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.

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.

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

Multi-scale data joint inversion of minerals and porosity in altered igneous reservoirs—A case study in the South China Sea

There are abundant igneous gas reservoirs in the South China Sea with significant value of research,and lithology classification,mineral analysis and porosity inversion are important links in reservoir evaluation.However,affected by the diverse lithology,complicated mineral and widespread alteration,conventional logging lithology classification and mineral inversion become considerably difficult.At the same time,owing to the limitation of the wireline log response equation,the quantity and accuracy of minerals can hardly meet the exploration requirements of igneous formations.To overcome those issues,this study takes the South China Sea as an example,and combines multi-scale data such as micro rock slices,petrophysical experiments,wireline log and element cutting log to establish a set of joint inversion methods for minerals and porosity of altered igneous rocks.Specifically,we define the lithology and mineral characteristics through core slices and mineral data,and establish an igneous multi-mineral volumetric model.Then we determine element cutting log correction method based on core element data,and combine wireline log and corrected element cutting log to perform the lithology classification and joint inversion of minerals and porosity.However,it is always difficult to determine the elemental eigenvalues of different minerals in inversion.This paper uses multiple linear regression methods to solve this problem.Finally,an integrated inversion technique for altered igneous formations was developed.The results show that the corrected element cutting log are in good agreement with the core element data,and the mineral and porosity results obtained from the joint inversion based on the wireline log and corrected element cutting log are also in good agreement with the core data from X-ray diffraction.The results demonstrate that the inversion technique is applicable and this study provides a new direction for the mineral inversion research of altered igneous formations.

SEMI-IMPLICIT SPECTRAL DEFERRED CORRECTION METHODS BASED ON SECOND-ORDER TIME INTEGRATION SCHEMES FOR NONLINEAR PDES

In[20],a semi-implicit spectral deferred correction(SDC)method was proposed,which is efficient for highly nonlinear partial differential equations(PDEs).The semi-implicit SDC method in[20]is based on first-order time integration methods,which are corrected iteratively,with the order of accuracy increased by one for each additional iteration.In this paper,we will develop a class of semi-implicit SDC methods,which are based on second-order time integration methods and the order of accuracy are increased by two for each additional iteration.For spatial discretization,we employ the local discontinuous Galerkin(LDG)method to arrive at fully-discrete schemes,which are high-order accurate in both space and time.Numerical experiments are presented to demonstrate the accuracy,efficiency and robustness of the proposed semi-implicit SDC methods for solving complex nonlinear PDEs.

An Arbitrarily High Order and Asymptotic Preserving Kinetic Scheme in Compressible Fluid Dynamic

We present a class of arbitrarily high order fully explicit kinetic numerical methods in compressible fluid dynamics,both in time and space,which include the relaxation schemes by Jin and Xin.These methods can use the CFL number larger or equal to unity on regular Cartesian meshes for the multi-dimensional case.These kinetic models depend on a small parameter that can be seen as a"Knudsen"number.The method is asymptotic preserving in this Knudsen number.Also,the computational costs of the method are of the same order of a fully explicit scheme.This work is the extension of Abgrall et al.(2022)[3]to multidimensional systems.We have assessed our method on several problems for two-dimensional scalar problems and Euler equations and the scheme has proven to be robust and to achieve the theoretically predicted high order of accuracy on smooth solutions.

Arbitrary High-Order Fully-Decoupled Numerical Schemes for Phase-Field Models of Two-Phase Incompressible Flows

Due to the coupling between the hydrodynamic equation and the phase-field equation in two-phase incompressible flows,it is desirable to develop efficient and high-order accurate numerical schemes that can decouple these two equations.One popular and efficient strategy is to add an explicit stabilizing term to the convective velocity in the phase-field equation to decouple them.The resulting schemes are only first-order accurate in time,and it seems extremely difficult to generalize the idea of stabilization to the second-order or higher version.In this paper,we employ the spectral deferred correction method to improve the temporal accuracy,based on the first-order decoupled and energy-stable scheme constructed by the stabilization idea.The novelty lies in how the decoupling and linear implicit properties are maintained to improve the efficiency.Within the framework of the spatially discretized local discontinuous Galerkin method,the resulting numerical schemes are fully decoupled,efficient,and high-order accurate in both time and space.Numerical experiments are performed to validate the high-order accuracy and efficiency of the methods for solving phase-field models of two-phase incompressible flows.

Errors and Correction of Precipitation Measurements in China

In order to discover the range of various errors in Chinese precipitation measurements and seek a correction method, 30 precipitation evaluation stations were set up countrywide before 1993. All the stations are reference stations in China. To seek a correction method for wind-induced error, a precipitation correction instrument called the ＂horizontal precipitation gauge＂ was devised beforehand. Field intercomparison observations regarding 29,000 precipitation events have been conducted using one pit gauge, two elevated operational gauges and one horizontal gauge at the above 30 stations. The range of precipitation measurement errors in China is obtained by analysis of intercomparison measurement results. The distribution of random errors and systematic errors in precipitation measurements are studied in this paper. A correction method, especially for wind-induced errors, is developed. The results prove that a correlation of power function exists between the precipitation amount caught by the horizontal gauge and the absolute difference of observations implemented by the operational gauge and pit gauge. The correlation coefficient is 0.99. For operational observations, precipitation correction can be carried out only by parallel observation with a horizontal precipitation gauge. The precipitation accuracy after correction approaches that of the pit gauge. The correction method developed is simple and feasible.

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.

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.

An Improved Method for Correction of Air Temperature Measured Using Different Radiation Shields

The variation of air temperature measurement errors using two different radiation shields （DTR502B Vaisala,Finland,and HYTFZ01,Huayun Tongda Satcom,China） was studied.Datasets were collected in the field at the Daxing weather station in Beijing from June 2011 to May 2012.Most air temperature values obtained with these two commonly used radiation shields were lower than the reference records obtained with the new Fiber Reinforced Polymers （FRP） Stevenson screen.In most cases,the air temperature errors when using the two devices were smaller on overcast and rainy days than on sunny days; and smaller when using the imported rather than the Chinese shield.The measured errors changed sharply at sunrise and sunset,and reached maxima at noon.Their diurnal variation characteristics were,naturally,related to changes in solar radiation.The relationships between the record errors,global radiation,and wind speed were nonlinear.An improved correction method was proposed based on the approach described by Nakamura and Mahrt （2005） （NM05）,in which the impact of the solar zenith angle （SZA） on the temperature error is considered and extreme errors due to changes in SZA can be corrected effectively.Measurement errors were reduced significantly after correction by either method for both shields.The error reduction rate using the improved correction method for the Chinese and imported shields were 3.3％ and 40.4％ higher than those using the NM05 method,respectively.

Development of an Instant Correction and Display System of Numerical Weather Prediction Products in China

This paper presents the development of numerical prediction products(NPP) correction and display system(NPPCDS) for rapid and effective post-processing and displaying of the T213 NPP(numerical prediction products of the medium range numerical weather prediction spectral model T213L31) through instant correction method. The NPPCDS consists of two modules: an automatic correction module and a graphical display module. The automatic correction module automatically corrects the T213 NPP at regularly scheduled time intervals, while the graphical display module interacts with users to display the T213 NPP and its correction results. The system helps forecasters extract the most relevant information at a quick glance without extensive post-processing. It is simple, easy to use, and computationally efficient, and has been running stably at Huludao Meteorological Bureau in Liaoning Province of China for the past three years. Because of its low computational costs, it is particularly useful for meteorological departments that lack advanced computing capacity and still need to make short-range weather forecasting.

ANALYSIS OF HUMAN PLACENTA BY ^(31)P NUCLEAR MAGNETIC RESONANCE AND THIN-LAYER CHROMATOGRAPHY SCANNING COMBINED WITH THE CORRECTIVE METHOD OF ABSORBANCE PROPORTIONAL COEFFICIENT

Five phospholipids in human placenta were determined by phosphorus 31 nuclear magnetic resonance(^(31)P NMR)spectroscopy and thin-layer chromatography(TLC) scanning combined with the corrective method of absorbance proportional coefficient. The NMR spectrometer used this investigation was a Bruker AM-500 spectrometer operating at 202.4 MHz for ^(31)P chemical shifts are relative to 85% phosphoric acid. TIC was carried out by silica gel H plate developed in chloroform-methanol-glacial acetic acid-ethanol-water(25:4:6:2:0.5),with Vaskovsky reagent as colour -developing agent of phospholipids.

Data correction of the force balanced accelerometer

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Land Surface Temperature Change in Hangzhou Urban Area in Recent 20 Years Based on Landsat Image

Since the reform and opening-up in 1978, the urbanization level of our country has been continuously improved and the urban development has made great progress. However, with the rapid expansion of urban construction land, the population density and building density have been greatly increased, resulting in the urban heat island effect, which has negative impact on the urban thermal environment and restricts the high-quality development of urbanization. This paper focuses on how the urban surface thermal environment of Hangzhou changes in 20 years. In this paper, the characteristics of land surface temperature (LST) in Hangzhou urban area from 2000 to 2020 were studied by using Landsat images. The radiative transfer equation method is used to retrieve the land surface temperature, and the retrieval results are analyzed. The results show that: 1) the land surface temperature in Hangzhou city area has a slight upward trend in the past 20 years;2) the area of high temperature area is expanding;3) the land surface temperature in the city center area has decreased significantly in the past 20 years, while the ground temperature in other areas around the city center has increased significantly.

Delta Compression Correction Method for Covert Communication in IoT

Covert communication can conceal the existence of wireless transmission and thus has the ability to address information security transfer issue in many applications of the booming Internet of Things(IoT).However,the proliferation of sensing devices has generated massive amounts of data,which has increased the burden of covert communication.Considering the spatiotemporal correlation of data collection causing redundancy between data,eliminating duplicate data before transmission is beneficial for shortening transmission time,reducing the average received signal power of warden,and ultimately realizing covert communication.In this paper,we propose to apply delta compression technology in the gateway to reduce the amount of data generated by IoT devices,and then sent it to the cloud server.To this end,a cost model and evaluation method that is closer to the actual storage mode of computer systems is been constructed.Based on which,the delta version sequence obtained by existing delta compression algorithms is no longer compact,manifested by the still high cost.In this situation,we designed the correction scheme based on instructions merging(CSIM)correction to save costs by merging instructions.Firstly,the delta version sequence is divided into five categories and corresponding merge rules were derived.Then,for any COPY/ADD class delta compression algorithm,merge according to strict to relaxed to selection rules while generating instructions.Finally,a more cost-effective delta version sequence can be gained.The experimental results on random data show that the delta version sequences output by the CSIM corrected 1.5-pass and greedy algorithms have better performance in cost reducing.

Effect of Sample Disturbance on Unconfined Compression Strength of Natural Marine Clays

Quantitatively correcting the unconfined compressive strength for sample disturbance is an important research project in the practice of ocean engineering and geotechnical engineering. In this study, the specimens of undisturbed natural marine clay obtained from the same depth at the same site were deliberately disturbed to different levels. Then, the specimens with different extents of sample disturbance were trimmed for both oedometer tests and unconfined compression tests. The degree of sample disturbance SD is obtained from the oedometer test data. The relationship between the unconfined compressive strength q u and SD is studied for investigating the effect of sample disturbance on q u. It is found that the value of q u decreases linearly with the increase in SD. Then, a simple method of correcting q u for sample disturbance is proposed. Its validity is also verified through analysis of the existing published data.