A LOW-REGULARITY FOURIER INTEGRATOR FOR THE DAVEY-STEWARTSON II SYSTEM WITH ALMOST MASS CONSERVATION

In this work,we propose a low-regularity Fourier integrator with almost mass conservation to solve the Davey-StewartsonⅡsystem(hyperbolic-elliptic case).Arbitrary order mass convergence could be achieved by the suitable addition of correction terms,while keeping the first order accuracy in H~γ×H^(γ+1)for initial data in H^(γ+1)×H^(γ+1)withγ>1.The main theorem is that,up to some fixed time T,there exist constantsτ_(0)and C depending only on T and‖u‖_(L^(∞)((0,T);H^(γ+1)))such that,for any 0<τ≤τ_(0),we have that‖u(t_(n),·)-u^(n)‖H_γ≤C_(τ),‖v(t_(n),·)-v^(n)‖_(Hγ+1)≤C_(τ),where u^(n)and v^(n)denote the numerical solutions at t_(n)=nτ.Moreover,the mass of the numerical solution M(u^(n))satisfies that|M(u^(n))-M(u_0)|≤Cτ~5.

PpARF6 acts as an integrator of auxin and ethylene signaling to promote fruit ripening in peach

Although auxin is known to induce ethylene biosynthesis in some Rosaceae fruit crops,the mechanisms underlying the auxin–ethylene interaction during fruit ripening remain largely unknown.Here,the regulatory role of an auxin response factor,PpARF6,in fruit ripening was investigated in peach.Peach fruits showed accelerated ripening after treatment with auxin and PpARF6 was found to be significantly induced.PpARF6 not only could induce ethylene synthesis by directly activating the transcription of ethylene biosynthetic genes,but also competed with EIN3-binding F-box proteins PpEBF1/2 for binding to ethylene-insensitive3-like proteins PpEIL2/3,thereby keeping PpEIL2/3 active.Moreover,PpARF6 showed an interaction with PpEIL2/3 to enhance the PpEIL2/3-activated transcription of ethylene biosynthetic genes.Additionally,ectopic overexpression of PpARF6 in tomato accelerated fruit ripening by promoting the expression of genes involved in ethylene synthesis and fruit texture.In summary,our results revealed a positive regulatory role of PpARF6 in peach fruit ripening via integrating auxin and ethylene signaling.

A Consistent Time Level Implementation Preserving Second-Order Time Accuracy via a Framework of Unified Time Integrators in the Discrete Element Approach

In this work,a consistent and physically accurate implementation of the general framework of unified second-order time accurate integrators via the well-known GSSSS framework in the Discrete Element Method is presented.The improved tangential displacement evaluation in the present implementation of the discrete element method has been derived and implemented to preserve the consistency of the correct time level evaluation during the time integration process in calculating the algorithmic tangential displacement.Several numerical examples have been used to validate the proposed tangential displacement evaluation;this is in contrast to past practices which only seem to attain the first-order time accuracy due to inconsistent time level implementation with different algorithms for normal and tangential directions.The comparisons with the existing implementation and the superiority of the proposed implementation are given in terms of the convergence rate with improved numerical accuracy in time.Moreover,several schemes via the unified second-order time integrators within the framework of the GSSSS family have been carried out based on the proposed correct implementation.All the numerical results demonstrate that using the existing state-of-the-art implementation reduces the time accuracy to be first-order accurate in time,while the proposed implementation preserves the correct time accuracy to yield second-order.

基于Cyber-Integrator语义平台的临床路径工作流管理方法研究

介绍一种基于Cyber-Integrator(CI)语义平台的临床路径(CP)工作流管理方法。阐明国内外语义技术在临床路径应用的成功案例,指出CP语义描述的可行性与不足,深入探讨如何利用CI语义平台来对CP工作流进行管理,包括描述、执行和控制等,说明此方法局限性并提出进一步研究方向。

基于ARM Integrator的Sigma-Delta音频DAC的实现

介绍了ARM公司的一款FPGA验证开发平台ARMIntegrator,以及基于该平台设计的Sigma-Delta音频DAC的实现.在详细介绍Integrator的各个模块的基础之上,利用开发平台的FPGA上验证实现了一个1阶的6位的Sigma-Delta型的DAC,主要包括Sigma-Delta DAC的原理与主要电路,FPGA验证实现过程中的DAC数字滤波器以及调制器的设计以及验证流程,通过virsi m仿真时序波形,验证了所设计的DAC正确性和可实现性.

Global satisfactory control for nonlinear integrator processes with long delay

Integrator processes with long delay are difficult to control. Nonlinear characteristics of actuators make the control problem more challenging. A technique is proposed in this paper for global satisfactory control （GSC） of such processes with relay-type nonlinearity. An oscillatory control signal is injected into the nonlinear process; the amplitude and frequency of the oscillatory signal are designed to linearise the nonlinear process in the sense of harmonic analysis; and a state feedback controller is configured to implement GSC over the linearised process. An illustrative example is given to demonstrate the effectiveness of

Geometric formulations and variational integrators of discrete autonomous Birkhoff systems

The variational integrators of autonomous Birkhoff systems are obtained by the discrete variational principle. The geometric structure of the discrete autonomous Birkhoff system is formulated. The discretization of mathematical pendulum shows that the discrete variational method is as effective as symplectic scheme for the autonomous Birkhoff systems.

Chebyshev spectral variational integrator and applications

The Chebyshev spectral variational integrator(CSVI) is presented in this paper. Spectral methods have aroused great interest in approximating numerically a smooth problem for their attractive geometric convergence rates. The geometric numerical methods are praised for their excellent long-time geometric structure-preserving properties.According to the generalized Galerkin framework, we combine two methods together to construct a variational integrator, which captures the merits of both methods. Since the interpolating points of the variational integrator are chosen as the Chebyshev points,the integration of Lagrangian can be approximated by the Clenshaw-Curtis quadrature rule, and the barycentric Lagrange interpolation is presented to substitute for the classic Lagrange interpolation in the approximation of configuration variables and the corresponding derivatives. The numerical float errors of the first-order spectral differentiation matrix can be alleviated by using a trigonometric identity especially when the number of Chebyshev points is large. Furthermore, the spectral variational integrator(SVI) constructed by the Gauss-Legendre quadrature rule and the multi-interval spectral method are carried out to compare with the CSVI, and the interesting kink phenomena for the Clenshaw-Curtis quadrature rule are discovered. The numerical results reveal that the CSVI has an advantage on the computing time over the whole progress and a higher accuracy than the SVI before the kink position. The effectiveness of the proposed method is demonstrated and verified perfectly through the numerical simulations for several classical mechanics examples and the orbital propagation for the planet systems and the Solar system.

Improvement of Boxcar Integrator and Its Application to Low Resistance Measurement of Inductive Load Coil

A boxcar integrator is described which is suitable for the low-repetition-rate signal processing. This boxcar integrator, named fixed-interval mode boxcar integrator, is able to reject harmonics other than the first harmonic component. It can also decrease the effective time constant In many situations, the antialiasing filter with narrow bandwidth will cause distortion of the input signal. The fixed-interval mode boxcar integrator with suitable gate width can achieve relative high performance without signal distortion because the bandwidth of its antialiasing filter can be wider than that in the fixed-Point boxcar integrator. ms boxcar integrator is used as majn part of signalprocessing circult in the low resisance measurement of inductive load coil. The results of experiments show that the fixed-interval boxcar integrator is suitable for low-repetition-rate use.

Symplectic-energy-first integrators of discrete mechanico-electrical dynamical systems

A discrete total variation calculus with variable time steps is presented for mechanico-electrical systems where there exist non-potential and dissipative forces. By using this discrete variation calculus, the symplectic-energy-first integrators for mechanico-electrical systems are derived. To do this, the time step adaptation is employed. The discrete variational principle and the Euler-Lagrange equation are derived for the systems. By using this discrete algorithm it is shown that mechanico-electrical systems are not symplectic and their energies are not conserved unless they are Lagrange mechanico-electrical systems. A practical example is presented to illustrate these results.

On Trigonometric Numerical Integrator for Solving First Order Ordinary Differential Equation

In this paper, we used an interpolation function with strong trigonometric components to derive a numerical integrator that can be used for solving first order initial value problems in ordinary differential equation. This numerical integrator has been tested for desirable qualities like stability, convergence and consistency. The discrete models have been used for a numerical experiment which makes us conclude that the schemes are suitable for the solution of first order ordinary differential equation.

A new explicit multisymplectic integrator for the Kawahara-type equation

We derive a new multisymplectic integrator for the Kawahara-type equation which is a fully explicit scheme and thus needs less computation cost. Multisympecticity of such scheme guarantees the long-time numerical behaviors. Nu- merical experiments are presented to verify the accuracy of this scheme as well as the excellent performance on invariant preservation for three kinds of Kawahara-type equations.

New way to construct high order Hamiltonian variational integrators

This paper develops a new approach to construct variational integrators. A simplified unconventional Hamilton＇s variational principle corresponding to initial value problems is proposed, which is convenient for applications. The displacement and mo- mentum are approximated with the same Lagrange interpolation. After the numerical integration and variational operation, the original problems are expressed as algebraic equations with the displacement and momentum at the interpolation points as unknown variables. Some particular variational integrators are derived. An optimal scheme of choosing initial values for the Newton-Raphson method is presented for the nonlinear dynamic system. In addition, specific examples show that the proposed integrators are symplectic when the interpolation point coincides with the numerical integration point, and both are Gaussian quadrature points. Meanwhile, compared with the same order symplectic Runge-Kutta methods, although the accuracy of the two methods is almost the same, the proposed integrators are much simpler and less computationally expensive.

EFFICIENT NUMERICAL INTEGRATORS FOR HIGHLY OSCILLATORY DYNAMIC SYSTEMS BASED ON MODIFIED MAGNUS INTEGRATOR METHOD

Based on the Magnus integrator method established in linear dynamic systems, an efficiently improved modified Magnus integrator method was proposed for the second-order dynamic systems with time-dependent high frequencies. Firstly, the secondorder dynamic system was reformulated as the first-order system and the frame of reference was transfered by introducing new variables so that highly oscillatory behaviour inherits from the entries in the meantime. Then the modified Magnus integrator method based on local linearization was appropriately designed for solving the above new form and some improved also were presented. Finally, numerical examples show that the proposed methods appear to be quite adequate for integration for highly oscillatory dynamic systems including Hamiltonian systems problem with long time and effectiveness.

Dynamic modeling of spacecraft solar panels deployment with Lie group variational integrator

The spacecraft with multistage solar panels have nonlinear coupling between attitudes of central body and solar panels, especially the rotation of central body is considered in space. The dynamics model is based for dynamics analysis and control, and the multistage solar panels means the dynamics modeling will be very complex. In this research, the Lie group variational integrator method is introduced, and the dynamics model of spacecraft with solar panels that connects together by flexible joints is built. The most obvious character of this method is that the attitudes of central body and solar panels are all described by three-dimensional attitude matrix. The dynamics models of spacecraft with one and three solar panels are established and simulated. The study shows Lie group variational integrator method avoids parameters coupling and effectively reduces difficulty of modeling. The obtained continuous dynamics model based on Lie group is a set of ordinary differential equations and equivalent with traditional dynamics model that offers a basis for the geometry control.

Best tracking performance for integrator and dead time plant

The optimal tracking performance for integrator and dead time plant in the case where plant uncertainty and control energy constraints are to be considered jointly is inrestigated. Firstly, an average cost function of the tracking error and the plant input energy over a class of stochastic model errors are defined. Then, we obtain an internal model controller design method that minimizes the average performance and further studies optimal tracking performance for integrator and dead time plant in the simultaneous presence of plant uncertainty and control energy constraint. The results can be used to evaluate optimal tracking performance and control energy in practical designs.

Extensive Numerical Tests of Leapfrog Integrator in Middle Thermostat Scheme in Molecular Simulations

Accurate and efficient integration of the equations of motion is indispensable for molecular dynamics(MD)simulations.Despite the massive use of the conventional leapfrog(LF)integrator in modern computational tools within the framework of MD propagation,further development for better performance is still possible.The alternative version of LF in the middle thermostat scheme(LFmiddle)achieves a higher order of accuracy and efficiency and maintains stable dynamics even with the integration time stepsize extended by several folds.In this work,we perform a benchmark test of the two integrators(LF and LF-middle)in extensive conventional and enhanced sampling simulations,aiming at quantifying the time-stepsizeinduced variations of global properties(e.g.,detailed potential energy terms)as well as of local observables(e.g.,free energy changes or bondlengths)in practical simulations of complex systems.The test set is composed of six chemically and biologically relevant systems,including the conformational change of dihedral flipping in the N-methylacetamide and an AT(AdenineThymine)tract,the intra-molecular proton transfer inside malonaldehyde,the binding free energy calculations of benzene and phenol targeting T4 lysozyme L99A,the hydroxyl bond variations in ethaline deep eutectic solvent,and the potential energy of the blue-light using flavin photoreceptor.It is observed that the time-step-induced error is smaller for the LFmiddle scheme.The outperformance of LF-middle over the conventional LF integrator is much more significant for global properties than local observables.Overall,the current work demonstrates that the LF-middle scheme should be preferably applied to obtain accurate thermodynamics in the simulation of practical chemical and biological systems.

Nonlinear control for global stabilization of multiple-integrator system by bounded controls

The global stabilization problem of the multiple-integrator system by bounded controls is considered. A nonlinear feedback law consisting of nested saturation functions is proposed. This type of nonlinear feedback law that is a modification and generalization of the result given in [1] needs only [（n ＋ 1）/2] （n is the dimensions of the system） saturation elements, which is fewer than that which the other nonlinear laws need. Furthermore, the poles of the closedloop system can be placed on any location on the left real axis when none of the saturation elements in the control laws is saturated. This type of nonlinear control law exhibits a simpler structure and can significantly improve the transient performances of the closed-loop system, and is very superior to the other existing methods. Simulation on a fourth-order system is used to validate the proposed method.

Multi-symplectic variational integrators for nonlinear Schrdinger equations with variable coefficients

In this paper, we propose a variational integrator for nonlinear Schrodinger equations with variable coefficients. It is shown that our variational integrator is naturally multi-symplectic. The discrete multi-symplectic structure of the integrator is presented by a multi-symplectic form formula that can be derived from the discrete Lagrangian boundary function. As two examples of nonlinear Schrodinger equations with variable coefficients, cubic nonlinear Schrodinger equations and Gross-Pitaevskii equations are extensively studied by the proposed integrator. Our numerical simulations demonstrate that the integrator is capable of preserving the mass, momentum, and energy conservation during time evolutions. Convergence tests are presented to verify that our integrator has second-order accuracy both in time and space.

Design and Analysis of a Gain-scaling Controller Applied to a Chain of Integrator System with Measurement Noise on Feedback Sensor

A control problem of a chain of integrator system with measurement noise on feedback sensor is considered. We propose a gain-scaling controller for compensating measurement noise of feedback sensor. Because control systems operate via feedback sensor＇s signal, the measurement noise in sensor＇ signal results in performance degradation or even system failure. Therefore, control systems often demand on compensating measurement noise. Our controller is equipped with a compensator and gain-scaling factor in order to reduce the effect of measurement noise on feedback sensor.