Configuration optimization of laser guide stars and wavefront correctors for multi-conjugation adaptive optics

Multi-conjugation adaptive optics（MCAOs） have been investigated and used in the large aperture optical telescopes for high-resolution imaging with large field of view（FOV）.The atmospheric tomographic phase reconstruction and projection of three-dimensional turbulence volume onto wavefront correctors,such as deformable mirrors（DMs） or liquid crystal wavefront correctors（LCWCs）,is a very important step in the data processing of an MCAO＇s controller.In this paper,a method according to the wavefront reconstruction performance of MCAO is presented to evaluate the optimized configuration of multi laser guide stars（LGSs） and the reasonable conjugation heights of LCWCs.Analytical formulations are derived for the different configurations and are used to generate optimized parameters for MCAO.Several examples are given to demonstrate our LGSs configuration optimization method.Compared with traditional methods,our method has minimum wavefront tomographic error,which will be helpful to get higher imaging resolution at large FOV in MCAO.

Collaborative Effect of Fines on Changes in Grain Distribution in the Process of Improving the Geotechnical Properties of an Alluvial Gravel 0/14

The technical and economic optimization of road projects has led to research into the use of materials obtained by mechanical stabilization for pavement construction. This research has enabled us to outline a solution capable of giving the sub-base layer the necessary and sufficient capacity to support the induced loads forecast for the traffic. This work evaluates the effect of adding fine silty clay (Cl) and clayey silt (Csp), two corrective materials to alluvial gravel (0/14), the main material, in the process of improving its cohesion and geotechnical properties. The results obtained show that the optimum mix is obtained with 10% by weight of Cl and 15% Csp. The granulometry of the mixes is spread out, but poorly calibrated. The Ag-Cl mixtures made at 10%, 15%, 20%, 25% 30% and Ag-Csp at 15%, 20%, 25%, 30%, and 35%, do not obey the law of mixtures. Mixing with 10% Cl reduces the sand equivalent of alluvial gravel by 60.23%, while mixing with 15% Cl reduces the sand equivalent by 6.82%. The addition of correctors increases the optimum water content and fine sand content of the mixes. Increasing the fine sand content reduces the optimum dry density, CBR index and static modulus. Mixes containing 10% Cl and 15% Csp have CBR values of CBRCl (96%) and CBRCsp (84%) and are not suitable for pavement base layers. In fact, the hardness of the grains has a Los Anges value of 41%, higher than the maximum permitted by the standard of 35%. The mixes obtained can be used as pavement base layers for traffic levels in a cumulative number of heavy goods vehicles 5 × 105 6 for an approximate life of 15 years.

Design and Analysis of Novel Three-Phase PFC for IM Drives

Induction motor drives(IMDs)can achieve high performance levels comparable to dc motor drives.A major problem in getting high dynamic performance in an IMD is the coupling between theflux and torque producing components of stator current.This is successfully overcome in FOC(Field-Oriented Control)IM,making it to the industry standard control.The performance of an IMD with an improved power quality converter at the front end is presented in this study.In the IMD,boost converter is employed to reduce power quality difficulties at the utility interface.As the boost converter contains only one switch,it results in a low processing time and cost.To ensure sinusoidal supply currents with high PF(Power Factor)and minimal THD(Total Harmonic Distortion),a novel PFC(Power Factor Corrector)control technique is proposed.To enhance the performance of the converter and to lower distortions at the motor side,PI(Proportional Integral)controller is incorporated at the PFC side.Thus it controls the DC bus voltage.The proposed boost converter improves power quality by lowering overall harmonic distortion of AC mains current,improving power factor correction,and regulating dc-link voltage.It is designed,modelled,and simulated in the MATLAB/simulink platform.Using a DSP(Digital Signal Processor),the suggested system’s performance is experimentally validated.The system’s performance is evaluated for speed and load torque,and the power quality indices are determined to meet IEEE-519 standards under all operating conditions.From the obtained results,it is evident that the proposed system mitigates the power quality issues effectively.

A Numerical Study of Several Species Population Models

This work considers a special case of Lotka-Volterra equations, which means that in the system of two ordinary differential equations, we take the four parameters equal to one. The reason is that we want just to illustrate the procedure to reduce that system to only one ordinary differential equation, such that we know its analytical solution. This idea will be applied to study the relations between a system of three ordinary differential equations, and a couple of partial differential equations. Lotka-Volterra equations are solved numerically by a fourth-order predictor-corrector method, which is initialized by an improved Euler method with a rather small time step because it is only a second-order algorithm. Then, it is proposed a model with three species, defined by ordinary differential equations.

The Chebyshev spectral element method using staggered predictor and corrector for elastic wave simulations

Based on strong and weak forms of elastic wave equations, a Chebyshev spectral element method （SEM） using the Galerkin variational principle is developed by discretizing the wave equation in the spatial and time domains and introducing the preconditioned conjugate gradient （PCG）-element by element （EBE） method in the spatial domain and the staggered predictor/corrector method in the time domain. The accuracy of our proposed method is verified by comparing it with a finite-difference method （FDM） for a homogeneous solid medium and a double layered solid medium with an inclined interface. The modeling results using the two methods are in good agreement with each other. Meanwhile, to show the algorithm capability, the suggested method is used to simulate the wave propagation in a layered medium with a topographic traction free surface. By introducing the EBE algorithm with an optimized tensor product technique, the proposed SEM is especially suitable for numerical simulation of wave propagations in complex models with irregularly free surfaces at a fast convergence rate, while keeping the advantage of the finite element method.

Wilson's disease: Prospective developments towards new therapies

Wilson's disease(WD) is an autosomal recessive disorder of copper metabolism, caused by mutations in the ATP7 B gene. A clear demand for novel WD treatment strategies has emerged. Although therapies using zinc salts and copper chelators can effectively cure WD, these drugs exhibit limitations in a substantial pool of WD patients who develop intolerance and/or severe side effects. Several lines of research have indicated intriguing potential for novel strategies and targets for development of new therapies. Here, we review these new approaches, which comprise correction of ATP7 B mutants and discovery of new compounds that circumvent ATP7B-deficiency, as well as cell and gene therapies. We also discuss whether and when these new therapeutic strategies will be translated into clinical use, according to the key requirements for clinical trials that remain to be met. Finally, we discuss the hope for the current rapidly developing research on molecular mechanisms underlying WD pathogenesis and for the related potential therapeutic targets to provide a solid foundation for the next generation of WD therapies that may lead to an effective, tolerable and safe cure.

HOMOGENIZATION OF SOME LINEAR AND SEMILINEAR SCHRDINGER EQUATIONS WITHREAL POTENTIAL

This paper considers the initial and boundary value problem of some linear and semilinear Schrodinger equation with real potential and H01 initial data. The author obtains the homogenization of linear and semilinear Schrodinger equations and gives correctors for the homogenization of linear and semilinear Schrodinger equations.

分数阶Jerk系统的动力学分析及在保密通信方面的应用

通过Adams-Bashforth-Moulton方法和predictor corrector algorithm方法并结合分数阶稳定性理论,辅助以相图、脉冲响应曲线、分叉图等分析了Jerk系统的动力学行为;引入反馈控制法对系统进行控制,最终得到理想的结果,并将其应用于保密通讯。Matlab数值仿真验证了其有效性。

Maximum Likelihood Estimation of the Identification Parameters and Its Correction

By taking the subsequence out of the input-output sequence of a system polluted by white noise, an independent observation sequence and its probability density are obtained and then a maximum likelihood estimation of the identification parameters is given. In order to decrease the asymptotic error, a corrector of maximum likelihood (CML) estimation with its recursive algorithm is given. It has been proved that the corrector has smaller asymptotic error than the least square methods. A simulation example shows that the corrector of maximum likelihood estimation is of higher approximating precision to the true parameters than the least square methods.

A predictor-corrector interior-point algorithmfor monotone variational inequality problems

Mehrotra's recent suggestion of a predictor corrector variant of primal dual interior point method for linear programming is currently the interior point method of choice for linear programming. In this work the authors give a predictor corrector interior point algorithm for monotone variational inequality problems. The algorithm was proved to be equivalent to a level 1 perturbed composite Newton method. Computations in the algorithm do not require the initial iteration to be feasible. Numerical results of experiments are presented.

Conformal optical system design with a single fixed conic corrector

A conformal optical system refers to the one whose first optical surface conforms to both aerodynamic and imaging requirements. Appropriate correction is required because a conformal dome induces significant aberrations. This paper intends to explain that an effective solution to the easy-fabrication conic surface corrector compensates aberrations induced by a coaxial aspheric dome. A conformal optical system with an ellipsoid MgF2 conformal dome, which has a fineness ratio of 2.0, is designed as an example. The field of regard angle is -4-30 degrees with a ＋2 degree instantaneous field of view. The system＇s ultimate value of modulation transfer function is close to the diffraction limit, which indicates that the performance of the conic conformal optical system with a fixed conic corrector meets the imaging requirements.

Dynamical Correction of Control Laws for Marine Ships’ Accurate Steering

The objective of this work is the analytical synthesis problem for marine vehicles autopilots design. Despite numerous known methods for a solution, the mentioned problem is very complicated due to the presence of an extensive population of certain dynamical conditions, requirements and restrictions, which must be satisfied by the appropriate choice of a steering control law. The aim of this paper is to simplify the procedure of the synthesis, providing accurate steering with desirable dynamics of the control system. The approach proposed here is based on the usage of a special unified multipurpose control law structure that allows decoupling a synthesis into simpler particular optimization problems. In particular, this structure includes a dynamical corrector to support the desirable features for the vehicle＇s motion under the action of sea wave disturbances. As a result, a specialized new method for the corrector design is proposed to provide an accurate steering or a trade-off between accurate steering and economical steering of the ship. This method guaranties a certain flexibility of the control law with respect to an actual environment of the sailing;its corresponding turning can be realized in real time onboard.

Error Analysis on Corrector Formula for Rectangular Rule

This paper presents truncation errors among Corrector Formula for left Rectangular rule and Corrector Formula for middle Rectangular rule respectively. It also displays an analysis on convergence order of compound corrector formulas for rectangular rule. Examples of numerical calculation have validated theoretical analysis.

An Efficient Multi-Scale Modelling Approach for ssDNA Motion in Fluid Flow

The paper presents a multi-scale modelling approach for simulating macromolecules in fluid flows. Macromolecule transport at low number densities is frequently encountered in biomedical devices, such as separators, detection and analysis systems. Accurate modelling of this process is challenging due to the wide range of physical scales involved. The continuum approach is not valid for low solute concentrations, but the large timescales of the fluid flow make purely molecular simulations prohibitively expensive. A promising multi-scale modelling strategy is provided by the meta-modelling approach considered in this paper. Meta-models are based on the coupled solution of fluid flow equations and equations of motion for a simplified mechanical model of macromolecules. The approach enables simulation of individual macromolecules at macroscopic time scales. Meta-models often rely on particle-corrector algorithms, which impose length constraints on the mechanical model. Lack of robustness of the particle-corrector algorithm employed can lead to slow convergence and numerical instability. A new FAst Linear COrrector （FALCO） algorithm is introduced in this paper, which significantly improves computational efficiency in comparison with the widely used SHAKE algorithm. Validation of the new particle corrector against a simple analytic solution is performed and improved convergence is demonstrated for ssDNA motion in a lid-driven micro-cavity.

Predictor-corrector interior-point algorithm for linearly constrained convex programming

Active set method and gradient projection method are curre nt ly the main approaches for linearly constrained convex programming. Interior-po int method is one of the most effective choices for linear programming. In the p aper a predictor-corrector interior-point algorithm for linearly constrained c onvex programming under the predictor-corrector motivation was proposed. In eac h iteration, the algorithm first performs a predictor-step to reduce the dualit y gap and then a corrector-step to keep the points close to the central traject ory. Computations in the algorithm only require that the initial iterate be nonn egative while feasibility or strict feasibility is not required. It is proved th at the algorithm is equivalent to a level-1 perturbed composite Newton method. Numerical experiments on twenty-six standard test problems are made. The result s show that the proposed algorithm is stable and robust.

A PCGM algorithm for solving linear equations

Based on the predictor corrector, we developed a new improved gradient method named the predictor corrector gradient algorithm (PCGM), which is useful for solving linear equations with symmetric positive definite of coefficient matrix.To improve the speed of convergence of traditional gradient method, we let values of original iterative formula be viewed as forecast values.Meanwhile, they are corrected by a new iterative formula through introducing corresponding step parameter.Therefore, a feasible and efficient algorithm is constructed.Numerical experiments indicate that PCGM method not only improve the accuracy and the speed of convergence, but also greatly reduce the number of steps to converge.The simple algorithm is easy to be realized and operated.

A parallel method for numerical solution of delay differential equations

A parallel diagonally iterated Runge Kutta (PDIRK) method is constructed to solve stiff initial value problems for delay differential equations. The order and stability of this PDIRK method has been analyzed, and the iteration parameters of the method are tuned in such a way that fast convergence to the value of corrector is achieved.

Optimal Filtering Correction forMarine Dynamical Positioning Control System

This paper focuses on the problem of control law optimization for marine vessels working in a dynamical positioning （DP） regime. The approach proposed here is based on the use of a special unified multipurpose control law structure constructed on the basis of nonlinear asymptotic observers, that allows the decoupling of a synthesis into simpler particular optimization problems. The primary reason for the observers is to restore deficient information concerning the unmeasured velocities of the vessel. Using a number of separate items in addition to the observers, it is possible to achieve desirable dynamical features of the closed loop connection. The most important feature is the so-called dynamical corrector, and this paper is therefore devoted to solving its optimal synthesis in marine vessels controlled by DP systems under the action of sea wave disturbances. The problem involves the need for minimal intensity of the control action determined by high frequency sea wave components. A specialized approach for designing the dynamical corrector is proposed and the applicability and effectiveness of the approach are illustrated using a practical example of underwater DP system synthesis.

Five Steps Block Predictor-Block Corrector Method for the Solution of <i>y''</i>= <i>f</i>(<i>x</i>,<i>y</i>,<i>y'</i>)

Theory has it that increasing the step length improves the accuracy of a method. In order to affirm this we increased the step length of the concept in [1] by one to get k = 5. The technique of collocation and interpolation of the power series approximate solution at some selected grid points is considered so as to generate continuous linear multistep methods with constant step sizes. Two, three and four interpolation points are considered to generate the continuous predictor-corrector methods which are implemented in block method respectively. The proposed methods when tested on some numerical examples performed more efficiently than those of [1]. Interestingly the concept of self starting [2] and that of constant order are reaffirmed in our new methods.

Optical System Design of Telescope Based on Mixed Modulation Diffractive Lens

Using of diffractive optical elements (DOE) in the Schupmann system offer a new way for the construction of ultra-large aperture telescope. The Fresnel Corrector, one of the DOEs, is the key device in the Schupmann system, which is used to correct the chromatic aberration introduced by the diffractive primary lens called Magnifying Glass. Generally, in a large aperture telescope (>20 m), the Fresnel Corrector is a diffractive lens with a large aperture and a small f-number, which is difficult to process. In this article, an improved device with a small F number but a large rim feature size, called amplitude and phase hybrid modulation Fresnel diffractive optical element (APHMFDOE), is used here as the Fresnel corrector. First, APHMFDOE with appropriate parameters is designed to match the dispersion of the Magnifying Glass so that the system meets the achromatic condition. Second, the optical characteristics of this improved system are simulated and compared with those of the general system based on the conventional Fresnel corrector. Our approach introduces a new dispersion correction device, which not only can eliminate the chromatic aberration caused by Magnifying Glass, but also can reduce the processing difficulty of Fresnel Corrector.