In order to better describe the phenomenon of biological invasion,this paper introduces a free boundary model of biological invasion.Firstly,the right free boundary is added to the equation with logistic terms.Secondl...In order to better describe the phenomenon of biological invasion,this paper introduces a free boundary model of biological invasion.Firstly,the right free boundary is added to the equation with logistic terms.Secondly,the existence and uniqueness of local solutions are proved by the Sobolev embedding theorem and the comparison principle.Finally,according to the relevant research data and contents of red fire ants,the diffusion area and nest number of red fire ants were simulated without external disturbance.This paper mainly simulates the early diffusion process of red fire ants.In the early diffusion stage,red fire ants grow slowly and then spread over a large area after reaching a certain number.展开更多
Grain boundary diffusion technology is pivotal in the preparation of high-performance NdFeB magnets.This study investigates the factors that affect the efficiency of grain boundary diffusion,starting from the properti...Grain boundary diffusion technology is pivotal in the preparation of high-performance NdFeB magnets.This study investigates the factors that affect the efficiency of grain boundary diffusion,starting from the properties of the diffusion matrix.Through the adjustment of the sintering process,we effectively prepared magnets with varied densities that serve as the matrix for grain boundary diffusion with TbH,diffusion.The mobility characteristics of the Nd-rich phase during the densification stage are leveraged to ensure a more extensive distribution of heavy rare earth elements within the magnets.According to the experimental results,the increase in coercivity of low-density magnets after diffusion is significantly greater than that of relatively high-density magnets.The coercivity values measured are 805.32 kA/m for low-density magnets and 470.3 kA/m for high-density magnets.Additionally,grain boundary diffusion notably enhances the density of initial low-density magnets,addressing the issue of low density during the sintering stage.Before the diffusion treatment,the Nd-rich phases primarily concentrate at the triangular grain boundaries,resulting in an increased number of cavity defects in the magnets.These cavity defects contain atoms in a higher energy state,making them more prone to transition.Consequently,the diffusion activation energy at the void defects is lower than the intracrystalline diffusion activation energy,accelerating atom diffusion.The presence of larger cavities also provides more space for atom migration,thereby promoting the diffusion process.After the diffusion treatment,the proportion of bulk Nd-rich phases significantly decreases,and they infiltrate between the grains to fill the cavity defects,forming continuous fine grain boundaries.Based on these observations,the study aims to explore how to utilize this information to develop an efficient technique for grain boundary diffusion.展开更多
Asymmetric tilt boundaries on conventional twin boundaries(TBs)are significant for understanding the role of twins on coordinating plastic deformation in many metallic alloys.However,the formation modes of many asymme...Asymmetric tilt boundaries on conventional twin boundaries(TBs)are significant for understanding the role of twins on coordinating plastic deformation in many metallic alloys.However,the formation modes of many asymmetric tilt boundaries are hard to be accounted for based on traditional theoretical models,and the corresponding solute segregation is complex.Herein,atomic structures of a specific asymmetric boundary on{1012}TBs were reveled using aberration-corrected high-angle annular dark-field scanning transmission electron microscopy(HAADF-STEM),molecular dynamics(MD)and density functional theory(DFT)simulations.Reaction between<a60>M dislocations and the{1012}TB can generate a~61°/25°asymmetric tilt boundary.The segregation of Gd and Zn atoms is closely related to the aggregateddislocations and the interfacial interstices of the asymmetric tilt boundary,which is energetically favorable in reducing the total system energy.展开更多
To explore the relationship between dynamic characteristics and wake patterns,numerical simulations were conducted on three equal-diameter cylinders arranged in an equilateral triangle.The simulations varied reduced v...To explore the relationship between dynamic characteristics and wake patterns,numerical simulations were conducted on three equal-diameter cylinders arranged in an equilateral triangle.The simulations varied reduced velocities and gap spacing to observe flow-induced vibrations(FIVs).The immersed boundary–lattice Boltzmann flux solver(IB–LBFS)was applied as a numerical solution method,allowing for straightforward application on a simple Cartesian mesh.The accuracy and rationality of this method have been verified through comparisons with previous numerical results,including studies on flow past three stationary circular cylinders arranged in a similar pattern and vortex-induced vibrations of a single cylinder across different reduced velocities.When examining the FIVs of three cylinders,numerical simulations were carried out across a range of reduced velocities(3.0≤Ur≤13.0)and gap spacing(L=3D,4D,and 5D).The observed vibration response included several regimes:the desynchronization regime,the initial branch,and the lower branch.Notably,the transverse amplitude peaked,and a double vortex street formed in the wake when the reduced velocity reached the lower branch.This arrangement of three cylinders proved advantageous for energy capture as the upstream cylinder’s vibration response mirrored that of an isolated cylinder,while the response of each downstream cylinder was significantly enhanced.Compared to a single cylinder,the vibration and flow characteristics of this system are markedly more complex.The maximum transverse amplitudes of the downstream cylinders are nearly identical and exceed those observed in a single-cylinder set-up.Depending on the gap spacing,the flow pattern varied:it was in-phase for L=3D,antiphase for L=4D,and exhibited vortex shedding for L=5D.The wake configuration mainly featured double vortex streets for L=3D and evolved into two pairs of double vortex streets for L=5D.Consequently,it well illustrates the coupling mechanism that dynamics characteristics and wake vortex change with gap spacing and reduced velocities.展开更多
The combination of dual-main-phase(DMP)(Nd,Ce)-Fe-B magnets and grain boundary diffusion process(GBDP)is currently a research topic for obtaining high-cost performance materials in rare earth permanent magnet fields.T...The combination of dual-main-phase(DMP)(Nd,Ce)-Fe-B magnets and grain boundary diffusion process(GBDP)is currently a research topic for obtaining high-cost performance materials in rare earth permanent magnet fields.The novel structural features of GBDP(Nd,Ce)-Fe-B magnets give a version of different domain reversal processes from those of non-diffused magnets.In this work,the in-situ magnetic domain evolution of the DMP magnets was observed at elevated temperatures,and the temperature demagnetization and coercivity mechanism of the GBDP dual-main-phase(Nd,Ce)-Fe-B magnets are discussed.The results show that the shell composition of different types of grains in DMP magnets is similar,while the magnetic microstructure results indicate the Ce-rich grains tend to demagnetize first.Dy-rich shell with a high anisotropic field caused by GBDP leads to an increase in the nucleation field,which enhances the coercivity.It is found that much more grains exhibit single domain characteristics in the remanent state for GBDP dual-main-phase(Nd,Ce)-Fe-B magnets.In addition,the grains that undergo demagnetization first are Ce-rich or Nd-rich grains,which is different from that of non-diffused magnets.These results were not found in previous studies but can be intuitively characterized from the perspective of magnetic domains in this work,providing a new perspective and understanding of the performance improvement of magnetic materials.展开更多
The grain boundary diffusion process(GBDP)has proven to be an effective method for enhancing the coercivity of sintered Nd-Fe-B magnets.However,the limited diffusion depth and thicker shell struc-ture have impeded the...The grain boundary diffusion process(GBDP)has proven to be an effective method for enhancing the coercivity of sintered Nd-Fe-B magnets.However,the limited diffusion depth and thicker shell struc-ture have impeded the further development of magnetic properties.Currently,the primary debates re-garding the mechanism of GBDP with Tb revolve around the dissolution-solidification mechanism and the atomic substitution mechanism.To clarify this mechanism,the microstructure evolution of sintered Nd-Fe-B magnets during the heating process of GBDP has been systematically studied by quenching at different tem peratures.In this study,it was found that the formation of TbFe_(2) phase is related to the dis-solution of _(2)Fe_(14)B grains during GBDP with Tb.The theory of mixing heat and phase separation further confirms that the Nd_(2)Fe_(14)B phase dissolves to form a mixed phase of Nd and TbFe_(2),which then solidifies into the(Nd,Tb)_(2)Fe_(14)B phase.Based on the discovery of the TbFe_(2) phase,the dissolution-solidification mechanism is considered the primary mechanism for GBDP.This is supported by the elemental content of the two typical core-shell structures observed.展开更多
This study aims to clarify the mechanisms for the grain boundary(GB)segregation through investigating the absorption of excess solute atoms at GBs in Al−Cu alloys by using the hybrid molecular dynamics/Monte Carlo sim...This study aims to clarify the mechanisms for the grain boundary(GB)segregation through investigating the absorption of excess solute atoms at GBs in Al−Cu alloys by using the hybrid molecular dynamics/Monte Carlo simulations.Two segregation mechanisms,substitutional and interstitial mechanisms,are observed.The intergranular defects,including dislocations,steps and vacancies,and the intervals in structural units are conductive to the prevalence of interstitial mechanism.And substitutional mechanism is favored by the highly ordered twin GBs.Furthermore,the two mechanisms affect the GB structure differently.It is quantified that interstitial mechanism is less destructive to GB structure than substitutional one,and often leads to a segregation level being up to about 6 times higher than the latter.These findings contribute to atomic scale insights into the microscopic mechanisms about how solute atoms are absorbed by GB structures,and clarify the correlation among intergranular structures,segregation mechanisms and kinetics.展开更多
Three types of NdFeB magnets with the same composition and different grain sizes were prepared,and then the grain boundary diffusion was conducted using metal Tb under the same technical parameters.The effect of grain...Three types of NdFeB magnets with the same composition and different grain sizes were prepared,and then the grain boundary diffusion was conducted using metal Tb under the same technical parameters.The effect of grain size on the grain boundary diffusion process and properties of sintered NdFeB magnets was investigated.The diffusion process was assessed using X-ray diffractometer,field emission scanning electron microscope,and electron probe microanalyzer.The magnetic properties of the magnet before and after diffusion were investigated.The results show that the grain refinement of the magnet leads to higher Tb utilization efficiency and results in higher coercivity at different temperatures.It can be attributed to the formation of a deeper and more complete core-shell structure,resulting in better magnetic isolation and higher anisotropy of the Nd_(2)Fe_(14)B grains.This work may shed light on developing high coercivity with low heavy rare earth elements through grain refinement.展开更多
Pb(Zr,Ti)O_(3)-Pb(Zn_(1/3)Nb_(2/3))O_(3) (PZT-PZN) based ceramics, as important piezoelectric materials, have a wide range of applications in fields such as sensors and actuators, thus the optimization of their piezoe...Pb(Zr,Ti)O_(3)-Pb(Zn_(1/3)Nb_(2/3))O_(3) (PZT-PZN) based ceramics, as important piezoelectric materials, have a wide range of applications in fields such as sensors and actuators, thus the optimization of their piezoelectric properties has been a hot research topic. This study investigated the effects of phase boundary engineering and domain engineering on (1-x)[0.8Pb(Zr_(0.5)Ti_(0.5))O_(3)-0.2Pb(Zn_(1/3)Nb_(2/3))O_(3)]-xBi(Zn_(0.5)Ti_(0.5))O_(3) ((1-x)(0.8PZT-0.2PZN)- xBZT) ceramic to obtain excellent piezoelectric properties. The crystal phase structure and microstructure of ceramic samples were characterized. The results showed that all samples had a pure perovskite structure, and the addition of BZT gradually increased the grain size. The addition of BZT caused a phase transition in ceramic samples from the morphotropic phase boundary (MPB) towards the tetragonal phase region, which is crucial for optimizing piezoelectric properties. By adjusting content of BZT and precisely controlling position of the phase boundary, the piezoelectric performance can be optimized. Domain structure is one of the key factors affecting piezoelectric performance. By using domain engineering techniques to optimize grain size and domain size, piezoelectric properties of ceramic samples have been significantly improved. Specifically, excellent piezoelectric properties (piezoelectric constant d_(33)=320 pC/N, electromechanical coupling factor kp=0.44) were obtained simultaneously for x=0.08. Based on experimental results and theoretical analysis, influence mechanisms of phase boundary engineering and domain engineering on piezoelectric properties were explored. The study shows that addition of BZT not only promotes grain growth, but also optimizes the domain structure, enabling the polarization reversal process easier, thereby improving piezoelectric properties. These research results not only provide new ideas for the design of high-performance piezoelectric ceramics, but also lay a theoretical foundation for development of related electronic devices.展开更多
Due to the coexistence of compressibility,viscosity,and threedimensional effects,laminar flow is difficult to maintain for high-speed boundary layer on complex geometries.The unstable disturbance waves in the boundary...Due to the coexistence of compressibility,viscosity,and threedimensional effects,laminar flow is difficult to maintain for high-speed boundary layer on complex geometries.The unstable disturbance waves in the boundary layer are excited and rapidly increase during the receptivity process,so sufficiently large Reynolds stress causes the basic flow velocity profile to change,and the formation of turbulence is inevitable.展开更多
The diffuse-interface immersed boundary method(IBM)possesses excellent capabilities for simulating flows around complex geometries and moving boundaries.In this method,the flow field is solved on a fixed Cartesian mes...The diffuse-interface immersed boundary method(IBM)possesses excellent capabilities for simulating flows around complex geometries and moving boundaries.In this method,the flow field is solved on a fixed Cartesian mesh,while the solid boundary is discretized into a series of Lagrangian points immersed in the flow field.The boundary condition is implemented by introducing a force term into the momentum equation,and the interaction between the immersed boundary and the fluid domain is achieved via an interpolation process.Over the past decades,the diffuse-interface IBM has gained popularity and spawned many variants,effectively handling a wide range of flow problems from isothermal to thermal flows,from laminar to turbulent flows,and from complex geometries to fluidstructure interaction scenarios.This paper first outlines the basic principles of the diffuse-interface IBM,then highlights recent advancements achieved by the authors’research group,and finally shows the method’s excellent numerical performance and wide applicability through several case studies involving complex moving boundary problems.展开更多
The traditional topology optimization method of continuum structure generally uses quadrilateral elements as the basic mesh.This approach often leads to jagged boundary issues,which are traditionally addressed through...The traditional topology optimization method of continuum structure generally uses quadrilateral elements as the basic mesh.This approach often leads to jagged boundary issues,which are traditionally addressed through post-processing,potentially altering the mechanical properties of the optimized structure.A topology optimization method of Movable Morphable Smooth Boundary(MMSB)is proposed based on the idea of mesh adaptation to solve the problem of jagged boundaries and the influence of post-processing.Based on the ICM method,the rational fraction function is introduced as the filtering function,and a topology optimization model with the minimum weight as the objective and the displacement as the constraint is established.A triangular mesh is utilized as the base mesh in this method.The mesh is re-divided in the optimization process based on the contour line,and a smooth boundary parallel to the contour line is obtained.Numerical examples demonstrate that the MMSB method effectively resolves the jagged boundary issues,leading to enhanced structural performance.展开更多
Vorticity is locally generated on a boundary at a rate measured by the boundary vorticity flux(BVF),which can be further decomposed into the sum of the orbital rotation and the generalized spin(specifically,the sum of...Vorticity is locally generated on a boundary at a rate measured by the boundary vorticity flux(BVF),which can be further decomposed into the sum of the orbital rotation and the generalized spin(specifically,the sum of shear and streaming vorticity)under the field description.For an incompressible viscous flow interacting with a stationary wall,the full expressions of the boundary fluxes of the orbital rotation and the spin are derived,for the first time,to elucidate their boundary creation mechanisms.Then,these new findings are successfully extended to the study of the boundary enstrophy dynamics,as well as the Lyman vorticity dynamics as an alternative interpretation to the boundary vorticity dynamics.Interestingly,it is found that the boundary coupling of the longitudinal and transverse processes is only embodied in the boundary spin flux,which is definitely not responsible for the generation of the boundary orbital-rotation flux.In addition,the boundary fluxes of enstrophy are directly associated with the boundary source of the second principal invariant of the velocity gradient tensor(VGT)and the two quadratic forms representing the spin-geometry interaction.The present exposition provides a new perspective and an additional dimension for understanding the vorticity dynamics on boundaries,which could be valuable in clarifying the formation mechanisms of near-wall coherent structures and flow noise at the fundamental level.展开更多
Numerical simulations were conducted on a 10-blade Sevik rotor ingesting wake downstream of two turbulence-generating grids.These simulations were based on implicit large-eddy simulation(ILES)and the boundary data imm...Numerical simulations were conducted on a 10-blade Sevik rotor ingesting wake downstream of two turbulence-generating grids.These simulations were based on implicit large-eddy simulation(ILES)and the boundary data immersion method(BDIM)for compressible flows,which were solved using a fully self-programmed Fortran code.Results show that the predicted thrust spectrum aligns closely with the experimental measurements.In addition,it captures the thrust dipole directivity of the noise around the rotating propeller due to random pressure pulsations on the blades,as well as the flow structures simultaneously.Furthermore,the differences in the statistical characteristics,flow structures,and low-frequency broadband thrust spectra due to different turbulence levels were investigated.This analysis indicates that the interaction between the upstream,which is characterized by a lower turbulence level and a higher turbulent length of scale,and the rotating propeller results in a lower amplitude in force spectra and a slight increase in the scale of tip vortices.展开更多
Cowl-induced incident Shock Wave/Boundary Layer Interactions (SWBLI) under the influence of gradual expansion waves are frequently observed in supersonic inlets. However, the analysis and prediction of interaction len...Cowl-induced incident Shock Wave/Boundary Layer Interactions (SWBLI) under the influence of gradual expansion waves are frequently observed in supersonic inlets. However, the analysis and prediction of interaction lengths have not been sufficiently investigated. First, this study presents a theoretical scaling analysis and validates it through wind tunnel experiments. It conducts detailed control volume analysis of mass conservation, considering the differences between inviscid and viscous cases. Then, three models for analysing interaction length under gradual expansion waves are derived. Related experiments using schlieren photography are conducted to validate the models in a Mach 2.73 flow. The interaction scales are captured at various relative distances between the shock impingement location and the expansion regions with wedge angles ranging from 12° to 15° and expansion angles of 9°, 12°, and 15°. Three trend lines are plotted based on different expansion angles to depict the relationship between normalised interaction length and normalised interaction strength metric. In addition, the relationship between the coefficients of the trend line and the expansion angles is introduced to predict the interaction length influenced by gradual expansion waves. Finally, the estimation of normalised interaction length is derived for various coefficients within a unified form.展开更多
When immersed in sand and dust environment,aero-engine blades are exposed to harsh erosion which may lead to failure if erosion is severe.Using Physical Vapor Deposition(PVD)to prepare hard ceramic coatings can greatl...When immersed in sand and dust environment,aero-engine blades are exposed to harsh erosion which may lead to failure if erosion is severe.Using Physical Vapor Deposition(PVD)to prepare hard ceramic coatings can greatly enhance the operational capabilities of aero-engine.However,due to the“line-of-sight”processing characteristic of PVD process,uneven coating deposition rates occur when preparing coatings on obstructed areas such as blisks.Quantitative research on such phenomena is few,and it is even rarer in the study of aero-engine coatings.Based on the analyses and considerations of the geometric shape of blade surfaces and the influence of both deposition and re-sputtering effect,an ideal model is established to analyze the deposition rate variation along blocked region in complex self-shadowing boundaries.The relative deposition rates at various locations on the blade surface within the inter-blade gaps are quantitatively calculated and experimentally validated.Furthermore,differences in erosion resistance of the coatings are tested.The conclusions are drawn as follows:the geometric configuration of the obstructed shape and resputtering phenomenon significantly influence the deposition rates within the inner wall of blade gaps.Taking the structural configuration as an example,in a 25 mm×60 mm×15 mm gap,the coating thickness can vary more than 252%from the thickest to the thinnest location.The deposition rates of various locations are proportional to the solid angle of incident ion in more obstructed regions,and the re-sputtering is more prominent in open regions.Obstructive boundaries directly affect the erosion resistance at various locations within the gaps,with erosion failure time decreasing by 40%in heavily blocked region compared to open region.展开更多
THE mechanical response and deformation mechanisms of pure nickel under nanoindentation were systematically investigated using molecular dynamics(MD)simulations,with a particular focus on the novel interplay between c...THE mechanical response and deformation mechanisms of pure nickel under nanoindentation were systematically investigated using molecular dynamics(MD)simulations,with a particular focus on the novel interplay between crystallographic orientation,grain boundary(GB)proximity,and pore characteristics(size/location).This study compares single-crystal nickel models along[100],[110],and[111]orientations with equiaxed polycrystalline models containing 0,1,and 2.5 nm pores in surface and subsurface configurations.Our results reveal that crystallographic anisotropy manifests as a 24.4%higher elastic modulus and 22.2%greater hardness in[111]-oriented single crystals compared to[100].Pore-GB synergistic effects are found to dominate the deformation behavior:2.5 nm subsurface pores reduce hardness by 25.2%through stress concentration and dislocation annihilation at GBs,whereas surface pores enable mechanical recovery via accelerated dislocation generation post-collapse.Additionally,size-dependent deformation regimes were identified,with 1 nm pores inducing negligible perturbation due to rapid atomic rearrangement,in contrast with persistent softening in 2.5 nm pores.These findings establish atomic-scale design principles for defect engineering in nickel-based aerospace components,demonstrating how crystallographic orientation,pore configuration,and GB interactions collectively govern nanoindentation behavior.展开更多
Hypersonic boundary-layer receptivity to freestream entropy and vorticity waves is investigated using direct numerical simula-tions for a Mach 6 flow over a 5.08 mm nose radius cone.Two frequencies of 33 kHz and 150 k...Hypersonic boundary-layer receptivity to freestream entropy and vorticity waves is investigated using direct numerical simula-tions for a Mach 6 flow over a 5.08 mm nose radius cone.Two frequencies of 33 kHz and 150 kHz are considered to be rep-resentative of the first and second instability modes,respectively.For the first mode,wall pressure fluctuations for both entropy and vorticity wave cases exhibit a strong modulation yet without a growing trend,indicating that the first mode is not generated despite its instability predicted by linear stability theory.The potential reason for this is the absence of postshock slow acoustic waves capable of synchronizing with the first mode.By contrast,for the second mode,a typical three-stage boundary-layer response is observed,consistent with that to slow acoustic waves studied previously.Furthermore,the postshock disturbances outside the boundary layer can be decomposed into the entropy(density/temperature fluctuations)and vorticity components(ve-locity fluctuations),and the latter is shown to play a leading role in generating the second mode,even for the case with entropy waves where the density/temperature fluctuations dominate the postshock regions.展开更多
This study was used oceanographic database in the Sea of Okhotsk between the period from 1929 to 2020(131286 stations).The paper used gas hydrate dissociation parameters for the“pure methane-seawater”system obtained...This study was used oceanographic database in the Sea of Okhotsk between the period from 1929 to 2020(131286 stations).The paper used gas hydrate dissociation parameters for the“pure methane-seawater”system obtained in the study by Dickens GR and Quinby-Hunt MS.The results have elucidated the spatiotemporal variability of distribution of such parameters at the upper boundary of the gas hydrate stability zone(GHSZ)as water temperature,salinity,and top depth of the stability zone.As the study has shown(based on average long-term spatial distributions),the minimum temperature and depth values of the GHSZ upper boundary in the Sea of Okhotsk occur off the western and southwestern parts of the water area.The maximum temperature and depth values of the GHSZ upper boundary are typical of the southeastern sea area and over the Kamchatka Peninsula slope.This study has also identified an area,where there are no thermobaric conditions for the emergence and stable existence of methane hydrates in the water column.The results presented agree well with the materials of observations conducted during expeditions and the previous data of predictive simulations for the Sea of Okhotsk.展开更多
In recent years,(0001)twist grain boundaries(BTGBs)located in primary α grain clusters were identified as fatigue crack nucleation sites in different Ti alloys.In the present study,crack initiation was investigated i...In recent years,(0001)twist grain boundaries(BTGBs)located in primary α grain clusters were identified as fatigue crack nucleation sites in different Ti alloys.In the present study,crack initiation was investigated in a bimodal Ti-5Al-4 V alloy subjected to low-cycle fatigue and dwell-fatigue loadings at room temperature.The low fraction of primary α grains was not associated with a lack of sensitivity to BTGB cracking.Transmission electron microscopy and electron back-scattered diffraction were used to characterize BTGBs in the initial microstructure.The fatigue mechanisms were then analyzed with a focus on dislocation activity.α_(p) grains adjacent to cracked BTGBs contained a high dislocation density.It was primarily composed of planar slip bands of dislocations.In addition,<c+a>dislocations were noticed in the vicinity of cracked BTGBs.They supposedly pertain to crack tip plasticity during growth,and no evidence of a role of an incoming slip event in crack nucleation was obtained.Also,basal slip bands extending across adjacent grains were found to emerge from BTGBs.This feature provides an easier path for crack extension when growth along the grain boundary becomes difficult owing to a deviation from the basal plane.Atom probe tomography analyses evidenced V and Fe segregation at a grain boundary with a significant deviation from the BTGB configuration.This suggests a possible contribution of local solute segregation to the high cracking resistance of general α_(p)/α_(p) grain boundaries.This work provides new insights into the mechanisms involved in cracking of BTGB in Ti alloys subjected to cyclic loadings.展开更多
基金Supported by National Natural Science Foundation of China(12101482)Postdoctoral Science Foundation of China(2022M722604)+2 种基金General Project of Science and Technology of Shaanxi Province(2023-YBSF-372)The Natural Science Foundation of Shaan Xi Province(2023-JCQN-0016)Shannxi Mathmatical Basic Science Research Project(23JSQ042)。
文摘In order to better describe the phenomenon of biological invasion,this paper introduces a free boundary model of biological invasion.Firstly,the right free boundary is added to the equation with logistic terms.Secondly,the existence and uniqueness of local solutions are proved by the Sobolev embedding theorem and the comparison principle.Finally,according to the relevant research data and contents of red fire ants,the diffusion area and nest number of red fire ants were simulated without external disturbance.This paper mainly simulates the early diffusion process of red fire ants.In the early diffusion stage,red fire ants grow slowly and then spread over a large area after reaching a certain number.
基金Project supported by the National Natural Science Foundation of China(52361033)National Key Research and Development Program(2022YFB3505400)+3 种基金Ministry of Industry and Information Technology Heavy Rare Earth Special Use of Sintered NdFeB Project(TC220H06J)Academic and Technical Leaders in Major Disciplines in Jiangxi Province(2022BCJ23007)Jiangxi Province Science and Technology Cooperation Key Project(20212BDH80007)Jiangxi Graduate Student Innovation Special Fund Project(YC2023-B213)。
文摘Grain boundary diffusion technology is pivotal in the preparation of high-performance NdFeB magnets.This study investigates the factors that affect the efficiency of grain boundary diffusion,starting from the properties of the diffusion matrix.Through the adjustment of the sintering process,we effectively prepared magnets with varied densities that serve as the matrix for grain boundary diffusion with TbH,diffusion.The mobility characteristics of the Nd-rich phase during the densification stage are leveraged to ensure a more extensive distribution of heavy rare earth elements within the magnets.According to the experimental results,the increase in coercivity of low-density magnets after diffusion is significantly greater than that of relatively high-density magnets.The coercivity values measured are 805.32 kA/m for low-density magnets and 470.3 kA/m for high-density magnets.Additionally,grain boundary diffusion notably enhances the density of initial low-density magnets,addressing the issue of low density during the sintering stage.Before the diffusion treatment,the Nd-rich phases primarily concentrate at the triangular grain boundaries,resulting in an increased number of cavity defects in the magnets.These cavity defects contain atoms in a higher energy state,making them more prone to transition.Consequently,the diffusion activation energy at the void defects is lower than the intracrystalline diffusion activation energy,accelerating atom diffusion.The presence of larger cavities also provides more space for atom migration,thereby promoting the diffusion process.After the diffusion treatment,the proportion of bulk Nd-rich phases significantly decreases,and they infiltrate between the grains to fill the cavity defects,forming continuous fine grain boundaries.Based on these observations,the study aims to explore how to utilize this information to develop an efficient technique for grain boundary diffusion.
基金supported by the Scientific and Technological Developing Scheme of Jilin Province under grants no.YDZJ202301ZYTS538the Chinese Academy of Sciences Youth Innovation Promotion Association under grants number 2023234+3 种基金the National Natural Science Foundation of China under grants number U21A20323the Scientific and Technological Developing Scheme of Jilin Province under grants no.SKL202302038the Major Scientific and Technological Projects of Hebei Province under grants No.23291001Zthe Scientific and Technology Project of Hanjiang District.
文摘Asymmetric tilt boundaries on conventional twin boundaries(TBs)are significant for understanding the role of twins on coordinating plastic deformation in many metallic alloys.However,the formation modes of many asymmetric tilt boundaries are hard to be accounted for based on traditional theoretical models,and the corresponding solute segregation is complex.Herein,atomic structures of a specific asymmetric boundary on{1012}TBs were reveled using aberration-corrected high-angle annular dark-field scanning transmission electron microscopy(HAADF-STEM),molecular dynamics(MD)and density functional theory(DFT)simulations.Reaction between<a60>M dislocations and the{1012}TB can generate a~61°/25°asymmetric tilt boundary.The segregation of Gd and Zn atoms is closely related to the aggregateddislocations and the interfacial interstices of the asymmetric tilt boundary,which is energetically favorable in reducing the total system energy.
基金Supported by the National Natural Science Foundation of China(52201350,52201394,and 52271301)the Innovation Group Project of Southern Marine Science and Engineering Guangdong Laboratory(Zhuhai)(Grant No.SML2022008).
文摘To explore the relationship between dynamic characteristics and wake patterns,numerical simulations were conducted on three equal-diameter cylinders arranged in an equilateral triangle.The simulations varied reduced velocities and gap spacing to observe flow-induced vibrations(FIVs).The immersed boundary–lattice Boltzmann flux solver(IB–LBFS)was applied as a numerical solution method,allowing for straightforward application on a simple Cartesian mesh.The accuracy and rationality of this method have been verified through comparisons with previous numerical results,including studies on flow past three stationary circular cylinders arranged in a similar pattern and vortex-induced vibrations of a single cylinder across different reduced velocities.When examining the FIVs of three cylinders,numerical simulations were carried out across a range of reduced velocities(3.0≤Ur≤13.0)and gap spacing(L=3D,4D,and 5D).The observed vibration response included several regimes:the desynchronization regime,the initial branch,and the lower branch.Notably,the transverse amplitude peaked,and a double vortex street formed in the wake when the reduced velocity reached the lower branch.This arrangement of three cylinders proved advantageous for energy capture as the upstream cylinder’s vibration response mirrored that of an isolated cylinder,while the response of each downstream cylinder was significantly enhanced.Compared to a single cylinder,the vibration and flow characteristics of this system are markedly more complex.The maximum transverse amplitudes of the downstream cylinders are nearly identical and exceed those observed in a single-cylinder set-up.Depending on the gap spacing,the flow pattern varied:it was in-phase for L=3D,antiphase for L=4D,and exhibited vortex shedding for L=5D.The wake configuration mainly featured double vortex streets for L=3D and evolved into two pairs of double vortex streets for L=5D.Consequently,it well illustrates the coupling mechanism that dynamics characteristics and wake vortex change with gap spacing and reduced velocities.
基金supported by the National Key Research and Development Program of China(Nos.2021YFB3503003,2021YFB3503100,and 2022YFB3505401).
文摘The combination of dual-main-phase(DMP)(Nd,Ce)-Fe-B magnets and grain boundary diffusion process(GBDP)is currently a research topic for obtaining high-cost performance materials in rare earth permanent magnet fields.The novel structural features of GBDP(Nd,Ce)-Fe-B magnets give a version of different domain reversal processes from those of non-diffused magnets.In this work,the in-situ magnetic domain evolution of the DMP magnets was observed at elevated temperatures,and the temperature demagnetization and coercivity mechanism of the GBDP dual-main-phase(Nd,Ce)-Fe-B magnets are discussed.The results show that the shell composition of different types of grains in DMP magnets is similar,while the magnetic microstructure results indicate the Ce-rich grains tend to demagnetize first.Dy-rich shell with a high anisotropic field caused by GBDP leads to an increase in the nucleation field,which enhances the coercivity.It is found that much more grains exhibit single domain characteristics in the remanent state for GBDP dual-main-phase(Nd,Ce)-Fe-B magnets.In addition,the grains that undergo demagnetization first are Ce-rich or Nd-rich grains,which is different from that of non-diffused magnets.These results were not found in previous studies but can be intuitively characterized from the perspective of magnetic domains in this work,providing a new perspective and understanding of the performance improvement of magnetic materials.
基金supported by the National Key Research and Development Program of China(2022YFB3505503)the National Natural Science Foundation of China(52201230)+2 种基金the Key R&D Program of Shandong Province(2022CXGC020307)the China Postdoctoral Science Foundation(2022M71204)the Beijing NOVA Program(Z211100002121092).
文摘The grain boundary diffusion process(GBDP)has proven to be an effective method for enhancing the coercivity of sintered Nd-Fe-B magnets.However,the limited diffusion depth and thicker shell struc-ture have impeded the further development of magnetic properties.Currently,the primary debates re-garding the mechanism of GBDP with Tb revolve around the dissolution-solidification mechanism and the atomic substitution mechanism.To clarify this mechanism,the microstructure evolution of sintered Nd-Fe-B magnets during the heating process of GBDP has been systematically studied by quenching at different tem peratures.In this study,it was found that the formation of TbFe_(2) phase is related to the dis-solution of _(2)Fe_(14)B grains during GBDP with Tb.The theory of mixing heat and phase separation further confirms that the Nd_(2)Fe_(14)B phase dissolves to form a mixed phase of Nd and TbFe_(2),which then solidifies into the(Nd,Tb)_(2)Fe_(14)B phase.Based on the discovery of the TbFe_(2) phase,the dissolution-solidification mechanism is considered the primary mechanism for GBDP.This is supported by the elemental content of the two typical core-shell structures observed.
基金supported by grants from the National Natural Science Foundation of China(Nos.52031017,51801237)the National Key Laboratory of Science and Technology on High-strength Structural Materials in Central South University,China(No.6142912200106).
文摘This study aims to clarify the mechanisms for the grain boundary(GB)segregation through investigating the absorption of excess solute atoms at GBs in Al−Cu alloys by using the hybrid molecular dynamics/Monte Carlo simulations.Two segregation mechanisms,substitutional and interstitial mechanisms,are observed.The intergranular defects,including dislocations,steps and vacancies,and the intervals in structural units are conductive to the prevalence of interstitial mechanism.And substitutional mechanism is favored by the highly ordered twin GBs.Furthermore,the two mechanisms affect the GB structure differently.It is quantified that interstitial mechanism is less destructive to GB structure than substitutional one,and often leads to a segregation level being up to about 6 times higher than the latter.These findings contribute to atomic scale insights into the microscopic mechanisms about how solute atoms are absorbed by GB structures,and clarify the correlation among intergranular structures,segregation mechanisms and kinetics.
基金Key Research and Development Program of Shandong Province(2021CXGC010310)Shandong Province Science and Technology Small and Medium Sized Enterprise Innovation Ability Enhancement Project(2023TSGC0287,2024TSGC0519)+1 种基金Shandong Provincial Natural Science Foundation(ZR2022ME222)National Natural Science Foundation of China(51702187)。
文摘Three types of NdFeB magnets with the same composition and different grain sizes were prepared,and then the grain boundary diffusion was conducted using metal Tb under the same technical parameters.The effect of grain size on the grain boundary diffusion process and properties of sintered NdFeB magnets was investigated.The diffusion process was assessed using X-ray diffractometer,field emission scanning electron microscope,and electron probe microanalyzer.The magnetic properties of the magnet before and after diffusion were investigated.The results show that the grain refinement of the magnet leads to higher Tb utilization efficiency and results in higher coercivity at different temperatures.It can be attributed to the formation of a deeper and more complete core-shell structure,resulting in better magnetic isolation and higher anisotropy of the Nd_(2)Fe_(14)B grains.This work may shed light on developing high coercivity with low heavy rare earth elements through grain refinement.
基金National Natural Science Foundation of China (52202139, 52072178)。
文摘Pb(Zr,Ti)O_(3)-Pb(Zn_(1/3)Nb_(2/3))O_(3) (PZT-PZN) based ceramics, as important piezoelectric materials, have a wide range of applications in fields such as sensors and actuators, thus the optimization of their piezoelectric properties has been a hot research topic. This study investigated the effects of phase boundary engineering and domain engineering on (1-x)[0.8Pb(Zr_(0.5)Ti_(0.5))O_(3)-0.2Pb(Zn_(1/3)Nb_(2/3))O_(3)]-xBi(Zn_(0.5)Ti_(0.5))O_(3) ((1-x)(0.8PZT-0.2PZN)- xBZT) ceramic to obtain excellent piezoelectric properties. The crystal phase structure and microstructure of ceramic samples were characterized. The results showed that all samples had a pure perovskite structure, and the addition of BZT gradually increased the grain size. The addition of BZT caused a phase transition in ceramic samples from the morphotropic phase boundary (MPB) towards the tetragonal phase region, which is crucial for optimizing piezoelectric properties. By adjusting content of BZT and precisely controlling position of the phase boundary, the piezoelectric performance can be optimized. Domain structure is one of the key factors affecting piezoelectric performance. By using domain engineering techniques to optimize grain size and domain size, piezoelectric properties of ceramic samples have been significantly improved. Specifically, excellent piezoelectric properties (piezoelectric constant d_(33)=320 pC/N, electromechanical coupling factor kp=0.44) were obtained simultaneously for x=0.08. Based on experimental results and theoretical analysis, influence mechanisms of phase boundary engineering and domain engineering on piezoelectric properties were explored. The study shows that addition of BZT not only promotes grain growth, but also optimizes the domain structure, enabling the polarization reversal process easier, thereby improving piezoelectric properties. These research results not only provide new ideas for the design of high-performance piezoelectric ceramics, but also lay a theoretical foundation for development of related electronic devices.
文摘Due to the coexistence of compressibility,viscosity,and threedimensional effects,laminar flow is difficult to maintain for high-speed boundary layer on complex geometries.The unstable disturbance waves in the boundary layer are excited and rapidly increase during the receptivity process,so sufficiently large Reynolds stress causes the basic flow velocity profile to change,and the formation of turbulence is inevitable.
基金partially supported by the National Natural Science Foundation of China(Nos.92271103,12202191)。
文摘The diffuse-interface immersed boundary method(IBM)possesses excellent capabilities for simulating flows around complex geometries and moving boundaries.In this method,the flow field is solved on a fixed Cartesian mesh,while the solid boundary is discretized into a series of Lagrangian points immersed in the flow field.The boundary condition is implemented by introducing a force term into the momentum equation,and the interaction between the immersed boundary and the fluid domain is achieved via an interpolation process.Over the past decades,the diffuse-interface IBM has gained popularity and spawned many variants,effectively handling a wide range of flow problems from isothermal to thermal flows,from laminar to turbulent flows,and from complex geometries to fluidstructure interaction scenarios.This paper first outlines the basic principles of the diffuse-interface IBM,then highlights recent advancements achieved by the authors’research group,and finally shows the method’s excellent numerical performance and wide applicability through several case studies involving complex moving boundary problems.
基金supported by the National Natural Science Foundation of China(Grant 12472113).
文摘The traditional topology optimization method of continuum structure generally uses quadrilateral elements as the basic mesh.This approach often leads to jagged boundary issues,which are traditionally addressed through post-processing,potentially altering the mechanical properties of the optimized structure.A topology optimization method of Movable Morphable Smooth Boundary(MMSB)is proposed based on the idea of mesh adaptation to solve the problem of jagged boundaries and the influence of post-processing.Based on the ICM method,the rational fraction function is introduced as the filtering function,and a topology optimization model with the minimum weight as the objective and the displacement as the constraint is established.A triangular mesh is utilized as the base mesh in this method.The mesh is re-divided in the optimization process based on the contour line,and a smooth boundary parallel to the contour line is obtained.Numerical examples demonstrate that the MMSB method effectively resolves the jagged boundary issues,leading to enhanced structural performance.
基金Project supported by the National Natural Science Foundation of China(No.12402262)。
文摘Vorticity is locally generated on a boundary at a rate measured by the boundary vorticity flux(BVF),which can be further decomposed into the sum of the orbital rotation and the generalized spin(specifically,the sum of shear and streaming vorticity)under the field description.For an incompressible viscous flow interacting with a stationary wall,the full expressions of the boundary fluxes of the orbital rotation and the spin are derived,for the first time,to elucidate their boundary creation mechanisms.Then,these new findings are successfully extended to the study of the boundary enstrophy dynamics,as well as the Lyman vorticity dynamics as an alternative interpretation to the boundary vorticity dynamics.Interestingly,it is found that the boundary coupling of the longitudinal and transverse processes is only embodied in the boundary spin flux,which is definitely not responsible for the generation of the boundary orbital-rotation flux.In addition,the boundary fluxes of enstrophy are directly associated with the boundary source of the second principal invariant of the velocity gradient tensor(VGT)and the two quadratic forms representing the spin-geometry interaction.The present exposition provides a new perspective and an additional dimension for understanding the vorticity dynamics on boundaries,which could be valuable in clarifying the formation mechanisms of near-wall coherent structures and flow noise at the fundamental level.
基金Supported by the National Key R&D Program of China(2022YFB3303500).
文摘Numerical simulations were conducted on a 10-blade Sevik rotor ingesting wake downstream of two turbulence-generating grids.These simulations were based on implicit large-eddy simulation(ILES)and the boundary data immersion method(BDIM)for compressible flows,which were solved using a fully self-programmed Fortran code.Results show that the predicted thrust spectrum aligns closely with the experimental measurements.In addition,it captures the thrust dipole directivity of the noise around the rotating propeller due to random pressure pulsations on the blades,as well as the flow structures simultaneously.Furthermore,the differences in the statistical characteristics,flow structures,and low-frequency broadband thrust spectra due to different turbulence levels were investigated.This analysis indicates that the interaction between the upstream,which is characterized by a lower turbulence level and a higher turbulent length of scale,and the rotating propeller results in a lower amplitude in force spectra and a slight increase in the scale of tip vortices.
基金co-supported by the National Natural Science Foundation of China (No. 12172175)the National Science and Technology Major Project, China (No. J2019-II0014-0035)the Science Center for Gas Turbine Project, China (Nos. P2022-C-II-002-001, P2022-A-II-002-001)
文摘Cowl-induced incident Shock Wave/Boundary Layer Interactions (SWBLI) under the influence of gradual expansion waves are frequently observed in supersonic inlets. However, the analysis and prediction of interaction lengths have not been sufficiently investigated. First, this study presents a theoretical scaling analysis and validates it through wind tunnel experiments. It conducts detailed control volume analysis of mass conservation, considering the differences between inviscid and viscous cases. Then, three models for analysing interaction length under gradual expansion waves are derived. Related experiments using schlieren photography are conducted to validate the models in a Mach 2.73 flow. The interaction scales are captured at various relative distances between the shock impingement location and the expansion regions with wedge angles ranging from 12° to 15° and expansion angles of 9°, 12°, and 15°. Three trend lines are plotted based on different expansion angles to depict the relationship between normalised interaction length and normalised interaction strength metric. In addition, the relationship between the coefficients of the trend line and the expansion angles is introduced to predict the interaction length influenced by gradual expansion waves. Finally, the estimation of normalised interaction length is derived for various coefficients within a unified form.
基金financially supported by the Shaanxi Provincial Science and Technology Innovation Team,China(No.2024RS-CXTD-26)。
文摘When immersed in sand and dust environment,aero-engine blades are exposed to harsh erosion which may lead to failure if erosion is severe.Using Physical Vapor Deposition(PVD)to prepare hard ceramic coatings can greatly enhance the operational capabilities of aero-engine.However,due to the“line-of-sight”processing characteristic of PVD process,uneven coating deposition rates occur when preparing coatings on obstructed areas such as blisks.Quantitative research on such phenomena is few,and it is even rarer in the study of aero-engine coatings.Based on the analyses and considerations of the geometric shape of blade surfaces and the influence of both deposition and re-sputtering effect,an ideal model is established to analyze the deposition rate variation along blocked region in complex self-shadowing boundaries.The relative deposition rates at various locations on the blade surface within the inter-blade gaps are quantitatively calculated and experimentally validated.Furthermore,differences in erosion resistance of the coatings are tested.The conclusions are drawn as follows:the geometric configuration of the obstructed shape and resputtering phenomenon significantly influence the deposition rates within the inner wall of blade gaps.Taking the structural configuration as an example,in a 25 mm×60 mm×15 mm gap,the coating thickness can vary more than 252%from the thickest to the thinnest location.The deposition rates of various locations are proportional to the solid angle of incident ion in more obstructed regions,and the re-sputtering is more prominent in open regions.Obstructive boundaries directly affect the erosion resistance at various locations within the gaps,with erosion failure time decreasing by 40%in heavily blocked region compared to open region.
基金The National Natural Science Foundation of China(Grant No.12462006)Beijing Institute of Structure and Environment Engineering Joint Innovation Fund(No.BQJJ202414).
文摘THE mechanical response and deformation mechanisms of pure nickel under nanoindentation were systematically investigated using molecular dynamics(MD)simulations,with a particular focus on the novel interplay between crystallographic orientation,grain boundary(GB)proximity,and pore characteristics(size/location).This study compares single-crystal nickel models along[100],[110],and[111]orientations with equiaxed polycrystalline models containing 0,1,and 2.5 nm pores in surface and subsurface configurations.Our results reveal that crystallographic anisotropy manifests as a 24.4%higher elastic modulus and 22.2%greater hardness in[111]-oriented single crystals compared to[100].Pore-GB synergistic effects are found to dominate the deformation behavior:2.5 nm subsurface pores reduce hardness by 25.2%through stress concentration and dislocation annihilation at GBs,whereas surface pores enable mechanical recovery via accelerated dislocation generation post-collapse.Additionally,size-dependent deformation regimes were identified,with 1 nm pores inducing negligible perturbation due to rapid atomic rearrangement,in contrast with persistent softening in 2.5 nm pores.These findings establish atomic-scale design principles for defect engineering in nickel-based aerospace components,demonstrating how crystallographic orientation,pore configuration,and GB interactions collectively govern nanoindentation behavior.
基金supported by the National Natural Science Foundation of China(GrantNo.12072231).
文摘Hypersonic boundary-layer receptivity to freestream entropy and vorticity waves is investigated using direct numerical simula-tions for a Mach 6 flow over a 5.08 mm nose radius cone.Two frequencies of 33 kHz and 150 kHz are considered to be rep-resentative of the first and second instability modes,respectively.For the first mode,wall pressure fluctuations for both entropy and vorticity wave cases exhibit a strong modulation yet without a growing trend,indicating that the first mode is not generated despite its instability predicted by linear stability theory.The potential reason for this is the absence of postshock slow acoustic waves capable of synchronizing with the first mode.By contrast,for the second mode,a typical three-stage boundary-layer response is observed,consistent with that to slow acoustic waves studied previously.Furthermore,the postshock disturbances outside the boundary layer can be decomposed into the entropy(density/temperature fluctuations)and vorticity components(ve-locity fluctuations),and the latter is shown to play a leading role in generating the second mode,even for the case with entropy waves where the density/temperature fluctuations dominate the postshock regions.
基金the POI FEB RAS,entitled“Study of the Structure and Dynamics of World’s Oceans Waters in Conditions of Current Climate Change”(reg.no.124022100079-4).
文摘This study was used oceanographic database in the Sea of Okhotsk between the period from 1929 to 2020(131286 stations).The paper used gas hydrate dissociation parameters for the“pure methane-seawater”system obtained in the study by Dickens GR and Quinby-Hunt MS.The results have elucidated the spatiotemporal variability of distribution of such parameters at the upper boundary of the gas hydrate stability zone(GHSZ)as water temperature,salinity,and top depth of the stability zone.As the study has shown(based on average long-term spatial distributions),the minimum temperature and depth values of the GHSZ upper boundary in the Sea of Okhotsk occur off the western and southwestern parts of the water area.The maximum temperature and depth values of the GHSZ upper boundary are typical of the southeastern sea area and over the Kamchatka Peninsula slope.This study has also identified an area,where there are no thermobaric conditions for the emergence and stable existence of methane hydrates in the water column.The results presented agree well with the materials of observations conducted during expeditions and the previous data of predictive simulations for the Sea of Okhotsk.
基金financially supported by the National Natural Science Foundation of China(No.U21A2050)support of the Chinese Scholarship Council(No.202006290165).
文摘In recent years,(0001)twist grain boundaries(BTGBs)located in primary α grain clusters were identified as fatigue crack nucleation sites in different Ti alloys.In the present study,crack initiation was investigated in a bimodal Ti-5Al-4 V alloy subjected to low-cycle fatigue and dwell-fatigue loadings at room temperature.The low fraction of primary α grains was not associated with a lack of sensitivity to BTGB cracking.Transmission electron microscopy and electron back-scattered diffraction were used to characterize BTGBs in the initial microstructure.The fatigue mechanisms were then analyzed with a focus on dislocation activity.α_(p) grains adjacent to cracked BTGBs contained a high dislocation density.It was primarily composed of planar slip bands of dislocations.In addition,<c+a>dislocations were noticed in the vicinity of cracked BTGBs.They supposedly pertain to crack tip plasticity during growth,and no evidence of a role of an incoming slip event in crack nucleation was obtained.Also,basal slip bands extending across adjacent grains were found to emerge from BTGBs.This feature provides an easier path for crack extension when growth along the grain boundary becomes difficult owing to a deviation from the basal plane.Atom probe tomography analyses evidenced V and Fe segregation at a grain boundary with a significant deviation from the BTGB configuration.This suggests a possible contribution of local solute segregation to the high cracking resistance of general α_(p)/α_(p) grain boundaries.This work provides new insights into the mechanisms involved in cracking of BTGB in Ti alloys subjected to cyclic loadings.
