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.

High-order targeted essentially non-oscillatory scheme for two-fluid plasma model

The weakly ionized plasma flows in aerospace are commonly simulated by the single-fluid model,which cannot describe certain nonequilibrium phenomena by finite collisions of particles,decreasing the fidelity of the solution.Based on an alternative formulation of the targeted essentially non-oscillatory(TENO)scheme,a novel high-order numerical scheme is proposed to simulate the two-fluid plasmas problems.The numerical flux is constructed by the TENO interpolation of the solution and its derivatives,instead of being reconstructed from the physical flux.The present scheme is used to solve the two sets of Euler equations coupled with Maxwell's equations.The numerical methods are verified by several classical plasma problems.The results show that compared with the original TENO scheme,the present scheme can suppress the non-physical oscillations and reduce the numerical dissipation.

Calibration of quantitative rescattering model for simulating vortex high-order harmonic generation driven by Laguerre–Gaussian beam with nonzero orbital angular momentum

We calibrate the macroscopic vortex high-order harmonic generation(HHG)obtained by the quantitative rescattering(QRS)model to compute single-atom induced dipoles against that by solving the time-dependent Schr?dinger equation(TDSE).We show that the QRS perfectly agrees with the TDSE under the favorable phase-matching condition,and the QRS can accurately predict the main features in the spatial profiles of vortex HHG if the phase-matching condition is not good.We uncover that harmonic emissions from short and long trajectories are adjusted by the phase-matching condition through the time-frequency analysis and the QRS can simulate the vortex HHG accurately only when the interference between two trajectories is absent.This work confirms that it is an efficient way to employ the QRS model in the single-atom response for precisely simulating the macroscopic vortex HHG.

Dynamic Spatio-Temporal Modeling in Disease Mapping

Spatio-temporal models are valuable tools for disease mapping and understanding the geographical distribution of diseases and temporal dynamics. Spatio-temporal models have been proven empirically to be very complex and this complexity has led many to oversimply and model the spatial and temporal dependencies independently. Unlike common practice, this study formulated a new spatio-temporal model in a Bayesian hierarchical framework that accounts for spatial and temporal dependencies jointly. The spatial and temporal dependencies were dynamically modelled via the matern exponential covariance function. The temporal aspect was captured by the parameters of the exponential with a first-order autoregressive structure. Inferences about the parameters were obtained via Markov Chain Monte Carlo (MCMC) techniques and the spatio-temporal maps were obtained by mapping stable posterior means from the specific location and time from the best model that includes the significant risk factors. The model formulated was fitted to both simulation data and Kenya meningitis incidence data from 2013 to 2019 along with two covariates;Gross County Product (GCP) and average rainfall. The study found that both average rainfall and GCP had a significant positive association with meningitis occurrence. Also, regarding geographical distribution, the spatio-temporal maps showed that meningitis is not evenly distributed across the country as some counties reported a high number of cases compared with other counties.

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.

Numerical modeling of wave equation by a truncated high-order finite-difference method

Finite-difference methods with high-order accuracy have been utilized to improve the precision of numerical solution for partial differential equations. However, the computation cost generally increases linearly with increased order of accuracy. Upon examination of the finite-difference formulas for the first-order and second-order derivatives, and the staggered finite-difference formulas for the first-order derivative, we examine the variation of finite-difference coefficients with accuracy order and note that there exist some very small coefficients. With the order increasing, the number of these small coefficients increases, however, the values decrease sharply. An error analysis demonstrates that omitting these small coefficients not only maintain approximately the same level of accuracy of finite difference but also reduce computational cost significantly. Moreover, it is easier to truncate for the high-order finite-difference formulas than for the pseudospectral for- mulas. Thus this study proposes a truncated high-order finite-difference method, and then demonstrates the efficiency and applicability of the method with some numerical examples.

A High-Order Conservative Semi-Lagrangian Solver for 3D Free Surface Flows with Sediment Transport on Voronoi Meshes

In this paper,we present a conservative semi-Lagrangian scheme designed for the numeri-cal solution of 3D hydrostatic free surface flows involving sediment transport on unstruc-tured Voronoi meshes.A high-order reconstruction procedure is employed for obtaining a piecewise polynomial representation of the velocity field and sediment concentration within each control volume.This is subsequently exploited for the numerical integration of the Lagrangian trajectories needed for the discretization of the nonlinear convective and viscous terms.The presented method is fully conservative by construction,since the transported quantity or the vector field is integrated for each cell over the deformed vol-ume obtained at the foot of the characteristics that arises from all the vertexes defining the computational element.The semi-Lagrangian approach allows the numerical scheme to be unconditionally stable for what concerns the advection part of the governing equations.Furthermore,a semi-implicit discretization permits to relax the time step restriction due to the acoustic impedance,hence yielding a stability condition which depends only on the explicit discretization of the viscous terms.A decoupled approach is then employed for the hydrostatic fluid solver and the transport of suspended sediment,which is assumed to be passive.The accuracy and the robustness of the resulting conservative semi-Lagrangian scheme are assessed through a suite of test cases and compared against the analytical solu-tion whenever is known.The new numerical scheme can reach up to fourth order of accu-racy on general orthogonal meshes composed by Voronoi polygons.

Constructing a raster-based spatio-temporal hierarchical data model for marine fisheries application

Marine information has been increasing quickly. The traditional database technologies have disadvantages in manipulating large amounts of marine information which relates to the position in 3-D with the time. Recently, greater emphasis has been placed on GIS （geographical information system）to deal with the marine information. The GIS has shown great success for terrestrial applications in the last decades, but its use in marine fields has been far more restricted. One of the main reasons is that most of the GIS systems or their data models are designed for land applications. They cannot do well with the nature of the marine environment and for the marine information. And this becomes a fundamental challenge to the traditional GIS and its data structure. This work designed a data model, the raster-based spatio-temporal hierarchical data model （RSHDM）, for the marine information system, or for the knowledge discovery fi＇om spatio-temporal data, which bases itself on the nature of the marine data and overcomes the shortages of the current spatio-temporal models when they are used in the field. As an experiment, the marine fishery data warehouse （FDW） for marine fishery management was set up, which was based on the RSHDM. The experiment proved that the RSHDM can do well with the data and can extract easily the aggregations that the management needs at different levels.

Multi-factor high-order intuitionistic fuzzy timeseries forecasting model

Fuzzy sets theory cannot describe the neutrality degreeof data, which has largely limited the objectivity of fuzzy time seriesin uncertain data forecasting. With this regard, a multi-factor highorderintuitionistic fuzzy time series forecasting model is built. Inthe new model, a fuzzy clustering algorithm is used to get unequalintervals, and a more objective technique for ascertaining membershipand non-membership functions of the intuitionistic fuzzy setis proposed. On these bases, forecast rules based on multidimensionalintuitionistic fuzzy modus ponens inference are established.Finally, contrast experiments on the daily mean temperature ofBeijing are carried out, which show that the novel model has aclear advantage of improving the forecast accuracy.

Spatio-temporal Changes and Associated Uncertainties of CENTURYmodelled SOC for Chinese Upland Soils, 1980-2010

Detailed information on the spatio-temporal changes of cropland soil organic carbon(SOC) can significantly contribute to the improvement of soil fertility and mitigate climate change. Nonetheless, information and knowledge on the national scale spatio-temporal changes and the corresponding uncertainties of SOC in Chinese upland soils remain limited. The CENTURY model was used to estimate the SOC storages and their changes in Chinese uplands from 1980 to 2010. With the Monte Carlo method, the uncertainties of CENTURY-modelled SOC dynamics associated with the spatial heterogeneous model inputs were quantified. Results revealed that the SOC storage in Chinese uplands increased from 3.03(1.59 to 4.78) Pg C in 1980 to 3.40(2.39 to 4.62) Pg C in 2010. Increment of SOC storage during this period was 370 Tg C, with an uncertainty interval of –440 to 1110 Tg C. The regional disparities of SOC changes reached a significant level, with considerable SOC accumulation in the Huang-Huai-Hai Plain of China and SOC loss in the northeastern China. The SOC lost from Meadow soils, Black soils and Chernozems was most severe, whilst SOC accumulation in Fluvo-aquic soils, Cinnamon soils and Purplish soils was most significant. In modelling large-scale SOC dynamics, the initial soil properties were major sources of uncertainty. Hence, more detailed information concerning the soil properties must be collected. The SOC stock of Chinese uplands in 2010 was still relatively low, manifesting that recommended agricultural management practices in conjunction with effectively economic and policy incentives to farmers for soil fertility improvement were indispensable for future carbon sequestration in these regions.

Spatio-temporal model for soil characteristic of reclamation land

The development of spatio-temporal data model is introduced. According to the soil characteristic of reclamation land, we adopt the base state with amendments model of multi-layer raster to organize the spatio-temporal data, using the combined data structure on linear quadtree and linear octree to code. The advantage of this model is that it can easily obtain the information of certain layer and integratedly analyze the data with other methods. Then, the methods of obtain and analyses are introduced. The method can provide a tool for the research of the soil characteristic change and spatial distribution in reclamation land.

Spatio-Temporal Dynamics and Structure Preserving Algorithm for Computer Virus Model

The present work is related to the numerical investigation of the spatio-temporal susceptible-latent-breaking out-recovered(SLBR)epidemic model.It describes the computer virus dynamics with vertical transmission via the internet.In these types of dynamics models,the absolute values of the state variables are the fundamental requirement that must be fulfilled by the numerical design.By taking into account this key property,the positivity preserving algorithm is designed to solve the underlying SLBR system.Since,the state variables associated with the phenomenon,represent the computer nodes,so they must take in absolute.Moreover,the continuous system(SLBR)acquires two steady states i.e.,the virus-free state and the virus existence state.The stability of the numerical design,at the equilibrium points,portrays an exceptional aspect about the propagation of the virus.The designed discretization algorithm sustains the stability of both the steady states.The computer simulations also endorse that the proposed discretization algorithm retains all the traits of the continuous SLBR model with spatial content.The stability and consistency of the proposed algorithm are verified,mathematically.All the facts are also ascertained by numerical simulations.

Grain Yield Prediction of Henan Province Based on Spatio-temporal Regression Model

By using correlation analysis method,regression analysis method and time sequence method,we combine time and space,to establish grain yield spatio-temporal regression prediction model of Henan Province and all prefecture-level cities.At first,we use the grain yield in prefecture-level cities of Henan in the year 2000 and 2005,to establish regression model,and then taking the grain yield in one year as independent variable,we predict the grain yield in the fifth year afterwards.Taking the dependent variable value as independent variable again,we predict the grain yield at an interval of the same years,and based on this,predict year by year forward until the year we need.The research shows that the grain yield of Henan Province in the year 2015 and 2020 is 59.849 6 and 67.929 3 million t respectively,consistent with the research results of other scholars to some extent.

Spatio-temporal epidemic type aftershock sequence model for Tangshan aftershock sequence

Shallow earthquakes usually show obvious spatio-temporal clustering patterns. In this study, several spatio-temporal point process models are applied to investigate the clustering characteristics of the well-known Tangshan sequence based on classical empirical laws and a few assumptions. The relative fit of competing models is compared by Akalke Information Criterion. The spatial clustering pattern is well characterized by the model which gives the best fit to the data. A simulated aftershock sequence is generated by thinning algorithm and compared with the real seismicity.

A High-Order Conservative Numerical Method for Gross-Pitaevskii Equation with Time-Varying Coefficients in Modeling BEC

We propose a high-order conservative method for the nonlinear Sehodinger/Gross-Pitaevskii equation with time- varying coefficients in modeling Bose Einstein condensation （BEC）. This scheme combined with the sixth-order compact finite difference method and the fourth-order average vector field method, finely describes the condensate wave function and physical characteristics in some small potential wells. Numerical experiments are presented to demonstrate that our numerical scheme is efficient by the comparison with the Fourier pseudo-spectral method. Moreover, it preserves several conservation laws well and even exactly under some specific conditions.

EEG Source Localization Using Spatio-Temporal Neural Network

Source localization of focal electrical activity from scalp electroencephalogram (sEEG) signal is generally modeled as an inverse problem that is highly ill-posed. In this paper, a novel source localization method is proposed to model the EEG inverse problem using spatio-temporal long-short term memory recurrent neural networks (LSTM). The network model consists of two parts, sEEG encoding and source decoding, to model the sEEG signal and receive the regression of source location. As there does not exist enough annotated sEEG signals correspond to specific source locations, simulated data is generated with forward model using finite element method (FEM) to act as a part of training signals. A framework for source localization is proposed to estimate the source position based on simulated training data. Experiments are done on simulated testing data. The results on simulated data exhibit good robustness on noise signal, and the proposed network solves the EEG inverse problem with spatio-temporal deep network. The result show that the proposed method overcomes the highly ill-posed linear inverse problem with data driven learning.

A high-order splitting scheme for the advection diffusion equation

A high-order splitting scheme for the advection-diffusion equation of pollutants is proposed in this paper. The multidimensional advection-diffusion equation is splitted into several one-dimensional equations that are solved by the scheme. Only three spatial grid points are needed in each direction and the scheme has fourth-order spatial accuracy. Several typically pure advection and advection-diffusion problems are simulated. Numerical results show that the accuracy of the scheme is much higher than that of the classical schemes and the scheme can he efficiently solved with little programming effort.

A corrected particle method with high-order Taylor expansion for solving the viscoelastic fluid flow

In this paper, a corrected particle method based on the smoothed particle hydrodynamics (SPH) method with high-order Taylor expansion (CSPH-HT) for solving the viscoelastic flow is proposed and investigated. The validity and merits of the CSPH-HT method are first tested by solving the nonlinear high order Kuramoto-Sivishinsky equation and simulating the drop stretching, respectively. Then the flow behaviors behind two stationary tangential cylinders of polymer melt, which have been received little attention, are investigated by the CSPH-HT method. Finally, the CSPH-HT method is extended to the simulation of the filling process of the viscoelastic fluid. The numerical results show that the CSPH-HT method possesses higher accuracy and stability than other corrected SPH methods and is more reliable than other corrected SPH methods.

A force control high-order single-step-β method (HSM) for substructure pseudo-dynamic testing

This paper proposes a new technique which introduces the high-order single-step-β method(HSM)into the experimental study on the substructure pseudo-dynamic testing(SPDT).The technique is based on the proposed concept of equivalent shear stiffness which can meet the requirement of the HSM algorithm.A study is done to theoretically validate the technique by the numerical analysis of two-storey shear building structure,in comparison of the proposed substructure pseudo-dynamic testing algorithm with the central difference method(CDM).Then,a full-scale SPDT model,the three-storey frame-supported reinforced concrete short-limb masonry shear wall structure,is designed and tested to simulate the seismic response of the corresponding six-storey structure and verify the proposed force control HSM technique.Meanwhile,the techniques of both stiffness correction and force control are suggested to control algorithmic error,control error and measurement error.The results indicate that the force control HSM can be used in the full-scale multi-degree-of-freedom(MDOF)substructure pseudo-dynamic testing before descent segment of structure restoring force properties.

Control of high-order harmonic generation with two-colour laser field

We numerically investigate the high-order harmonic generation with two-colour optical field, taking into consideration the propagation effects. Some harmonics can be dramatically enhanced at a certain delay between the fundamental pulse and its second harmonics. Choice of the enhanced harmonics can be realised by changing the time delay between the two laser pulses.