Ghost images reconstructed from fractional-order moments with thermal light

We present the joint probability density function(PDF) between the bucket signals and reference signals in thermal light ghost imaging, by regarding these signals as stochastic variables. The joint PDF allows us to examine the fractional-order moments of the bucket and the reference signals, in which the correlation orders are fractional numbers,other than positive integers in previous studies. The experimental results show that various images can be reconstructed from fractional-order moments. Negative(positive) ghost images are obtained with negative(positive) orders of the bucket signals. The visibility and peak signal-to-noise ratios of the diverse ghost images depend greatly on the fractional orders.

True-temperature inversion algorithm for a multi-wavelength pyrometer based on fractional-order particle-swarm optimization

Herein,a method of true-temperature inversion for a multi-wavelength pyrometer based on fractional-order particle-swarm optimization is proposed for difficult inversion problems with unknown emissivity.Fractional-order calculus has the inherent advantage of easily jumping out of local extreme values;here,it is introduced into the particle-swarm algorithm to invert the true temperature.An improved adaptive-adjustment mechanism is applied to automatically adjust the current velocity order of the particles and update their velocity and position values,increasing the accuracy of the true temperature values.The results of simulations using the proposed algorithm were compared with three algorithms using typical emissivity models:the internal penalty function algorithm,the optimization function(fmincon)algorithm,and the conventional particle-swarm optimization algorithm.The results show that the proposed algorithm has good accuracy for true-temperature inversion.Actual experimental results from a rocket-motor plume were used to demonstrate that the true-temperature inversion results of this algorithm are in good agreement with the theoretical true-temperature values.

Intelligent Fractional-Order Controller for SMES Systems in Renewable Energy-Based Microgrid

An autonomous microgrid that runs on renewable energy sources is presented in this article.It has a supercon-ducting magnetic energy storage(SMES)device,wind energy-producing devices,and an energy storage battery.However,because such microgrids are nonlinear and the energy they create varies with time,controlling and managing the energy inside them is a difficult issue.Fractional-order proportional integral(FOPI)controller is recommended for the current research to enhance a standalone microgrid’s energy management and performance.The suggested dedicated control for the SMES comprises two loops:the outer loop,which uses the FOPI to regulate the DC-link voltage,and the inner loop,responsible for regulating the SMES current,is constructed using the intelligent FOPI(iFOPI).The FOPI+iFOPI parameters are best developed using the dandelion optimizer(DO)approach to achieve the optimum performance.The suggested FOPI+iFOPI controller’s performance is contrasted with a conventional PI controller for variations in wind speed and microgrid load.The optimal FOPI+iFOPI controller manages the voltage and frequency of the load.The behavior of the microgrid as a reaction to step changes in load and wind speed was measured using the proposed controller.MATLAB simulations were used to evaluate the recommended system’s performance.The results of the simulations showed that throughout all interruptions,the recommended microgrid provided the load with AC power with a constant amplitude and frequency.In addition,the required load demand was accurately reduced.Furthermore,the microgrid functioned incredibly well despite SMES and varying wind speeds.Results obtained under identical conditions were compared with and without the best FOPI+iFOPI controller.When utilizing the optimal FOPI+iFOPI controller with SMES,it was found that the microgrid performed better than the microgrid without SMES.

Sensitivity Analysis of Electromagnetic Scattering from Dielectric Targets with Polynomial Chaos Expansion and Method of Moments

In this paper,an adaptive polynomial chaos expansion method(PCE)based on the method of moments(MoM)is proposed to construct surrogate models for electromagnetic scattering and further sensitivity analysis.The MoM is applied to accurately solve the electric field integral equation(EFIE)of electromagnetic scattering from homogeneous dielectric targets.Within the bistatic radar cross section(RCS)as the research object,the adaptive PCE algorithm is devoted to selecting the appropriate order to construct the multivariate surrogate model.The corresponding sensitivity results are given by the further derivative operation,which is compared with those of the finite difference method(FDM).Several examples are provided to demonstrate the effectiveness of the proposed algorithm for sensitivity analysis of electromagnetic scattering from homogeneous dielectric targets.

The deterministic condition for the ground reaction force acting point on the combined knee valgus and tibial internal rotation moments in early phase of cutting maneuvers in female athletes

Background:Combined knee valgus and tibial internal rotation(VL+IR)moments have been shown to stress the anterior cruciate ligament(ACL)in several in vitro cadaveric studies.To utilize this knowledge for non-contact ACL injury prevention in sports,it is necessary to elucidate how the ground reaction force(GRF)acting point(center of pressure(CoP))in the stance foot produces combined knee VL+IR moments in risky maneuvers,such as cuttings.However,the effects of the GRF acting point on the development of the combined knee VL+IR moment in cutting are still unknown.Methods:We first established the deterministic mechanical condition that the CoP position relative to the tibial rotational axis differentiates the GRF vector’s directional probability for developing the combined knee VL+IR moment,and theoretically predicted that when the CoP is posterior to the tibial rotational axis,the GRF vector is more likely to produce the combined knee VL+IR moment than when the CoP is anterior to the tibial rotational axis.Then,we tested a stochastic aspect of our theory in a lab-controlled in vivo experiment.Fourteen females performed 60˚cutting under forefoot/rearfoot strike conditions(10 trials each).The positions of lower limb markers and GRF data were measured,and the knee moment due to GRF vector was calculated.The trials were divided into anterior-and posterior-CoP groups depending on the CoP position relative to the tibial rotational axis at each 10 ms interval from 0 to 100 ms after foot strike,and the occurrence rate of the combined knee VL+IR moment was compared between trial groups.Results:The posterior-CoP group showed significantly higher occurrence rates of the combined knee VL+IR moment(maximum of 82.8%)at every time point than those of the anterior-CoP trials,as theoretically predicted by the deterministic mechanical condition.Conclusion:The rearfoot strikes inducing the posterior CoP should be avoided to reduce the risk of non-contact ACL injury associated with the combined knee VL+IR stress.

Firing activities in a fractional-order Hindmarsh–Rose neuron with multistable memristor as autapse

Considering the fact that memristors have the characteristics similar to biological synapses, a fractional-order multistable memristor is proposed in this paper. It is verified that the fractional-order memristor has multiple local active regions and multiple stable hysteresis loops, and the influence of fractional-order on its nonvolatility is also revealed. Then by considering the fractional-order memristor as an autapse of Hindmarsh–Rose(HR) neuron model, a fractional-order memristive neuron model is developed. The effects of the initial value, external excitation current, coupling strength and fractional-order on the firing behavior are discussed by time series, phase diagram, Lyapunov exponent and inter spike interval(ISI) bifurcation diagram. Three coexisting firing patterns, including irregular asymptotically periodic(A-periodic)bursting, A-periodic bursting and chaotic bursting, dependent on the memristor initial values, are observed. It is also revealed that the fractional-order can not only induce the transition of firing patterns, but also change the firing frequency of the neuron. Finally, a neuron circuit with variable fractional-order is designed to verify the numerical simulations.

Reliability analysis of torpedo loading based on fractional-order optimization model

A fractional-order cumulative optimization GM(1,2)model based on grey theory is proposed to study the relationship between torpedo loading and working reliabilities.In this model,the average relative error function related to order and background value is established.Taking the average relative error function as the objective function,the optimal value of the two parameters is obtained through the optimization method,and the minimum value of the average relative error is determined.The calculation example shows that this method can greatly improve the accuracy of the model and more accurately reflect the relationship between torpedo loading and working reliabilities compared with the traditional GM(1,2)model.

BIFURCATION CONTROL FOR A FRACTIONAL-ORDER DELAYED SEIR RUMOR SPREADING MODEL WITH INCOMMENSURATE ORDERS

A fractional-order delayed SEIR rumor spreading model with a nonlinear incidence function is established in this paper,and a novel strategy to control the bifurcation of this model is proposed.First,Hopf bifurcation is investigated by considering time delay as bifurcation parameter for the system without a feedback controller.Then,a state feedback controller is designed to control the occurrence of bifurcation in advance or to delay it by changing the parameters of the controller.Finally,in order to verify the theoretical results,some numerical simulations are given.

Quasi-synchronization of fractional-order complex networks with random coupling via quantized control

We investigate the quasi-synchronization of fractional-order complex networks(FCNs) with random coupling via quantized control. Firstly, based on the logarithmic quantizer theory and the Lyapunov stability theory, a new quantized feedback controller, which can make all nodes of complex networks quasi-synchronization and eliminate the disturbance of random coupling in the system state, is designed under non-delay conditions. Secondly, we extend the theoretical results under non-delay conditions to time-varying delay conditions and design another form of quantization feedback controller to ensure that the network achieves quasi-synchronization. Furthermore, the error bound of quasi-synchronization is obtained.Finally, we verify the accuracy of our results using two numerical simulation examples.

Robust Stability Analysis of Smith Predictor Based Interval Fractional-Order Control Systems:A Case Study in Level Control Process

The robust stability study of the classic Smith predictor-based control system for uncertain fractional-order plants with interval time delays and interval coefficients is the emphasis of this work.Interval uncertainties are a type of parametric uncertainties that cannot be avoided when modeling real-world plants.Also,in the considered Smith predictor control structure it is supposed that the controller is a fractional-order proportional integral derivative(FOPID)controller.To the best of the authors'knowledge,no method has been developed until now to analyze the robust stability of a Smith predictor based fractional-order control system in the presence of the simultaneous uncertainties in gain,time-constants,and time delay.The three primary contributions of this study are as follows:ⅰ)a set of necessary and sufficient conditions is constructed using a graphical method to examine the robust stability of a Smith predictor-based fractionalorder control system—the proposed method explicitly determines whether or not the FOPID controller can robustly stabilize the Smith predictor-based fractional-order control system;ⅱ)an auxiliary function as a robust stability testing function is presented to reduce the computational complexity of the robust stability analysis;andⅲ)two auxiliary functions are proposed to achieve the control requirements on the disturbance rejection and the noise reduction.Finally,four numerical examples and an experimental verification are presented in this study to demonstrate the efficacy and significance of the suggested technique.

Unusual magnetic relaxation in a single-molecule magnet with toroidal magnetic moments

We report the synthesis and characterization of a single-molecule magnet composed of triangular clusters of dysprosium ions.The structural study shows that the symmetry changes from one polar point group(mm2)at room temperature to another polar point group(m)at low temperature.Magnetic studies and theory calculations illustrate that the vortex distribution of magnetic dipoles in the triangular dysprosium clusters forms a toroidal magnetic moment.Interestingly,the analysis of AC magnetic susceptibility reveals the coexistence of three distinct magnetic relaxation processes,corresponding to the Raman,Orbach,and QTM relaxation pathways,respectively.The sum of three modified Debye functions is successfully used to describe the multiple relaxation behavior.

Free vibration of thermo-elastic microplate based on spatiotemporal fractional-order derivatives with nonlocal characteristic length and time

A fractional-order thermo-elastic model taking into account the small-scale effects of the thermo-elastic coupled behavior is developed to study the free vibration of a higher-order shear microplate.The nonlocal strain gradient theory is modified with the introduction of the fractional-order derivatives and the nonlocal characteristic length.The Fourier heat conduction is replaced by the non-Fourier heat conduction with the introduction of the fractional order and the memory characteristic time.Numerical calculations are performed to analyze the effects of the nonlocal strain gradient parameters,the spatiotemporal fractional order,the nonlocal characteristic length,and the memory characteristic time on the natural frequencies,the vibration attenuation,and the phase shift between the temperature field and the displacement field.The numerical results show that the new thermo-elastic model with the spatiotemporal fractional order can provide more exquisite descriptions of the thermo-elastic behavior at a small scale.

Numerical Simulation of the Fractional-Order Lorenz Chaotic Systems with Caputo Fractional Derivative

Although some numerical methods of the fractional-order chaotic systems have been announced,high-precision numerical methods have always been the direction that researchers strive to pursue.Based on this problem,this paper introduces a high-precision numerical approach.Some complex dynamic behavior of fractional-order Lorenz chaotic systems are shown by using the present method.We observe some novel dynamic behavior in numerical experiments which are unlike any that have been previously discovered in numerical experiments or theoretical studies.We investigate the influence of α_(1),α_(2),α_(3) on the numerical solution of fractional-order Lorenz chaotic systems.The simulation results of integer order are in good agreement with those of othermethods.The simulation results of numerical experiments demonstrate the effectiveness of the present method.

Dynamic connectedness and network in the high moments of cryptocurrency,stock,and commodity markets

This study examines the connectedness in high-order moments between cryptocurrency,major stock(U.S.,U.K.,Eurozone,and Japan),and commodity(gold and oil)markets.Using intraday data from 2020 to 2022 and the time and frequency connectedness models of Diebold and Yilmaz(Int J Forecast 28(1):57–66,2012)and Barunik and Křehlik(J Financ Econom 16(2):271–296,2018),we investigate spillovers among the markets in realized volatility,the jump component of realized volatility,realized skewness,and realized kurtosis.These higher-order moments allow us to identify the unique characteristics of financial returns,such as asymmetry and fat tails,thereby capturing various market risks such as downside risk and tail risk.Our results show that the cryptocurrency,stock,and commodity markets are highly connected in terms of volatility and in the jump component of volatility,while their connectedness in skewness and kurtosis is smaller.Moreover,jump and volatility connectedness are more persistent than that of skewness and kurtosis connectedness.Our rolling-window analysis of the connectedness models shows that connectedness varies over time across all moments,and tends to increase during periods of high uncertainty.Finally,we show the potential of gold and oil as hedging and safe-haven investments for other markets given that they are the least connected to other markets across all moments and investment horizons.Our findings provide useful information for designing effective portfolio management and cryptocurrency regulations.

Explaining Pomeranchuk Effect by Parity of Magnetic Moments of Leptons and Hadrons for Superconductivity in 3He and Graphene*

The mystery of superconductivity has intrigued scientists for 110 years now. The author in 2014 specifically predicted the superconductivity in carbon, sulfur and hydrogen compounds and generally predicted carbonaceous, hydrogeneous and sulfurous compounds in 2005 with reference to scattering to asymmetric orbital motions and associated spin and orbital exchanges between nuclei and electrons. The emphasis was in 2005 upon stronger electron and nuclear interactions and electron-phonon effects. But here the author develops more the un-gerade parity of the p and f orbitals and their contributions to the superconductivity at lower pressures and higher temperatures. On the bases of such, the role of parity from the origin and inflation of the Universe is noted and dark and bright energies and matters in the mature Universe are reasoned. Moreover, the superconductors are all reasoned by positive and negative nuclear magnetic moments (NMMs) with availability of un-gerade parities of p and f subshells and their orbitals. In addition to superconductivity, such positive and negative NMMs by Little Effect is presented for explaining Pomeranchuk Effect and thereby further explaining superconductivity and superfluidity of 3He. On the bases of successes of Little Effect via positive and negative NMMs, in particular negative NMMs of 3He, the superconductivity in twisted graphene is explained and also its recently discovered Pomeranchuk Effect.

Moments of Inertia, Magnetic Dipole Moments, and Electric Quadrupole Moments of the Lithium Isotopes

The single-particle Schrödinger fluid model is designed mainly to calculate the moments of inertia of the axially symmetric deformed nuclei by assuming that each nucleon in the nucleus is moving in a single-particle potential which is deformed with time t, through its parametric dependence on a classical shape variable α(t). Also, the Nilsson model is designed for the calculations of the single-particle energy levels, the magnetic dipole moments, and the electric quadrupole moments of axially symmetric deformed nuclei by assuming that all the nucleons are moving in the field of an anisotropic oscillator potential. On the other hand, the nuclear superfluidity model is designed for the calculations of the nuclear moments of inertia and the electric quadrupole moments of deformed nuclei which have no axes of symmetry by assuming that the nucleons are moving in a quadruple deformed potential. Furthermore, the cranked Nilsson model is designed for the calculations of the total nuclear energy and the quadrupole moments of deformed nuclei which have no axes of symmetry by modifying the Nilsson potential to include second and fourth order oscillations. Accordingly, to investigate whether the six p-shell isotopes 6Li, 7Li, 8Li, 9Li, 10Li, and 11Li have axes of symmetry or not, we applied the four mentioned models to each nucleus by calculating their moments of inertia, their magnetic dipole moments, and their electric quadrupole moments by varying the deformation parameter β and the non-axiality parameter γ in wide ranges of values for this reason. Hence for the assumption that these isotopes are deformed and have axes of symmetry, we applied the single-particle Schrödinger fluid model and the Nilsson model. On the other hand, for the assumption that these isotopes are deformed and have no axes of symmetry, we applied the cranked Nilsson model and the nuclear super fluidity model. As a result of our calculations, we can conclude that the nucleus 6Li may be assumed to be deformed and has an axis of symmetry.

基于LQ-moments的洪水频率分布参数计算方法研究

为改善频率曲线高尾部对实测洪水大值段的拟合效果,提高大重现期洪水设计值精度,研究LQmoments(LQM)法在洪水频率分布参数估计中的应用。LQM法是L-moments(LM)法的扩展方法,具有较好的不偏性和稳健性。以6个年最大洪峰流量系列为例,进行P-Ⅲ分布和GEV分布LQM法的参数估计,以累积相对偏差平方和(δ)、RMSE和平均绝对误差(MAE)为标准,评价和比较LQM法和LM法对P-Ⅲ和GEV分布参数的估计精度和拟合效果。结果表明,P-Ⅲ分布LQM法取得了很好的拟合效果,6个洪峰流量系列中,5个系列的最优参数估计方法为LQM法,其中3个系列的最优分布为P-Ⅲ分布;与LM法相比,LQM法能更好地拟合洪水序列大值部分,提高大重现期设计值估计精度,是洪水频率分布参数估计的有效方法。

High-speed train cooperativecontrol based on fractional-ordersliding mode adaptive algorithm

Purpose–This study aims to propose an adaptive fractional-order sliding mode controller to solve the problem of train speed tracking control and position interval control under disturbance environment in moving block system,so as to improve the tracking efficiency and collision avoidance performance.Design/methodology/approach–The mathematical model of information interaction between trains is established based on algebraic graph theory,so that the train can obtain the state information of adjacent trains,and then realize the distributed cooperative control of each train.In the controller design,the sliding mode control and fractional calculus are combined to avoid the discontinuous switching phenomenon,so as to suppress the chattering of sliding mode control,and a parameter adaptive law is constructed to approximate the time-varying operating resistance coefficient.Findings–The simulation results show that compared with proportional integral derivative(PID)control and ordinary sliding mode control,the control accuracy of the proposed algorithm in terms of speed is,respectively,improved by 25%and 75%.The error frequency and fluctuation range of the proposed algorithm are reduced in the position error control,the error value tends to 0,and the operation trend tends to be consistent.Therefore,the control method can improve the control accuracy of the system and prove that it has strong immunity.Originality/value–The algorithm can reduce the influence of external interference in the actual operating environment,realize efficient and stable tracking of trains,and ensure the safety of train control.

Circuit implementation of a new hyperchaos in fractional-order system

This paper introduces a new four-dimensional （4D） hyperchaotic system, which has only two quadratic nonlinearity parameters but with a complex topological structure. Some complicated dynamical properties are then investigated in detail by using bifurcations, Poincare mapping, LE spectra. Furthermore, a simple fourth-order electronic circuit is designed for hardware implementation of the 4D hyperchaotic attractors. In particular, a remarkable fractional-order circuit diagram is designed for physically verifying the hyperchaotic attractors existing not only in the integer-order system but also in the fractional-order system with an order as low as 3.6.

Chaotic dynamics of the fractional-order Ikeda delay system and its synchronization

In this paper we numerically investigate the chaotic behaviours of the fractional-order Ikeda delay system. The results show that chaos exists in the fractional-order Ikeda delay system with order less than 1. The lowest order for chaos to be a, ble to appear in this system is found to be 0.1. Master-slave synchronization of chaotic fractional-order Ikeda delay systems with linear coupling is also studied.