Atmospheric transmission algorithm for pulsed X-rays from high-altitude nuclear detonations based on scattering correction

In high-altitude nuclear detonations,the proportion of pulsed X-ray energy can exceed 70%,making it a specific monitoring signal for such events.These pulsed X-rays can be captured using a satellite-borne X-ray detector following atmospheric transmission.To quantitatively analyze the effects of different satellite detection altitudes,burst heights,and transmission angles on the physical processes of X-ray transport and energy fluence,we developed an atmospheric transmission algorithm for pulsed X-rays from high-altitude nuclear detonations based on scattering correction.The proposed method is an improvement over the traditional analytical method that only computes direct-transmission X-rays.The traditional analytical method exhibits a maximum relative error of 67.79% compared with the Monte Carlo method.Our improved method reduces this error to within 10% under the same conditions,even reaching 1% in certain scenarios.Moreover,its computation time is 48,000 times faster than that of the Monte Carlo method.These results have important theoretical significance and engineering application value for designing satellite-borne nuclear detonation pulsed X-ray detectors,inverting nuclear detonation source terms,and assessing ionospheric effects.

Monte Carlo method for evaluation of surface emission rate measurement uncertainty

The aim of this study is to evaluate the uncertainty of 2πα and 2πβ surface emission rates using the windowless multiwire proportional counter method.This study used the Monte Carlo method (MCM) to validate the conventional Guide to the Expression of Uncertainty in Measurement (GUM) method.A dead time measurement model for the two-source method was established based on the characteristics of a single-channel measurement system,and the voltage threshold correction factor measurement function was indirectly obtained by fitting the threshold correction curve.The uncertainty in the surface emission rate was calculated using the GUM method and the law of propagation of uncertainty.The MCM provided clear definitions for each input quantity and its uncertainty distribution,and the simulation training was realized with a complete and complex mathematical model.The results of the surface emission rate uncertainty evaluation for four radioactive plane sources using both methods showed the uncertainty’s consistency E_(n)<0.070 for the comparison of each source,and the uncertainty results of the GUM were all lower than those of the MCM.However,the MCM has a more objective evaluation process and can serve as a validation tool for GUM results.

High-Order Decoupled and Bound Preserving Local Discontinuous Galerkin Methods for a Class of Chemotaxis Models

In this paper,we explore bound preserving and high-order accurate local discontinuous Galerkin(LDG)schemes to solve a class of chemotaxis models,including the classical Keller-Segel(KS)model and two other density-dependent problems.We use the convex splitting method,the variant energy quadratization method,and the scalar auxiliary variable method coupled with the LDG method to construct first-order temporal accurate schemes based on the gradient flow structure of the models.These semi-implicit schemes are decoupled,energy stable,and can be extended to high accuracy schemes using the semi-implicit spectral deferred correction method.Many bound preserving DG discretizations are only worked on explicit time integration methods and are difficult to get high-order accuracy.To overcome these difficulties,we use the Lagrange multipliers to enforce the implicit or semi-implicit LDG schemes to satisfy the bound constraints at each time step.This bound preserving limiter results in the Karush-Kuhn-Tucker condition,which can be solved by an efficient active set semi-smooth Newton method.Various numerical experiments illustrate the high-order accuracy and the effect of bound preserving.

Superconvergence of Direct Discontinuous Galerkin Methods:Eigen-structure Analysis Based on Fourier Approach

This paper investigates superconvergence properties of the direct discontinuous Galerkin(DDG)method with interface corrections and the symmetric DDG method for diffusion equations.We apply the Fourier analysis technique to symbolically compute eigenvalues and eigenvectors of the amplification matrices for both DDG methods with different coefficient settings in the numerical fluxes.Based on the eigen-structure analysis,we carry out error estimates of the DDG solutions,which can be decomposed into three parts:(i)dissipation errors of the physically relevant eigenvalue,which grow linearly with the time and are of order 2k for P^(k)(k=2,3)approximations;(ii)projection error from a special projection of the exact solution,which is decreasing over the time and is related to the eigenvector corresponding to the physically relevant eigenvalue;(iii)dissipative errors of non-physically relevant eigenvalues,which decay exponentially with respect to the spatial mesh sizeΔx.We observe that the errors are sensitive to the choice of the numerical flux coefficient for even degree P^(2)approximations,but are not for odd degree P^(3)approximations.Numerical experiments are provided to verify the theoretical results.

An improved algorithm based on equivalent sound velocity profile method at large incident angle

With the development of ultra-wide coverage technology,multibeam echo-sounder(MBES)system has put forward higher requirements for localization accuracy and computational efficiency of ray tracing method.The classical equivalent sound speed profile(ESSP)method replaces the measured sound velocity profile(SVP)with a simple constant gradient SVP,reducing the computational workload of beam positioning.However,in deep-sea environment,the depth measurement error of this method rapidly increases from the central beam to the edge beam.By analyzing the positioning error of the ESSP method at edge beam,it is discovered that the positioning error increases monotonically with the incident angle,and the relationship between them could be expressed by polynomial function.Therefore,an error correction algorithm based on polynomial fitting is obtained.The simulation experiment conducted on an inclined seafloor shows that the proposed algorithm exhibits comparable efficiency to the original ESSP method,while significantly improving bathymetry accuracy by nearly eight times in the edge beam.

FITTING CORRECTION METHOD OF RING ARTIFACTS FOR RECONSTRUCTING CONE-BEAM CT IMAGES

In high-resolution cone-beam computed tomography （CBCT） using the flat-panel detector, imperfect or defect detector elements cause ring artifacts due to the none-uniformity of their X-ray response. They often disturb the image quality. A dedicated fitting correction method for high-resolution micro-CT is presented. The method converts each elementary X-ray response curve to an average one, and eliminates response inconsistency among pixels. Other factors of the method are discussed, such as the correction factor variability by different sampling frames and nonlinear factors over the whole spectrum. Results show that the noise and artifacts are both reduced in reconstructed images

What is the Most Effective Method of Error Correction in L2 Writing?

The efficacy of error correction and various kinds of correction approaches is one of the key issues in second language writing faced by both teachers and researchers. The current paper reviews the definition of error correction and examines the different views on whether error correction in L2 writing should be corrected. In particular, the paper discusses and analyses the three common correction methods: direct correction, peer feedback and indirect correction. Teachers are encouraged to weigh and analyze the advantages and disadvantages of these methods according to the current literature, employ the most beneficial error correction method in L2 writing, and adapt its suitability to their teaching context.

A Correction Method Suitable for Dynamical Seasonal Prediction

Based on the hindcast results of summer rainfall anomalies over China for the period 1981-2000 by the Dynamical Climate Prediction System （IAP-DCP） developed by the Institute of Atmospheric Physics, a correction method that can account for the dependence of model＇s systematic biases on SST anomalies is proposed. It is shown that this correction method can improve the hindcast skill of the IAP-DCP for summer rainfall anomalies over China, especially in western China and southeast China, which may imply its potential application to real-time seasonal prediction.

Low/distortion on Exterior Surface of Auto Body and Its Correction Method

Surface low/distortion is one of the most challenging surface deflections that have a great effect on the exterior appearance of automobiles.Most studies on surface distortion/deflection have focused on evaluation and visualization techniques,the research work on correction or prevention of surface low/distortion is limited,and there is no perfect surface low/distortion corrective method that can satisfy the needs of the engineering.A B-spline based geometry morphing algorithm is proposed and then a new program based on UG-NX platform is developed to modify the die face in the surface low/distortion areas.To verify this developed system,the experimental dies that can replicate the surface low/distortion phenomenon successfully is put to use.Five geometric variables are introduced to describe the basic geometry of typical depression features of automotive outer panels.The experimental dies are then designed to reflect various combinations of these geometric parameters.The stamping experiments are conducted on cold rolled grade 5（CR5） sheet steel and various static measurements,such as oil-stoning,laser scanner,etc,are performed to measure and record the surface low/distortions.Three approaches including good bearing,holds in blank and die face morphing that aim to correct low/distortions are tried out and surface low/distortions are observed in the specimen with reverse draw depth of 10 mm.The measurement results show that die morphing is a practical and effective method to correct the surface low/distortion.The correction method proposed can be used to minimize the occurrence of surface low/distortion in die manufacturing,which has certain reference significance to the correction of surface low/distortion.

Analogue correction method of errors and its application to numerical weather prediction

In this paper, an analogue correction method of errors （ACE） based on a complicated atmospheric model is further developed and applied to numerical weather prediction （NWP）. The analysis shows that the ACE can effectively reduce model errors by combining the statistical analogue method with the dynamical model together in order that the information of plenty of historical data is utilized in the current complicated NWP model, Furthermore, in the ACE, the differences of the similarities between different historical analogues and the current initial state are considered as the weights for estimating model errors. The results of daily, decad and monthly prediction experiments on a complicated T63 atmospheric model show that the performance of the ACE by correcting model errors based on the estimation of the errors of 4 historical analogue predictions is not only better than that of the scheme of only introducing the correction of the errors of every single analogue prediction, but is also better than that of the T63 model.

Use of Plastic Correction Formula to Improve Accuracy of Welding Residual Stress Test with Blind-Hole Method

The blind-hole method is the most widely used approach to experimentally determine the distribution of residual stress. This paper aims to improve test accuracy of welding residual stress and conducts an experimental study on the strain release factors involved when using the blind-hole method for Q235 and Q345, two steels commonly used in building structures. The ranges of strain release factors A and B in the elastic stage, the effects of strain release factors on residual stress calculated values, and the plastic corrected strain release factors are analyzed considering of the effect of plastic deformation around the blind hole on measurement accuracy. Finally, a simplified calculation formula to determine strain release factors is proposed for use with the blind-hole method. Results show that in the elastic stage, strain release factor A for Q235 and Q345 ranges from-0.399 to-0.525 and strain release factor B from-0.791 to-0.960. Changing the strain release factors A and B shows that calculated residual tensile stress varies in relation to a decrease in both factor values. However, there is a increase in calculated residual compressive stress with a decrease in the strain release factor A value, but there is an decrease with a decrease in strain release factor B value. Calculated residual stress applied to elastic strain release factors is compared with that applied to amended plastic strain release factors for Q235 steel. The maximum deviation between calculated residual stress and test stress is reduced from 21.1 to 1.0%,and for Q345 steel from 26.5 to 1.2%. It is thus evident that the plastic correction formula proposed in this paper can be used in calculations when conducting a residual stress test.

Accuracy of the half-power bandwidth method with a third-order correction for estimating damping in multi-DOF systems

A third-order correction was recently suggested to improve the accuracy of the half-power bandwidth method in estimating the damping of single DOF systems.This paper analyzes the accuracy of the half-power bandwidth method with the third-order correction in damping estimation for multi-DOF linear systems.Damping ratios in a two-DOF linear system are estimated using its displacement and acceleration frequency response curves,respectively.A wide range of important parameters that characterize the shape of these response curves are taken into account.Results show that the third-order correction may greatly improve the accuracy of the half-power bandwidth method in estimating damping in a two-DOF system.In spite of this,the half-power bandwidth method may significantly overestimate the damping ratios of two-DOF systems in some cases.

A time domain induced polarization relaxation time spectrum inversion method based on a damping factor and residual correction

Relaxation time spectra （RTS） derived from time domain induced polarization data （TDIP） are helpful to assess oil reservoir pore structures. However, due to the sensitivity to the signal-to-noise ratio （SNR）, the inversion accuracy of the traditional singular value decomposition （SVD） inversion method reduces with a decrease of SNR. In order to enhance the inversion accuracy and improve robustness of the inversion method to the SNR, an improved inversion method, based on damping factor and spectrum component residual correction, is proposed in this study. The numerical inversion results show that the oscillation of the RTS derived from the SVD method increased with a decrease of SNR, which makes it impossible to get accurate inversion components. However, the SNR has little influence on inversion components of the improved method, and the RTS has high inversion accuracy and robustness. Moreover, RTS derived from core sample data is basically in accord with the pore-size distribution curve, and the RTS derived from the actual induced polarization logging data is smooth and continuous, which indicates that the improved method is practicable.

ON THE METHODS FOR FINDING ROOTS OF ALGEBRAIC EQUATIONS WITH WEIERSTRASS' CORRECTIONS

This is a study of the Durand-Kerner and Nourein methods for finding the roots of a given algebraic equation simultaneously. We consider the conditions under which the iterative methods fail. The numerical example is presented.

Tooth surface error correction of hypoid gears machined by duplex helical method

In this work,synchronous cutting of concave and convex surfaces was achieved using the duplex helical method for the hypoid gear,and the problem of tooth surface error correction was studied.First,the mathematical model of the hypoid gears machined by the duplex helical method was established.Second,the coordinates of discrete points on the tooth surface were obtained by measurement center,and the normal errors of the discrete points were calculated.Third,a tooth surface error correction model is established,and the tooth surface error was corrected using the Levenberg-Marquard algorithm with trust region strategy and least square method.Finally,grinding experiments were carried out on the machining parameters obtained by Levenberg-Marquard algorithm with trust region strategy,which had a better effect on tooth surface error correction than the least square method.After the tooth surface error is corrected,the maximum absolute error is reduced from 30.9μm before correction to 6.8μm,the root mean square of the concave error is reduced from 15.1 to 2.1μm,the root mean square of the convex error is reduced from 10.8 to 1.8μm,and the sum of squared errors of the concave and convex surfaces was reduced from 15471 to 358μm^(2).It is verified that the Levenberg-Marquard algorithm with trust region strategy has a good accuracy for the tooth surface error correction of hypoid gear machined by duplex helical method.

Convergence Properties of Local Defect Correction Algorithm for the Boundary Element Method

Sometimes boundary value problems have isolated regions where the solution changes rapidly.Therefore,when solving numerically,one needs a fine grid to capture the high activity.The fine grid can be implemented as a composite coarse-fine grid or as a global fine grid.One cheaper way of obtaining the composite grid solution is the use of the local defect correction technique.The technique is an algorithm that combines a global coarse grid solution and a local fine grid solution in an iterative way to estimate the solution on the corresponding composite grid.The algorithm is relatively new and its convergence properties have not been studied for the boundary element method.In this paper the objective is to determine convergence properties of the algorithm for the boundary element method.First,we formulate the algorithm as a fixed point iterative scheme,which has also not been done before for the boundary element method,and then study the properties of the iteration matrix.Results show that we can always expect convergence.Therefore,the algorithm opens up a real alternative for application in the boundary element method for problems with localised regions of high activity.

Types and Correction Methods of Matrix Effect during Zircon LA-ICP-MS U-Pb Dating

Matrix effect primarily impacts the accuracy and precision of zircon LA-ICP-MS U-Pb data.This paper describes three types of matrix effect in zircon LA-ICPMS U-Pb dating,i.e.,the element matrix effect,high Ddpa or uranium matrix effect and alpha dose matrix effect,and illustrates the correction of these three effects.In addition,we point out the limitation and possible problems of the existing correction methods.

New Estimates for the Rate of Convergence of the Method of Subspace Corrections

We discuss estimates for the rate of convergence of the method of successive subspace corrections in terms of condition number estimate for the method of parallel subspace corrections.We provide upper bounds and in a special case,a lower bound for preconditioners defined via the method of successive subspace corrections.

PARALLEL ALGORITHMS OF ONE-LEG METHOD AND ITERATED DEFECT CORRECTION METHODS

The parallel algorithms of iterated defect correction methods (PIDeCM’s) are constructed, which are of efficiency and high order B-convergence for general nonlinear stiff systems in ODE’S. As the basis of constructing and discussing PIDeCM’s. a class of parallel one-leg methods is also investigated, which are of particular efficiency for linear systems.

Correction of cosine oscillation to the improved correlation method of estimating the amplitude of gravitational background signal

In the measurement of G with the angular acceleration method,the improved correlation method developed by Wu et al.（Wu W H,Tian Y,Luo J,Shao C G,Xu J H and Wang DH 2016 Rev.Sci.Instrum.87 094501） is used to accurately estimate the amplitudes of the prominent harmonic components of the gravitational background signal with time-varying frequency.Except the quadratic slow drift,the angular frequency of the gravitational background signal also includes a cosine oscillation coming from the useful angular acceleration signal,which leads to a deviation from the estimated amplitude.We calculate the correction of the cosine oscillation to the amplitude estimation.The result shows that the corrections of the cosine oscillation to the amplitudes of the fundamental frequency and second harmonic components obtained by the improved correlation method are within respective errors.