A Derivative Recovery Spectral Volume Model for the Analysis of Constituents Transport in One-Dimensional Flows

The treatment of advective fluxes in high-order finite volume models is well established, but this is not the case for diffusive fluxes, due to the conflict between the discontinuous representation of the solution and the continuous structure of analytic solutions. In this paper, a derivative reconstruction approach is proposed in the context of spectral volume methods, for the approximation of diffusive fluxes, aiming at the reconciliation of this conflict. Two different reconstructions are used for advective and diffusive fluxes： the advective reconstruction makes use of the information contained in a spectral cell, and allows the formation of discontinuities at the spectral cells boundaries; the diffusive reconstruction makes use of the information contained in contiguous spectral cells, imposing the continuity of the reconstruction at the spectral cells boundaries. The method is demonstrated by a number of numerical experiments, including the solution of shallow-water equations, complemented with the advective-diffusive transport equation of a conservative substance, showing the promising abilities of the numerical scheme proposed.

ANALYSIS OF TWO ANY ORDER SPECTRAL VOLUME METHODS FOR 1-D LINEAR HYPERBOLIC EQUATIONS WITH DEGENERATE VARIABLE COEFFICIENTS

In this paper,we analyze two classes of spectral volume(SV)methods for one-dimensional hyperbolic equations with degenerate variable coefficients.Two classes of SV methods are constructed by letting a piecewise k-th order(k≥1 is an integer)polynomial to satisfy the conservation law in each control volume,which is obtained by refining spectral volumes(SV)of the underlying mesh with k Gauss-Legendre points(LSV)or Radaus points(RSV)in each SV.The L^(2)-norm stability and optimal order convergence properties for both methods are rigorously proved for general non-uniform meshes.Surprisingly,we discover some very interesting superconvergence phenomena:At some special points,the SV flux function approximates the exact flux with(k+2)-th order and the SV solution itself approximates the exact solution with(k+3/2)-th order,some superconvergence behaviors for element averages errors have been also discovered.Moreover,these superconvergence phenomena are rigorously proved by using the so-called correction function method.Our theoretical findings are verified by several numerical experiments.

Whole-volume histogram analysis of spectral-computed tomography iodine maps characterizes HER2 expression in gastric cancer

BACKGROUND Although surgery remains the primary treatment for gastric cancer(GC),the identification of effective alternative treatments for individuals for whom surgery is unsuitable holds significance.HER2 overexpression occurs in approximately 15%-20%of advanced GC cases,directly affecting treatment-related decisions.Spectral-computed tomography(sCT)enables the quantification of material compositions,and sCT iodine concentration parameters have been demonstrated to be useful for the diagnosis of GC and prediction of its invasion depth,angioge-nesis,and response to systemic chemotherapy.No existing report describes the prediction of GC HER2 status through histogram analysis based on sCT iodine maps(IMs).AIM To investigate whether whole-volume histogram analysis of sCT IMs enables the prediction of the GC HER2 status.METHODS This study was performed with data from 101 patients with pathologically confirmed GC who underwent preoperative sCT examinations.Nineteen parameters were extracted via sCT IM histogram analysis:The minimum,maximum,mean,standard deviation,variance,coefficient of variation,skewness,kurtosis,entropy,percentiles(1st,5th,10th,25th,50th,75th,90th,95th,and 99th),and lesion volume.Spearman correlations of the parameters with the HER2 status and clinicopathological parameters were assessed.Receiver operating characteristic curves were used to evaluate the parameters’diagnostic performance.RESULTS Values for the histogram parameters of the maximum,mean,standard deviation,variance,entropy,and percentiles were significantly lower in the HER2+group than in the HER2–group(all P<0.05).The GC differentiation and Lauren classification correlated significantly with the HER2 status of tumor tissue(P=0.001 and 0.023,respectively).The 99th percentile had the largest area under the curve for GC HER2 status identification(0.740),with 76.2%,sensitivity,65.0%specificity,and 67.3%accuracy.All sCT IM histogram parameters correlated positively with the GC HER2 status(r=0.237-0.337,P=0.001-0.017).CONCLUSION Whole-lesion histogram parameters derived from sCT IM analysis,and especially the 99th percentile,can serve as imaging biomarkers of HER2 overexpression in GC.

Improving the High Order Spectral Volume Formulation Using a Diffusion Regulator

The concept of diffusion regulation(DR)was originally proposed by Jaisankar for traditional second order finite volume Euler solvers.This was used to decrease the inherent dissipation associated with using approximate Riemann solvers.In this paper,the above concept is extended to the high order spectral volume(SV)method.The DR formulation was used in conjunction with the Rusanov flux to handle the inviscid flux terms.Numerical experiments were conducted to compare and contrast the original and the DR formulations.These experiments demonstrated(i)retention of high order accuracy for the new formulation,(ii)higher fidelity of the DR formulation,when compared to the original scheme for all orders and(iii)straightforward extension to Navier Stokes equations,since the DR does not interfere with the discretization of the viscous fluxes.In general,the 2D numerical results are very promising and indicate that the approach has a great potential for 3D flow problems.

A High Order Spectral Volume Formulation for Solving Equations Containing Higher Spatial Derivative Terms II:Improving the Third Derivative Spatial Discretization Using the LDG2 Method

In this paper,the second in a series,we improve the discretization of the higher spatial derivative terms in a spectral volume(SV)context.The motivation for the above comes from[J.Sci.Comput.,46(2),314–328],wherein the authors developed a variant of the LDG(Local Discontinuous Galerkin)flux discretization method.This variant(aptly named LDG2),not only displayed higher accuracy than the LDG approach,but also vastly reduced its unsymmetrical nature.In this paper,we adapt the LDG2 formulation for discretizing third derivative terms.A linear Fourier analysis was performed to compare the dispersion and the dissipation properties of the LDG2 and the LDG formulations.The results of the analysis showed that the LDG2 scheme(i)is stable for 2nd and 3rd orders and(ii)generates smaller dissipation and dispersion errors than the LDG formulation for all the orders.The 4th order LDG2 scheme is howevermildly unstable:as the real component of the principal eigen value briefly becomes positive.In order to circumvent the above,a weighted average of the LDG and the LDG2 fluxes was used as the final numerical flux.Even a weight of 1.5%for the LDG(i.e.,98.5%for the LDG2)was sufficient tomake the scheme stable.Thisweighted scheme is still predominantly LDG2 and hence generated smaller dissipation and dispersion errors than the LDG formulation.Numerical experiments are performed to validate the analysis.In general,the numerical results are very promising and indicate that the approach has a great potential for higher dimension Korteweg-de Vries(KdV)type problems.

A High Order Spectral Volume Formulation for Solving Equations Containing Higher Spatial Derivative Terms:Formulation and Analysis for Third Derivative Spatial Terms Using the LDG Discretization Procedure

In this paper,we develop a formulation for solving equations containing higher spatial derivative terms in a spectral volume(SV)context;more specifically the emphasis is on handling equations containing third derivative terms.This formulation is based on the LDG(Local Discontinuous Galerkin)flux discretization method,originally employed for viscous equations containing second derivatives.A linear Fourier analysis was performed to study the dispersion and the dissipation properties of the new formulation.The Fourier analysis was utilized for two purposes:firstly to eliminate all the unstable SV partitions,secondly to obtain the optimal SV partition.Numerical experiments are performed to illustrate the capability of this formulation.Since this formulation is extremely local,it can be easily parallelized and a h-p adaptation is relatively straightforward to implement.In general,the numerical results are very promising and indicate that the approach has a great potential for higher dimension Korteweg-de Vries(KdV)type problems.

An Implicit LU-SGS Scheme for the Spectral Volume Method on Unstructured Tetrahedral Grids

An efficient implicit lower-upper symmetric Gauss-Seidel(LU-SGS)solution approach has been applied to a high order spectral volume(SV)method for unstructured tetrahedral grids.The LU-SGS solver is preconditioned by the block element matrix,and the system of equations is then solved with a LU decomposition.The compact feature of SV reconstruction facilitates the efficient solution algorithm even for high order discretizations.The developed implicit solver has shown more than an order of magnitude of speed-up relative to the Runge-Kutta explicit scheme for typical inviscid and viscous problems.A convergence to a high order solution for high Reynolds number transonic flow over a 3D wing with a one equation turbulence model is also indicated.

Spectral Beam Combining of Fiber Lasers by Using Reflecting Volume Bragg Gratings

By employing three reflecting volume Bragg gratings, a near-infrared 4-channel spectral-beam-combining system is demonstrated to present 720 W combined power with a combining efficiency of 94.7%. The combined laser beam is near-diffraction-limited with a beam factor M^2-1.54. During this 4-channel beam-combining process, no special active cooling measures are used to evaluate the volume Bragg gratings as combining elements are under the higher power laser operation. Thermal expansion and period distortion are verified in a 2 k W 2-channel beam-combining process, and the heat issue in the transmission case is found to be more remarkable than that in the diffraction e-se. Transmitted and diffracted beams experience wave-front aberrations with different degrees, thus leading to distinct beam deterioration.

Preoperative prediction of lymphovascular and perineural invasion in gastric cancer using spectral computed tomography imaging and machine learning

BACKGROUND Lymphovascular invasion(LVI)and perineural invasion(PNI)are important prognostic factors for gastric cancer(GC)that indicate an increased risk of metastasis and poor outcomes.Accurate preoperative prediction of LVI/PNI status could help clinicians identify high-risk patients and guide treatment deci-sions.However,prior models using conventional computed tomography(CT)images to predict LVI or PNI separately have had limited accuracy.Spectral CT provides quantitative enhancement parameters that may better capture tumor invasion.We hypothesized that a predictive model combining clinical and spectral CT parameters would accurately preoperatively predict LVI/PNI status in GC patients.AIM To develop and test a machine learning model that fuses spectral CT parameters and clinical indicators to predict LVI/PNI status accurately.METHODS This study used a retrospective dataset involving 257 GC patients(training cohort,n=172;validation cohort,n=85).First,several clinical indicators,including serum tumor markers,CT-TN stages and CT-detected extramural vein invasion(CT-EMVI),were extracted,as were quantitative spectral CT parameters from the delineated tumor regions.Next,a two-step feature selection approach using correlation-based methods and information gain ranking inside a 10-fold cross-validation loop was utilized to select informative clinical and spectral CT parameters.A logistic regression(LR)-based nomogram model was subsequently constructed to predict LVI/PNI status,and its performance was evaluated using the area under the receiver operating characteristic curve(AUC).RESULTS In both the training and validation cohorts,CT T3-4 stage,CT-N positive status,and CT-EMVI positive status are more prevalent in the LVI/PNI-positive group and these differences are statistically significant(P<0.05).LR analysis of the training group showed preoperative CT-T stage,CT-EMVI,single-energy CT values of 70 keV of venous phase(VP-70 keV),and the ratio of standardized iodine concentration of equilibrium phase(EP-NIC)were independent influencing factors.The AUCs of VP-70 keV and EP-NIC were 0.888 and 0.824,respectively,which were slightly greater than those of CT-T and CT-EMVI(AUC=0.793,0.762).The nomogram combining CT-T stage,CT-EMVI,VP-70 keV and EP-NIC yielded AUCs of 0.918(0.866-0.954)and 0.874(0.784-0.936)in the training and validation cohorts,which are significantly higher than using each of single independent factors(P<0.05).CONCLUSION The study found that using portal venous and EP spectral CT parameters allows effective preoperative detection of LVI/PNI in GC,with accuracy boosted by integrating clinical markers.

Enhancing silicon spectral emission in LIBS using Tesla coil discharge

Laser-induced breakdown spectroscopy(LIBS)is a powerful technique for elemental analysis,offering rapid analysis,minimal sample preparation,wide elemental coverage,and portability.To enhance the detection sensitivity of LIBS,increasing the spectral emission intensity is crucial.This paper explores the use of Tesla coil(TC)discharge as an alternative to spark discharge in silicon LIBS.The study examines the influence of TC discharge on both time-integrated and timeresolved spectra,with and without TC discharge;the corresponding electron temperature and density are obtained.The results show that TC discharge significantly amplifies the spectral intensity,improving signal sensitivity in LIBS analysis.Specifically,in the laser energy range from 7.4 to 24.0 mJ,TC discharge increased the average spectral line intensities of Si(II)385.60 nm and Si(I)390.55 nm by factors of 8.4 and 5.1,respectively.Additionally,the average electron temperature and density were enhanced by approximately 3.2%and 4.2%,respectively,under TC discharge.The advantages of TC discharge include higher energy deposition,extended discharge duration,reduced electrode erosion,and enhanced safety.This research contributes to advancing LIBS technology and expanding its applications in various fields.

Experimental investigation of spectral evolution in flash radiation by hypervelocity impact on aluminum plates

In this study,a series of hypervelocity impact tests were carried out based on a two-stage light gas gun,and the sequence spectrum and radiation evolution data of the impact products under different impact conditions were obtained.The diameter of the projectile is 3-5 mm,the impact velocity is 3.13-6.58 km/s,and the chamber pressure is 0.56-990 Pa.The spectrum of ejected debris cloud in the 250-310 nm band were obtained using a transient spectral measurement system and a multi-channel radiometer measurement system.The test results reveal that the flash radiation intensity increases as a power function with the kinetic energy of the impact.Furthermore,the peak value of the line spectrum decreases as the chamber vacuum degree increases,while the radiation width gradually expands.The line spectrum in the spectral characterization curve corresponds to the ejected debris clouds splitting phase,which does not produce significant line spectrum during material fragmentation and is dominated by the continuum spectrum produced by blackbody radiation.There will appear one or three characteristic peaks in the flash radiation time curve,the first and second peaks correspond to the penetration phase and the third peak corresponds to the expansion phase of the ejected debris clouds on the time scale,the first and second peaks are more sensitive to the chamber vacuum degree,and when the pressure is higher than 99 Pa,the first and second characteristic peaks will disappear.The radiant heat attenuation of the flash under different impact conditions is significantly different,the attenuation exponent has a power function relationship with the impact velocity and the chamber vacuum degree,while the attenuation exponent has a linear relationship with the diameter of the projectile,the specific expression of the attenuation exponent is obtained by fitting.The findings from this research can serve as a valuable reference for remote diagnostic technologies based on flash radiation characteristics.

Comparison of a Spectral Bin and Two Multi-Moment Bulk Microphysics Schemes for Supercell Simulation:Investigation into Key Processes Responsible for Hydrometeor Distributions and Precipitation

There are more uncertainties with ice hydrometeor representations and related processes than liquid hydrometeors within microphysics parameterization(MP)schemes because of their complicated geometries and physical properties.Idealized supercell simulations are produced using the WRF model coupled with“full”Hebrew University spectral bin MP(HU-SBM),and NSSL and Thompson bulk MP(BMP)schemes.HU-SBM downdrafts are typically weaker than those of the NSSL and Thompson simulations,accompanied by less rain evaporation.HU-SBM produces more cloud ice(plates),graupel,and hail than the BMPs,yet precipitates less at the surface.The limiting mass bins(and subsequently,particle size)of rimed ice in HU-SBM and slower rimed ice fall speeds lead to smaller melting-level net rimed ice fluxes than those of the BMPs.Aggregation from plates in HU-SBM,together with snow–graupel collisions,leads to a greater snow contribution to rain than those of the BMPs.Replacing HU-SBM’s fall speeds using the formulations of the BMPs after aggregating the discrete bin values to mass mixing ratios and total number concentrations increases net rain and rimed ice fluxes.Still,they are smaller in magnitude than bulk rain,NSSL hail,and Thompson graupel net fluxes near the surface.Conversely,the melting-layer net rimed ice fluxes are reduced when the fall speeds for the NSSL and Thompson simulations are calculated using HU-SBM fall speed formulations after discretizing the bulk particle size distributions(PSDs)into spectral bins.The results highlight precipitation sensitivity to storm dynamics,fall speed,hydrometeor evolution governed by process rates,and MP PSD design.

Estimating wheat spike-leaf composite indicator(SLI)dynamics by coupling spectral indices and machine learning

The contribution of spike photosynthesis to grain yield(GY)has been overlooked in the accurate spectral prediction of yield.Thus,it’s essential to construct and estimate a yield-related phenotypic trait considering spike photosynthesis.Based on field and spectral reflectance data from 19 wheat cultivars under two nitrogen fertilization conditions in two years,our objectives were to(i)construct a yield-related phenotypic trait(spike–leaf composite indicator,SLI)accounting for the contribution of the spike to photosynthesis,(ii)develop a novel spectral index(enhanced triangle vegetation index,ETVI3)sensitive to SLI,and(iii)establish and evaluate SLI estimation models by integrating spectral indices and machine learning algorithms.The results showed that SLI was sensitive to nitrogen fertilizer and wheat cultivar variation as well as a better predictor of yield than the leaf area index.ETVI3 maintained a strong correlation with SLI throughout the growth stage,whereas the correlations of other spectral indices with SLI were poor after spike emergence.Integrating spectral indices and machine learning algorithms improved the estimation accuracy of SLI,with the most accurate estimates of SLI showing coefficient of determination,root mean square error(RMSE),and relative RMSE values of 0.71,0.047,and 26.93%,respectively.These results provide new insights into the role of fruiting organs for the accurate spectral prediction of GY.This high-throughput SLI estimation approach can be applied for wheat yield prediction at whole growth stages and may be assisted with agronomical practices and variety selection.

Decoupling of temporal/spatial broadening effects in Doppler wind LiDAR by 2D spectral analysis

Pulse echo accumulation is commonly employed in coherent Doppler wind LiDAR(light detection and ranging)under the assumption of steady wind.Here,the measured spectral data are analyzed in the time dimension and frequency dimension to cope with the temporal wind shear and achieve the optimal accumulation time.A hardware-efficient algorithm combining the interpolation and cross-correlation is used to enhance the wind retrieval accuracy by reducing the frequency sampling interval and then reduce the spectral width calculation error.Moreover,the temporal broadening effect and spatial broadening effect are decoupled according to the strategy we developed.

A research on the effect of plasma spectrum collection device on LIBS spectral intensity

Only a small amount of spectral information is collected because the collection solid angle of the optical fiber probe and lens is very limited when collecting spectral information.To overcome this limitation,this study presents a novel method for acquiring plasma spectral information from various spatial directions.A parabolic-shaped plasma spectral collection device(PSCD)is employed to effectively collect more spectral information into the spectrometer,thereby enhancing the overall spectral intensity.The research objects in this study were soil samples containing different concentrations of heavy metals Pb,Cr,and Cd.The results indicate that the PSCD significantly enhances the spectral signal,with an enhancement rate of up to 45%.Moreover,the signal-to-noise ratio also increases by as much as 36%.Simultaneously,when compared to the absence of a device,it is found that there is no significant variation in plasma temperature when the PSCD is utilized.This observation eliminates the impact of the spatial effect caused by the PSCD on the spectral intensity.Consequently,a concentrationspectral intensity relationship curve is established under the PSCD.The results revealed that the linear fitting R^(2)for Pb,Cr,and Cd increased by 0.011,0.001,and 0.054,respectively.Additionally,the limit of detection(LOD)decreased by 0.361 ppm,0.901 ppm,and 0.602 ppm,respectively.These findings indicate that the spectral enhancement rate elevates with the increase in heavy metal concentration.Hence,the PSCD can effectively enhance the spectral intensity and reduce the detection limit of heavy metals in soil.

Review on article of preoperative prediction in chronic hepatitis B virus patients using spectral computed tomography and machine learning

This letter comments on the article that developed and tested a machine learning model that predicts lymphovascular invasion/perineural invasion status by combining clinical indications and spectral computed tomography characteristics accurately.We review the research content,methodology,conclusions,strengths and weaknesses of the study,and introduce follow-up research to this work.

System error iterative identification for underwater positioning based on spectral clustering

The observation error model of the underwater acous-tic positioning system is an important factor to influence the positioning accuracy of the underwater target.For the position inconsistency error caused by considering the underwater tar-get as a mass point,as well as the observation system error,the traditional error model best estimation trajectory(EMBET)with little observed data and too many parameters can lead to the ill-condition of the parameter model.In this paper,a multi-station fusion system error model based on the optimal polynomial con-straint is constructed,and the corresponding observation sys-tem error identification based on improved spectral clustering is designed.Firstly,the reduced parameter unified modeling for the underwater target position parameters and the system error is achieved through the polynomial optimization.Then a multi-sta-tion non-oriented graph network is established,which can address the problem of the inaccurate identification for the sys-tem errors.Moreover,the similarity matrix of the spectral cluster-ing is improved,and the iterative identification for the system errors based on the improved spectral clustering is proposed.Finally,the comprehensive measured data of long baseline lake test and sea test show that the proposed method can accu-rately identify the system errors,and moreover can improve the positioning accuracy for the underwater target positioning.

Efficient simulation of spatially correlated non-stationary ground motions by wavelet-packet algorithm and spectral representation method

Although the classical spectral representation method(SRM)has been widely used in the generation of spatially varying ground motions,there are still challenges in efficient simulation of the non-stationary stochastic vector process in practice.The first problem is the inherent limitation and inflexibility of the deterministic time/frequency modulation function.Another difficulty is the estimation of evolutionary power spectral density(EPSD)with quite a few samples.To tackle these problems,the wavelet packet transform(WPT)algorithm is utilized to build a time-varying spectrum of seed recording which describes the energy distribution in the time-frequency domain.The time-varying spectrum is proven to preserve the time and frequency marginal property as theoretical EPSD will do for the stationary process.For the simulation of spatially varying ground motions,the auto-EPSD for all locations is directly estimated using the time-varying spectrum of seed recording rather than matching predefined EPSD models.Then the constructed spectral matrix is incorporated in SRM to simulate spatially varying non-stationary ground motions using efficient Cholesky decomposition techniques.In addition to a good match with the target coherency model,two numerical examples indicate that the generated time histories retain the physical properties of the prescribed seed recording,including waveform,temporal/spectral non-stationarity,normalized energy buildup,and significant duration.

S^(2)ANet:Combining local spectral and spatial point grouping for point cloud processing

Background Despite the recent progress in 3D point cloud processing using deep convolutional neural networks,the inability to extract local features remains a challenging problem.In addition,existing methods consider only the spatial domain in the feature extraction process.Methods In this paper,we propose a spectral and spatial aggregation convolutional network(S^(2)ANet),which combines spectral and spatial features for point cloud processing.First,we calculate the local frequency of the point cloud in the spectral domain.Then,we use the local frequency to group points and provide a spectral aggregation convolution module to extract the features of the points grouped by the local frequency.We simultaneously extract the local features in the spatial domain to supplement the final features.Results S^(2)ANet was applied in several point cloud analysis tasks;it achieved stateof-the-art classification accuracies of 93.8%,88.0%,and 83.1%on the ModelNet40,ShapeNetCore,and ScanObjectNN datasets,respectively.For indoor scene segmentation,training and testing were performed on the S3DIS dataset,and the mean intersection over union was 62.4%.Conclusions The proposed S^(2)ANet can effectively capture the local geometric information of point clouds,thereby improving accuracy on various tasks.

DiriNet:An Estimation Network for Spectral Response Function and Point Spread Function

Hyper-and multi-spectral image fusion is an important technology to produce hyper-spectral and hyper-resolution images,which always depends on the spectral response function andthe point spread function.However,few works have been payed on the estimation of the two degra-dation functions.To learn the two functions from image pairs to be fused,we propose a Dirichletnetwork,where both functions are properly constrained.Specifically,the spatial response function isconstrained with positivity,while the Dirichlet distribution along with a total variation is imposedon the point spread function.To the best of our knowledge,the neural network and the Dirichlet regularization are exclusively investigated,for the first time,to estimate the degradation functions.Both image degradation and fusion experiments demonstrate the effectiveness and superiority of theproposed Dirichlet network.