Nanoporous metals (NPMs) have great potential applications in many technological areas, such as catalysis, sensing, actuation, and fuel cells, because of their unique physical and chemical properties. The cognition of related mechanical properties is one of the important bases for achieving functionalized applications. A series of large-scale molecular dynamics (MD) simulations is performed to study the mechanical properties of nanoporous sliver (NPS) under uniaxial tension. Three different topology architectures of NPS, including cube, gyroid and diamond structures, are constructed and investigated. The effects of topology architecture and relative density on the mechanical properties are discussed. The LAMMPS is used to perform MD simulations and the embedded atom method potential is utilized to describe the interatomic interactions. The applied strain rate is 10⁹ s^-1 and the applied strain increment is 0.001 in each loading step. The results show that the plastic properties of NPS mainly depend on those of ligaments and the breakage of NPS mainly occurs in ligament areas. Meanwhile, the gyroid structure has better plasticity than other structures, due to the existence of ligament in spiral form. For one structure, the ultimate strength and the Young's modulus increase with the increase of relative density. Analysis shows that the basic mechanical properties of NPS largely depend on the relative density, similar to those of porous materials. The modulus as a function of relative density displays a power-law relation and the exponents depend on the topology architectures. The exponents of three structures are in a range between 1 and 2, showing that the bending of ligament and the tension of ligament are both included during the deformation. The variation trends of modulus of diamond and gyroid structures are similar to the variation of relative density, whose possible reason is that diamond and gyroid structures are both constructed by triply periodic minimal surfaces. With the same relative density, the modulus of diamond structure is in good agreement with that of gyroid structure, and the modulus of cube structure is the minimum. The strength shows a linear relation with the relative density, indicating that the yielding behavior of NPS is dominated by the axial yielding of ligament. When three types of NPSs have the same relative density, the strength of diamond structure is the maximum, cube structure second, and gyroid structure is the minimum. In diamond structure NPS, the structure of triangular framework is formed between ligaments, resulting in a relatively higher strength. The present study will provide an atomistic insight into the understanding of deformation mechanisms of nanoporous metals, and it will provide data support for designing NPMs with optimal mechanical properties by controlling geometric structure.

In this paper, the classical molecular dynamics method is used to investigate the permeability of pressure-driven water fluid in the hybrid structure of graphene-carbon nanotube (CNT). The results indicate that the permeability of water molecules for the hybrid structure of graphene-CNT is obviously higher than that for the assembled structure of graphene-CNT. The combination between the graphene sheet and CNT in the hybrid structure is found to be a key point to improve the permeability of water molecules. Subsequently, the potential of mean force (PMF) is calculated in order to explain the influences of the combined structure on the permeabilities for the water fluid passing through both the hybrid and assembled graphene-CNT structures. The result shows that the PMF for the water molecules penetrating through the assembled structure is larger than that for the hybrid structure appreciably. It implies that the structure of the combined chemical bonds in the hybrid structure can efficiently improve the permeability of water molecules. As for the water penetrating through the hybrid structured graphene-CNT, the permeability of water increases with water pressure rising, and decreases with the electric field intensity increasing. The water molecules cannot pass through the proposed hybrid structure below a pressure threshold of 100 MPa. The permeability of water in the hybrid structure decreases with the increasing charge quantity on CNT below a threshold of 0.8e. The PMF for water penetrating through the hybrid structure decreases with charge quantity decreasing. The results suggest that the water permeability can be controlled by regulating the water pressure and the electric field intensity. Furthermore, the influences of the temperature and the axis spacing of two CNTs in the hybrid structure on the water permeability are considered. The permeability of water in the hybrid structure increases with the increasing temperature above a threshold of 200 K. The PMF for water penetrating through the hybrid structure increases with the decreasing temperature. Interestingly, the water permeability decreases with the increasing axis spacing. As the axial spacing increases, the water permeability decreases gradually and even approaches to two times of the permeability in the case of the hybrid structure with a single CNT channel. The findings can provide a theoretical basis for designing nanopumps or osmotic membranes based on the graphene-CNT hybrid structures.

In this paper, we study the effects of external electric field and Al content on the transverse and longitudinal g-factor (g_┴ and g_//) and its anisotropy (δg) of wurtzite AlGaN/GaN quantum wells (QWs). The Δg_┴=(g_┴-g₀)=g_┴^bulk + g^w and Δg_//=(g_//-g₀)=g_//^bulk are mainly contributed by the bulk structure (g_//^bulk and g_┴^bulk) respectively, but the difference between g_//^bulk and g_┴^bulk is small and almost remains unchanged when the external electric field and Al content are varied. So the anisotropy of the g factor in AlGaN/GaN QWs induced by the bulk wurtzite structure is small, while the anisotropy induced by the quantum confined effect (g^w) is considerable. When the direction of the external electric field is the same as (opposite to) the polarization electric field, the magnitudes of g_//^bulk and g_┴^bulk both increase (decrease) with increasing external electric field. This is induced mainly by the variations of envelope function and confined energy with the electric field. With the external electric field changing from -1.5×10⁸ V·m^-1 to 1.5×10⁸ V· m^-1, the confined energy ε₁ increases slowly, and the magnitude of the envelope function at the left heterointerface increases. So the contribution to Δg_┴ from the heterointerface Γ_Inter is positive and increases slowly, and that from the well Γ_W is negative and increases slowly in magnitude. The magnitude of Γ_Inter is larger than that of Γ_W, but the magnitude of the latter increases more rapidly. All the above factors make the g-factor anisotropy δg>0 and decrease in magnitude with electric field increasing. With increasing Al content of the barrier, both <β>₁ (g_┴^bulk) and <γ>₁ (g_//^bulk) decrease if the strain effects are ignored (S_{1, 2}=0), because the confined energy decreases and the peak of the envelope function shifts towards the left heterointerface. By considering the strain effects (S_{1, 2} ≠ 0), the magnitude of <β>₁ (g_┴^bulk) and <γ>₁ (g_//^bulk) increase with Al content increasing. The strain effect has a great influence on the confined potential V(z), leading to the rapid increase of β(z) when z > z_p, which the situation for γ (z) is similar to. With increasing Al content, the magnitudes of Γ_Inter and Γ_W both increase, but the magnitude of Γ_Inter is larger and increases more rapidly. Therefore δg increases slowly. The magnitude of Δ g_┴ first decreases with increasing Al content, then it increases with Al content increasing, and since g_┴^bulk <0 it increases more rapidly in magnitude. Results show that the g-factor and its anisotropy in AlGaN/GaN QWs can be greatly modulated by the external electric field, the Al content in the barrier, the strain effects and the quantum confined effect. Results obtained here are of great importance for designing the spintronic devices.

The HfO_x-based resistive random access memory (RRAM) has been extensively investigated as one of the emerging nonvolatile memory (NVM) candidates due to its excellent memory performance and compatibility with CMOS process. In this study, the influences of deposition ambient, especially the oxygen partial pressure during thin film sputtering, on the resistive switching characteristics are discussed in detail for possible nonvolatile memory applications. The Ni/HfO_x/TiN RRAMs are fabricated, and the HfO_x films with different oxygen content are deposited by a radio frequency magnetron sputtering at room temperature under different oxygen partial pressures. The oxygen partial pressures in the sputter deposition process are 2%, 4% and 6% relative to engineer oxygen content in the HfO_x film. Current-voltage (I-V) measurements, X-ray photoelectron spectroscopy, and atomic force microscopy are performed to explain the possible nature of the stable resistive switching phenomenon. Through the current-voltage measurement, typical resistive switching behavior is observed in Ni/HfO_x/TiN device cells. It is found that with the increase of the oxygen partial pressure during the preparation of HfO_x films, the stoichiometric ratio of O in the film is improved, the root mean square (RMS) of the surface roughness of the film slightly decreases due to the slower deposition rate under a higher oxygen partial pressure, and the high resistance state (HRS) current decreases. In addition, by controlling the oxygen content of the device, the endurance performance of the device is improved, which reaches up to 10³ under a 6% oxygen partial pressure. The HfO_x films prepared at a higher oxygen partial pressure supply enough oxygen ions to preserve the switching effect. As the oxygen partial pressure increases, the uniformity of the switching voltage is improved, which can be attributed to the fact that better oxidation prevents the point defects (oxygen vacancies) from aggregating into extended defects. Through the linear fitting and temperature test, it is found that the conduction mechanism of Ni/HfO_x/TiN RRAM device cells in low resistance state is an ohmic conduction mechanism, while in high resistance state it is a Schottky emission mechanism. The interface between TE and the oxide layer (HfO_x) is expected to influence the resistive switching phenomenon. The activation energy of the device is investigated based on the Arrhenius plots in HRS. A switching model is proposed according to the theory of oxygen vacancy conductive filament. Furthermore, the self-compliance behavior is found and explained.

A novel approach to using tunable diode laser absorption spectroscopy (TDLAS) is developed for measuring the laser intensity and absorbance of gas with highly broadened and congested spectra by wavelength division multiplex (WDM) technology. Direct absorption spectroscopy with non-linear algorithm is utilized, because this fitting method offers benefits in dealing with blended spectral features according to the relationship between transmitted laser intensity and absorbance by Beer law. Compared with traditional TDLAS sensing with WDM, this approach has some advantages of transmissions demultiplexing without additional optic gratings and detectors. Following the published theory, the absorbance and transmitted laser intensity are incorporated into an improved non-linear fitting model. A solution to a simulation of CO₂ blended spectrum at a pressure of 5 atm is exploited to demonstrate the ability to recover the absorption in a high pressure environment, inferring the optimal combination of parameters in the model. The influences of these nonideal laser effects, such as nonlinear and linear coefficients, are investigated by the multiplexed transmission simulations at rovibrational transitions of H₂O near 7444 cm^-1 and 7185 cm^-1. Errors in absorbance fitting is larger when nonlinear or linear coefficients of two lasersbecome closer. The satisfied results can be obtained when linear coefficients ratio is limited whitin a range from 0.05 to 0.67. In addition, the essential transition spacing in multiplexed transmissions, larger than the full width of transitions, is considered to be able to improve the fitting accuracy. This approach is validated in a static absorption cell over a pressure range from 1 to 10 atm at room temperature to demonstrate the ability to measure the blended CO₂ spectrum from 63307 cm^-1 to 6337 cm^-1 by a single DFB laser. The sensor method resolves laser intensity with a nonlinear coefficient of 1.4×10^-4 and recovers absorbance with a root mean square (RMS) precision of 3.2%, which demonstrates the applicability of this sensor to high-pressure gas sensing systems. Another approach to validating the gas temperature and measuring H₂O by WDM is presented in a gas-liquid two phase pulsed detonation engine running with a filling fraction of 100%. Two fiber coupled lasers, respectively, near 7185.6 cm^-1 and 7444.35 cm^-1 are scanned at 20 kHz to achieve a temporal resolution of 50 μs for monitoring detonation exhaust. A fixed spectrum interval (about 0.7 cm^-1) of transitions in multiplexed transmission is created through temperature adjustment in DFB laser to provide more independent absorption information. Recovered linear coefficients of 0.18 and 0.46 in two DFB lasers are in good agreement with the results from the simulations. An instantaneous temperature measurement of 1183 K in the exhaust 7.45 ms after detonation wave provides the confirmation of the ability of this method to infer the temperature and H₂O time histories in the whole detonation process. In conclusion, the novel approach based on TDLAS has tremendous potential applications in high pressure combustion diagnosis and WDM spectrum analysis.

Gas sensor has been widely used to monitor the air quality. Metal oxide semiconductor (MOS) is one of the most popular materials used for gas sensors due to its low-cost, easy preparation and good sensing properties. However, the working temperature of tungsten oxide gas sensor is still high, which restricts its applications in special environment. Researchers try to lower the working temperature of WO₃ by doping or changing morphology. Tungsten oxide nanowire has great potential to be applied to the gas sensing field because of its high specific surface area. In this work, one-dimensional WO₃ nanowire structure is synthesized by sputtering W and followed by the twostep thermally oxidation method. The first step of oxidation is carried out in vacuum tube furnace to obtain the WO₂ nanowires and the second step of oxidation is an air annealing treatment in which we will control the temperatures (S0, without treatment; S1, 300℃; S2, 400℃) to study the morphologies and gas sensing properties. The obtained WO₃ nanowires are investigated by field emission scanning electron microscopy (FESEM), X-ray diffraction (XRD), X-ray photoelectron spectroscopy (XPS), and transmission electron microscope (TEM) techniques. The SEM results indicate that WO₃ nanowires grow along different directions in space. Nanowires have an average length of 1 μm and a diameter of 40 nm. Besides, nanowires have better crystallinity after higher-temperature (400℃) annealing as indicated by the XRD results, which means less surface defects and surface states. The XPS spectrum indicates the existence of oxygen vacancy in nanowires after 300℃ annealing. The TEM results show that nanowires preferred growth direction is changed after different annealing treatments and the crystal lattice of nanowires after 400℃ has better order than that of nanowires after 300℃. The influences of annealing temperature in the second step on the sensing properties to variousconcentration NO₂ gases are investigated at working temperature ranging from room temperature (RT) to 150℃. The results show that the WO₃ nanowires after 300℃ annealing show better response than after 400℃ annealing and without annealing treatment. The best response of nanowires to 6 ppm NO₂ is 2.5 at RT after 300℃ annealing treatment, and the lowest NO₂ detection limit is 0.5 ppm. The room temperature enhancement in gas sensing property may be attributed to the large WO₃ nanowire surface states caused by oxidation degree controlled twostep thermal oxidation method. Besides, p-type response to testing gas is found. This might be caused by the lattice defect and the adsorption of oxygen from atmosphere which leads to the formation of surface inversion layer. And the dominated carriers of nanowires will convert from electrons into holes. In conclusion, these results demonstrate that the WO₃ nanowires have great potential applications in future NO₂ gas detection with low consumption and good performance.

The accurate modeling and parameter identification of lithium-ion battery are of great significance in real-time control and high-performance operation for advanced battery management system (BMS) in electrified vehicles (EVs). However, it is difficult to obtain the information about the interior state inside battery, because it cannot be directly measured by some electric devices. In order to accurately identify the key state parameters of lithium-ion cell applied to electric ground vehicles, an extended single particle model of lithium-ion cell with electrolyte dynamics behaviors is first built up based on the porous electrode theory and concentration theory in this article. Compared with the conventional single particle cell model, the parameter description of the solid electrolyte interface film is incorporated into this model, and the coupled effects of temperature-dependent and electrolyte-dependent electrochemical parameters on the cell discharge are also taken into consideration. Based on this extended single particle cell model, a simplified parameter sensitivity analysis method and a comprehensive parameter identification scheme for lithium-ion cell are proposed herein, in which a sensitivity analysis of the capacity to a subset of electrochemical parameters that are hypothesized to evolve throughout the battery's life, is conducted to determine the highly sensitive parameters to be identified under some particular operation scenarios, and further to solve the parameter optimization problem using the genetic algorithm. Based on this method, the test data under the working condition of 1 C discharge rate at 23℃ are employed to evaluate the identified parameters of lithium-ion battery cell with a peak value of voltage error less than 3.8%. Afterwards, the effectiveness and feasibility of the proposed parameter identification scheme are validated by the comparative study of the simulated output voltage and the experimental output voltage under the same input current profile. Specifically, the 0.05 C discharge and HPPC (hybrid pulse power characterization) current profile are used to verify the evaluated parameters under the 1 C discharge condition, and the maximum relative errors of voltage with 0.05 C galvanostatic discharge profile at 23 and 45℃ are 3.4% and 2.6% by using our proposed SPMe_SEI model, and 5.7% and 4.0% by using the traditional SPMe model, respectively. Moreover, the maximum relative errors of voltage with HPPC discharge profile at 23 and 45℃ are 1.9% and 1.5% by using our proposed SPMe_SEI model, and 2.1% and 1.8% by using the traditional SPMe model, respectively. It is concluded that the proposed parameter identification scheme for a lithium-ion cell model can provide a solid theory foundation for facilitating the estimation of state-of-health in BMS application.

The relationship between the sequential and structural features of intrinsically disordered peptides (IDPs) has attracted much attention during the recent decade. One essential problem relating to sequence-structure relationship is how the distribution of charged residues affects the structure of IDP. In this work, we address this problem with simulations on a series of random peptides composed of arginine and aspartic acids. With the ABSINTH implicit solvation model, the structural ensembles are generated with Markov Chain Monte Carlo method and replica-exchange sampling. The relations between various structural features (including the gyration radius, the tail distance, the distance between residues, and asphericity) and the distribution of charged residues are analyzed. Several limit cases (with parts of interactions switched off) are also calculated for comparison. The conversion from extended conformations to compact structures is observed, following the demixing of negatively and positively charged residues along the sequence. For the cases with well-mixed charges, the intra-chain electrostatic repulsions and attractions are balanced, which results in a generic Flory random coil-like conformation. Differently, for the case with well-separated charged residues, the electrostatic attraction between residues distant along the sequence induces a semi-compact hairpin-like conformation. This is consistent with the observations of Pappu group. Our results suggest that the structural dependence on charge distribution would not be sensitive to the selection of amino acid, and is determined by the patterns of charges, which demonstrates the robustness of the mechanism that the charge distribution modulates the structural features in the IDP system. Our results may broaden our understanding of the sequence-structure relation of IDP system.

Broadband wireless communication is implemented primarily in a complicated environment. The complex environment with time-varying multi-path propagation characteristics will seriously affect the performance of communication. To solve the problem of insecurity in information transmission in wireless channels, in this paper a system is modeled by using the multi-input single output eavesdropping channel model and the security of information transmission through time reversal technology is ensured. Another problem is that the information focuses on the receiving point. Owing to the temporal and spatial focusing characteristics of the time reversal technology the information near the receiving point can be eavesdropped easily. To solve this problem, a secure transmission scheme based on time reversal technology with artificial noise interference on the transmitter side is proposed. One of the core technologies to solve this problem is to introduce the environment adaptive technique–time reversal in the wireless link. Further, the problem of a wiretap channel in physical layer security research has become a popular research topic in recent years. To solve the problems about the physical layer wiretap channel and multi-path fading in wireless channels, a novel concept combining time reversal technology with physical layer security technology is proposed. In this paper, a physical layer secure transmission scheme based on the joint time reversal technique and artificial noise at the sending end is proposed for the wireless multi-path channel. First, in a typical wiretap channel model the time reversal technique is used to improve the security of the information transmission process by using the properties of spatial and temporal focusing. It refers to the fact that information can be focused at a given moment and in space. Second, as the information is easily eavesdropped near the focus point, artificial noise is added to the sending end to disrupt the ability of the eavesdropper to eavesdrop. The artificial noise has no effect on legitimate user due to the use of null-space artificial noise in legitimate user. Based on this scheme, a closed expression, such as secure signal-to-interference and signal-to-noise ratio, an achievable secrecy rate and bit error rate are obtained, and the influences of the number of antennas, signal-to-noise ratio, and artificial noise are analyzed. The theoretical analysis and simulation results show that the proposed scheme has a higher secrecy signal-to-noise ratio, a higher rate of secrecy, and a lower bit error rate of the legitimate user than the the existing physical layer security schemes.

In this paper, we mainly study the simplification and improvement of Santilli's methods in Birkhoffian system, which is a more general type of basic dynamic system. The theories and methods of Birkhoffian dynamics have been used in hadron physics, quantum physics, rotational relativity theory, and fractional dynamics. As is well known, Lagrangian inverse problem, Hamiltonian inverse problem, and Birkhoffian inverse problem are the main objects of the dynamic inverse problems. The results given by Douglas (Douglas J 1941 Trans. Amer. Math. Soc. 50 71) and Havas[Havas P 1957 Nuovo Cimento Suppl. Ser. X5 363] show that only the self-adjoint Newtonian systems can be represented by Lagrange's equations, so the Lagrangian inverse problem is not universal for a holonomic constrained mechanical system. Furthermore, from the equivalence between Lagrange's equation and Hamilton's equation, Hamiltonian inverse problem is not universal. A natural question is then raised:whether there exists a self-adjoint dynamical model whose inverse problem is universal for holonomic constrained mechanical systems, in the field of analytical mechanics.
An in-depth study of this issue in the 1980s by R. M. Santilli shows that a universal self-adjoint model exists for a holonomic constrained mechanic system that satisfies the basic conditions of locality, analyticity, and formality. The Birkhoff's equation is a natural extension of the Hamilton's equation, which shows the geometric properties of a nonconservative system as a general symplectic structure. This more general symplectic structure provides the geometry for the study of the non-conservative system preserving structure algorithms. Therefore, it is particularly important to study the problem of the Birkhoffian representation for the holonomic constrained system.
For the inverse problem of Birkhoff's dynamics, studied mainly are the condition under which the mechanical systems can be represented by Birkhoff's equations and the construction method of Birkhoff's functions. However, due to the extensiveness and complexity of the holonomic nonconservative system, Birkhoff's dynamical functions do not have so simple construction method as Lagrange function and Hamilton function. The research results of this issue are very few. The existing construction methods are mainly for three constructions proposed by Santilli[Santilli R M 1983 Foundations of Theoretical Mechanics Ⅱ (New York:Springer-Verlag) pp25-28], and there are still many technical problems to be solved in the applications of these methods.
In order to solve these problems, this article mainly focuses on the following content. First, according to the existence theorem of Cauchy-Kovalevskaya type equations, we prove that the autonomous system always has an autonomous Birkhoffian representation. Second, a more concise method is given to prove that Santilli's second method can be simplified. An equivalent relationship implied in Santilli's third method is found, an improved Santilli's third method is proposed, and the MATLAB programmatic calculation of the method is studied. Finally, the full text is summarized and the results are discussed.

During the plastic deformation of hexagonal metals, it is easy to generate the point defect clusters with complex shapes and configurations due to their anisotropic properties. The interactions among these clusters and between these clusters and moving dislocations significantly influence the physical and mechanical properties of hexagonal materials. However, none of these issues in particular concerning the evolutions of vacancy clusters, the formation of microvoids, and the crack nucleation and propagation, is comprehensively understood on an atomic scale. In the present work, we first employ the activation-relaxation technique, in combination with ab initio and interatomic potential calculations, to systematically investigate vacancy cluster configurations in titanium and the transformation between these clusters. The results indicate the stable and metastable configurations of vacancy clusters at various sizes and activation energies of their dissociation, combination and migration. It is found that the formation and migration energies decrease with the size of vacancy cluster increasing. Small vacancy clusters stabilize at configurations with special symmetry, while large clusters transform into microvoids or microcracks. High-throughput molecular dynamics simulations are subsequently employed to investigate the influences of these clusters on plastic deformation under tensile loading. The clusters are found to facilitate the crack nucleation by providing lower critical stress, which decreases with the size of the vacancy clusters increasing. Under tensile loading, cracks are first nucleated at small clusters and then grow up, while large clusters form microvoids and cracks directly grow up.

In order to overcome the difficulty in real-time effectively acquiring the target parameters of differential game guidance in a complex underwater environment,the differential game guidance of underwater nonlinear tracking control based on continuous time generalised predictive correction is proposed.Since the target parameter and the detection precision are seriously affected by the acoustic homing device detection period,noise,and interference,it is easy to lose or misjudge the target signal.Hence a combination of the dynamic tracking game model for differential games and the acoustic homing detection method of underwater tracking is used for making the on-line prediction and compensation correction to the deviation tendency of target manoeuvres deviating from the self-guided sound zero axis.This is carried out by using a continuous time generalized predictive control algorithm,according to the discrepancy between the predicted advance> and the expected value.The manoeuvring target can then be located in the maximum capture probability sector of the tracker device in real time.In order to solve the estimation difficulty problem of the remaining time of the dynamic differential game antagonism,and improve the response speed and the control precision of the system,the zero-efficiency control parameter and the predictive control algorithm are introduced to optimize the differential game.In this way,the infinite time domain differential game can be transformed into a multiple-time domain differential game with feedback correction.Through the complementing advantages of dynamic programming and predictive optimization,the real-time compensation and correction to the interceptor differential game guidance is realised,and the disadvantages of the differential game in the process constraints and stochastic disturbance are overcome. In order to adjust the favourable advance> of the self-guided detection rapidly,the learning prediction function of rolling optimization feedback correction is adopted.The initial moment of the differential response is pushed forward along with the entire forecast period by rolling optimization.To verify the validity of the algorithm,this is applied to the underwater nonlinear tracking game,and the guidance performance is compared with the differential game guidance and the integrated control algorithm of differential game and discrete predictive control.The results show that this can achieve the optimum control of the high precision underwater manoeuvring target on-line tracking and prediction correction with the detection mode limited in uncertain disturbances,because this is flexible in the choosing of sampling time and does not need control weighting for non-minimum phase system.This can also solve the problem of the initial bias and random disturbance taking into account the control constraints and interference suppression performance,and can improve the robustness to environmental interference.

Shilnikov criteria believe that the emergence of chaos requires at least one unstable equilibrium, and an attractor is associated with the unstable equilibrium. However, some special chaotic systems have been proposed recently, each of which has one stable equilibrium, or no equilibrium at all, or has a linear equilibrium (infinite equilibrium). These special dynamical systems can present chaotic characteristics, and the attractors in these chaotic systems are called hidden attractors due to the fact that the attraction basins of chaotic systems do not intersect with small neighborhoods of any equilibrium points. Since they were first found and reported in 2011, the dynamical systems with hidden attractors have attracted much attention. Additionally, the fractional-order system, which can give a clearer physical meaning and a more accurate description of the physical phenomenon, has been broadly investigated in recent years. Motivated by these two considerations, in this paper, we propose a fractional-order chaotic system with hidden attractors, and the finite time synchronization of the fractional-order chaotic systems is also studied.
Most of the researches mainly focus on dynamic analysis and control of integer-order chaotic systems with hidden attractors. In this paper, based on the Sprott E system, a fractional-order chaotic system is constructed by adding an appropriate constant term. The fractional-order chaotic system has only one stable equilibrium point, but it can generate various hidden attractors. Basic dynamical characteristics of the system are analyzed carefully through phase diagram, Poincare mapping and power spectrum, and the results show that the fractional-order system can present obvious chaotic characteristics. Based on bifurcation diagram of system order, it can be found that the fractional-order system can have period attractors, doubling period attractors, and chaotic attractors with various orders. Additionally, a finite time synchronization of the fractional-order chaotic system with hidden attractors is realized based on the finite time stable theorem, and the proposed controller is robust and can guarantee fast convergence. Finally, numerical simulation is carried out and the results verify the effectiveness of the proposed controller.
The fractional-order chaotic system with hidden attractors has more complex and richer dynamic characteristics than integer-order chaotic systems, and chaotic range of parameters is more flexible, meanwhile the dynamics is more sensitive to system parameters. Therefore, the fractional-order chaotic system with hidden attractors can provide more key parameters and present better performance for practical applications, such as secure communication and image encryption, and it deserves to be further investigated.

Turing proposed a model for the development of patterns found in nature in 1952. Turing instability is known as diffusion-driven instability, which states that a stable spatially homogeneous equilibrium may lose its stability due to the unequal spatial diffusion coefficients. The Gierer-Mainhardt model is an activator and inhibitor system to model the generating mechanism of biological patterns. The reaction-diffusion system is often used to describe the pattern formation model arising in biology. In this paper, the mechanism of the pattern formation of the Gierer-Meinhardt model is deduced from the reactive diffusion model. It is explained that the steady equilibrium state of the nonlinear ordinary differential equation system will be unstable after adding of the diffusion term and produce the Turing pattern. The parameters of the Turing pattern are obtained by calculating the model. There are a variety of numerical methods including finite difference method and finite element method. Compared with the finite difference method and finite element method, which have low order precision, the spectral method can achieve the convergence of the exponential order with only a small number of nodes and the discretization of the suitable orthogonal polynomials. In the present work, an efficient high-precision numerical scheme is used in the numerical simulation of the reaction-diffusion equations. In spatial discretization, we construct Chebyshev differentiation matrices based on the Chebyshev points and use these matrices to differentiate the second derivative in the reaction-diffusion equation. After the spatial discretization, we obtain the nonlinear ordinary differential equations. Since the spectral differential matrix obtained by the spectral collocation method is full and cannot use the fast solution of algebraic linear equations, we choose the compact implicit integration factor method to solve the nonlinear ordinary differential equations. By introducing a compact representation for the spectral differential matrix, the compact implicit integration factor method uses matrix exponential operations sequentially in every spatial direction. As a result, exponential matrices which are calculated and stored have small sizes, as those in the one-dimensional problem. This method decouples the exact evaluation of the linear part from the implicit treatment of the nonlinear reaction terms. We only solve a local nonlinear system at each spatial grid point. This method combines with the advantages of the spectral method and the compact implicit integration factor method, i.e., high precision, good stability, and small storage and so on. Numerical simulations show that it can have a great influence on the generation of patterns that the system control parameters take different values under otherwise identical conditions. The numerical results verify the theoretical results.

With the development of the networks, the coupling between networks has become increasingly significant. Here, the networks can be described as interdependent networks. An interdependent network can have two different kinds of links, a connectivity link and a dependency link, which are fundamental properties of interdependent networks. During the past several years, interdependent complex network science has attracted a great deal of attention. This is mainly because the rapid increase in computing power has led to an information and communication revolution. Investigating and improving our understanding of interdependent networks will enable us to make the networks (such as infrastructures) we use in daily life more efficient and robust. As a significant collective behavior, synchronization phenomena and processes are common in nature and play a vital role in the interaction between dynamic units. At the same time, the time delay problem is an important issue to be investigated, especially in biological and physical networks. As a matter of fact, time delays exist commonly in the real networks. A signal or influence traveling through a network is often associated with time delay. In this paper, the local adaptive heterogeneous synchronization is investigated for interdependent networks with delayed coupling consisting of two sub-networks, which are one-by-one inter-coupled. The delays exist both in the intra-coupling and in the inter-coupling between two sub-networks, the intra-coupling and inter-coupling relations of the networks satisfy the requirements for nonlinearity and smoothness, and the nodes between two sub-networks have different dynamical systems, namely heterogeneous systems. Based on the Lyapunov stability theory, linear matrix inequality, and adaptive control technique, with proper controllers and adaptive laws for the networks, the sufficient conditions are proposed to synchronize the sub-networks of the interdependent networks into heterogeneous isolated systems, respectively. In order to illustrate the main results of the theoretical analysis clearly, some numerical simulations for an interdependent network with NW small world sub-network and BA sub-network are presented, in which each sub-network has 100 nodes and the heterogeneous systems are Lorenz and Rössler systems. The numerical simulations show that using the controllers and adaptive laws proposed, the network obtains the local heterogeneous synchronization quickly, that is, the nodes of two sub-networks are synchronized into Lorenz and Rössler systems separately. Thus, they verify the feasibility and correctness of the proposed techniques. It is worth noting that the presented results are delay-independent. In the future, our research will be directed to the further investigation of the delay-dependent synchronization of interdependent networks by using the current results as a basis.

The compactness and robustness of the vacuum setup are the major limitations to develop transportable and space-borne optical clocks. The first step in the engineering challenge is to reduce volume and weight with respect to a stationary system. In this paper, we present the realization of a miniaturized vacuum system by building two anti-Helmholtz coils inside the vacuum magneto-optical-trap (MOT) chamber. The built-in coils are specially designed to minimize the distance between the coils, and in this way it is possible to reduce the current needed to realize a typical magnetic gradient of 40 Gs/cm required for blue MOT. When the MOT coil current is 2 A, an axial magnetic field gradient of 43 Gs/cm is obtained in the center of the MOT, which is enough for the first stage Doppler cooling. This novel design allows us to reduce size, weight and power consumption with respect to a traditional laser cooling apparatus, and simultaneously avoid complicating the water cooling equipment. Our vacuum system has a size of 60 cm×20 cm×15 cm, about 1/10 of the original system in the laboratory. In addition, the circularly polarized Zeeman slowing laser is sent to counter propagating atomic beam, and atoms at a few hundred meters per second are now routinely slowed down to velocities of tens of meters per second. As a result, about 16.4% of the atoms are actually trapped into the blue MOT. The final temperature of the blue MOT is approximately 10.6 mK, and the internal diameter is 1.5 mm by observing the expansion of the atoms from the MOT. The populations of cold atoms finally trapped in the MOT are 1.6×10⁶ of ⁸⁸Sr and 1.5×10⁵ of ⁸⁷Sr. The ¹S₀ → ¹P₁ transition used for the blue MOT is not perfectly closed due to the decay channel of the 5p¹P₁ → 4d¹D₂, and a part of atoms are stored in the ³P₂ and ³P₀ states. To prevent the atoms from losing, 707 and 679 nm repumping lasers are employed to recycle these atoms in the ³P₁ state, and then the atoms decay to the ground state ¹S₀. Now the typical number of loaded atoms dramatically increases by 5 times compared with before. The slowing efficiency of Zeeman slower is also optimized for the operation with deceleration related to the parameter of magnet length, which uses more effectively available magnetic field distribution, in contrast to the usual constant deceleration mode. Our future work will focus on constructing a Zeeman slower combined with permanent magnets or an electric magnet for better tuning of the magnetic field.

X-ray detector is a core component for X-ray astronomical observation and pulsar navigation.The on-orbit observation performance of X-ray detector will change gradually,owing to the influences of emission vibration,radiation damage of high-energy particles,and the aging of the components.The on-orbit calibration of X-ray detector facilitates the accurate acquisition and the precise modeling of X-ray radiation of the observation celestial bodies.In this paper a new method of calibrating the performance of X-ray detector is studied by using the radiation spectrum of the pulsar, which can effectively eliminate the influences from detector background and space environment noise.The on-orbit performance of the first focusing X-ray detector in China has been evaluated by analyzing the observations of the X-ray pulsar-based navigation satellite-1(XPNAV-1) for the Crab pulsar.The XPNAV-1 was launched in November 2016, with the aim of conducting the test of the feasibility of applying the regular emission of X-ray signals from pulsars to spacecraft navigation.Now,the first batch of scientific data about the Crab pulsar observations gained by the focusing X-ray detector for almost one month has been released.The pulse profiles of 124 observations and the total observational spectrum of Crab pulsar are achieved from those data.According to the international accurate X-ray radiation parameters of Crab pulsar,which have been determined by other X-ray space satellites,together with the absorption effect of the neutral hydrogen gas in the universe,the effective area of the focusing X-ray detector is estimated.The result shows that the effective area of the focusing X-ray detector on XPNAV-1 in an energy range of 0.6-1.9 keV is better than 2 cm².The maximum effective area is 3.06 cm² at an energy of 0.7 keV,which means that its detection efficiency is about 10%.As the observed energy increases,the effective area decreases.The area of the focusing X-ray detector in an energy range of 2-3.5 keV is about 1 cm²,and it is about 0.1 cm² at energies above 5 keV,and its estimation accuracy is affected seriously by the statistical errors of X-ray photons.At the same time,another method of calibrating the effective area is studied by considering the energy response matrix of detector.The energy response matrix of the focusing X-ray detector is estimated by using the five ground test values of energy resolution.The effective area of the focusing X-ray detector is re-calibrated.However,the result shows that the energy response matrix exerts little effect on the effective area of the focusing X-ray detector.Finally,we suggest that the XPNAV-1 should observe some supernova remnants to monitor the changes of energy resolution and energy linearity and so on.

The accurate calculation of the isotope shift factors is helpful in extracting the mean-square charge radius of the nucleus,which is an important nuclear parameter to investigate the nuclear properties and improve nuclear structure theories.However,for atomic systems with many electrons the uncertainties of the calculated isotope shift factors are difficult to evaluate accurately,since high sensitivity of the isotope shift factor to the electron correlation and limitation of the computational resource.Based on the calculations of the isotope shift factors of the 3s^{2 1}S₀→ 3s3p ^3,1P₁^o transitions in Al+by using the multi-configuration Dirac-Hartree-Fock method,the convergences of these physical quantities with the expansion of the configuration space are investigated in detail.In our calculation,the electron correlations are divided into the first-order correlation and the higher-order correlations according to the perturbation theory,and captured by using the active space approach.The effect of the first-order correlation are considered by including configuration state functions (CSFs) that are generated by the single and double substitutions from the occupied orbitals in the single reference configuration set.After the first-order correlation effect are taken into account adequately,the reference configuration sets are augumented by adding the dominant CSFs from the first-order correlation configuration space,in order to consider the higher-order correlation effect.We find that the convergence of the mass shift factors (including the normal shift factor and the specific mass shift factor) is linearly correlated with the convergence of the level energies in our computational model.For the transitions,the linear correlation of the convergence between the mass shift factors and the transition energies is not so good as that for the levels involved in the transitions due to the limited computational resource,but it can be improved with the expansion by including more higher-order correlation related 2s and 2p core electrons.Furthermore,we made use of the linear correlation to estimate the uncertainties of our isotope shift factors, and obtain the reasonable value of error.The authors hope that the linear correlation between the convergence of the mass shift factors and the level or transition energies can be proved and explained in more atomic systems,and the linear correlation can be used to evaluate accurately the uncertainties of the mass shift factors for the atoms and ions with many electrons in the near future.

Inorganic-organic metal halide perovskite solar cells (PSCs) have drawn tremendous attention as a promising next-generation solar-cell technology because of their high efficiencies and low production cost. Since the first report in 2009, the recorded power conversion efficiency (PCE) of PSCs has rapidly risen to 22.1% by using 2, 2', 7, 7'-tetrakis (N,Ndi-p-methoxyphenyl-amine) 9,9-spirobifluorene (spiro-MeoTAD) as hole transport material (HTM), with the efforts devoted to the device architecture optimization, material compositional engineer and interface engineering. Nevertheless, the synthesis and cost of the organic HTM (OHTM) become a major challenging issue and therefore alternative materials are required. In the past few years, the applications of inorganic HTMs (IHTMs) in PSCs have shown large improvement in PCE and stability. For example, PSCs with CuO_x as IHTM reached a PCE of 19.0% with better stability. Even more exciting, the theoretical PCE of PSC based on Cu₂O HTM reaches 24.4%. So, Cu₂O is a promising IHTM for future optimized PSC and the large area uniform preparation is very important. In this paper, Cu₂O films have been successfully prepared using electron beam evaporation followed by air annealing. The influences of annealing temperature and time on the composition, structure, and photoelectric characteristics of film are investigated in detail. It is found that the as-deposited film is a mixture of Cu₂O and Cu. With the increase of annealing temperature, material composition is transformed from mixture to pure Cu₂O phase, and then to CuO, due to the oxidation in air. In an annealing temperature between 100℃ to 150℃, pure Cu₂O film can be obtained with an average transmission rate over 70%, optical band-gap of 2.5 eV, HOMO level of -5.32 eV, and a carrier mobility of 30 cm²·V^-1·s^-1. When the film is treated with a UV lamp, the structure and composition of the film can be changed more easily because of the enhancement of oxidation. Finally, reverted planar PSCs with the structure of Ag/PCBM/CH₃NH₃PbI₃/HTMs/ITO are constructed and compared carefully based on HTMs of Cu₂O, with poly(3,4-ethylenedioxythiophene)-poly(styrenesulfonate)(PEDOT:PSS), and Cu2O/PEDOT:PSS layers, respectively. An optimum thickness of 40 nm of Cu₂O HTM is achieved with high carrier extraction rate. However, the performances of all of the PSCs are inferior to those of PEDOT:PSS-based devices, due to the formation of pinholesin absorber layer resulting from the strong hydrophobicity of Cu₂O film. However, the efficiency of PSC based on Cu2O/PEDOT:PSS double-HTM is deteriorated because of the chemical interaction between PEDOT:PSS and Cu₂O. These findings provide some important guidelines for the design of HTMs.

The strong light scattering in complex media, due to the highly inhomogeneous distributions of refractive indexes, is regarded as a fundamental impediment in numerous optical applications such as optical communications, biophotonics, and optical tweezer. Recently, many optical techniques based on the coherence of light source with long coherent length have been developed and widely used to suppress and control light scattering and propagation in complex media. Here, we propose and experimentally demonstrate the control and time reversal of only one part instead of all of light passing through complex media and different optical paths by combining digital phase conjugation and coherence gating based on partially coherent light source. Interference of reference and objective beams and corresponding phase maps are measured by the charge coupled device (CCD) and four-step phase-shift measuring technique only when the optical path difference between two beams is less than coherence length. Time reversal is achieved by spatial light modulator (SLM). In the experiment we further analyze the phase map and time reversal with different optical path differences and different coherence lengths of source. The experimental results demonstrate that for each optical path difference, the time reversal of only the part of light coming from the same scattering> and identical optical path is achieved by digital phase conjugation and coherent gating of broadband light source.

Underwater polarization imaging is a valuable technology for underwater detection and exploration, since it can provide abundant information about target scene via the removal of background light from raw images. However, in a conventional polarization imaging method, the reconstructed image has limited quality caused by the inaccurate estimation of degree of polarization (DoP) and noise amplification, which finally leads to the incomplete removal of background light. The situation becomes worse if the target and background light reach an almost equal DoP.
To date, various approaches including acoustic imaging, photoacoustic imaging, and polarization imaging have been implemented to realize underwater imaging. Notably, underwater polarization imaging is of particular interest due to its simple system structure, low cost and excellent performance in recovering target information. It mainly involves the separation of the backscattered light denoted as background light from the target scattered light acting as the target light. Removal of the background light from the raw image gives rise to a clear target image, which has been the focus of polarization imaging for a long period. The most representative approach was presented by Schechner[Schechner Y Y, Karpel N 2005 IEEE Journal of Oceanic Engineering 30 570] who utilized the DoP of background light and target light to recover clear image. Further optimization of the approach was also conducted by researchers including Schechner[Tali T, Schechner Y Y 2009 IEEE Transactions on Pattern Analysis and Machine Intelligence 31 385], Huang[Huang B J, Liu T G, Hu H F, Han J H, Yu M X 2016 Optics Express 24 9826], et al. However, the influence of noise amplification in the process on the reconstruction results has always been ignored, which accounts for the results to some extent though the explanation is unsatisfactory.
In this paper, we present a multi-scale polarization imaging strategy to suppress the noise amplification effect and its influence on the final results. It originates from the difference in polarization image between two diverse layers. Specifically, the image is divided into two layers, one of which is characterized by high contrast but remarkably difference between the target and background, known as base layer B_TI; the other layer is low-contrast but contains the detailed information about the target, known as detail layer D_TI. Special processes are applied to the two layers according to their characteristics, respectively. For the base layer B_TI, combined bilateral filtering is used to suppress noise. As for the detail layer, it is first processed by wavelet transform with considering its multi-resolution characteristic. After the wavelet coefficient correction via adjusting the kernel function w(x, f), the details in target image is perfected with keeping iterations. During the updating procedure, the image noise can be further suppressed. Underwater experiments are conducted in the laboratory to demonstrate the validity of the proposed method. Besides, quantitative analyses also verify the improvement in final target image.
Compared with conventional underwater polarization imaging methods, the proposed method is good at dealing with various target conditions, since it handles noise amplification without requiring any additional equipment. Furthermore, the proposed method is easy to incorporate in a conventional polarization imaging system to achieve underwater images with better quality and valid detail information. Therefore, the proposed method has more potential applications in underwater imaging.

Modulation instability (MI) of the isosceles-triangle symmetric continuous wave in equilateral three-core fibers (ETCFs) is studied in detail. The so-called isosceles-triangle symmetric continuous wave state is the planar wave where the fields in its two cores are identical but different from the field in the third core, and the premise of its existence is that the total power (P) exceeds a minimum value (P_min) that depends on the linear coupling coefficient and nonlinear coefficient of ETCFs. For a given total power P (P ≥ qslant P_min), set the power in one core to be P₁, and the powers in the other two cores to be P₂ (P=P₁ + 2P₂), then two kinds of filed distributions will be found. The first kind is for P₁ > P₂ with P₁ becoming more and more large as total power P increases. By the linear stability analysis method, the main characteristics of MI in ETCFs are found which are quite similar to those of the asymmetric continuous wave states in two core optical fibers (TCFs). The other kind is that P₁ becomes more and more small and P₂ becomes more and more large as total power P increases. Through the same method, the main characteristics of MI in ETCFs are found which are distinctively different from those of the asymmetric continuous wave states in TCFs. On the one hand, MI can be generated in both normal and anomalous dispersion regimes without perturbations. In addition, the zero-perturbation frequency corresponds to the largest gain of MI in the normal dispersion regime. On the other hand, the coupling coefficient dispersion, which can dramatically modify the spectra of MI in TCFs, plays a minor role in both normal and anomalous dispersion regimes in ETCFs. In practical application, the findings in this paper are of guiding significance for studying the nonlinear effects of mode-division multiplexing system based on the multimode or multicore optical fibers.

Sodium laser guide star (LGS) becomes an essential part in modern astronomical adaptive optics system, especially for the next generation extremely large ground based telescope. The LGS technology has experienced the developmental stages as natural guide star, Rayleigh LGS, sodium LGS and constellation of LGS. The sky coverage is still limited in that the LGS cannot not be used to detect the tip/tilt aberrations. While the polychromatic laser guide star (PLGS) is one of the most effective ways to enlarge the sky coverage to 100%. Previous simulation models are insufficient for the accurate calculation of the return flux, especially for the simulation model of PLGS which is generated by one-photon excitation of mesospheric sodium atoms. The simulation model based on Bloch equations proposed in this paper can be used to compute the return flux of one-photon excited PLGS precisely. Doppler broadening, beam atom exchanging, collisions and recoil are taken into account in the model. The return flux is validated by the return efficiency. The simulation results indicate that with one-photon excitation of sodium atoms, a return efficiency of 330 nm is minimum compared with those of other wavelengths; the saturation power density will decrease with recoil increasing and increase with collision rate increasing; an optimal line-width exists up to maximum the photon return efficiency. In the best case, when the power density is 10 W/m² at the sodium layer, the maximum return efficiency at 330 nm is 0.907 photons/s/sr/atom/(W/m²) with an optimal laser line-width of 18 MHz.

We construct a nonlinear equation between the return signal and the boundary value of extinction coefficient according to the lidar equation. And according to the nonlinear equation, we put forward a new method to solve the nonlinear equation by using Broyden algorithm. The Broyden algorithm is a concrete application of the quasi-Newton method. It has faster convergence and less iteration times, and does not need to calculate the derivative value. After choosing a suitable initial value, the boundary value can be obtained through the algorithm. A 532 nm single-band Mie scattering imaging lidar system is developed in Hefei, Southern China, for real-time atmospheric aerosol/particle remote sensing. Atmospheric measurement has been performed in Science Island during night time, and the time-range distribution of atmospheric backscattering signal was recorded on April 6, 2017, by employing the imaging lidar system. Then, the boundary values are achieved based on the Broyden algorithm and the least square algorithm. It adopts the Klett backward integration method to retrieve the horizontal distribution of extinction coefficients in a range of 1 km after the acquisition of the signal by changing the distance, then the horizontal atmospheric transmittance can be achieved based on the path integral. We also conduct a contrast experiment with the one-way transmission of the horizontal light near the ground within the range of 1 km at the same time. The initial site is situated in the experimental room besides the Dongpu reservoir and the end site is located on the second floor of our office building. The important things in this experiment are that the light reaching the target surface must be fully received and the laser power should be monitored at the double-end. Then we can obtain the transmittance by the direct method. By comparing the transmittance from the direct method with the transmittance from imaging lidar between the two different ways, i.e., Broyden algorithm and least square algorithm, then the correlation coefficients are obtained to be both over 0.95 in the period. And the method introduced in this paper is a little better than the least square algorithm with a value of 0.968. Besides, the average relative errors between the two inverse methods and the direct method are 4.66% and 9.10%, respectively. The average relative errors obtained by using the least square algorithm is about twice that by using the Broyden algorithm. It can be concluded that the algorithm introduced in this paper is effective and has certain advantages for the inverse problem.

Since recently one is interested in underwater communications, imaging, sensing and lidar appeared, it is important to study characteristic parameters of the adaptive optical imaging system in oceanic turbulence. Until now, the characteristic parameters of the adaptive optical imaging system in atmospheric turbulence have investigated widely and in depth, but those in oceanic turbulence have been examined seldom. It is known that the atmospheric turbulence is induced by the temperature fluctuation. However, the oceanic turbulence is induced by both the temperature fluctuation and the salinity fluctuation. The temperature and salinity spectra have similar ''bumped'' profiles, with bumps occurring at different wave numbers. Thus, the behavior of light propagation in oceanic turbulence is very different from that in atmospheric turbulence. In this paper, the influence of oceanic turbulence on characteristic parameters (i.e., strehl ratio, Greenwood time constant, and isoplanatic>) of the adaptive optical imaging system is studied. The approximate analytical expression of the Strehl ratio for the short-exposure imaging case is derived. It is demonstrated by the numerical calculation method that this Strehl ratio approximate expression is accurate enough except the near field when D_G/r₀=1 (where D_G is the pupil diameter of the optical system, r₀ is the seeing parameter in oceanic turbulence), and the relative error maximum of this Strehl ratio approximate expression in the far field is much smaller than that in the near field. In addition, the analytical expressions of the Greenwood time constant and the isoplanatic> in oceanic turbulence are also obtained in this paper. It is shown that the values of the three characteristic parameters (i.e., Strehl ratio, the Greenwood time constant and the isoplanatic>) decrease when salinity-induced optical turbulence dominates gradually. The Strehl ratio, the Greenwood time constant and the isoplanatic> also decrease as the rate of dissipation of kinetic energy per unit mass of seawater decreases or the rate of dissipation of mean-squared temperature increases. It is known that the isoplanatic> at wavelength λ=0.5 μm are roughly 7-10 μrad for a nearly vertical path from Earth to space in atmospheric turbulence. However, it is shown in this paper that the isoplanatic> may be on the order of μrad after 100 m propagation distance in oceanic turbulence. Therefore, the influence of oceanic turbulence on the isoplanatic> is very large. The results obtained in this paper will be useful in the applications of adaptive optics imaging systems involving oceanic turbulence channels.

Aperiodic signal is widely used in different engineering fields.It is important to detect or enhance a weak aperiodic signal.In this work,we investigate the aperiodic vibrational resonance (AVR) in a fractional-order bistable system excited by an aperiodic binary signal and a square waveform signal simultaneously.The weak aperiodic binary signal is the characteristic signal which usually carries the useful information.The square waveform signal is the auxiliary signal which is used to induce the AVR.By tuning the amplitude of the auxiliary signal,the AVR may occur and the aperiodic binary signal is enhanced.The occurrence of the AVR is measured by the cross-correlated coefficient between the input aperiodic binary signal and the output time series.When the cross-correlated coefficient achieves a large enough value, the AVR may occur and the weak aperiodic signal is enhanced excellently by the auxiliary signal.If the aperiodic binary signal has large pulse width and the system has small parameters (usually on the order of 1),the AVR can be realized by tuning the amplitude of the square waveform.If the aperiodic binary signal has small pulse width,the AVR cannot be realized in the system with small parameters directly.For this case,we realize the AVR by the re-scaled method and the twice sampling method separately.By the re-scaled method,through a scale transformation,the equivalent system with large system parameters can match the input characteristic signal with arbitrary small pulse width.When the re-scaled method is used,the scale parameter is a key factor.By the twice sampling method,the reconstructed characteristic signal after the twice sampling has a large pulse width.Then,it can match the original system with small system parameters.When the twice sampling method is used,the ratio of the twice sampling frequency to the first sampling frequency is a key factor.Although these two methods have different physical processes,they can achieve the same goal. The AVR also depends on the fractional-order value closely.Specifically,with the increase of the fractional-order,the resonance region in the cross-correlated coefficient curve turns wider.Moreover,the amplitude of the square waveform signal which induces the optimal AVR to turn larger.Simultaneously,the similarity between the optimal output and the input binary aperiodic signal is enhanced.The method and the results of this paper not only can be used to enhance the weak aperiodic binary signal but also have a certain reference value in processing other kinds of aperiodic signals, such as the linear or nonlinear frequency modulated signal,etc.Furthermore,the results in this paper also present rich dynamical behaviors of a fractional-order system and may provide reference value in the study of fractional-order systems.

High Reynolds number helical vortex system possesses a dominant characteristic of helicopter rotor flow field, whose spatiotemporal evolution is one of the most important factors affecting the aerodynamic performance. In such a type of flow field, vortex interaction due to flow unsteadiness and non-linearity possesses the most common characteristic, whose complexity and tightly coupling property make it very hard to understand its physical behaviors. Also, the multi-scale characteristic of the helical vortex evolution poses a severe challenge to the computational fluid dynamics community. In this paper, a hybrid numerical method, blending 5th order weighted essentially non-oscillatory and 6th order cenitral schemes, implemented in a finite volume overset grid framework based on adaptive mesh refinement technique, are adopted to capture the evolution of vortical structure in a high resolution manner. The highly-resolved flow field of Caradonna-Tung rotor with two blades in hover, with a tip Mach number of 0.439 and a tip Reynolds number of 1.92×10⁶, is obtained using delayed detached eddy simulation method. The averaged pressure coefficient distributions at 50%R, 68%R, 80%R, and 96%R stations show good agreement with experiment data, and the vortex trajectories during the stable stage, as well as the instantaneous turbulent kinetic energy distribution in the wake region, and also validate the computed result. In order to reveal the underlying physical mechanism of the helical vortex structure evolution, proper orthogonal decomposition analysis and Lagrangian coherent structures are adopted as a post processing procedure, which brings more details about the unsteady vortex system. The evolution characteristics of the vortex system are revealed as follows. 1) Trailing edge vortex sheet rolling-up and interaction with tip vortex strongly affect vortical stability and downstream nonlinear vortex-vortex behaviors. 2) The vortical system exhibits the spatiotemporal stability at an age less than 720°, and the vorticity decays with age and trajectories by power law, the distribution of circumferential velocity and the evolution of vortex core radius agree well with theoretical models. 3) Results of proper orthogonal decomposition analysis show that the mode of free stream and point vortex combination plays critical roles in the state transition of flow field. 4) Lagrangian coherent structure further gives the evolution process of helical vortex, and reveals the flow characteristics of vortex pairing and co-rotating, showing the effect of trailing edge vortex roll up phenomenon in the vortical system evolution.

The freezing of water droplet is a ubiquitous phenomenon in nature. Although the freezing process of water droplet impacting on cold surfaces is widely observed on a macroscopic scale, the study of freezing process on a micro-scale is still deficient, and it is definitely difficult to study micro-droplets and nano-droplets using experimental methods due to the obstacles in both generation and observation. For these reasons, simulation methods using molecular dynamics (MD) have been proposed to study micro-droplets and nano-droplets, as molecular dynamics can trace each atom, count up the collective behavior of a group of atoms and describe the detail interaction between atoms. In this paper, a three-dimensional model is established by molecular dynamics simulation to study the freezing process of water droplets impinging on a cold solid surface on a nanoscale. We select the micro-canonical ensemble (NVE) as a statistical system and the TIP4P/ice model as a potential energy function to simulate oxygen atoms, hydrogen atoms and water molecules. The LJ/126 model is used to simulate the interaction between water molecules and solid atoms. Different wettability walls are simulated by adjusting the potential energy parameters. For all the simulations, the velocity-rescale method is used to keep the temperature constant and the Verlet algorithm is adopted to solve the Newton equations. In the velocity-rescale method, the temperature is calculated by using the profile-unbiased thermostat. The freezing process inside the water droplet is determined by the temperature distribution of water molecules along the vertical direction, which is more concise than by the location coordinates of the microscopic atoms. Through the numerical experimentations, we find that when the surface temperature decreases, the completely freezing time of drops is reduced; meanwhile, the time required for water temperature to drop down to the wall temperature is increased. Moreover, the heat transfer inside the water droplet slows down with the decreasing of wall hydrophilicity while the total freezing time is prolonged.

In the re-entry process of hypersonic vehicle in near space,the violent interaction between the vehicle and the surrounding air will ionize the air and leaves a complex environment in the vicinity of the vehicle surface.Both the flow field and the communication between the vehicle and the controlling center on the earth are significantly affected by the generated plasma layers.This will result in serious system operation problems such as the communication blackout or radio blackout.Numerical modelling is one of the most widely used methods to investigate such complicated physical-chemical processes involving coupled magneto-hydrodynamics,heat transfer,dissociation,ionization,excitation and their reverse processes.Due to the strong collision,non-uniform and non-equilibrium characteristics of the plasma layers formed in the vicinity of the vehicle surface,a self-consistent physical-mathematical model,as well as a database for the transport properties of non-equilibrium plasmas,describing the non-equilibrium features of plasmas is one of the pre-requisites for numerical simulations.This paper focuses on the non-equilibrium plasmas produced near the bluff body surface in the re-entry process of hypersonic vehicles in near space,and a new non-equilibrium plasma model which has been developed previously by our group is employed for conducting two-dimensional (2D) simulations on the characteristics of the non-equilibrium argon plasma jets based on the multiphase gas discharge plasma experimental platform-2015(MPX-2015) established in our laboratory.The modelling is conducted under two different flow conditions, i.e.,the sub-sonic flow condition and the super-sonic flow condition.Under the sub-sonic flow condition,the 2D nonequilibrium modeling results are consistent well with the experimental measurements which validates the reliability of the non-equilibrium physical-mathematical model,as well as the developed computer codes in this study.The modeling results under the super-sonic flow conditions show that the spatial uniformity of the plasma layer surrounding the bluff body,as well as the total heat flux to the bluff body surface from plasmas,decreases significantly with the increase of the plasma jet velocity;while the local electron number density increases in the vicinity of the head of the bluff body, the thickness of the plasma layer surrounding the bluff body first decreases,and then increases.These modelling results provide a theoretical guidance for conducting experimental studies under a super-sonic flow condition on MPX-2015. In the future research,we will extend the physical-mathematical model to investigate of the transient,non-equilibrium features of the air discharge plasmas,and the complicated interactions between the plasma jet and the surrounding air, and/or the downstream bluff body under different operating conditions.Simultaneously,we will also try to develop the in-situ experimental methods to obtain the spatiotemporal distributions of the temperature,velocity and species concentrations in the plasma layer,and conduct a comparison between modelling results and measured data.