellation (NC) were employed to enhance ∂V/∂Φ, the former showing a degradation in the linear flux range but otherwise the same with NC. For a weakly damped SQUID with β_{c} ≈ 3, it is directly connected to the preamplifier without APF or NC, and a low SQUID system noise of about 4 μΦ_{0}/√Hz is measured, which is close to its intrinsic noise.

We report the optical response characteristics of Al/Ti bilayer transition edge sensors (TESs), which are mainly comprised of Al/Ti bilayer thermometers and suspended SiN membranes for thermal isolation. The measurement was performed in a ^{3}He sorption refrigerator and the device's response to optical pulses was investigated using a pulsed laser source. Based on these measurements, we obtained the effective recovery time (τ_{ eff}) of the devices at different biases and discussed the dependence of τ_{eff} on the bias. The device with a 940 μm × 940 μm continuous suspended SiN membrane demonstrated a fast response speed with τ_{ eff} = 3.9 μs, which indicates a high temperature sensitivity (α = T/R ·d R/dT = 326). The results also showed that the TES exhibits good linearity under optical pulses of variable widths.

Synergistic effects of the total ionizing dose (TID) on the single event upset (SEU) sensitivity in static random access memories (SRAMs) were studied by using protons. The total dose was cumulated with high flux protons during the TID exposure, and the SEU cross section was tested with low flux protons at several cumulated dose steps. Because of the radiation-induced off-state leakage current increase of the CMOS transistors, the noise margin became asymmetric and the memory imprint effect was observed.

Nitrogen plasma passivation (NPP) on (111) germanium (Ge) was studied in terms of the interface trap density, roughness, and interfacial layer thickness using plasma-enhanced chemical vapor deposition (PECVD). The results show that NPP not only reduces the interface states, but also improves the surface roughness of Ge, which is beneficial for suppressing the channel scattering at both low and high field regions of Ge MOSFETs. However, the interfacial layer thickness is also increased by the NPP treatment, which will impact the equivalent oxide thickness (EOT) scaling and thus degrade the device performance gain from the improvement of the surface morphology and the interface passivation. To obtain better device performance of Ge MOSFETs, suppressing the interfacial layer regrowth as well as a trade-off with reducing the interface states and roughness should be considered carefully when using the NPP process.

An analytical model for the channel potential and the threshold voltage of the short channel dual-material-gate lightly doped drain (DMG-LDD) metal-oxide-semiconductor field-effect transistor (MOSFET) is presented using the parabolic approximation method. The proposed model takes into account the effects of the LDD region length, the LDD region doping, the lengths of the gate materials and their respective work functions, along with all the major geometrical parameters of the MOSFET. The impact of the LDD region length, the LDD region doping, and the channel length on the channel potential is studied in detail. Furthermore, the threshold voltage of the device is calculated using the minimum middle channel potential, and the result obtained is compared with the DMG MOSFET threshold voltage to show the improvement in the threshold voltage roll-off. It is shown that the DMG-LDD MOSFET structure alleviates the problem of short channel effects (SCEs) and the drain induced barrier lowering (DIBL) more efficiently. The proposed model is verified by comparing the theoretical results with the simulated data obtained by using the commercially available ATLAS^{TM} 2D device simulator.

An extensive and complete experimental investigation with a full layout design of the channel direction was carried out for the first time to clarify the orientation dependence of germanium p-channel metal-oxide-semiconductor field-effect transistors (PMOSFETs). By comparison of gate trans-conductance, drive current, and hole mobility, we found that the performance trend with the substrate orientation for Ge PMOSFET is (110) > (111) ～ (100), and the best channel direction is (110)/[110]. Moreover, the (110) device performance was found to be easily degraded as the channel direction got off from the [110] orientation, while (100) and (111) devices exhibited less channel orientation dependence. This experimental result shows good matching with the simulation reports to give a credible and significant guidance for Ge PMOSFET design.

In this paper, a new equivalent circuit model of GaN-based light emitting diodes (LEDs) is established. The impact of the series resistance to luminous efficacy is simulated using the MATLAB software. GaN-based LEDs with different n-contact electrode materials (LEDs with Ni/Au and LEDs with Cr/Au) are fabricated. By comparing and analyzing the results of performances, we concluded that both the series resistance and the carrier loss could affect the luminous efficacy severely. LEDs with lower series resistance have higher luminous efficacy and its efficiency droop is alleviated simultaneously. To improve luminous efficacy, the fabrication process should be optimized for lower series resistance.

A controllable etching process for indium zinc oxide (IZO) films was developed by using a weak etchant of oxalic acid with a slow etching ratio. With controllable etching time and temperature, a patterned IZO electrode with smoothed surface morphology and slope edge was achieved. For the practical application in organic light emitting devices (OLEDs), a suppression of the leak current in the current-voltage characteristics of OLEDs was observed. It resulted in a 1.6 times longer half lifetime in the IZO-based OLEDs compared to that using an indium tin oxide (ITO) anode etched by a conventional strong etchant of aqua regia.

A series of experiments are conducted to confirm whether the vectors calculated for an early section of a continuous non-invasive fetal electrocardiogram (fECG) recording can be directly applied to subsequent sections in order to reduce the computation required for real-time monitoring. Our results suggest that it is generally feasible to apply the initial optimal maternal and fetal ECG combination vectors to extract the fECG and maternal ECG in subsequent recorded sections.

In this paper, a micro capacitive sensor with nanometer resolution is presented for ultra-precision measurement of micro components, which is fabricated by the MEMS (micro electromechanical systems) non-silicon technique. Based on the sensor, a micro capacitive tactile probe is constructed by stylus assembly and packaging design for dimension metrology on micro/nano scale, in which a data acquiring system is developed with AD7747. Some measurements of the micro capacitive tactile probe are performed on a nano positioning and measuring machine (NMM). The measurement results show good linearity and hysteresis with a range of 11.6 μm and resolution of better than 5 nm. Hence, the micro capacitive tactile probe can be integrated on NMM to realize measurement of micro structures with nanometer accuracy.

A concurrent multiscale method of coupling atomistic and continuum models is presented in the two-dimensional system. The atomistic region is governed by molecular dynamics while the continuum region is represented by constructing the mass and stiffness matrix dependent on the coarsening of the grids, which ensures that they merge seamlessly. The low-pass phonon filter embedded in the handshaking region is utilized to effectively eliminate the spurious reflection of high-frequency phonons, while keeping the low-frequency phonons transparent. These schemes are demonstrated by numerically calculating the reflection and transmission coefficient, and by the further application of dynamic crack propagation subjected to mode-I tensile loading.

Emitted multi-crystalline silicon and black silicon solar cells are conformal doped by ion implantation using the plasma immersion ion implantation (PⅢ) technique. The non-uniformity of emitter doping is lower than 5%. The secondary ion mass spectrometer profile indicates that the PⅢ technique obtained 100-nm shallow emitter and the emitter depth could be impelled by furnace annealing to 220 nm and 330 nm at 850 ℃ with one and two hours, respectively. Furnace annealing at 850 ℃ could effectively electrically activate the dopants in the silicon. The efficiency of the black silicon solar cell is 14.84% higher than that of the mc-silicon solar cell due to more incident light being absorbed.

The improvement of the acetone-soaking treatment to the performance of polymer solar cells based on the P3HT/PCBM bulk heterojunction is reported. Undergoing acetone-soaking, the PCBM does not distribute uniformly in the vertical direction, a PCBM enrichment layer forms on the top of the active layer, which is beneficial to the collection of the carriers and blocking the inverting diffusion carriers. X-ray photoelectron spectroscopy (XPS) analysis reveals that the PCBM weight ratio on the top of the active layer increases by 20% after the acetone-soaking treatment. Due to the nonuniform distribution of PCBM, the short-circuit current density, the open-circuit voltage, and the fill factor are enhanced significantly. Finally, the power conversion efficiency of the acetone-soaking device increases by 31% compared with the control device.

Natural disasters cause significant damage to roads, making route selection a complicated logistical problem. To overcome this complexity, we present a method of using a trapezoidal fuzzy number to select the optimal transport path. Using the given trapezoidal fuzzy edge coefficients, we calculate a fuzzy integrated matrix, and incorporate the fuzzy multi-weights into fuzzy integrated weights. The optimal path is determined by taking two sets of vertices and transforming undiscovered vertices into discoverable ones. Our experimental results show that the model is highly accurate, and requires only a few measurement data to confirm the optimal path. The model provides an effective, feasible, and convenient method to obtain weights for different road sections, and can be applied to road planning in intelligent transportation systems.

As the controllability of complex networks has attracted much attention recently, how to design and optimize the robustness of network controllability has become a common and urgent problem in the engineering field. In this work, we propose a method that modifies any given network with strict structural perturbation to effectively enhance its robustness against malicious attacks, called dynamic optimization of controllability. Unlike other structural perturbations, the strict perturbation only swaps the links and keeps the in- and out-degree unchanged. A series of extensive experiments show that the robustness of controllability and connectivity can be improved dramatically. Furthermore, the effectiveness of our method is explained from the views of underlying structure. The analysis results indicate that the optimization algorithm makes networks more homogenous and assortative.

Motivated by the relationship of the dynamic behaviors and network structure, in this paper, we present two efficient dynamic community detection algorithms. The phases of the nodes in the network can evolve according to our proposed differential equations. In each iteration, the phases of the nodes are controlled by several parameters. It is found that the phases of the nodes are ultimately clustered into several communities after a short period of evolution. They can be adopted to detect the communities successfully. The second differential equation can dynamically adjust several parameters, so it can obtain satisfactory detection results. Simulations on some test networks have verified the efficiency of the presented algorithms.

Recent research results indicate that individual awareness can play an important influence on epidemic spreading in networks. By local stability analysis, a significant conclusion is that the embedded awareness in an epidemic network can increase its epidemic threshold. In this paper, by using limit theory and dynamical system theory, we further give global stability analysis of a susceptible-infected-susceptible (SIS) epidemic model on networks with awareness. Results show that the obtained epidemic threshold is also a global stability condition for its endemic equilibrium, which implies the embedded awareness can enhance the epidemic threshold globally. Some numerical examples are presented to verify the theoretical results.

For the potential vorticity (PV) invariant, there is a PV-based complete-form vorticity equation, which we use heuristically in the present paper to answer the following question: for the Ertel-Rossby invariant (ERI), is there a corresponding vorticity tendency equation? Such an ERI-based thermally-coupled vorticity equation is derived and discussed in detail in this study. From the obtained new vorticity equation, the vertical vorticity change is constrained by the vertical velocity term, the term associated with the slope of the generalized momentum surface, the term related to the horizontal vorticity change, and the baroclinic or solenoid term. It explicitly includes both the dynamical and thermodynamic factors' influence on the vorticity change. For the ERI itself, besides the traditional PV term, the ERI also includes the moisture factor, which is excluded in dry ERI, and the term related to the gradients of pressure, kinetic energy, and potential energy that reflects the fast-manifold property. Therefore, it is more complete to describe the fast motions off the slow manifold for severe weather than the PV term. These advantages are naturally handed on and inherited by the ERI-based thermally-coupled vorticity equation. Then the ERI-based thermally-coupled vorticity equation is further transformed and compared with the traditional vorticity equation. The main difference between the two equations is the term which describes the contribution of the solenoid term to the vertical vorticity development. In a barotropic flow, the solenoid term disappears, then the ERI-based thermally-coupled vorticity equation can regress to the traditional vorticity equation.

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