Observer-based robust high-order fully actuated attitude autopilot design for spinning glide-guided projectiles

This paper investigates the design of an attitude autopilot for a dual-channel controlled spinning glideguided projectile(SGGP),addressing model uncertainties and external disturbances.Based on fixed-time stable theory,a disturbance observer with integral sliding mode and adaptive techniques is proposed to mitigate total disturbance effects,irrespective of initial conditions.By introducing an error integral signal,the dynamics of the SGGP are transformed into two separate second-order fully actuated systems.Subsequently,employing the high-order fully actuated approach and a parametric approach,the nonlinear dynamics of the SGGP are recast into a constant linear closed-loop system,ensuring that the projectile's attitude asymptotically tracks the given goal with the desired eigenstructure.Under the proposed composite control framework,the ultimately uniformly bounded stability of the closed-loop system is rigorously demonstrated via the Lyapunov method.Validation of the effectiveness of the proposed attitude autopilot design is provided through extensive numerical simulations.

Tunable spectral continuous shift of high-order harmonic generation in atoms by a plasmon-assisted shaping pulse

We delve into the phenomenon of high-order harmonic generation within a helium atom under the influence of a plasmon-assisted shaping pulse.Our findings reveal an intriguing manipulation of the frequency peak position in the harmonic emission by adjusting the absolute phase parameter within the frequency domain of the shaping pulse.This phenomenon holds potential significance for experimental setups necessitating precisely tuned single harmonics.Notably,we observe a modulated shift in the created harmonic photon energy,spanning an impressive range of 1.2 eV.This frequency peak shift is rooted in the asymmetry exhibited by the rising and falling edges of the laser pulse,directly influencing the position of the peak frequency emission.Our study quantifies the dependence of this tuning range and the asymmetry of the laser pulse,offering valuable insights into the underlying mechanisms driving this phenomenon.Furthermore,our investigation uncovers the emergence of semi-integer order harmonics as the phase parameter is altered.We attribute this discovery to the intricate interference between harmonics generated by the primary and secondary return cores.This observation introduces an innovative approach for generating semi-integer order harmonics,thus expanding our understanding of high-order harmonic generation.Ultimately,our work contributes to the broader comprehension of complex phenomena in laser-matter interactions and provides a foundation for harnessing these effects in various applications,particularly those involving precise spectral control and the generation of unique harmonic patterns.

A global model of intensity autocorrelation to determine laser pulse duration

We present a new global model of collinear autocorrelation based on second harmonic generation nonlinearity.The model is rigorously derived from the nonlinear coupled wave equation specific to the autocorrelation measurement configuration,without requiring a specific form of the incident pulse function.A rigorous solution of the nonlinear coupled wave equation is obtained in the time domain and expressed in a general analytical form.The global model fully accounts for the nonlinear interaction and propagation effects within nonlinear crystals,which are not captured by the classical local model.To assess the performance of the global model compared to the classic local model,we investigate the autocorrelation signals obtained from both models for different incident pulse waveforms and different full-widthes at half-maximum(FWHMs).When the incident pulse waveform is Lorentzian with an FWHM of 200 fs,the global model predicts an autocorrelation signal FWHM of 399.9 fs,while the classic local model predicts an FWHM of 331.4 fs.The difference between the two models is 68.6 fs,corresponding to an error of 17.2%.Similarly,for a sech-type incident pulse with an FWHM of 200 fs,the global model predicts an autocorrelation signal FWHM of 343.9 fs,while the local model predicts an FWHM of 308.8 fs.The difference between the two models is 35.1 fs,with an error of 10.2%.We further examine the behavior of the models for Lorentzian pulses with FWHMs of 100 fs,200 fs and 500 fs.The differences between the global and local models are 17.1 fs,68.6 fs and 86.0 fs,respectively,with errors approximately around 17%.These comparative analyses clearly demonstrate the superior accuracy of the global model in intensity autocorrelation modeling.

Electron correlation in two-electron atoms:A Bohmian analysis of high-order harmonic generation in high-frequency domain

In studying interactions between intense laser fields and atoms or molecules,the role of electron correlation effects on the dynamical response is an important and pressing issue to address.Utilizing Bohmian mechanics(BM),we have theoretically explored the two-electron correlation characteristics while generating high-order harmonics in xenon atoms subjected to intense laser fields.We initially employed Bohmian trajectories to reproduce the dynamics of the electrons and subsequently utilized time-frequency analysis spectra to ascertain the emission time windows for high-order harmonics.Within these time windows,we classified the nuclear region Bohmian trajectories and observed that intense high-order harmonics are solely generated when paired Bohmian particles(BPs)concurrently appear in the nuclear region and reside there for a duration within a re-collision time window.Furthermore,our analysis of characteristic trajectories producing high-order harmonics led us to propose a two-electron re-collision model to elucidate this phenomenon.The study demonstrates that intense high-order harmonics are only generated when both electrons are in the ground state within the re-collision time window.This work discusses the implications of correlation effects between two electrons and offers valuable insights for studying correlation in multi-electron high-order harmonic generation.

A Probing Model of Secret Key Generation Based on Channel Autocorrelation Function

Secret key generation(SKG)is a promising solution to the problem of wireless communications security.As the first step of SKG,channel probing affects it significantly.Although there have been some probing schemes,there is a lack of research on the optimization of the probing process.This study investigates how to optimize correlated parameters to maximize the SKG rate(SKGR)in the time-division duplex(TDD)mode.First,we build a probing model which includes the effects of transmitting power,the probing period,and the dimension of sample vectors.Based on the model,the analytical expression of the SKGR is given.Next,we formulate an optimization problem for maximizing the SKGR and give an algorithm to solve it.We conclude the SKGR monotonically increases as the transmitting power increases.Relevant mathematical proofs are given in this study.From the simulation results,increasing appropriately the probing period and the dimension of the sample vector could increase the SKGR dramatically compared to a yardstick,which indicates the importance of optimizing the parameters related to the channel probing phase.

Elliptically polarized high-order harmonic generation of Ar atom in an intense laser field

High-order harmonic generation(HHG) of Ar atom in an elliptically polarized intense laser field is experimentally investigated in this work.Interestingly,the anomalous ellipticity dependence on the laser ellipticity(ε) in the lower-order harmonics is observed,specifically in the 13rd-order,which displays a maximal harmonic intensity at ε ≈ 0.1,rather than at ε = 0 as expected.This contradicts the general trend of harmonic yield,which typically decreases with the increase of laser ellipticity.In this study,we attribute this phenomenon to the disruption of the symmetry of the wave function by the Coulomb effect,leading to the generation of a harmonic with high ellipticity.This finding provides valuable insights into the behavior of elliptically polarized harmonics and opens up a potential way for exploring new applications in ultrafast spectroscopy and light–matter interactions.

High-order Bragg forward scattering and frequency shift of low-frequency underwater acoustic field by moving rough sea surface

Acoustic scattering modulation caused by an undulating sea surface on the space-time dimension seriously affects underwater detection and target recognition.Herein,underwater acoustic scattering modulation from a moving rough sea surface is studied based on integral equation and parabolic equation.And with the principles of grating and constructive interference,the mechanism of this acoustic scattering modulation is explained.The periodicity of the interference of moving rough sea surface will lead to the interference of the scattering field at a series of discrete angles,which will form comb-like and frequency-shift characteristics on the intensity and the frequency spectrum of the acoustic scattering field,respectively,which is a high-order Bragg scattering phenomenon.Unlike the conventional Doppler effect,the frequency shifts of the Bragg scattering phenomenon are multiples of the undulating sea surface frequency and are independent of the incident sound wave frequency.Therefore,even if a low-frequency underwater acoustic field is incident,it will produce obvious frequency shifts.Moreover,under the action of ideal sinusoidal waves,swells,fully grown wind waves,unsteady wind waves,or mixed waves,different moving rough sea surfaces create different acoustic scattering processes and possess different frequency shift characteristics.For the swell wave,which tends to be a single harmonic wave,the moving rough sea surface produces more obvious high-order scattering and frequency shifts.The same phenomena are observed on the sea surface under fully grown wind waves,however,the frequency shift slightly offsets the multiple peak frequencies of the wind wave spectrum.Comparing with the swell and fully-grown wind waves,the acoustic scattering and frequency shift are not obvious for the sea surface under unsteady wind waves.

High-order harmonic generation of ZnO crystals in chirped and static electric fields

High harmonic generation in ZnO crystals under chirped single-color field and static electric field are investigated by solving the semiconductor Bloch equation(SBE). It is found that when the chirp pulse is introduced, the interference structure becomes obvious while the harmonic cutoff is not extended. Furthermore, the harmonic efficiency is improved when the static electric field is included. These phenomena are demonstrated by the classical recollision model in real space affected by the waveform of laser field and inversion symmetry. Specifically, the electron motion in k-space shows that the change of waveform and the destruction of the symmetry of the laser field lead to the incomplete X-structure of the crystal-momentum-resolved(k-resolved) inter-band harmonic spectrum. Furthermore, a pre-acceleration process in the solid four-step model is confirmed.

Arbitrary High-Order Fully-Decoupled Numerical Schemes for Phase-Field Models of Two-Phase Incompressible Flows

Due to the coupling between the hydrodynamic equation and the phase-field equation in two-phase incompressible flows,it is desirable to develop efficient and high-order accurate numerical schemes that can decouple these two equations.One popular and efficient strategy is to add an explicit stabilizing term to the convective velocity in the phase-field equation to decouple them.The resulting schemes are only first-order accurate in time,and it seems extremely difficult to generalize the idea of stabilization to the second-order or higher version.In this paper,we employ the spectral deferred correction method to improve the temporal accuracy,based on the first-order decoupled and energy-stable scheme constructed by the stabilization idea.The novelty lies in how the decoupling and linear implicit properties are maintained to improve the efficiency.Within the framework of the spatially discretized local discontinuous Galerkin method,the resulting numerical schemes are fully decoupled,efficient,and high-order accurate in both time and space.Numerical experiments are performed to validate the high-order accuracy and efficiency of the methods for solving phase-field models of two-phase incompressible flows.

High-Order Soliton Solutions and Hybrid Behavior for the (2 + 1)-Dimensional Konopelchenko-Dubrovsky Equations

In this paper, the evolutionary behavior of N-solitons for a (2 + 1)-dimensional Konopelchenko-Dubrovsky equations is studied by using the Hirota bilinear method and the long wave limit method. Based on the N-soliton solution, we first study the evolution from N-soliton to T-order (T=1,2) breather wave solutions via the paired-complexification of parameters, and then we get the N-order rational solutions, M-order (M=1,2) lump solutions, and the hybrid behavior between a variety of different types of solitons combined with the parameter limit technique and the paired-complexification of parameters. Meanwhile, we also provide a large number of three-dimensional figures in order to better show the degeneration of the N-soliton and the interaction behavior between different N-solitons.

Generation of tunable high-order Laguerre– Gaussian petal-like modes from a mid-infrared optical vortex parametric oscillator

High-order Laguerre–Gaussian(LG)petal-like beams have become a topic of significant interest due to their potential application in next-generation optical trapping,quantum optics,and materials processing technologies.In this work,we demonstrate the generation of high-order LG beams with petal-like spatial profiles and tunable orbital angular momentum(OAM)in the mid-infrared wavelength region.These beams are generated using idler-resonant optical parametric oscillation(OPO)in a KTiOAsO_(4)(KTA)crystal.By adjusting the length of the resonant cavity,the OAM of the mid-infrared idler field can be tuned and we demonstrate tuning in the range of 0 to10.When using a maximum pump energy of 20.2 mJ,the maximum output energy of high-order modes LG_(0.45),LG_(0.48),and LG_(0.410) were 0.8,0.53,and 0.46 mJ,respectively.The means by which high-order LG modes with petal-like spatial profiles and tunable OAM were generated from the OPO is theoretically modeled by examining the spatial overlap efficiency of the beam waists of the pump and resonant idler fields within the center of the KTA crystal.The methodology presented in this work offers a simple and flexible method to wavelength-convert laser emission and generate high-order LG modes.

Measurement of spatiotemporal characteristics of femtosecond laser pulses by a modified single-shot autocorrelation

To overcome the shortcomings of the single-shot autocorrelation SSA where only one pulse width is obtained when the SSA is applied to measure the pulse width of ultrashort laser pulses a modified SSA for measuring the spatiotemporal characteristics of ultrashort laser pulses at different spatial positions is proposed. The spatiotemporal characteristics of femtosecond laser pulses output from the Ti sapphire regenerative amplifier system are experimentally measured by the proposed method. It was found that the complex spatial characteristics are measured accurately.The pulse widths at different spatial positions are various which obey the Gaussian distribution.The pulse width at the same spatial position becomes narrow with the increase in input average power when femtosecond laser pulses pass through a carbon disulfide CS2 nonlinear medium.The experimental results verify that the proposed method is valid for measuring the spatiotemporal characteristics of ultrashort laser pulses at different spatial positions.

HIGH-ORDER RUNGE-KUTTA DISCONTINUOUS GALERKIN FINITE ELEMENT METHOD FOR 2-D RESONATOR PROBLEM

The Runge-Kutta discontinuous Galerkin finite element method （RK-DGFEM） is introduced to solve the classical resonator problem in the time domain. DGFEM uses unstructured grid discretization in the space domain and it is explicit in the time domain. Consequently it is a best mixture of FEM and finite volume method （FVM）. RK-DGFEM can obtain local high-order accuracy by using high-order polynomial basis. Numerical experiments of transverse magnetic （TM） wave propagation in a 2-D resonator are performed. A high-order Lagrange polynomial basis is adopted. Numerical results agree well with analytical solution. And different order Lagrange interpolation polynomial basis impacts on simulation result accuracy are discussed. Computational results indicate that the accuracy is evidently improved when the order of interpolation basis is increased. Finally, L^2 errors of different order polynomial basis in RK-DGFEM are presented. Computational results show that L^2 error declines exponentially as the order of basis increases.

A truncated implicit high-order finite-difference scheme combined with boundary conditions

In this paper, first we calculate finite-difference coefficients of implicit finite- difference methods （IFDM） for the first and second-order derivatives on normal grids and first- order derivatives on staggered grids and find that small coefficients of high-order IFDMs exist. Dispersion analysis demonstrates that omitting these small coefficients can retain approximately the same order accuracy but greatly reduce computational costs. Then, we introduce a mirrorimage symmetric boundary condition to improve IFDMs accuracy and stability and adopt the hybrid absorbing boundary condition （ABC） to reduce unwanted reflections from the model boundary. Last, we give elastic wave modeling examples for homogeneous and heterogeneous models to demonstrate the advantages of the proposed scheme.

Design of a spatial sampling scheme considering the spatial autocorrelation of crop acreage included in the sampling units

Information on crop acreage is important for formulating national food polices and economic planning. Spatial sampling, a combination of traditional sampling methods and remote sensing and geographic information system （GIS） technology, provides an efficient way to estimate crop acreage at the regional scale. Traditional sampling methods require that the sampling units should be independent of each other, but in practice there is often spatial autocorrelation among crop acreage contained in the sampling units. In this study, using Dehui County in Jilin Province, China, as the study area, we used a thematic crop map derived from Systeme Probatoire d＇Observation de la Terre （SPOT-5） imagery, cultivated land plots and digital elevation model data to explore the spatial autocorrelation characteristics among maize and rice acreage included in sampling units of different sizes, and analyzed the effects of different stratification criteria on the level of spatial autocorrelation of the two crop acreages within the sampling units. Moran＇s/, a global spatial autocorrelation index, was used to evaluate the spatial autocorrelation among the two crop acreages in this study. The results showed that although the spatial autocorrelation level among maize and rice acreages within the sampling units generally decreased with increasing sampling unit size, there was still a significant spatial autocorrelation among the two crop acreages included in the sampling units （Moran＇s / varied from 0.49 to 0.89）, irrespective of the sampling unit size. When the sampling unit size was less than 3000 m, the stratification design that used crop planting intensity （CPI） as the stratification criterion, with a stratum number of 5 and a stratum interval of 20% decreased the spatial autocorrelation level to almost zero for the maize and rice area included in sampling units within each stratum. Therefore, the traditional sampling methods can be used to estimate the two crop acreages. Compared with CPI, there was still a strong spatial correlation among the two crop acreages included in the sampling units belonging to each stratum when cultivated land fragmentation and ground slope were used as stratification criterion. As far as the selection of stratification criteria and sampling unit size is concerned, this study provides a basis for formulating a reasonable spatial sampling scheme to estimate crop acreage.

LPI radar signal detection based on the combination of FFT and segmented autocorrelation plus PAHT

This paper proposes a desirable method to detect different kinds of low probability of intercept (LPI) radar signals, targeted at the main intra-pulse modulation method of LPI radar signals including the signals of linear frequency modulation, phase code, and frequency code. Firstly, it improves the coherent integration of LPI radar signals by adding the periodicity of the ambiguity function. Then, it develops a frequency domain detection method based on fast Fourier transform (FFT) and segmented autocorrelation function to detect signals without features of linear frequency modulation by virtue of the distribution characteristics of noise signals in the frequency domain. Finally, this paper gives a verification of the performance of the method for different signal-to-noise ratios by conducting simulation experiments, and compares the method with existing ones. Additionally, this method is characterized by the straightforward calculation and high real-time performance, which is conducive to better detecting all kinds of LPI radar signals.

STUDY ON SPATIAL AUTOCORRELATION OF URBAN LAND PRICE DISTRIBUTION IN CHANGZHOU CITY OF JIANGSU PROVINCE

This paper uses a spatial statistics method based on the calculation of spatial autocorrelation as a possible approach for modeling and quantifying the distribution of urban land price in Changzhou City, Jiangsu Province. GIS and spatial statistics provide a useful way for describing the distribution of urban land price both spatially and temporally, and have proved to be useful for understanding land price distribution pattern better. In this paper, we apply the statistical analysis method to 8379 urban land price samples collected from Changzhou Land Market, and it is turned out that the proposed approach can effectively identify the spatial clusters and local point patterns in dataset and forms a general method for conceptualizing the land price structure. The results show that land price structure in Changzhou City is very complex and that even where there is a high spatial autocorrelation, the land price is still relatively heterogeneous. Furthermore, lands for different uses have different degrees of spatial autocorrelation. Spatial autocorrelation of commercial lands is more intense than that of residential and industrial lands in regional central district. This means that treating land price as integration of homogeneous units can limit analysis of pattern, over-simplifying the structure of land price, but the methods, just as the autocorrelation approaches, are useful tools for quantifying the variables of land price.

Vertex degree autocorrelation topological index and its application in QSAR study of organic chemicals

Considering the calculated result and higher degeneracy existing in the calculation of autocorrelation topological index totally depend on experimental parameters, a new group of autocorrelation topological index as A t, B t, C t and D t was designed and developed based on the vertex degree of molecular topology and autocorrelation function of mathematics. Autocorrelation function f(i) was calculated from the square root of the vertex degree, revised vertex degree and their combination, and they are (δ i) 1/2 , (δ V i) 1/2 ,(δ V i+δ i) 1/2  and (δ E i-δ i) 1/2 / N. With the matrix description method achieved, and the unit input in matrix of unsaturated bond and heteroatoms revised based on the adjacency matrix and distance matrix of organic molecular graph, the corresponding computer software has also been designed and developed. Better results have been obtained for the application of these indexes in QSAR study of organic chemicals.

High-order ghost imaging with N-colour thermal light

High-order ghost imaging with thermal light consisting of N different frequencies is investigated. The high-order intensity correlation and intrinsic correlation functions are derived for such N-colour light. It is found that they are similar in form to those for the monochromatic case, thus most of the conclusions we obtained previously for monochromatic Nth-order ghost imaging are still applicable. However, we find that the visibility of the N-colour ghost image depends strongly on the wavelength used to illuminate the object, and increases as this wavelength increases when the test arm is fixed. On the contrary, changes of wavelength in the reference arms do not lead to any change of the visibility.

On iterative learning control design for tracking iteration-varying trajectories with high-order internal model

In this paper, iterative learning control （ILC） design is studied for an iteration-varying tracking problem in which reference trajectories are generated by high-order internal models （HOLM）. An HOlM formulated as a polynomial operator between consecutive iterations describes the changes of desired trajectories in the iteration domain and makes the iterative learning problem become iteration varying. The classical ILC for tracking iteration-invariant reference trajectories, on the other hand, is a special case of HOlM where the polynomial renders to a unity coefficient or a special first-order internal model. By inserting the HOlM into P-type ILC, the tracking performance along the iteration axis is investigated for a class of continuous-time nonlinear systems. Time-weighted norm method is utilized to guarantee validity of proposed algorithm in a sense of data-driven control.