A Priori and A Posteriori Error Estimates of Streamline Diffusion Finite Element Method for Optimal Control Problem Governed by Convection Dominated Diffusion Equation

In this paper,we investigate a streamline diffusion finite element approxi- mation scheme for the constrained optimal control problem governed by linear con- vection dominated diffusion equations.We prove the existence and uniqueness of the discretized scheme.Then a priori and a posteriori error estimates are derived for the state,the co-state and the control.Three numerical examples are presented to illustrate our theoretical results.

Microstructure in the Weld Metal of Austenitic-Pearlitic Dissimilar Steels and Diffusion of Element in the Fusion Zone

Microstructure and alloy element distribution in the welded joint between austenitic stainless steel (1Cr18Ni9Ti) and pearlitic heat-resistant steel (1Cr5Mo) were researched by means of light microscopy, scanning electron microscopy (SEM) and electron probe microanalysis (EPMA). Microstructure, divisions of the fusion zone and elemental diffusion distributions in the welded joints were investigated. Furthermore, solidification microstructure and S-ferrite distribution in the weld metal of these steels are also discussed.

Studies on diffusion and profiles of elements in deep-sea manganese nodules

Elemental compositions are measured in manganese nodules collected from the Northern Mid-Pacific floor by inductively-coupled plasma atomic emission spectrometry (1CP-AES) and their growth rates are determined by radiometric methods. The result shows that depth distributions of elements in nodules vary with depth as follows; (i) increase, (ii) decrease and (iii) fluctuation. These internodule variations in elemental compositions are considered to be caused by diffusion and migration of elements in nodules and heterogeneities in textures of nodules. In the present paper, a diffusive model is used to elucidate the inward-increase profile of some elements in nodules. The effective diffusive coefficients are estimated to be of the order of 10-9 cm2/a for Ni, V and Zn in the nodules, which is less than the value reported for radionuclides.

Analysis of Linear Triangular Elements for Convection-diffusion Problems by Streamline Diffusion Finite Element Methods

This paper is devoted to studying the superconvergence of streamline diffusion finite element methods for convection-diffusion problems. In [8], under the condition that ε ≤ h^2 the optimal finite element error estimate was obtained in L^2-norm. In the present paper, however, the same error estimate result is gained under the weaker condition that ε≤h.

Adaptive Finite Element Method for Steady Convection-Diffusion Equation

This paper examines the numerical solution of the convection-diffusion equation in 2-D. The solution of this equation possesses singularities in the form of boundary or interior layers due to non-smooth boundary conditions. To overcome such singularities arising from these critical regions, the adaptive finite element method is employed. This scheme is based on the streamline diffusion method combined with Neumann-type posteriori estimator. The effectiveness of this approach is illustrated by different examples with several numerical experiments.

Effect of temperature on interface diffusion in micro solder joint under current stressing

The effects of temperature on Cu pad consumption and intermetallic compound（IMC） growth were investigated under current stressing. The Cu/Sn-3.0Ag-0.5Cu（SAC305）/Cu solder joints were used, with a certain current density of 0.76×104A/cm^2 at 100, 140, 160 and 180 °C. The constitutive equations of cathode Cu pad consumption and anode interface IMC growth are established, respectively, based on the loading time and sample temperature. The cathode Cu pad consumption（δ） increases linearly with the loading time and the consumption rate shows parabolic curve relationships with sample temperature. The anode interface IMC thickness（δ1） increased is linearly with the square root of loading time and the interface IMC growth coefficient shows parabolic curve relationship with sample temperature. The δ and δ1 have different variation laws under current stressing, due to the current facilitating larger amount of IMC formation in the bulk solder.

Preparation of Wear Resistant Materials by Melting and Diffusion Process

A wear-resistant material reinforced with VCp was manufactured by the in-mold melting process, in which the high-vanadium alloy-rods were melted by high temperature liquid steel and elements diffused into the liquid. Microstructure of the material was examined by OM, SEM, and XRD, and alloy elements in the diffusion layer were studied by EDS, and the hardness of the material was tested by HRS. The experimental results show that the material gradually changes hardness, which is due to the uniformly existents of carbide particles on martensite matrix and the gradient distribution of vanadium and carbide.

A new computational approach for modeling diffusion tractography in the brain

Computational models provide additional tools for studying the brain,however,many techniques are currently disconnected from each other.There is a need for new computational approaches that span the range of physics operating in the brain.In this review paper,we offer some new perspectives on how the embedded element method can fill this gap and has the potential to connect a myriad of modeling genre.The embedded element method is a mesh superposition technique used within finite element analysis.This method allows for the incorporation of axonal fiber tracts to be explicitly represented.Here,we explore the use of the approach beyond its original goal of predicting axonal strain in brain injury.We explore the potential application of the embedded element method in areas of electrophysiology,neurodegeneration,neuropharmacology and mechanobiology.We conclude that this method has the potential to provide us with an integrated computational framework that can assist in developing improved diagnostic tools and regeneration technologies.

High-current pulsed electron beam modification on microstructure and performance of Cu/CuW diffusion bonding joints

This study investigates the influence of high-current pulsed electron beam(HCPEB)modification on the microstructure and shear strength of Cu/CuW joints.Reliable solid-state diffusion bonding of modified-Cu(MCu)and modified-CuW(M-CuW)was achieved by HCPEB modification pretreatment at a temperature of 800-900℃and a pressure of 5 MPa for 10-50 min.Experiments demonstrate that HCPEB modification facilitates the dissolution of W and Cu,resulting in the formation of a Cu_(0.4)W_(0.6)solid solution and thus enhancing the uniform distribution of microstructures.Additionally,HCPEB-induced defects play a beneficial role in promoting the diffusion process by providing fast diffusion paths for elements.The optimal joints with the maximum shear strength of 213.7 MPa were obtained through bonding M-Cu and M-CuW at 900℃and 5 MPa for 30 min,which attributes to the combined effects of fine-grained strengthening and solid solution strengthening.Overall,the application of HCPEB modification showcases its effectiveness in promoting element diffusion and enhancing the mechanical performance of the joints.

Evolution of secondary phases and properties of 7B04 aluminum alloy during DC homogenization

The effects of the direct current （DC） on the evolutions of hardness and morphology of the secondary phases in 7B04 aluminum alloy homogenized at 380？465 ℃ for 2 h were investigated in detail by electric conductivity measurement, hardness test, X-ray diffraction analysis, field emission scanning electron microscopy and energy dispersive spectrometry. The results show that with increasing temperature from 380 to 465 ℃, the electric conductivity of normal homogenized sample decreases from 34.9%IACS to 28.7%IACS, the hardness increases from HV 96 to HV 146, and the area fraction of secondary phase reduces from 4.5% to 1.89%. While, DC homogenized sample has a higher hardness, a lower electric conductivity and a smaller area fraction of secondary phases at the same temperature. The DC enhances the homogenization process by promoting the diffusibility of the solute atoms and the mobility of vacancy.

Abnormal interfacial bonding mechanisms of multi-material additive-manufactured tungsten-stainless steel sandwich structure

Tungsten(W)and stainless steel(SS)are well known for the high melting point and good corrosion resistance respectively.Bimetallic W-SS structures would offer potential applications in extreme environments.In this study,a SS→W→SS sandwich structure is fabricated via a special laser powder bed fusion(LPBF)method based on an ultrasonic-assisted powder deposition mechanism.Material characterization of the SS→W interface and W→SS interface was conducted,including microstructure,element distribution,phase distribution,and nano-hardness.A coupled modelling method,combining computational fluid dynamics modelling with discrete element method,simulated the melt pool dynamics and solidification at the material interfaces.The study shows that the interface bonding of SS→W(SS printed on W)is the combined effect of solid-state diffusion with different elemental diffusion rates and grain boundary diffusion.The keyhole mode of the melt pool at the W→SS(W printed on SS)interface makes the pre-printed SS layers repeatedly remelted,causing the liquid W to flow into the sub-surface of the pre-printed SS through the keyhole cavities realizing the bonding of the W→SS interface.The above interfacial bonding behaviours are significantly different from the previously reported bonding mechanism based on the melt pool convection during multiple material LPBF.The abnormal material interfacial bonding behaviours are reported for the first time.

Diffusion behavior at void tip and its contributions to void shrinkage during solid-state bonding

Solid-state diffusion bonding is an advanced joining technique, which has been widely used to join similar or dissimilar materials. Generally, it is easy to observe the diffusion behavior during dissimilar bonding, but for similar bonding the diffusion behavior has yet been observed via experiments. In this study, the diffusion behavior at void tip was firstly observed during similar bonding of stainless steel. Scanning electron microscopy with energy dispersive spectroscopy was used to examine the interface charac- teristic and diffusion behavior. The results showed that a diffusion region was discovered at void tip. Element concentrations of diffusion region were more than those of void region, but less than those of bonded region. This behavior indicated that the diffusion was ongoing at void tip, but the perfect bond has yet formed. The diffusion region was attributed to the interface diffusion from adjacent region to void tip due to the stress gradient along bonding interface. The mass accumulation at void tip transformed the sharp void tip into smooth one at the beginning of void shrinkage, and then resulted in shorter voids.

Oxidation Performance and Interdiffusion Behaviour of two MCrAlY Coatings on a Fourth-Generation Single-Crystal Superalloy

The oxidation behaviour of a fourth-generation single-crystal superalloy without coating and with two types of MCrAlY coatings at 1140℃was studied.The results showed that both coatings greatly improved the oxidation resistance of the superalloy,and the addition of Hf further improved the oxidation resistance by pinning the oxide layer into the coating.Before and after oxidation,obvious Cr and Al interdiffusion was detected.Inward Cr diffusion induces the precipitation of a topologically close-packed phase,while the diffusion of Al affects the structure of theγ/γ’phase,the solubility of refractory elements,and the formation of an interdiffusion zone.

Distortion correction for the elemental images of integral imaging by introducing the directional diffuser

A distortion correction method for the elemental images of integral imaging（Ⅱ） by utilizing the directional diffuser is demonstrated. In the traditional Ⅱ, the distortion originating from lens aberration wraps elemental images and degrades the image quality severely. According to the theoretical analysis and experiments, it can be proved that the farther the three-dimensional image is displayed from the lens array, the more serious the distortion is. To analyze the process of eliminating lens distortion, one lens and its corresponding elemental image are separated from the traditional Ⅱ. By introducing the directional diffuser, the aperture stop of the separated optical system changes from the eye＇s pupil to the lens. In terms of contrast experiments, the distortion of the improved display system is corrected effectively. In the experiment, when the distance between the reconstructed image and lens array is equal to 120 mm, the largest lens distortion is decreased from 46.6% to 3.3%.

Ultra-fast amorphization of crystalline alloys by ultrasonic vibrations

The amorphization of alloys is of both broad scientific interests and engineering significance.Despite considered as an efficient strategy to regulate and even achieve record-breaking properties of metallic materials,a facile and rapid method to trigger solid-state amorphization is still being pursued.Here we report such a method to utilize ultrasonic vibration to trigger amorphization of intermetallic compound.The ultrasonic vibrations can cause tunable amorphization at room temperature and low stress(2 MPa)conveniently.Remarkably,the ultrasonic-induced amorphization could be achieved in 60 s,which is 360 times faster than the ball milling(2.16×10^(4) s)with the similar proportion of amorphization.The elements redistribute uniformly and rapidly via the activated short-circuit diffusion.Both experimental evidences and simulations show that the amorphous phase initiates and expands at nanograin boundaries,owing to the induction of lattice instability.This work provides a groundbreaking strategy for developing novel materials with tunable structures and properties.

Mechanism of adding rhenium to improve hot corrosion resistance of nickel-based single-crystal superalloys

Hot corrosion behavior in sulfate salt at 950℃ of Rene N5 single-crystal superalloys with 3 wt%rhenium(NSR)was investigated compared with that of nickel-based single-crystal superalloys without rhenium(NS).After 30-h corrosion,the surface of the NS superalloy is seriously corroded.Many holes and exfoliation appear on the surface.The NSR superalloys exhibit better hot corrosion resistance than the NS superalloys.After 30-h corrosion,a continuous and compact Al_(2)O_(3) film is observed on its surface.The Al_(2)O_(3) film with dense structure formed on the surface provides protection for the matrix.The characterization results show that A1 is aggregated in theγ’phase,while Re is aggregated in the y phase during the formation of oxide scale.Considering that Re can inhibit the diffusion of A1 in the nickel matrix,it is inferred that Re can inhibit the outward diffusion of A1 and prevent the decrease of Al concentration in theγ’phase.High concentration of Al hinders the decomposition of Al_(2)O_(3) due to the reaction of acid and basic dissolution.Al_(2)O_(3) keeps its structure intact and provides protection for the matrix.

Effects of Ni on austenite stability and fracture toughness in high Co-Ni secondary hardening steel

Three kinds of high Co Ni secondary hardening steels with different Ni contents were studied. The nanoscale austenite layers formed at the interface of matensite laths were observed. Both observation and diffusion kinetic simulation results showed that both Ni and Co did not obtain enough time to get the equilibrium content in this system. The Ni content in austenite layers decreased significantly, and Co content increased slightly with the decrease of Ni content in overall composition. The austenite stability was estimated by Olson-Cohen model, in which both chemical and mechanical driving force could be calculated by equilibrium thermodynamic and Mohr＇s circle methods, respectively. Simulation and mechanical test results showed that The decrease of Ni content in austenite layers would cause the change of austenite stability and decrease the fracture toughness of the steels. When the Ni content in the overall composition was lower than 7 wt. %, the Ni content in y phase would be lower than 20 wt.%. And the simulation value of M; （stress induced critical martensite transformation temperature） would be up to 80 ℃, which was about 60℃ higher than room temperature. Based on the analysis, the Ni content in the overall composition of high Co Ni secondary hardening steels should be higher than 8 wt. % in order to obtain a good fracture toughness.