Benchmarking calculations of excitation energies and transition properties with spectroscopic accuracy of highly charged ions used for the fusion plasma and astrophysical plasma

Atomic radiative data such as excitation energies, transition wavelengths, radiative rates, and level lifetimes with high precision are the essential parameters for the abundance analysis, simulation, and diagnostics in fusion and astrophysical plasmas. In this work, we mainly focus on reviewing our two projects performed in the past decade. One is about the ions with Z■30 that are generally of astrophysical interest, and the other one is about the highly charged krypton(Z = 36)and tungsten(Z = 74) ions that are relevant in research of magnetic confinement fusion. Two different and independent methods, namely, multiconfiguration Dirac–Hartree–Fock(MCDHF) and the relativistic many-body perturbation theory(RMBPT) are usually used in our studies. As a complement/extension to our previous works for highly charged tungsten ions with open M-shell and open N-shell, we also mainly focus on presenting and discussing our complete RMBPT and MCDHF calculations for the excitation energies, wavelengths, electric dipole(E1), magnetic dipole(M1), electric quadrupole(E2), and magnetic quadrupole(M2) transition properties, and level lifetimes for the lowest 148 levels belonging to the 3l3configurations in Al-like W61+. We also summarize the uncertainties of our systematical theoretical calculations, by cross-checking/validating our datasets from our RMBPT and MCDHF calculations, and by detailed comparisons with available accurate observations and other theoretical calculations. The data are openly available in Science Data Bank at https://doi.org/10.57760/sciencedb.10569.

High accuracy non-equidistant method for singular perturbation reaction-diffusion problem

Singular perturbation reaction-diffusion problem with Dirichlet boundary condition is considered. It is a multi-scale problem. Presence of small parameter leads to boundary layer phenomena in both sides of the region. A non-equidistant finite difference method is presented according to the property of boundary layer. The region is divided into an inner boundary layer region and an outer boundary layer region according to transition point of Shishkin. The steps sizes are equidistant in the outer boundary layer region. The step sizes are gradually increased in the inner boundary layer region such that half of the step sizes are different from each other. Truncation error is estimated. The proposed method is stable and uniformly convergent with the order higher than 2. Numerical results are given, which are in agreement with the theoretical result.

A SET OF 12-PARAMETER RECTANGULAR PLATE ELEMENT WITH HIGH ACCURACY

Using the method of undetermined function, a set of 12 parameter rectangular plate element with double set parameter and geometry symmetry is constructed. Their consistency error are O(h\+2) , one order higher than the usual 12 parameter rectangular plate elements.

ADFE METHOD WITH HIGH ACCURACY FOR NONLINEAR PARABOLIC INTEGRO-DIFFERENTIAL SYSTEM WITH NONLINEAR BOUNDARY CONDITIONS

Alternating direction finite element (ADFE) scheme for d-dimensional nonlinear system of parabolic integro-differential equations is studied. By using a local approximation based on patches of finite elements to treat the capacity term qi(u), decomposition of the coefficient matrix is realized, by using alternating direction, the multi-dimensional problem is reduced to a family of single space variable problems, calculation work is simplified; by using finite element method, high accuracy for space variant is kept; by. using inductive hypothesis reasoning, the difficulty coming from the nonlinearity of the coefficients and boundary conditions is treated; by introducing Ritz-Volterra projection, the difficulty coming from the memory term is solved. Finally, by using various techniques for priori estimate for differential equations, the unique resolvability and convergence properties for both FE and ADFE schemes are rigorously demonstrated, and optimal H-1 and L-2 norm space estimates and O((Deltat)(2)) estimate for time variant are obtained.

Positioning accuracy of IGPS

The positioning accuracy of a short-haul target-locating system,the inverse-GPS(IGPS) ,was analyzed in detail. The relationship between IGPS and the positioning error was discussed. The multiplicative error minimal bound of the geometric dilution of precision (GDOP) about the four-base-station IGPS was also investigated. In order to clarify the practical implementation of IGPS,the multiplicative and additive error factors which affect the positioning accuracy and theoretical estimation of positioning accuracy were presented. By analyzing the experiments of locating a target's position in virtual three-dimensional areas,the positioning performance of IGPS was illustrated. The results show that the multiplicative and additive error factors should be eliminated in IGPS to improve the positioning accuracy.

A new alternating group explicit-implicit algorithm with high accuracy for dispersive equation

In this paper, a new alternating group explicit-implicit （nAGEI） scheme for dispersive equations with a periodic boundary condition is derived. This new unconditionally stable scheme has a fourth-order truncation error in space and a convergence ratio faster than some known alternating methods such as ASEI and AGE. Comparison in accuracy with the AGEI and AGE methods is presented in the numerical experiment.

A COUPLING METHOD OF DIFFERENCE WITH HIGH ORDER ACCURACY AND BOUNDARY INTEGRAL EQUATION FOR EVOLUTIONARY EQUATION AND ITS ERROR ESTIMATES

In the present paper, a new numerical method for solving initial-boundary value problems of evolutionary equations is proposed and studied, combining difference method with high accuracy with boundary integral equation method. The numerical approximate schemes for both problems on a bounded or unbounded domain in R3 are proposed and their prior error estimates are obtained.

A Compact Explicit Difference Scheme of High Accuracy for Extended Boussinesq Equations

Presented here is a compact explicit difference scheme of high accuracy for solving the extended Boussinesq equations. For time discretization, a three-stage explicit Runge-Kutta method with TVD property is used at predicting stage, a cubic spline function is adopted at correcting stage, which made the time discretization accuracy up to fourth order; For spatial discretization, a three-point explicit compact difference scheme with arbitrary order accuracy is employed. The extended Boussinesq equations derived by Beji and Nadaoka are solved by the proposed scheme. The numerical results agree well with the experimental data. At the same time, the comparisons of the two numerical results between the present scheme and low accuracy difference method are made, which further show the necessity of using high accuracy scheme to solve the extended Boussinesq equations. As a valid sample, the wave propagation on the rectangular step is formulated by the present scheme, the modelled results are in better agreement with the experimental data than those of Kittitanasuan.

Trajectory Control: Directional MWD Inversely New Wellbore Positioning Accuracy Prediction Method

The deviation control of directional drilling is essentially the controlling of two angles of the wellbore actually drilled, namely, the inclination and azimuth. In directional drilling the bit trajectory never coincides exactly with the planned path, which is usually a plane curve with straight, building, holding, and dropping sections in succession. The drilling direction is of course dependant on the direction of the resultant forces acting on the bit and it is quite a tough job to hit the optimum target at the hole bottom as required. The traditional passive methods for correcting the drilling path have not met the demand to improve the techniques of deviation control. A method for combining wellbore surveys to obtain a composite, more accurate well position relies on accepting the position of the well from the most accurate survey instrument used in a given section of the wellbore. The error in each position measurement is the sum of many independent root sources of error effects. The relationship between surveys and other influential factors is considered, along with an analysis of different points of view. The collaborative work describes, establishes a common starting point of wellbore position uncertainty model, definition of what constitutes an error model, mathematics of position uncertainty calculation and an error model for basic directional service.

Comparison of density and positioning accuracy of PS extracted from super-resolution PSI with those from traditional PSI

In the application of persistent scatterer interferometry(PSI),deformation information is extracted from persistent scatterer(PS)points.Thus,the density and position of PS points are critical for PSI.To increase the PS density,a time-series InSAR chain termed as"super-resolution persistent scatterer interferometry"(SR-PSI)is proposed.In this study,we investigate certain important properties of SR-PSI.First,we review the main workflow and dataflow of SR-PSI.It is shown that in the implementation of the Capon algorithm,the diagonal loading(DL)approach should be only used when the condition number of the covariance matrix is sufficiently high to reduce the discontinuities between the joint images.We then discuss the density and positioning accuracy of PS when compared with traditional PSI.The theory and experimental results indicate that SR-PSI can increase the PS density in urban areas.However,it is ineffective for the rural areas,which should be an important consideration for the engineering application of SR-PSI.Furthermore,we validate that the positioning accuracy of PS can be improved by SRPSI via simulations.

A HIGH ACCURACY DIFFERENCE SCHEME FOR THE SINGULAR PERTURBATION PROBLEM OF THE SECOND-ORDER LINEAR ORDINARY DIFFERENTIAL EQUATION IN CONSERVATION FORM

In this paper, combining the idea of difference method and finite element method, we construct a difference scheme for a self-adjoint problem in conservation form. Its solution uniformly converges to that of the original differential equation problem with order h3.

A FAMILY OF HIGH-ORDER ACCURACY EXPLICIT DIFFERENCE SCHEMES WITH BRANCHING STABILITY FOR SOLVING 3-D PARABOLIC PARTIAL DIFFERENTIAL EQUATION

A family of high-order accuracy explict difference schemes for solving 3-dimension parabolic P. D. E. is constructed. The stability condition is r = Deltat/Deltax(2) Deltat/Deltay(2) = Deltat/Deltaz(2) < 1/2 ,and the truncation error is 0(<Delta>t(2) + Deltax(4)).

HIGH ACCURACY FINITE VOLUME ELEMENT METHOD FOR TWO-POINT BOUNDARY VALUE PROBLEM OF SECOND ORDER ORDINARY DIFFERENTIAL EQUATIONS

In this paper, a high accuracy finite volume element method is presented for two-point boundary value problem of second order ordinary differential equation, which differs from the high order generalized difference methods. It is proved that the method has optimal order error estimate O(h3) in H1 norm. Finally, two examples show that the method is effective.

Numerical Simulation for Accuracy of Velocity Analysis in Small-Scale High-Resolution Marine Multichannel Seismic Technology

When used with large energy sparkers, marine multichannel small-scale high-resolution seismic detection technology has a high resolution, high-detection precision, a wide applicable range, and is very flexible. Positive results have been achieved in submarine geological research, particularly in the investigation of marine gas hydrates. However, the amount of traveltime difference information is reduced for the velocity analysis under conditions of a shorter spread length, thus leading to poorer focusing of the velocity spectrum energy group and a lower accuracy of the velocity analysis. It is thus currently debatable whether the velocity analysis accuracy of short-arrangement multichannel seismic detection technology is able to meet the requirements of practical application in natural gas hydrate exploration. Therefore, in this study the bottom boundary of gas hydrates(Bottom Simulating Reflector, BSR) is used to conduct numerical simulation to discuss the accuracy of the velocity analysis related to such technology. Results show that a higher dominant frequency and smaller sampling interval are not only able to improve the seismic resolution, but they also compensate for the defects of the short-arrangement, thereby improving the accuracy of the velocity analysis. In conclusion, the accuracy of the velocity analysis in this small-scale, high-resolution, multi-channel seismic detection technology meets the requirements of natural gas hydrate exploration.

Feasibility and Diagnostic Accuracy for Assessment of Coronary Artery Stenosis of Prospectively Electrocardiogram-gated High-pitch Spiral Acquisition Mode Dual-source CT Coronary Angiography in Patients with Relatively Higher Heart Rates: in Comparison wit

Objective To prospectively investigate the diagnostic accuracy for coronary artery stenosis of prospectively electrocardiogram-triggered spiral acquisition mode (high pitch mode) dual-source computed tomography coronary angiography (CTCA) in patients with relatively higher heart rates (HR) compared with catheter coronary angiography (CCA). Methods Forty-seven consecutive patients with relatively higher HR (>65 and <100 bpm) (20 male, 27 female; age 55±10 years) who both underwent dual-source CTCA and CCA were prospectively included in this study. All patients were performed CTCA using high pitch mode setting at 20%-30% of the R-R interval for the image acquisition. All coronary segments were evaluated by two blinded and independent observers with regard to image quality on a three-point scale (1: excellent to 3: non-diagnostic) and for the presence of significant coronary stenoses (defined as diameter narrowing exceeding 50%). Considered CCA as the standard of reference, the sensitivity, specificity, positive predictive value and negative predictive value were calculated. Radiation dose values were calculated using the dose-length product. Results Image quality was rated as being score 1 in 92.4% of segments, score 2 in 6.1% of segmentsand score 3 in 1.5% of segments. The average image quality score per segment was 1.064±0.306. The HR variability of patients with image score 1, 2 and 3 were 2.29±1.06 bpm, 5.17±1.37 bpm, 8.88±1.53 bpm, respectively. The average HR variability of patients with different image scores were significantly different (F=170.402, P=0.001). The sensitivity, specificity, positive and negative predictive values were 92.6%, 97.0%, 87.6%, 98.3%, respectively, per segment and 90.0%, 95.2%, 85.3%, 96.9%, respectively, per vessel and 100%, 63.6%, 90.0%, 100%, respectively, per patient. The effective radiation dose was on average 0.86±0.16 mSv. Conclusion In patients with HR more than 65 bpm and below 100 bpm without cardiac arrhythmia, the prospectively electrocardiogram-gated high-pitch spiral acquisition mode with image acquired timing set at 20%-30% of the R-R interval provides a high diagnostic accuracy for the assessment of coronary stenoses combined with a 1.5% of non-diagnostic coronary segments and a radiation dose below 1 mSv.

Error Analysis on the Positioning Accuracy of a Pneumatic Vibration Isolator

A method of error analysis on the positioning accuracy of a pneumatic vibration isolator was proposed.First,the necessity of positioning accuracy was studied,in addition to the key factors associated with positioning accuracy.These analyses indicated that the positioning accuracy of the pneumatic vibration isolator was mainly attributed to the position error of the push button and the gap between the spindle and valve stem.Second,the error model of the positioning accuracy of the pneumatic vibration isolator was established through geometric simplification and geometric calculation.There are different methods used to calculate the position error of the push button for the different valves.Finally,an example analysis evaluating the impact of a specific two-position three-way valve on the positioning accuracy was given by means of error distribution.Experimental results validated the accuracy of the error model and the example analysis.This error model can be used to guide the structural parameter optimization design according to the requirements for positioning accuracy.

A High-order Accuracy Explicit Difference Scheme with Branching Stability for Solving Higher-dimensional Heat-conduction Equation

为解决 4-dimensional heatconduction 方程的明确的差别计划是的高顺序的精确性 constructed.The 稳定性状况是 r = t/x2 = t/y2 =t/] z2 = t/w23/8，和截断错误是 O (t2 + x4 ) 。

HIGH ORDER ACCURACY SCHEME FOR 2-D TRANSONIC FLOWS

According to Taylor's expansion formula, a kind of derivatives computation method is presented, which can achieve arbitrary order of accuracy. Then it is combined with a flux difference splitting technique and a flux limiter to construct the desiredscheme that is suitable for non-oscillatory shock-capturing calculation. TVD typeRunge-Kutta method is used for temporal discretization. Several steady and unsteadynumerical experiments demonstrate that the scheme is a robust solver for transonicflows with high accuracy and high resolution of shock wave structures.

Practical Research of IKONOS-2 Geopositioning and Its Accuracy in Tibet of China

This paper presents the studies of the refining of IKONOS-2 RPC, the transform of the datum, the mode of the control point distribution and the method of IKONOS stereo triangulation, so that IKONOS imagery can be used to collect the precise geospatial data and produce the large scale map.The transform between the IKONOS-2 image space and the national coordinate system based on the RPC have been developed, and the results of block adjustment with various control schemes in a practical project near Himalayas have been examined and analysed. The encouraging results of high positioning accuracy have been obtained.