We show that a class of spectral problems are related to the spectral problem of the Volterra lattice through a gauge transformation. The transformation is given. We hope that our discussion can draw attention to the study of gauge transformation theory of differential-difference integrable systems.

Measurement-device-independent quantum key distribution (MDI-QKD) can be immune to all detector side-channel attacks and guarantee the information-theoretical security even with uncharacterized single photon detectors. MDI-QKD has been demonstrated in both laboratories and field-tests by using attenuated lasers combined with the decoy-state technique. However, it is a critical assumption that the sources used by legitimate participants are trusted in MDI-QKD. Hence, it is possible that a potential security risk exists. Here we propose a new scheme of polarization-encoding-based MDI-QKD with a single untrusted source, by which the complexity of the synchronization system can be reduced and the success rate of the Bell-state measurement can be improved. Meanwhile, the decoy-state method is employed to avoid the security issues introduced by a non-ideal single photon source. We also derive a security analysis of the proposed system. In addition, it seems to be a promising candidate for the implementation for QKD network in the near future.

Influences of topological defect and dislocation on conductivity behavior of charge carriers in external electromagnetic fields are studied. Particularly the quantum Hall effect is investigated in detail. It is found that the nontrivial deformations of spacetime due to topological defect and dislocation produce an electric current at the leading order of perturbation theory. This current then induces a deformation on the Hall conductivity. The corrections on the Hall conductivity depend on the external electric fields, the size of the sample and the momentum of the particle.

The high frequency gravitational waves (around $10^{8}$–$10^{12}$ Hz) could interact with a specially designed electromagnetic resonance system. It is found that the power of transverse perturbative photon flux (PPF) of an electromagnetic resonance system can be improved significantly by virtue of an astigmatic Gaussian beam. Correspondingly the signal-to-noise ratio (SNR) would also be improved. When the eccentric ratio of waist satisfying $w_{0x}:w_{0y}>1$, the peak value of signal photon flux could be raised by 2–4 times with typical systematic parameters, while the background photon flux would be depressed. Therefore, the ratio of transverse PPF to background photon flux (i.e., SNR) can be further improved 3–8 times with dimensionless amplitude of relic gravitational wave $h_{\rm t}=10^{-36}$.

The viscous polytropic gas model as one model of dark energy is hot-spot and keystone to the modern cosmology. We study the evolution of the viscous polytropic dark energy model interacting with the dark matter in the Einstein cosmology. Setting the autonomous dynamical system for the interacting viscous polytropic dark energy with dark matter and using the phase space analysis method to investigate the dynamical evolution and its critical stability, we find that the viscosity property of the dark energy creates a benefit for the stable critical dynamical evolution of the interaction model between dark matter and dark energy in the flat Friedmann–Robertson–Walker universe and the viscosity of dark energy will soften the coincidence problem just like the interacting dark energy model.

We present a hybrid singular spectrum analysis (SSA) and fuzzy entropy method to filter noisy nonlinear time series. With this approach, SSA decomposes the noisy time series into its constituent components including both the deterministic behavior and noise, while fuzzy entropy automatically differentiates the optimal dominant components from the noise based on the complexity of each component. We demonstrate the effectiveness of the hybrid approach in reconstructing the Lorenz and Mackey–Glass attractors, as well as improving the multi-step prediction quality of these two series in noisy environments.

We investigate the moving matter-wave solitons in spin–orbit coupled Bose–Einstein condensates (BECs) by a perturbation method. Starting with the one-dimensional Gross–Pitaevskii equations, we derive a new KdV-like equation to which an approximate solution is obtained by assuming weak Raman coupling and strong spin–orbit coupling. The derivation of the KdV-like equation may be useful to understand the properties of solitons excitation in spin–orbit coupled BECs. We find different types of moving solitons: dark–bright, bright–bright and dark–dark solitons. Interestingly, moving dark–dark soliton for attractive intra- and inter-species interactions is found, which depends on the Raman coupling. The amplitude and velocity of the moving solitons strongly depend on the Raman coupling and spin–orbit coupling.

Complex networks are important paradigms for analyzing the complex systems as they allow understanding the structural properties of systems composed of different interacting entities. In this work we propose a reliable method for constructing complex networks from chaotic time series. We first estimate the covariance matrices, then a geodesic-based distance between the covariance matrices is introduced. Consequently the network can be constructed on a Riemannian manifold where the nodes and edges correspond to the covariance matrix and geodesic-based distance, respectively. The proposed method provides us with an intrinsic geometry viewpoint to understand the time series.

The 1st-order symmetry energy coefficient of nuclear matter induced merely by the neutron–proton (n–p) mass difference is derived analytically, which turns out to be completely model-independent. Based on this result, the 1st-order symmetry energy $E_{\rm sym,1}^{({\rm npDM})}(A)$ of heavy nuclei such as $^{208}$Pb induced by the n–p mass difference is investigated with the help of a local density approximation combined with the Skyrme energy density functionals. Although $E_{\rm sym,1}^{({\rm npDM})}(A)$ is small compared with the second-order symmetry energy, it cannot be dropped simply for an accurate estimation of nuclear masses as it is still larger than the rms deviation given by some accurate mass formulas. It is therefore suggested that one perhaps needs to distinguish the neutron mass from the proton one in the construction of nuclear density functionals.

The properties of the low-lying states and the shape coexistence in $^{98}$Sr are investigated within the framework of the proton–neutron interacting boson model (IBM2). By considering the relative energy of the $d$ proton boson to be different from that of the neutron boson, it is found that the calculated energy levels and the $B(E2)$ transition strengths agree with the experimental data perfectly. Particularly, the second 0$^+$ state, which is associated with the shape coexistence phenomenon and has the lowest energy $E(0^+_2)$ among all known even–even nuclei, is reproduced very well. The behavior of the calculated quadrupole shape invariants is consistent with the experimental results.

Starting with a bare nucleon-nucleon interaction, for the first time the full relativistic Brueckner–Hartree–Fock equations are solved for finite nuclei in a Dirac–Woods–Saxon basis. No free parameters are introduced to calculate the ground-state properties of finite nuclei. The nucleus $^{16}$O is investigated as an example. The resulting ground-state properties, such as binding energy and charge radius, are considerably improved as compared with the non-relativistic Brueckner–Hartree–Fock results and much closer to the experimental data. This opens the door for ab initio covariant investigations of heavy nuclei.

We report on the magic wavelength measurement of our optical lattice clock based on fermion strontium atoms at the National Institute of Metrology (NIM). A Ti:sapphire solid state laser locked to a reference cavity inside a temperature-stabilized vacuum chamber is employed to generate the optical lattice. The laser frequency is measured by an erbium fiber frequency comb. The trap depth is modulated by varying the lattice laser power via an acousto-optic modulator. We obtain the frequency shift coefficient at this lattice wavelength by measuring the differential frequency shift of the clock transition of the strontium atoms at different trap depths, and the frequency shift coefficient at this lattice wavelength is obtained. We measure the frequency shift coefficients at different lattice frequencies around the magic wavelength and linearly fit the measurement data, and the magic wavelength is calculated to be 368554672(44) MHz.

The $^{27}$Al$^+$ ion optical clock is one of the most attractive optical clocks due to its own advantages such as low black-body radiation shift at room temperature and insensitivity to the magnetic drift. However, it cannot be laser-cooled directly in the absence of 167 nm laser to date. This problem can be solved by sympathetic cooling. In this work, a linear Paul trap is used to trap both $^{40}$Ca$^{+}$ and $^{27}$Al$^+$ ions simultaneously, and a single Doppler-cooled $^{40}$Ca$^+$ ion is employed to sympathetically cool a single $^{27}$Al$^+$ ion. Thus a 'bright-dark' two-ion crystal has been successfully synthesized. The temperature of the crystal has been estimated to be about 7 mK by measuring the ratio of carrier and sideband spectral intensities. Finally, the dark ion is proved to be an $^{27}$Al$^+$ ion by precise measuring of the ion crystal's secular motion frequency, which means that it is a great step for our $^{27}$Al$^+$ quantum logic clock.

Two-photon absorption (TPA) and nonlinear refraction in AlN single crystals are revealed with the single beam $Z$-scan technique. A large TPA coefficient of 13$\pm$3 cm/GW at 355 nm and third-order nonlinear refractive indices of $-$1.91$\pm$0.38 $\times$ 10$^{-13}$ cm$^{2}$/W at 355 nm, 1.79$\pm$0.36 $\times$ 10$^{-13}$ cm$^{2}$/W at 532 nm and 1.61$\pm$0.32 $\times$ 10$^{-12}$ cm$^{2}$/W at 1064 nm are derived. It is inferred that the TPA-generated free carriers are responsible for the large negative nonlinear refractive index at 355 nm, while the oxygen impurity induced bandgap narrowing may account for the large third-order nonlinear refractive indices at 532 nm and 1064 nm. The large nonlinear optical responses of AlN promise wide applications in the deep ultraviolet nonlinear optical devices.

A widely tunable microwave photonic (MWP) notch filter with high linearity based on a dual-parallel Mach–Zehnder modulator (DPMZM) is proposed and experimentally demonstrated. The motivation of this work lies in the fact that the MWP notch filter previously reported has nonlinear distortions generally induced by the nonlinear property of electro-optic devices. In this scheme, even-order modulated sidebands at the DPMZM output are effectively suppressed by properly adjusting bias voltages of the DPMZM, which are the dominant factor to induce the nonlinear distortions into the MWP notch filter. The proposed scheme is theoretically analyzed and experimentally verified.

We investigate spin squeezing effects of trapped ions in an off-resonance optical potential system using the arbitrary range spin–spin interaction and transverse field model. The collective spin noises at any time are analyzed exactly. The general expression of spin squeezing factor is presented for arbitrary-range spin interaction. For the nearest-neighbor and next-nearest neighbor spin interaction model, the analytic solutions are reduced from the general expressions. It is shown that the maximum spin squeezing is enhanced for the general arbitrary-range spin interaction compared with the nearest-neighbor interaction model as the long-range interaction with arbitrary sites enforces stronger correlation.

Ultrashort pulses complicate the frequency conversion in a nonlinear crystal, where group velocity mismatch becomes the main obstacle due to dispersion. We present a design for group velocity compensated second harmonic generation in a modulated nonlinear structure, embedded in a liquid crystal box. In this structure, nonlinear crystals act as sources of signal and liquid crystals compensate for group velocity mismatch originating from nonlinear crystals. There are the advantages of the flexible, controllable birefringence of liquid crystals. Meanwhile, a method calculating the parameters of this type of structure is presented. To make it clear, an example is provided. Furthermore, the structure can also be shaped as a waveguide to support integration into other optical devices, applicable to all-optical processing systems.

The influences of phase and group velocity matching on cumulative second harmonic generation of Lamb waves are investigated in numerical perspective. Finite element simulations of nonlinear Lamb wave propagation are performed for Lamb wave mode pairs with exact and approximate phase velocity matching, with and without group velocity matching, respectively. The evolution of time-domain second harmonic Lamb waves is analyzed with the propagation distance. The amplitudes of primary and second harmonic waves are calculated to characterize the acoustic nonlinearity. The results verify that phase velocity matching is necessary for generation of the cumulative second harmonic Lamb wave in numerical perspective, while group velocity matching is demonstrated to not be a necessary condition.

For close range (almost 8–15 km) propagation, bottom-bounce energy (BBE) usually suffers from a great transmission loss due to a large grazing angle interacting with the ocean bottom, and the surface duct energy leakage (SDEL) might be able to make a significant contribution to shadow zone insonification. This study aims at making a comparison between SDEL and BBE in a shadow zone with a source depth of 50 m for close range propagation. Analysis of experimental data shows that for lower frequencies the SDEL can be comparable with the BBE up to a range of 12 km. Numerical simulations suggest that the transmission loss (TL) of 90 dB is a proper value to quantify the role of the SDEL in shadow zone insonification. When TL of the SDEL is about 90 dB, it is believed to be comparable with the BBE. Studies on the effect of mix layer depth (MLD) on the SDEL indicate that larger MLD and lower frequencies can help to create favorable conditions for SDEL and that there exists an optimal MLD for SDEL at certain frequency. Statistics of MLD distribution in the South China Sea (SCS) show that winter is favorable for SDEL and the situation reverses in summer. Eddies are known to occur frequently in the SCS and the study on the effect of eddies on the SDEL suggests that the presence of an eddy will influence the SDEL significantly by modifying the MLD.

The effect of the solid matrix and porosity of the porous medium are first introduced to the study of power-law nanofluids, and the Marangoni boundary layer flow with heat generation is investigated. Two cases of solid matrix of porous medium including glass balls and aluminum foam are considered. The governing partial differential equations are simplified by dimensionless variables and similarity transformations, and are solved numerically by using a shooting method with the fourth–fifth-order Runge–Kutta integration technique. It is indicated that the increase of the porosity leads to the enhancement of heat transfer in the surface of the Marangoni boundary layer flow.

The propagation of surface modes in warm non-magnetized quantum plasma is investigated. The surface modes are assumed to propagate on the plane between vacuum and warm quantum plasma. The quantum hydrodynamic model including quantum diffraction effect (the Bohm potential) and quantum statistical pressure is used to derive a new dispersion relation of surface modes. The new dispersion relation of surface modes is analyzed in some special interesting cases. It is shown that the dispersion relation can be reduced to the earlier results in some special cases. The results indicate that the quantum effects can facilitate the propagation of surface modes in such a semi-bounded plasma system. This work is helpful to understand the physical characteristics of the surface modes and the bounded quantum plasma.

A new low-energy negative-ion induced luminescence setup was recently developed at the injector of the GIC4117 $2\times1.7$ MV Tandem accelerator in Beijing Normal University. In situ luminescence measurements are performed on silica glass by using 20 keV H$^{-}$ ions at room temperature. Gauss fitting of the spectra revealed six overlapping components at about 2.7 eV, 2.4 eV, 1.9 eV, 1.8 eV, 4.2 eV, and 3.6 eV, which except for the new observed emission band at 3.6 eV are assigned to the creation of type II oxygen-deficient centers, E$'$ centers, non-bridging oxygen hole centers with different precursor states, and type-I oxygen-deficient centers. The fitted results of the saturation concentration show that self-trapped exciton recombination at type-II oxygen-deficient centers is the main luminescence emission process. The evolution of the luminescence intensity and full width at half maximums as a function of ion fluence is also discussed. It is found that the number of recombination centers reaches its maximum at lower fluence, and the area ratio between blue bands and red bands is much lower than that under high energy H$^{+}$ ion irradiation.

By means of density functional theory calculations, an orthogonal boron-carbon-nitrogen compound called (3,0)-BC$_2$N is predicted, which can be obtained by transversely compressing (3,0) carbon nanotubes (CNTs) and boron nitride nanotubes (BNNTs). Its structural stability, elastic properties, mechanical properties and electronic structure are systematically investigated. The results show that (3,0)-BC$_2$N is a superhard material with a direct bandgap. However, its similar structures, (3,0)-C and (3,0)-BN are indirect semiconductors. Strikingly, (3,0)-C is harder than diamond. We also simulate the x-ray diffraction of (3,0)-BC$_2$N to support future experimental investigations. In addition, our study shows that the transition from (3,0) CNTS and BNNTs to (3,0)-BC$_2$N is irreversible.

Plastic deformation of small crystals occurs by power-law distributed strain avalanches whose universality is still debated. In this work we introduce a continuum crystal plasticity model for the deformation of microsized single crystals, which is able to reproduce the main experimental observations such as flow intermittency and statistics of strain avalanches. We report exact predictions for scaling exponents and scaling functions associated with random distribution of avalanche sizes. In this way, the developed model provides a routine for a quantitative characterization of the statistical aspects of strain avalanches in microsized single crystals.

The resonant excitation is used to generate photo-excited carriers in quantum wells to observe the process of the carriers transportation by comparing the photoluminescence results between quantum wells with and without a p-n junction. It is observed directly in experiment that most of the photo-excited carriers in quantum wells with a p-n junction escape from quantum wells and form photocurrent rather than relax to the ground state of the quantum wells. The photo absorption coefficient of multiple quantum wells is also enhanced by a p-n junction. The results pave a novel way for solar cells and photodetectors making use of low-dimensional structure.

Magnetite (Fe$_{3}$O$_{4}$) nanoparticles with different sizes and shapes are synthesized by the thermal decomposition method. Two approaches, non-injection one-pot and hot-injection methods, are designed to investigate the growth mechanism in detail. It is found that the size and shape of nanoparticles are determined by adjusting the precursor concentration and duration time, which can be well explained by the mechanism based on the LaMer model in our synthetic system. The monodisperse Fe$_{3}$O$_{4}$ nanoparticles have a mean diameter from 5 nm to 16 nm, and shape evolution from spherical to triangular and cubic. The magnetic properties are size-dependent, and Fe$_{3}$O$_{4}$ nanoparticles in small size about 5 nm exhibit superparamagnetic properties at room temperature and maximum saturation magnetization approaches to 78 emu/g, whereas Fe$_{3}$O$_{4}$ nanoparticles develop ferromagnetic properties when the diameter increases to about 16 nm.

We present the experimental results of nitrogen-vacancy (NV) electron spin decoherence, which are linked to the coexistence of electron spin bath of nitrogen impurity (P1 center) and $^{13}$C nuclear spin bath. In previous works, only one dominant decoherence source is studied: P1 electron spin bath for type-Ib diamond; or $^{13}$C nuclear spin bath for type-IIa diamond. In general, the thermal fluctuation from both spin baths can be eliminated by the Hahn echo sequence, resulting in a long coherence time ($T_2$) of about 400 μs. However, in a high-purity type-IIa diamond where $^{13}$C nuclear spin bath is the dominant decoherence source, dramatic decreases of NV electron spin $T_2$ time caused by P1 electron spin bath are observed under certain magnetic field. We further apply the engineered Hahn echo sequence to confirm the decoherence mechanism of multiple spin baths and quantitatively estimate the contribution of P1 electron spin bath. Our results are helpful to understand the NV decoherence mechanisms, which will benefit quantum computing and quantum metrology.

The Cu$_{2}$ZnSnS$_{4}$ (CZTS)-based solar cell is numerically simulated by a one-dimensional solar cell simulation software analysis of microelectronic and photonic structures (AMPS-1D). The device structure used in the simulation is Al/ZnO:Al/nZn(O,S)/pCZTS/Mo. The primary motivation of this simulation work is to optimize the composition in the ZnO$_{1-x}$S$_{x}$ buffer layer, which would yield higher conversion efficiency. By varying S/(S+O) ratio $x$, the conduction band offset (CBO) at CZTS/Zn(O,S) interface can range from $-$0.23 eV to 1.06 eV if the full range of the ratio is considered. The optimal CBO of 0.23 eV can be achieved when the ZnO$_{1-x}$S$_{x}$ buffer has an S/(S+O) ratio of 0.6. The solar cell efficiency first increases with increasing sulfur content and then decreases abruptly for $x>0.6$, which reaches the highest value of 17.55% by our proposed optimal sulfur content $x=0.6$. Our results provide guidance in dealing with the ZnO$_{1-x}$S$_{x}$ buffer layer deposition for high efficiency CZTS solar cells.

The carrier-density-dependent spin relaxation dynamics for modulation-doped GaAs/Al$_{0.3}$Ga$_{0.7}$As quantum wells is studied using the time-resolved magneto-Kerr rotation measurements. The electron spin relaxation time and its in-plane anisotropy are studied as a function of the optically injected electron density. Moreover, the relative strength of the Rashba and the Dresselhaus spin–orbit coupling fields, and thus the observed spin relaxation time anisotropy, is further tuned by the additional excitation of a 532 nm continuous wave laser, demonstrating an effective spin relaxation manipulation via an optical gating method.

Silver films (Ag) and silver–gold films (Ag–Au) with thickness $\sim$15 nm are coated on Bk7 glasses through thermal evaporation. After doping gold of 5.2%, the grain size of the Ag film reduces from 13.6 nm to 9.1 nm, also the surface roughness decreases from 1.45 nm to 0.94 nm. A UV lamp is used as the irradiation light source to accelerate the corrosion process in the atmosphere. After 17 h irradiation, the pure silver film surface turns dark, and the transmittances reduce from 350 nm to 500 nm, while the Ag–Au film degrades much less, almost negligibly after UV radiation. Additional x-ray photoelectron spectroscopy and atomic force micrographs data are provided to show atomic content of films and their surface morphologies. It is suggested that small grain size and high packing density of alloy film prevent reaction of silver with oxygen in the atmosphere, which leads to high stability of the Ag–Au film.

The dependence of perpendicular magnetic anisotropy (PMA) on the barrier layer MgO thickness in MgO/CoFeB /Ta multilayers is investigated. The results show that the strongest PMA occurs in a small window of about 2–4 nm with the increase of MgO thickness from 1–10 nm. The crystalline degree of MgO and the change of interatomic distance along the out-of-plane direction may be the main reasons for the change of PMA in these multilayers. Moreover, the roughnesses of 2- and 4-nm-thick MgO samples are 3.163 and 1.8 nm, respectively, and both the samples show PMA. These results could be used to tune the magnetic characteristic of the ultra thin CoFeB film for future applications in perpendicular magnetic devices.

GaN nanorods are fabricated using inductively coupled plasma etching with Ni nano-island masks. The poly [2-methoxy-5-(2-ethyl)hexoxy-1,4-phenylenevinylene] (MEH-PPV)/GaN-nanorod hybrid structure is fabricated by depositing the MEH-PPV film on the GaN nanorods by using the spin-coating process. In the hybrid structure, the spatial separation is minimized to achieve high-efficiency non-radiative resonant energy transfer. Optical properties of a novel device consisting of MEH-PPV/GaN-nanorod hybrid structure is studied by analyzing photoluminescence (PL) spectra. Compared with the pure GaN nanorods, the PL intensity of the band edge emission of GaN in the MEH-PPV/GaN-nanorods is enhanced as much as three times, and the intensity of the yellow band is suppressed slightly. The obtained results are analyzed by energy transfer between the GaN nanorods and the MEH-PPV. An energy transfer model is proposed to explain the phenomenon.

Recently, great efforts have been made in the fabrication of arbitrary warped devices to satisfy the requirement of wearable and lightweight electronic products. Direct growth of high crystalline quality films on flexible substrates is the most desirable method to fabricate flexible devices owing to the advantage of simple and compatible preparation technology with current semiconductor devices, while it is a very challenging work, and usually amorphous, polycrystalline or discontinuous single crystalline films are achieved. Here we demonstrate the direct growth of high-quality Bi$_{2}$Te$_{3}$ single crystalline films on flexible polyimide substrates by the modified hot wall epitaxy technique. Experimental results reveal that adjacent crystallites are coherently coalesced to form a continuous film, although amounts of disoriented crystallites are generated due to fast growth rate. By inserting a quartz filter into the growth tube, the number density of disoriented crystallites is effectively reduced owing to the improved spiral interaction. Furthermore, flexible Bi$_{2}$Te$_{3}$ photoconductors are fabricated and exhibit strong near-infrared photoconductive response under different degrees of bending, which also confirms the obtained flexible films suitable for electronic applications.

The liquid state undercoolability and crystal growth kinetics of ternary Ni-5%Cu-5%Sn and Ni-10%Cu-10%Sn alloys are investigated by the glass fluxing method. In these two alloys, experimental maximum undercoolings of 304 K (0.18$T_{\rm L})$ and 286 K (0.17$T_{\rm L})$ are achieved and the dendritic growth velocities attain 39.8 and 25.1 m/s, respectively. The transition of morphology from coarse dendrite into equiaxed structure occurs and the grain size of the $\alpha$ (Ni) phase decreases remarkably when the undercooling increases. Both the lattice constant and microhardness increase obviously with the enhancement of undercooling. The enrichment of Cu and Sn solute contents reduces the dendritic growth velocity, while enhances the lattice constant and microhardness of $\alpha$ (Ni) phase.

Nearly lattice-matched InAlGaN/GaN heterostructure is grown on sapphire substrates by pulsed metal organic chemical vapor deposition and excellent high electron mobility transistors are fabricated on this heterostructure. The electron mobility is 1668.08 cm$^{2}$/V$\cdot$s together with a high two-dimensional-electron-gas density of $1.43\times10^{13}$ cm$^{-2}$ for the InAlGaN/GaN heterostructure of 20 nm InAlGaN quaternary barrier. High electron mobility transistors with gate dimensions of $1\times50$ μm$^{2}$ and 4 μm source-drain distance exhibit the maximum drain current of 763.91 mA/mm, the maximum extrinsic transconductance of 163.13 mS/mm, and current gain and maximum oscillation cutoff frequencies of 11 GHz and 21 GHz, respectively.

Recently, a stable hollow Sc$_{20}$C$_{60}$ cage with $T_{h}$ point group symmetry has been proposed, due to its volleyball-like shape called volleyballene. Here the structural and electronic properties for Sc$_{20}$C$_{60}$ cage with a europium atom are further studied based on density functional theory. The results give two stable low-lying Eu@Sc$_{20}$C$_{60}$ isomers, called cage-a and cage-b, respectively, which still retain the cage-like shape of Sc$_{20}$C$_{60}$ volleyballene. After a Eu atom is encaged into the Sc$_{20}$C$_{60}$ volleyballene, the HOMO–LUMO gaps decrease from 1.47 eV of the Sc$_{20}$C$_{60}$ cage to 0.46 eV of cage-a and 0.21 eV of cage-b. Due to the half-filled 4$f$-electron orbital states of the Eu atom, the two low-lying Eu@Sc$_{20}$C$_{60}$ isomers have net magnetic moments of 7$\mu _{\rm B}$. This study further provides the possible applications for the Sc$_{20}$C$_{60}$ volleyballene, and enriches the species of magnetic cage-like molecules, which provides more information for magnetic storage and magnetic control.

Considering the feature of distributions of parameters within the micro-hollow cathode discharge, we use a simple method to separate the sheath region characterized by drastic changes of plasma parameters and the bulk plasma region characterized by smooth changes of plasma parameters. A zero-dimensional chemical kinetic model is used to analyze the dissociation mechanism of CO$_{2}$ in the bulk plasma region of a micro-hollow cathode discharge and is validated by comparisons with previous modeling and experimental results. The analysis of the chemical kinetic processes has shown that the electron impact dissociation and heavy species impact dissociation are dominant in different stages of the micro-hollow cathode discharge process for a given applied voltage. The analysis of energy consumption distributions under different applied voltages reveals that the main reason of the conversion improvement with the increase of the applied voltage is that more input energy is distributed to the heavy species impact dissociation.

We provide a way to precisely control the geometry of a SiN$_x$ nanopore by adjusting the applied electric pulse. The pore is generated by applying the current pulse across a SiN$_x$ membrane, which is immersed in potassium chloride solution. We can generate single conical and cylindrical pores with different electric pulses. A theoretical model based on the Poisson and Nernst–Planck equations is employed to simulate the ion transport properties in the channel. In turn, we can analyze pore geometries by fitting the experimental current-voltage ($I$–$V$) curves. For the conical pores with a pore size of 0.5–2 nm in diameter, the slope angles are around $-2.5^{\circ}$ to $-10^{\circ}$. Moreover, the pore orifice can be enlarged slightly by additional repeating pulses. The conic pore lumen becomes close to a cylindrical channel, resulting in a symmetry $I$–$V$ transport under positive and negative biases. A qualitative understanding of these effects will help us to prepare useful solid-nanopores as demanded.

The time delays in both synthesis and degradation reactions, reflecting the non-Markovian behavior, are introduced in the stochastic gene transcriptional dynamics. The effects of the time delays on the stationary probability distribution, mean first passage time and stochastic resonance are discussed in detail based on the delayed stochastic differential equation and the corresponding delay Fokker–Planck equation. The time delays in synthesis reactions and in degradation reactions play a completely opposite role. The time delay in synthesis (degradation) reaction enhances (reduces) the mean first passage time, and tends to reduce (enhance) the signal-to-noise ratio. Finally, the effect of Gauss-distributed time delays on the transcriptional system is explored to test whether the previous approximation of employing a certain delay time works well or not.

We directly grow a lattice matched GaInP/GaInAs/GaInNAs/Ge (1.88 eV/1.42 eV/1.05 eV/0.67 eV) four-junction (4J) solar cell on a Ge substrate by the metal organic chemical vapor deposition technology. To solve the current limit of the GaInNAs sub cell, we design three kinds of anti-reflection coatings and adjust the base region thickness of the GaInNAs sub cell. Developed by a series of experiments, the external quantum efficiency of the GaInNAs sub cell exceeds 80%, and its current density reaches 11.24 mA/cm$^{2}$. Therefore the current limit of the 4J solar cell is significantly improved. Moreover, we discuss the difference of test results between 4J and GaInP/GaInAs/Ge solar cells under the 1 sun AM0 spectrum.

The air transportation network, one of the common multilayer complex systems, is composed of a collection of individual airlines, and each airline corresponds to a different layer. An important question is then how many airlines are really necessary to represent the optimal structure of a multilayer air transportation system. Here we take the Chinese air transportation network (CATN) as an example to explore the nature of multiplex systems through the procedure of network aggregation. Specifically, we propose a series of structural measures to characterize the CATN from the multilayered to the aggregated network level. We show how these measures evolve during the network aggregation process in which layers are gradually merged together and find that there is an evident structural transition that happened in the aggregated network with nine randomly chosen airlines merged, where the network features and construction cost of this network are almost equivalent to those of the present CATN with twenty-two airlines under this condition. These findings could shed some light on network structure optimization and management of the Chinese air transportation system.