A new strain-based pentagonal membrane finite element for solid mechanics problems

Polygonal finite elements remain an attractive option in finite element analysis due to their flexibility in modelingarbitrary shapes compared to triangles.In this study,a pentagonal membrane element was developed with thestrain approach for the first time.The element possesses invariance,and the equilibrium constraint was appliedto the assumed strain field using corrective coefficients.Inspired by the advancing front technique,a pentagonalmesh was generated,and the mesh quality was enhanced with Laplacian smoothing.The performance of thedeveloped pentagonal element was assessed in a few numerical tests,and the results revealed its suitability inmodeling the bending of beams.Besides,the numerical results are enhanced when pentagonal elements are usedin mesh transitions along boundaries to smoothen curved edges and capture distributed loads.

Investigation of the block toppling evolution of a layered model slope by centrifuge test and discrete element modeling

Primary toppling usually occurs in layered rock slopes with large anti-dip angles.In this paper,the block toppling evolution was explored using a large-scale centrifuge system.Each block column in the layered model slope was made of cement mortar.Some artificial cracks perpendicular to the block column were prefabricated.Strain gages,displacement gages,and high-speed camera measurements were employed to monitor the deformation and failure processes of the model slope.The centrifuge test results show that the block toppling evolution can be divided into seven stages,i.e.layer compression,formation of major tensile crack,reverse bending of the block column,closure of major tensile crack,strong bending of the block column,formation of failure zone,and complete failure.Block toppling is characterized by sudden large deformation and occurs in stages.The wedge-shaped cracks in the model incline towards the slope.Experimental observations show that block toppling is mainly caused by bending failure rather than by shear failure.The tensile strength also plays a key factor in the evolution of block toppling.The simulation results from discrete element method(DEM)is in line with the testing results.Tensile stress exists at the backside of rock column during toppling deformation.Stress concentration results in the fragmented rock column and its degree is the most significant at the slope toe.

Design of low-alloying and high-performance solid solution-strengthened copper alloys with element substitution for sustainable development

Solid solution-strengthened copper alloys have the advantages of a simple composition and manufacturing process,high mechanical and electrical comprehensive performances,and low cost;thus,they are widely used in high-speed rail contact wires,electronic component connectors,and other devices.Overcoming the contradiction between low alloying and high performance is an important challenge in the development of solid solution-strengthened copper alloys.Taking the typical solid solution-strengthened alloy Cu-4Zn-1Sn as the research object,we proposed using the element In to replace Zn and Sn to achieve low alloying in this work.Two new alloys,Cu-1.5Zn-1Sn-0.4In and Cu-1.5Zn-0.9Sn-0.6In,were designed and prepared.The total weight percentage content of alloying elements decreased by 43%and 41%,respectively,while the product of ultimate tensile strength(UTS)and electrical conductivity(EC)of the annealed state increased by 14%and 15%.After cold rolling with a 90%reduction,the UTS of the two new alloys reached 576 and 627MPa,respectively,the EC was 44.9%IACS and 42.0%IACS,and the product of UTS and EC(UTS×EC)was 97%and 99%higher than that of the annealed state alloy.The dislocations proliferated greatly in cold-rolled alloys,and the strengthening effects of dislocations reached 332 and 356 MPa,respectively,which is the main reason for the considerable improvement in mechanical properties.

Genesis of the Nuri Cu-W-Mo Deposit,Tibet,China:Constraints from in situ Trace Elements and Sr Isotopic Analysis of Scheelite

The Nuri deposit is the only Cu-W-Mo polymetallic deposit with large-scale WO3 resources in the eastern section of the Gangdese metallogenic belt,Tibet,China.However,the genetic type of this deposit has been controversial since its discovery.Based on a study of the geological characteristics of the deposit,this study presents mineralization stages,focusing on the oxide stage and the quartz-sulfide stage where scheelite is mainly formed,referred to as Sch-A and Sch-B,respectively.Through LA-ICP-MS trace element and Sr isotope analyses,the origin,evolutionary process of the oreforming fluid and genesis of the ore deposit are investigated.Scanning Electron Microscope-Cathodoluminescence(SEMCL)observations reveal that Sch-A consists of three generations,with dark gray homogenous Sch-A1 being replaced by relatively lighter and homogeneous Sch-A2 and Sch-A3,with Sch-A2 displaying a gray CL image color with vague and uneven growth bands and Sch-A3 has a light gray CL image color with hardly any growth band.In contrast,Sch-B exhibits a‘core-rim’structure,with the core part(Sch-B1)being dark gray and displaying a uniform growth band,while the rim part(Sch-B2)is light gray and homogeneous.The normalized distribution pattern of rare earth elements in scheelite and Sr isotope data suggest that the early ore-forming fluid in the Nuri deposit originated from granodiorite porphyry and,later on,some country rock material was mixed in,due to strong water-rock interaction.Combining the O-H isotope data further indicates that the ore-forming fluid in the Nuri deposit originated from magmatic-hydrothermal sources,with contributions from metamorphic water caused by water-rock interaction during the mineralization process,as well as later meteoric water.The intense water-rock interaction likely played a crucial role in the precipitation of scheelite,leading to varying Eu anomalies in different generations of scheelite from the oxide stage to the quartz-sulfide stage,while also causing a gradual decrease in oxygen fugacity(fO2)and a slow rise in pH value.Additionally,the high Mo and low Sr contents in the scheelite are consistent with typical characteristics of magmatic-hydrothermal scheelite.Therefore,considering the geological features of the deposit,the geochemical characteristics of scheelite and the O-H isotope data published previously,it can be concluded that the genesis of the Nuri deposit belongs to porphyry-skarn deposit.

Method to measure tree-ring width,density,elemental composition,and stable carbon and oxygen isotopes using one sample

Tree-ring width(RW),density,elemental com-position,and stable carbon and oxygen isotope(δ^(13)C,δ^(18)O)are widely used as proxies to assess climate change,ecology,and environmental pollution;however,a specific pretreat-ment has been needed for each proxy.Here,we developed a method by which each proxy can be measured in the same sample.First,the sample is polished for ring width meas-urement.After obtaining the ring width data,the sample is cut to form a 1-mm-thick wood plate.The sample is then mounted in a vertical sample holder,and gradually scanned by an X-ray beam.Simultaneously,the count rates of the fluorescent photons of elements(for chemical characteriza-tion)and a radiographic grayscale image(for wood density)are obtained,i.e.the density and the element content are obtained.Then,cellulose is isolated from the 1-mm wood plate by removal of lignin,and hemicellulose.After producing this cellulose plate,cellulose subsamples are separated by knife under the microscope for inter-annual and intra-annual stable carbon and oxygen isotope(δ^(13)C,δ^(18)O)analysis.Based on this method,RW,density,elemental composition,δ^(13)C,and δ^(18)O can be measured from the same sample,which reduces sample amount and treatment time,and is helpful for multi-proxy comparison and combination research.

A stable implicit nodal integration-based particle finite element method(N-PFEM)for modelling saturated soil dynamics

In this study,we present a novel nodal integration-based particle finite element method(N-PFEM)designed for the dynamic analysis of saturated soils.Our approach incorporates the nodal integration technique into a generalised Hellinger-Reissner(HR)variational principle,creating an implicit PFEM formulation.To mitigate the volumetric locking issue in low-order elements,we employ a node-based strain smoothing technique.By discretising field variables at the centre of smoothing cells,we achieve nodal integration over cells,eliminating the need for sophisticated mapping operations after re-meshing in the PFEM.We express the discretised governing equations as a min-max optimisation problem,which is further reformulated as a standard second-order cone programming(SOCP)problem.Stresses,pore water pressure,and displacements are simultaneously determined using the advanced primal-dual interior point method.Consequently,our numerical model offers improved accuracy for stresses and pore water pressure compared to the displacement-based PFEM formulation.Numerical experiments demonstrate that the N-PFEM efficiently captures both transient and long-term hydro-mechanical behaviour of saturated soils with high accuracy,obviating the need for stabilisation or regularisation techniques commonly employed in other nodal integration-based PFEM approaches.This work holds significant implications for the development of robust and accurate numerical tools for studying saturated soil dynamics.

Paleoenvironmental Characteristics of Paleogene Lacustrine Source Rocks in the Western Bozhong Sag,Bohai Bay Basin,China:Evidence from Biomarkers,Major and Trace Elements

The organic matter(OM)enrichment mechanisms and depositional environment characteristics of lacustrine source rocks in the western Bozhong Sag,Bohai Bay Basin in Northeast China remain controversial.To address these issues,based on Rock-Eval pyrolysis,kerogen macerals,H/C and O/C ratios,GC-MS,major and trace elements,the Dongying Formation Member(Mbr)3(E_(3)d_(3)),the Shahejie Formation mbrs 1 and 2(E_(2)s_(1+2)),and the Shahejie Mbr 3(E_(2)s_(3))source rocks in the western Bozhong Sag were studied.The above methods were used to reveal their geochemical properties,OM origins and depositional environments,all of which indicate that E_(2)s_(1+2)and E_(2)s_(3)are excellent source rocks,and that E_(3)d_(3)is of the second good quality.E_(3)d_(3)source rocks were formed under a warm and humid climate,mainly belong to fluvial/delta facies,the E_(3)d_(3)sediments formed under weakly oxidizing and freshwater conditions.Comparatively,the depositional environments of E_(2)s_(1+2)source rocks were arid and cold climate,representing saline or freshwater lacustrine facies,and the sediments of E_(2)s_(1+2)belong to anoxic or suboxic settings with large evaporation and salinity.During the period of E_(2)s_(3),the climate became warm and humid,indicating the freshwater lacustrine facies,and E_(2)s_(3)was characterized by freshwater and abundant algae.Moreover,compared with other intervals,the OM origin of E_(3)d_(3)source rocks has noticeable terrestrial input.The OM origin of the E_(2)s_(1+2)and E_(2)s_(3)are mainly plankton and bacteria.Tectonic subsidence and climate change have affected the changes of the depositional environment in the western Bozhong Sag,thus controlling the distribution of the source rocks,the geochemical characteristics in the three intervals of lacustrine source rocks have distinct differences.Overall,these factors are effective to evaluate the paleoenvironmental characteristics of source rocks by biomarkers,major and trace elements.The established models may have positive implications for research of lacustrine source rocks in offshore areas with few drillings.

Enriched Constant Elements in the Boundary Element Method for Solving 2D Acoustic Problems at Higher Frequencies

The boundary element method(BEM)is a popular method for solving acoustic wave propagation problems,especially those in exterior domains,owing to its ease in handling radiation conditions at infinity.However,BEM models must meet the requirement of 6–10 elements per wavelength,using the conventional constant,linear,or quadratic elements.Therefore,a large storage size of memory and long solution time are often needed in solving higher-frequency problems.In this work,we propose two new types of enriched elements based on conventional constant boundary elements to improve the computational efficiency of the 2D acoustic BEM.The first one uses a plane wave expansion,which can be used to model scattering problems.The second one uses a special plane wave expansion,which can be used tomodel radiation problems.Five examples are investigated to showthe advantages of the enriched elements.Compared with the conventional constant elements,the new enriched elements can deliver results with the same accuracy and in less computational time.This improvement in the computational efficiency is more evident at higher frequencies(with the nondimensional wave numbers exceeding 100).The paper concludes with the potential of our proposed enriched elements and plans for their further improvement.

Effect of Rare-Earth Element Substitution in Superconducting R_(3)Ni_(2)O_(7) under Pressure

Recently,high temperature(T_(c)≈80 K)superconductivity(SC)has been discovered in La_(3)Ni_(2)O_(7)(LNO)under pressure.This raises the question of whether the superconducting transition temperature T_(c) could be further enhanced under suitable conditions.One possible route for achieving higher T_(c) is element substitution.Similar SC could appear in the Fmmm phase of rare-earth(RE)R_(3)Ni_(2)O_(7)(RNO,R=RE element)material series under suitable pressure.The electronic properties in the RNO materials are dominated by the Ni 3d orbitals in the bilayer NiO_(2) plane.In the strong coupling limit,the SC could be fully characterized by a bilayer single 3d_(x^(2)−y^(2))-orbital t–J‖–J⊥ model.With RE element substitution from La to other RE element,the lattice constant of the Fmmm RNO material decreases,and the resultant electronic hopping integral increases,leading to stronger superexchanges between the 3d_(x^(2)−y^(2)) orbitals.Based on the slave-boson mean-field theory,we explore the pairing nature and the evolution of T_(c) in RNO materials under pressure.Consequently,it is found that the element substitution does not alter the pairing nature,i.e.,the inter-layer s-wave pairing is always favored in the superconducting RNO under pressure.However,the T_(c) increases from La to Sm,and a nearly doubled T_(c) could be realized in SmNO under pressure.This work provides evidence for possible higher T_(c) R_(3)Ni_(2)O_(7) materials,which may be realized in further experiments.

Robust T_c in element molybdenum up to 160 GPa

Element superconductors with the single atoms provide clean and fundamental platforms for studying superconductivity.Although elements with d electrons are usually not favored by conventional BCS,the record superconducting critical temperature(T_(c))in element scandium(S_(c))has further ignited the intensive attention on transition metals.The element molybdenum(M_o)with a half-full d-orbital is studied in our work,which fills the gap in the study of Mo under high pressure and investigates the pressure dependence of superconductivity.In this work,we exhibit a robust superconductivity of Mo in the pressure range of 5 GPa to 160 GPa via high-pressure electrical transport measurements,the T_(c) varies at a rate of0.013 K/GPa to 8.56 K at 160 GPa.Moreover,the superconductivity is evidenced by the T_(c) shifting to lower temperature under applied magnetic fields,and the upper critical magnetic fields are extrapolated by the WHH equation and GL equation;the results indicate that the maximum upper critical magnetic field is estimated to be 8.24 T at 137 GPa.We further investigate the superconducting mechanism of Mo,the theoretical calculations indicate that the superconductivity can be attributed to the strong coupling between the electrons from the partially filled d band and the phonons from the frequency zone of 200-400 cm^(-1).

Galerkin-based quasi-smooth manifold element(QSME)method for anisotropic heat conduction problems in composites with complex geometry

The accurate and efficient analysis of anisotropic heat conduction problems in complex composites is crucial for structural design and performance evaluation. Traditional numerical methods, such as the finite element method(FEM), often face a trade-off between calculation accuracy and efficiency. In this paper, we propose a quasi-smooth manifold element(QSME) method to address this challenge, and provide the accurate and efficient analysis of two-dimensional(2D) anisotropic heat conduction problems in composites with complex geometry. The QSME approach achieves high calculation precision by a high-order local approximation that ensures the first-order derivative continuity.The results demonstrate that the QSME method is robust and stable, offering both high accuracy and efficiency in the heat conduction analysis. With the same degrees of freedom(DOFs), the QSME method can achieve at least an order of magnitude higher calculation accuracy than the traditional FEM. Additionally, under the same level of calculation error, the QSME method requires 10 times fewer DOFs than the traditional FEM. The versatility of the proposed QSME method extends beyond anisotropic heat conduction problems in complex composites. The proposed QSME method can also be applied to other problems, including fluid flows, mechanical analyses, and other multi-field coupled problems, providing accurate and efficient numerical simulations.

亲子鉴定中Penta E基因座发生等位基因丢失1例

目的本文以等位基因丢失为切入点,重点说明在亲子鉴定过程中出现等位基因丢失如何证明并解决。方法本机构在进行亲子鉴定检测过程中,通过对20个染色体STR基因座进行PCR复合扩增,毛细管电泳后荧光检测,发现被检父与孩子仅在Penta E基因座上有不符合遗传规律现象。增加基因座进行检测,并验证被检父与孩子是否符合同一父系,判断其亲子关系。结果两个试剂盒共39个基因座检测显示,仅Penta E基因座不符合遗传规律,且为6步突变,其峰面积与相邻基因座杂合子的单峰面积相近,考虑为等位基因丢失。更换试剂盒再次进行实验,验证了该案例的两个个体的Penta E基因座发生等位基因“19”丢失的情况。结论等位基因丢失导致杂合子被误判为纯合子,影响累积亲权指数计算结果,可更换不同引物序列的检测试剂盒重新检测,以保证鉴定结果的准确性。

Features of rare earth elements geochemistry in coals of Central Kazakhstan

This research presents the results of a comprehensive study of mineralogical and geochemical features of REE distribution in coals of Central Kazakhstan deposits—Karaganda coal basin and Shubarkol deposit,which have large hard coal reserves and are industrially important for the coal industry of Kazakhstan;the research is based on 205 samples of clayey interlayers and coal seams.It shows basic patterns of distribution and features of concentration for impurity elements,gives an estimate of the impurity elements concentration,including REE,defines conditions and factors of their accumulation,and studies features of their forms in coal and coal-bearing rocks,which allows estimating the mechanisms of their migration and conditions of accumulation.According to the results of geochemical indicators,the article establishes the factors of REE dislocation,reveals the composition of margin rocks that have influenced REE concentration in coal seams,and the presented latest data on mineralogy allowed to establish the ways of their transportation to the paleobasin during the synand epigenetic periods of formation of the coal deposits of Central Kazakhstan being researched.It was found that the coals are insignificantly enriched with heavy lanthanides from Ho to Lu.The distribution curves of UCC normalized REE values in the coals are similar and coincide,but they are less than the average value for world coal,and amount to only one-third of the UCC.It was found that the highest concentrations of all REE are characteristic of clayey interlayers and oxidized coals.The La/Yb ratio in this case increases upwards along the section,indicating mainly clastogenic mechanism of REE delivery to the coals.In coal and clay samples,the predominant mineral form of REE is light lanthanide phosphates.Identified particles of REE from minerals and their composition peculiarities suppose autigene nature of their formation.The formation of the bulk of autigene minerals occurred during the maturation of brown coals and their transformation into hard ones.

Trace elements in magmatic and hydrothermal quartz:Implications on the genesis of the Xingluokeng Tungsten Deposit,South China

The Xingluokeng deposit is the largest gran-ite-related tungsten deposit within the Wuyi metallogenic belt in South China.The Xingluokeng intrusion primarily consists of porphyritic biotite granite,biotite granite,andfine-grained granite.The deposit is represented by veinlet-disseminated mineralization with K-feldspathization and biotitization,alongside quartz-vein mineralization with gre-isenization and sericitization.This study investigates in-situ analyses of quartz compositions from both the intrusion and hydrothermal veinlets and veins.Trace element correlations indicate that trivalent Al^(3+)and Fe^(3+)replace Si^(4+)within the quartz lattice,with monovalent cations(such as Li^(+),Na^(+),and K^(+))primarily serving as charge compensators.Low Ge/Al ratios(<0.013)of quartz from granites suggest a mag-matic origin.The low Al/Ti and Ge/Ti ratios,accompanied by high Ti contents in quartz,suggest that the porphyritic biotite granite and biotite granite are characterized by rela-tively low levels of differentiation and high crystallization temperatures.In contrast,thefine-grained granite exhibits a higher degree of fractionation,lower crystallization tem-peratures,and a closer association with tungsten miner-alization.Ti contents in quartz from quartz veins indicate Qz-Ⅰformed at temperatures above 400°C,while Qz-Ⅱto Qz-Ⅴformed at temperatures below 350°C.Variations in different generations of quartz,as indicated by Al content and(Al+Fe)/(Li+Na+K)ratio,suggest that Qz-Ⅰprecipi-tated from a less acidicfluid with a stable pH,whereas Qz-Ⅱto Qz-Ⅴoriginated from a more acidicfluid with notable pH variations.Consequently,alkaline alteration and acidic alteration supplied the essential Ca and Fe for the precipita-tion of scheelite and wolframite,respectively,highlighting a critical mechanism in tungsten mineralization at the Xin-gluokeng deposit.

Distribution, health and ecological risk assessments of trace elements in Nigerian oil sands

The Nigerian oil sands represent the largest oil sand deposit in Africa, yet there is little published information on the distribution and potential health and ecological risks of trace elements in the oil resource. In the present study, we investigated the distribution pattern of 18trace elements(including biophile and chalcophile elements) as well as the estimated risks associated with exposure to these elements. The results of the study indicated that Fe was the most abundant element, with a mean concentration of 22,131 mg/kg while Br had the lowest mean concentration of 48 mg/kg. The high occurrence of Fe and Ti suggested a possible occurrence of ilmenite(Fe TiO_(3)) in the oil sands. Source apportionment using positive matrix factorization showed that the possible sources of detected elements in the oil sands were geogenic, metal production, and crustal. The contamination factor, geo-accumulation index, modified degree of contamination, pollution load index, and Nemerow pollution index indicated that the oil sands are heavily polluted by the elements. Health risk assessment showed that children were relatively more susceptible to the potentially toxic elements in the oil sands principally via ingestion exposure route(HQ > 1E-04). Cancer risks from inhalation are unlikely due to CR < 1E-06 but ingestion and dermal contact pose severe risks(CR > 1E-04). The high concentrations of the elements pose serious threats due to the potential for atmospheric transport, bioaccessibility, and bioavailability.

Element UI中利用Upload控件实现文件上传的方法

为了介绍如何利用Element UI中的Upload控件上传图片,以发微博功能举例,描述了反向代理服务器在图片上传过程中的作用,列举了包括全局配置文件、上传图片或删除图片、保存图片路径等步骤,并对单张图片上传功能进行说明。采用多张图片路径合并成字符串的方式来保存数据,以便更加有效地储存、读取图片信息。

Effects of heating temperature and atmosphere on element distribution and microstructure in high-Mn/Al austenitic low-density steel

The elemental distribution and microstructure near the surface of high-Mn/Al austenitic low-density steel were investigated after isothermal holding at temperatures of 900-1200℃ in different atmospheres,including air,N_(2),and N_(2)+CO_(2).No ferrite was formed near the surface of the experimental steel during isothermal holding at 900 and 1000℃ in air,while ferrite was formed near the steel sur-face at holding temperatures of 1100 and 1200℃.The ferrite fraction was larger at 1200℃ because more C and Mn diffused to the sur-face,exuded from the steel,and then reacted with N and O to form oxidation products.The thickness of the compound scale increased owing to the higher diffusion rate at higher temperatures.In addition,after isothermal holding at 1100℃ in N_(2),the Al content near the surface slightly decreased,while the C and Mn contents did not change.Therefore,no ferrite was formed near the surface.However,the near-surface C and Al contents decreased after holding at 1100℃in the N_(2)+CO_(2)mixed atmosphere,resulting in the formation of a small amount of ferrite.The compound scale was thickest in N_(2),followed by the N_(2)+CO_(2)mixed atmosphere,and thinnest in air.Overall,the element loss and ferrite fraction were largest after holding in air at the same temperature.The differences in element loss and ferrite frac-tion between in N_(2) and N_(2)+CO_(2)atmospheres were small,but the compound scale formed in N_(2) was significantly thicker.According to these results,N_(2)+CO_(2)is the ideal heating atmosphere for the industrial production of high-Mn/Al austenitic low-density steel.

Crystal plasticity finite element simulations on extruded Mg-10Gd rod with texture gradient

The mechanical properties of an extruded Mg-10Gd sample, specifically designed for vascular stents, are crucial for predicting its behavior under service conditions. Achieving homogeneous stresses in the hoop direction, essential for characterizing vascular stents, poses challenges in experimental testing based on standard specimens featuring a reduced cross section. This study utilizes an elasto-visco-plastic self-consistent polycrystal model(ΔEVPSC) with the predominant twinning reorientation(PTR) scheme as a numerical tool, offering an alternative to mechanical testing. For verification, various mechanical experiments, such as uniaxial tension, compression, notched-bar tension, three-point bending, and C-ring compression tests, were conducted. The resulting force vs. displacement curves and textures were then compared with those based on the ΔEVPSC model. The computational model's significance is highlighted by simulation results demonstrating that the differential hardening along with a weak strength differential effect observed in the Mg-10Gd sample is a result of the interplay between micromechanical deformation mechanisms and deformation-induced texture evolution. Furthermore, the study highlights that incorporating the axisymmetric texture from the as-received material incorporating the measured texture gradient significantly improves predictive accuracy on the strength in the hoop direction. Ultimately, the findings suggest that the ΔEVPSC model can effectively predict the mechanical behavior resulting from loading scenarios that are impossible to realize experimentally, emphasizing its valuable contribution as a digital twin.

Electromagnetic responses on microstructures of duplex stainless steels based on 3D cellular and electromagnetic sensor finite element models

Microstructures determine mechanical properties of steels,but in actual steel product process it is difficult to accurately control the microstructure to meet the requirements.General microstructure characterization methods are time consuming and results are not rep-resentative for overall quality level as only a fraction of steel sample was selected to be examined.In this paper,a macro and micro coupled 3D model was developed for nondestructively characterization of steel microstructures.For electromagnetic signals analysis,the relative permeability value computed by the micro cellular model can be used in the macro electromagnetic sensor model.The effects of different microstructure components on the relative permeability of duplex stainless steel(grain size,phase fraction,and phase distribu-tion)were discussed.The output inductance of an electromagnetic sensor was determined by relative permeability values and can be val-idated experimentally.The findings indicate that the inductance value of an electromagnetic sensor at low frequency can distinguish dif-ferent microstructures.This method can be applied to real-time on-line characterize steel microstructures in process of steel rolling.

THE SUPERCLOSENESS OF THE FINITE ELEMENT METHOD FOR A SINGULARLY PERTURBED CONVECTION-DIFFUSION PROBLEM ON A BAKHVALOV-TYPE MESH IN 2D

For singularly perturbed convection-diffusion problems,supercloseness analysis of the finite element method is still open on Bakhvalov-type meshes,especially in the case of 2D.The difficulties arise from the width of the mesh in the layer adjacent to the transition point,resulting in a suboptimal estimate for convergence.Existing analysis techniques cannot handle these difficulties well.To fill this gap,here a novel interpolation is designed delicately for the smooth part of the solution,bringing about the optimal supercloseness result of almost order 2 under an energy norm for the finite element method.Our theoretical result is uniform in the singular perturbation parameterεand is supported by the numerical experiments.