Self-vibrating systems comprised of active materials have great potential for application in the fields of energy harvesting,actuation,bionic instrumentation,and autonomous robotics.However,it is challenging to obtain...Self-vibrating systems comprised of active materials have great potential for application in the fields of energy harvesting,actuation,bionic instrumentation,and autonomous robotics.However,it is challenging to obtain analytical solutions describing these systems,which hinders analysis and design.In this work,we propose a self-vibrating liquid crystal elastomer(LCE)fiber-spring system exposed to spatially-constant gradient light,and determine analytical solutions for its amplitude and period.First,using a dynamic model of LCE,we obtain the equations governing the self-vibration.Then,we analyze two different motion states and elucidate the mechanism of self-vibration.Subsequently,we derive analytical solutions for the amplitude and frequency using the multi-scale method,and compare the solutions with numerical results.The analytical outcomes are shown to be consistent with the numerical calculations,while taking far less computational time.Our findings reveal the utility of the multi-scale method in describing self-vibration,which may contribute to more efficient and accurate analyses of self-vibrating systems.展开更多
This work presents a novel approach to achieve nonlinear vibration response based on the Hamilton principle.We chose the 5-MW reference wind turbine which was established by the National Renewable Energy Laboratory(NR...This work presents a novel approach to achieve nonlinear vibration response based on the Hamilton principle.We chose the 5-MW reference wind turbine which was established by the National Renewable Energy Laboratory(NREL),to research the effects of the nonlinear flap-wise vibration characteristics.The turbine wheel is simplified by treating the blade of a wind turbine as an Euler-Bernoulli beam,and the nonlinear flap-wise vibration characteristics of the wind turbine blades are discussed based on the simplification first.Then,the blade’s large-deflection flap-wise vibration governing equation is established by considering the nonlinear term involving the centrifugal force.Lastly,it is truncated by the Galerkin method and analyzed semi-analytically using the multi-scale analysis method,and numerical simulations are carried out to compare the simulation results of finite elements with the numerical simulation results using Campbell diagram analysis of blade vibration.The results indicated that the rotational speed of the impeller has a significant impact on blade vibration.When the wheel speed of 12.1 rpm and excitation amplitude of 1.23 the maximum displacement amplitude of the blade has increased from 0.72 to 3.16.From the amplitude-frequency curve,it can be seen that the multi-peak characteristic of blade amplitude frequency is under centrifugal nonlinearity.Closed phase trajectories in blade nonlinear vibration,exhibiting periodic motion characteristics,are found through phase diagrams and Poincare section diagrams.展开更多
Prediction of melt index （MI）, the most important parameter in determining the product＇s grade and quality control of polypropylene produced in practical industrial processes, is studied. A novel soft-sensor model ...Prediction of melt index （MI）, the most important parameter in determining the product＇s grade and quality control of polypropylene produced in practical industrial processes, is studied. A novel soft-sensor model with principal component analysis （PCA）, radial basis function （RBF） networks, and multi-scale analysis （MSA） is proposed to infer the MI of manufactured products from real process variables, where PCA is carried out to select the most relevant process features and to eliminate the correlations of the input variables, MSA is introduced to a^quire much more information and to reduce the uncertainty of the system, and RBF networks are used to characterize the nonlinearity of the process. The research results show that the proposed method provides promising prediction reliability and accuracy, and supposed to have extensive application prospects in propylene polymerization processes.展开更多
The trade-offs and synergies of forest ecosystem service are important research topics for several disciplines.The multi-scale analysis of service trade-offs and synergies assists in the implementation of more effecti...The trade-offs and synergies of forest ecosystem service are important research topics for several disciplines.The multi-scale analysis of service trade-offs and synergies assists in the implementation of more effective forest resource management.Based on multi-source data including forest distribution,topography,NDVI,meteorology and soil conditions,key forest ecosystem services,including total forest volume,carbon storage,water yield,soil retention and habitat quality were mapped and evaluated for the Funiu Mountain Region through integrated deployment of the CASA model,the InVEST3.2 model and the ArcGIS10.2 software.The characteristics of trade-offs and synergies among different ecosystem services were then mapped and considered across multiple spatial scales(i.e.,by region,north and south slopes,vertical belt)using the spatial overlay analysis method.The main results are as follows:(1)Mean forest volume is 49.26 m^(3)/ha,carbon density is 156.94 t/ha,water yield depth is 494.46 mm,the unit amount of soil retention is 955.4 t/ha,and the habitat quality index is 0.79.(2)The area of forests with good synergy is 28.79%,and the area of forests with poor synergy is 10.15%,while about 61.06%of forests show severe trade-offs and weak trade-offs.The overall benefits of forest ecosystem services in the study area are still low.In the future,bad synergy and severe trade-off areas should be the focus of forest resource management and efficiency regulation.(3)Synergy between ecosystem services is better for forest on south slope than that on north slope.Deciduous broad-leaved forest belt at moderate elevations on south slope in the mountains(SIII)has the highest synergies,while that at low elevations on north slope(NI)exhibits the lowest synergy levels.展开更多
Urban faults in Shenzhen are potential threats to city security and sustainable development. In consideration of the importance of the Shenzhen fault zone, the author provide a detailed interpretation on gravity data ...Urban faults in Shenzhen are potential threats to city security and sustainable development. In consideration of the importance of the Shenzhen fault zone, the author provide a detailed interpretation on gravity data model. Bouguer gravity covering the whole Shenzhen City was calculated with a 1-km resolution. Wavelet multi-scale analysis（MSA） was applied to the Bouguer gravity data to obtain the multilayer residual anomalies corresponding to different depths. In addition, 2D gravity models were constructed along three profiles. The Bouguer gravity anomaly shows an NE-striking high-low-high pattern from northwest to southeast, strongly related to the main faults. According to the results of MSA, the correlation between gravity anomaly and faults is particularly significant from 4 to 12 km depth. The residual gravity with small amplitude in each layer indicates weak tectonic activity in the crust. In the upper layers, positive anomalies along most of faults reveal the upwelling of high-density materials during the past tectonic movements. The multilayer residual anomalies also yield important information about the faults, such as the vertical extension and the dip direction. The maximum depth of the faults is about 20 km. In general, NE-striking faults extend deeper than NW-striking faults and have a larger dip angle.展开更多
This paper deals with modeling of the phenomenon of fretting fatigue in heterogeneous materials using the multi-scale computational homogenization technique and finite element analysis(FEA).The heterogeneous material ...This paper deals with modeling of the phenomenon of fretting fatigue in heterogeneous materials using the multi-scale computational homogenization technique and finite element analysis(FEA).The heterogeneous material for the specimens consists of a single hole model(25% void/cell,16% void/cell and 10% void/cell)and a four-hole model(25%void/cell).Using a representative volume element(RVE),we try to produce the equivalent homogenized properties and work on a homogeneous specimen for the study of fretting fatigue.Next,the fretting fatigue contact problem is performed for 3 new cases of models that consist of a homogeneous and a heterogeneous part(single hole cell)in the contact area.The aim is to analyze the normal and shear stresses of these models and compare them with the results of the corresponding heterogeneous models based on the Direct Numerical Simulation(DNS)method.Finally,by comparing the computational time and%deviations,we draw conclusions about the reliability and effectiveness of the proposed method.展开更多
Identifying the active and inactive period of earthquakes in Chinese mainland is of great importance for guiding mid-short term, especially short term, earthquake forecast.……
The void evolution of large-section plastic mold steel during multi-directional forging(MDF)was investigated using multiscale analysis.To simulate the forging process of the plastic mold steel(SDP1 steel)and realize m...The void evolution of large-section plastic mold steel during multi-directional forging(MDF)was investigated using multiscale analysis.To simulate the forging process of the plastic mold steel(SDP1 steel)and realize micro-void reconstruction in a representative volume element(RVE),MDF experiment and void-characteristic evaluation of the SDP1 steel were carried out.Traditional upsetting and stretching forging(TUSF)and MDF were simulated to comparatively analyze the evolution of temperature,effective stress,and effective strain.By embedding RVE with a micro-void and using boundary condition by point tracking into the forging process,the single-void evolution in TUSF and MDF was studied.The effect of void orientation on single-void evolution was also investigated.The multi-scale analysis revealed the following results.(1)Compared with TUSF,MDF achieved a higher efficiency in void closure.(2)The closing efficiency of the void increased with the increase in angle h(the angle between the Z and long axes of the void).(3)The closing efficiency increased with the increase in the orientation angle during the forging process.On the basis of the important role of the main stress in each forging step on the void closure,an integral formula of the main stress was proposed.When main compressive-stress integration reached-0.4,the closed state of the void could be accurately determined.展开更多
A new finite element method （FEM） of B-spline wavelet on the interval （BSWI） is proposed. Through analyzing the scaling functions of BSWI in one dimension, the basic formula for 2D FEM of BSWI is deduced. The 2D F...A new finite element method （FEM） of B-spline wavelet on the interval （BSWI） is proposed. Through analyzing the scaling functions of BSWI in one dimension, the basic formula for 2D FEM of BSWI is deduced. The 2D FEM of 7 nodes and 10 nodes are constructed based on the basic formula. Using these proposed elements, the multiscale numerical model for foundation subjected to harmonic periodic load, the foundation model excited by external and internal dynamic load are studied. The results show the pro- posed finite elements have higher precision than the tradi- tional elements with 4 nodes. The proposed finite elements can describe the propagation of stress waves well whenever the foundation model excited by extemal or intemal dynamic load. The proposed finite elements can be also used to con- nect the multi-scale elements. And the proposed finite elements also have high precision to make multi-scale analysis for structure.展开更多
The spatial structures of China’s Major Function Zoning are important constraining indicators in all types of spatial planning and key parameters for accurately downscaling major functions.Taking the proportion of ur...The spatial structures of China’s Major Function Zoning are important constraining indicators in all types of spatial planning and key parameters for accurately downscaling major functions.Taking the proportion of urbanization zones,agricultural development zones and ecological security zones as the basic parameter,this paper explores the spatial structures of major function zoning at different scales using spatial statistics,spatial modeling and landscape metrics methods.The results show:First,major function zones have spatial gradient structures,which are prominently represented by latitudinal and longitudinal gradients,a coastal distance gradient,and an eastern-central-western gradient.Second,the pole-axis system structure and core-periphery structure exist at provincial scales.The general principle of the pole-axis structure is that as one moves along the distance axis,the proportion of urbanization zones decreases and the proportion of ecological security zones increases.This also means that the proportion of different function zones has a ring-shaped spatial differentiation principle with distance from the core.Third,there is a spatial mosaic structure at the city and county scale.This spatial mosaic structure has features of both spatial heterogeneity,such as agglomeration and dispersion,as well as of mutual,adjacent topological correlation and spatial proximity.The results of this study contribute to scientific knowledge on major function zones and the principles of spatial organization,and it acts as an important reference for China’s integrated geographical zoning.展开更多
Particle size distribution(PSD) is an important parameter in the process of fluidization,and it always plays a crucial role in a gas-solid fluidized system.A PSD model for on-line PSD determination based on acoustic e...Particle size distribution(PSD) is an important parameter in the process of fluidization,and it always plays a crucial role in a gas-solid fluidized system.A PSD model for on-line PSD determination based on acoustic emission(AE) measurement was developed according to the mechanism of particle collision with the inner wall of the cylinder and multi-scale wavelet decomposition analysis.This PSD model illuminates the quantitative relationship between the energy percentage of AE signals for different scales and the PSD,which indicates the feasibility of the application of the PSD model.Experiments were undertaken both in lab and plant gas-solid fluidized setup with polyethylene particles,and the parameters of the PSD model were calibrated and revised.The experimental conditions and results proved that the PSD model was suitable for on-line measurement and was sufficiently sensible and accurate.Concerning agglomeration,the PSD model also showed exact serviceability on detecting the onset of agglomeration by abnormal PSD,and the result agreed with that from the radiation method.Ultimately,AE measurement was found to be a reliable and credible means for understanding the PSD information that affects the behavior of a system,which can provide valuable guidance for practical applications.展开更多
In present study, the subgrid scale （SGS） stress and dissipation for multiscale formulation of large eddy simulation are analyzed using the data of turbulent channel flow at Ret = 180 obtained by direct numerical si...In present study, the subgrid scale （SGS） stress and dissipation for multiscale formulation of large eddy simulation are analyzed using the data of turbulent channel flow at Ret = 180 obtained by direct numerical simulation. It is found that the small scale SGS stress is much smaller than the large scale SGS stress for all the stress components. The dominant contributor to large scale SGS stress is the cross stress between small scale and subgrid scale motions, while the cross stress between large scale and subgrid scale motions make major contributions to small scale SGS stress. The energy transfer from resolved large scales to subgrid scales is mainly caused by SGS Reynolds stress, while that between resolved small scales and subgrid scales are mainly due to the cross stress. The multiscale formulation of SGS models are evaluated a priori, and it is found that the small- small model is superior to other variants in terms of SGS dissipation.展开更多
Because of the challenge of compounding lightweight,high-strength Ti/Al alloys due to their considerable disparity in properties,Al 6063 as intermediate layer was proposed to fabricate TC4/Al 6063/Al 7075 three-layer ...Because of the challenge of compounding lightweight,high-strength Ti/Al alloys due to their considerable disparity in properties,Al 6063 as intermediate layer was proposed to fabricate TC4/Al 6063/Al 7075 three-layer composite plate by explosive welding.The microscopic properties of each bonding interface were elucidated through field emission scanning electron microscope and electron backscattered diffraction(EBSD).A methodology combining finite element method-smoothed particle hydrodynamics(FEM-SPH)and molecular dynamics(MD)was proposed for the analysis of the forming and evolution characteristics of explosive welding interfaces at multi-scale.The results demonstrate that the bonding interface morphologies of TC4/Al 6063 and Al 6063/Al 7075 exhibit a flat and wavy configuration,without discernible defects or cracks.The phenomenon of grain refinement is observed in the vicinity of the two bonding interfaces.Furthermore,the degree of plastic deformation of TC4 and Al 7075 is more pronounced than that of Al 6063 in the intermediate layer.The interface morphology characteristics obtained by FEM-SPH simulation exhibit a high degree of similarity to the experimental results.MD simulations reveal that the diffusion of interfacial elements predominantly occurs during the unloading phase,and the simulated thickness of interfacial diffusion aligns well with experimental outcomes.The introduction of intermediate layer in the explosive welding process can effectively produce high-quality titanium/aluminum alloy composite plates.Furthermore,this approach offers a multi-scale simulation strategy for the study of explosive welding bonding interfaces.展开更多
Shale gas, as a clean, low-carbon, and abundant unconventional natural gas resource, plays a crucial role in achieving clean energy transformation and carbon neutrality. The Fuling shale gas reservoir in Sichuan Basin...Shale gas, as a clean, low-carbon, and abundant unconventional natural gas resource, plays a crucial role in achieving clean energy transformation and carbon neutrality. The Fuling shale gas reservoir in Sichuan Basin stands out as China's most promising area for shale gas exploration and recovery. However, the continuous recovery of shale gas in the southern Sichuan Basin has led to well interference events in hundreds of wells, with the furthest well distance reaching over 2000 m. This study introduces a multi-scale approach for transient analysis of a multi-well horizontal pad with well interference in shale gas reservoirs. The approach utilizes Laplace transform technology, boundary element theory, and the finite difference method to address the complexities of the system. Well interference is managed using the pressure superposition principle. To validate the proposed multi-scale method, a commercial numerical simulator is employed. The comprehensive pressure behavior of a multi-well horizontal pad in a shale gas reservoir is analyzed, encompassing wellbore storage effect, skin effect, bilinear flow, linear flow, pseudo-radial flow of primary fractures, well interference period, dual-porosity flow, pseudo-radial flow of the total system, and boundary-dominated flow. A case study is conducted on the typical well, the well with the longest production history in the Fuling shale gas reservoir. The rate transient analysis is conducted to integrate up to 229 days of shale gas production daily data and wellhead pressure data, enabling the generation of pressure behavior under unit flow rate. The results indicate that the linear flow, transitional flow, and boundary-dominated flow are more likely to be observed in the actual data. Secondary fractures are considered to be the primary pathways for fluid migration during well interference events. The evaluated formation permeability is 2.58 × 10^(-2) mD, the well spacing is 227.8 m, the diffusion coefficient is 1.49 × 10^(-4), and the skin factor is 0.09.展开更多
To improve design accuracy and reliability of structures,this study solves the uncertain natural frequencies with consideration for geometric nonlinearity and structural uncertainty.Frequencies of the laminated plate ...To improve design accuracy and reliability of structures,this study solves the uncertain natural frequencies with consideration for geometric nonlinearity and structural uncertainty.Frequencies of the laminated plate with all four edges clamped(CCCC)are derived based on Navier's method and Galerkin's method.The novelty of the current work is that the number of unknowns in the displacement field model of a CCCC plate with free midsurface(CCCC-2 plate)is only three compared with four or five in cases of other exposed methods.The present analytical method is proved to be accurate and reliable by comparing linear natural frequencies and nonlinear natural frequencies with other models available in the open literature.Furthermore,a novel method for analyzing effects of mean values and tolerance zones of uncertain structural parameters on random frequencies is proposed based on a self-developed Multiscale Feature Extraction and Fusion Network(MFEFN)system.Compared with a direct Monte Carlo Simulation(MCS),the MFEFNbased procedure significantly reduces the calculation burden with a guarantee of accuracy.Our research provides a method to calculate nonlinear natural frequencies under two boundary conditions and presentes a surrogate model to predict frequencies for accuracy analysis and optimization design.展开更多
In high-performance electric sports vehicles,the application of woven composite materials with the purpose of lightweight has become an inevitable choice.It is considerably difference between traditional metal materia...In high-performance electric sports vehicles,the application of woven composite materials with the purpose of lightweight has become an inevitable choice.It is considerably difference between traditional metal materials and composites for the lightweight design strategy of electric vehicle structures,due to the multi-scale and anisotropic characteristics of fiber reinforced composites.Nevertheless,most of scholars are focus on the meso-scale mechanical responses of woven composites,and few studies are involved in their multi-scale mechanical behaviors and hierarchical design strategy of composite structures in electric vehicles.In this work,a multiscale analysis strategy was proposed to investigate mechanical behaviors of composite front firewall.Subsequently,a hierarchical optimization strategy with the objective of lightweight design of composite front firewall was carried out.Finally,a reasonable layout scheme of composite front firewall was quantitatively obtained.The maximum errors between the predicted and theoretical/experimental results in terms of equivalent engineering constants of fiber yarns and 2D twill woven composites(2DTWCs)were 8.8 GPa and 7%,respectively.It indicates that the multi-scale models can be used to evaluate the mechanical properties of 2DTWCs.Additionally,the total weight of optimized composite front firewall was reduced by 36%in comparison with the reference,and simultaneously the total stiffness was improved by 26%.Hence,it is an effective strategy to design lightweight composite structures of electric vehicles.We hope the proposed multi-scale and hierarchical design strategy could promote the further development of composite structures in high-performance electric sports vehicles.展开更多
Second-generation high-temperature superconducting(HTS)conductors,specifically rare earth-barium-copper-oxide(REBCO)coated conductor(CC)tapes,are promising candidates for high-energy and high-field superconducting app...Second-generation high-temperature superconducting(HTS)conductors,specifically rare earth-barium-copper-oxide(REBCO)coated conductor(CC)tapes,are promising candidates for high-energy and high-field superconducting applications.With respect to epoxy-impregnated REBCO composite magnets that comprise multilayer components,the thermomechanical characteristics of each component differ considerably under extremely low temperatures and strong electromagnetic fields.Traditional numerical models include homogenized orthotropic models,which simplify overall field calculation but miss detailed multi-physics aspects,and full refinement(FR)ones that are thorough but computationally demanding.Herein,we propose an extended multi-scale approach for analyzing the multi-field characteristics of an epoxy-impregnated composite magnet assembled by HTS pancake coils.This approach combines a global homogenization(GH)scheme based on the homogenized electromagnetic T-A model,a method for solving Maxwell's equations for superconducting materials based on the current vector potential T and the magnetic field vector potential A,and a homogenized orthotropic thermoelastic model to assess the electromagnetic and thermoelastic properties at the macroscopic scale.We then identify“dangerous regions”at the macroscopic scale and obtain finer details using a local refinement(LR)scheme to capture the responses of each component material in the HTS composite tapes at the mesoscopic scale.The results of the present GH-LR multi-scale approach agree well with those of the FR scheme and the experimental data in the literature,indicating that the present approach is accurate and efficient.The proposed GH-LR multi-scale approach can serve as a valuable tool for evaluating the risk of failure in large-scale HTS composite magnets.展开更多
To effectively extract multi-scale information from observation data and improve computational efficiency,a multi-scale second-order autoregressive recursive filter(MSRF)method is designed.The second-order autoregress...To effectively extract multi-scale information from observation data and improve computational efficiency,a multi-scale second-order autoregressive recursive filter(MSRF)method is designed.The second-order autoregressive filter used in this study has been attempted to replace the traditional first-order recursive filter used in spatial multi-scale recursive filter(SMRF)method.The experimental results indicate that the MSRF scheme successfully extracts various scale information resolved by observations.Moreover,compared with the SMRF scheme,the MSRF scheme improves computational accuracy and efficiency to some extent.The MSRF scheme can not only propagate to a longer distance without the attenuation of innovation,but also reduce the mean absolute deviation between the reconstructed sea ice concentration results and observations reduced by about 3.2%compared to the SMRF scheme.On the other hand,compared with traditional first-order recursive filters using in the SMRF scheme that multiple filters are executed,the MSRF scheme only needs to perform two filter processes in one iteration,greatly improving filtering efficiency.In the two-dimensional experiment of sea ice concentration,the calculation time of the MSRF scheme is only 1/7 of that of SMRF scheme.This means that the MSRF scheme can achieve better performance with less computational cost,which is of great significance for further application in real-time ocean or sea ice data assimilation systems in the future.展开更多
Distinct from the case with width-dominated shallow wetland flows,the longitudinal evolution of contaminant concentration in the most-typical pattern of wetland as dominated by free-water-surface-effect is characteriz...Distinct from the case with width-dominated shallow wetland flows,the longitudinal evolution of contaminant concentration in the most-typical pattern of wetland as dominated by free-water-surface-effect is characterized by a multi-scale analysis in the present study.An environmental dispersion model for the evolution of the mean concentration is deduced as an extension of Taylor's classical formulation by Mei’s multi-scale analysis.Corresponding environmental dispersivity is found identical to that determined by the method of concentration moments.展开更多
The SKP1 gene is an important component of the SCF(SKP1-Cullin1-F-box)complex and serves as a bridge connecting the F-box and Cullin1genes(F-box-SKP1-Cullin1).The pattern of S-RNase being ubiquitously labelled by the ...The SKP1 gene is an important component of the SCF(SKP1-Cullin1-F-box)complex and serves as a bridge connecting the F-box and Cullin1genes(F-box-SKP1-Cullin1).The pattern of S-RNase being ubiquitously labelled by the SCF complex and degraded by the 26S protease accounts for the bulk of the available self-incompatibility studies.In this study,15 ClSKP1s from the‘Xiangshui'lemon genome and ubiquitome exist in the same SKP1 conserved domain(CD)as SKP1s in other species.The q PCR results showed that SKP1-6 and SKP1-14 have tissue expression patterns specific for expression in pollen.In addition,SKP1-6 and SKP1-14 in the stigma,style and ovary were significantly upregulated after self-pollination compared to those after cross-pollination.A subcellular location showed that SKP1-6 and SKP1-14 were located in the nucleus.In addition,yeast two-hybrid(Y2H)assays,bimolecular fluorescence complementation(BiFC)and luciferase complementation imaging(LCI)assays showed that SKP1-6 interacted with F-box1,F-box33,F-box34,F-box17,F-box19,Cullin1-2 and 26S proteasome subunit 4 homolog A(26S PS4HA).SKP1-14 interacted with F-box17,F-box19,F-box35,Cullin1-2 and 26S PS4HA.The interaction of Cullin1-2 and the F-box with SKP1 as a bridge was verified by a yeast three-hybrid experiment.The ability of S3-RNase to inhibit pollen and pollen tube growth and development was assessed using in vitro pollen co-culture experiments with recombinant S3-RNase proteins.Overall,this study provides important experimental evidence and theoretical basis for understanding the mechanism of self-incompatibility in plants by revealing the key role of the SCF complex in‘Xiangshui'lemon,which is bridged by ClSKP1-6,in self-incompatibility.The results of this study are of great significance for the future indepth exploration of the molecular mechanism of the SCF complex and its wide application in the self-incompatibility of plants.展开更多
基金supported by the National Natural Science Foundation of China(No.12172001)the University Natural Science Research Project of Anhui Province(No.2022AH020029)+1 种基金the Anhui Provincial Natural Science Foundation(Nos.2208085Y01 and 2008085QA23)the Housing and Urban-Rural Development Science and Technology Project of Anhui Province(No.2023-YF129),China.
文摘Self-vibrating systems comprised of active materials have great potential for application in the fields of energy harvesting,actuation,bionic instrumentation,and autonomous robotics.However,it is challenging to obtain analytical solutions describing these systems,which hinders analysis and design.In this work,we propose a self-vibrating liquid crystal elastomer(LCE)fiber-spring system exposed to spatially-constant gradient light,and determine analytical solutions for its amplitude and period.First,using a dynamic model of LCE,we obtain the equations governing the self-vibration.Then,we analyze two different motion states and elucidate the mechanism of self-vibration.Subsequently,we derive analytical solutions for the amplitude and frequency using the multi-scale method,and compare the solutions with numerical results.The analytical outcomes are shown to be consistent with the numerical calculations,while taking far less computational time.Our findings reveal the utility of the multi-scale method in describing self-vibration,which may contribute to more efficient and accurate analyses of self-vibrating systems.
基金supported by the National Natural Science Foundation of China(No.51965034).
文摘This work presents a novel approach to achieve nonlinear vibration response based on the Hamilton principle.We chose the 5-MW reference wind turbine which was established by the National Renewable Energy Laboratory(NREL),to research the effects of the nonlinear flap-wise vibration characteristics.The turbine wheel is simplified by treating the blade of a wind turbine as an Euler-Bernoulli beam,and the nonlinear flap-wise vibration characteristics of the wind turbine blades are discussed based on the simplification first.Then,the blade’s large-deflection flap-wise vibration governing equation is established by considering the nonlinear term involving the centrifugal force.Lastly,it is truncated by the Galerkin method and analyzed semi-analytically using the multi-scale analysis method,and numerical simulations are carried out to compare the simulation results of finite elements with the numerical simulation results using Campbell diagram analysis of blade vibration.The results indicated that the rotational speed of the impeller has a significant impact on blade vibration.When the wheel speed of 12.1 rpm and excitation amplitude of 1.23 the maximum displacement amplitude of the blade has increased from 0.72 to 3.16.From the amplitude-frequency curve,it can be seen that the multi-peak characteristic of blade amplitude frequency is under centrifugal nonlinearity.Closed phase trajectories in blade nonlinear vibration,exhibiting periodic motion characteristics,are found through phase diagrams and Poincare section diagrams.
基金Supported by the National Natural Science Foundation of China (No. 20106008)National HI-TECH Industrialization Program of China (No. Fagai-Gaoji-2004-2080)Science Fund for Distinguished Young Scholars of Zhejiang University (No. 111000-581645).
文摘Prediction of melt index （MI）, the most important parameter in determining the product＇s grade and quality control of polypropylene produced in practical industrial processes, is studied. A novel soft-sensor model with principal component analysis （PCA）, radial basis function （RBF） networks, and multi-scale analysis （MSA） is proposed to infer the MI of manufactured products from real process variables, where PCA is carried out to select the most relevant process features and to eliminate the correlations of the input variables, MSA is introduced to a^quire much more information and to reduce the uncertainty of the system, and RBF networks are used to characterize the nonlinearity of the process. The research results show that the proposed method provides promising prediction reliability and accuracy, and supposed to have extensive application prospects in propylene polymerization processes.
基金National Natural Science Foundation of China,No.41671090National Basic Research Program(973 Program),No.2015CB452702。
文摘The trade-offs and synergies of forest ecosystem service are important research topics for several disciplines.The multi-scale analysis of service trade-offs and synergies assists in the implementation of more effective forest resource management.Based on multi-source data including forest distribution,topography,NDVI,meteorology and soil conditions,key forest ecosystem services,including total forest volume,carbon storage,water yield,soil retention and habitat quality were mapped and evaluated for the Funiu Mountain Region through integrated deployment of the CASA model,the InVEST3.2 model and the ArcGIS10.2 software.The characteristics of trade-offs and synergies among different ecosystem services were then mapped and considered across multiple spatial scales(i.e.,by region,north and south slopes,vertical belt)using the spatial overlay analysis method.The main results are as follows:(1)Mean forest volume is 49.26 m^(3)/ha,carbon density is 156.94 t/ha,water yield depth is 494.46 mm,the unit amount of soil retention is 955.4 t/ha,and the habitat quality index is 0.79.(2)The area of forests with good synergy is 28.79%,and the area of forests with poor synergy is 10.15%,while about 61.06%of forests show severe trade-offs and weak trade-offs.The overall benefits of forest ecosystem services in the study area are still low.In the future,bad synergy and severe trade-off areas should be the focus of forest resource management and efficiency regulation.(3)Synergy between ecosystem services is better for forest on south slope than that on north slope.Deciduous broad-leaved forest belt at moderate elevations on south slope in the mountains(SIII)has the highest synergies,while that at low elevations on north slope(NI)exhibits the lowest synergy levels.
基金supported by the National Natural Science Foundation of China (Nos.41504015,41429401)the National 973 Project of China (No.2013CB733302)+2 种基金 China Postdoctoral Science Foundation (No.2015M572146)the National High Technology Research and Development Program of China (No.2011AA060503)the Surveying and Mapping Basic Research Program of National Administration of Surveying,Mapping and Geoinformation (No.15-01-08)
文摘Urban faults in Shenzhen are potential threats to city security and sustainable development. In consideration of the importance of the Shenzhen fault zone, the author provide a detailed interpretation on gravity data model. Bouguer gravity covering the whole Shenzhen City was calculated with a 1-km resolution. Wavelet multi-scale analysis（MSA） was applied to the Bouguer gravity data to obtain the multilayer residual anomalies corresponding to different depths. In addition, 2D gravity models were constructed along three profiles. The Bouguer gravity anomaly shows an NE-striking high-low-high pattern from northwest to southeast, strongly related to the main faults. According to the results of MSA, the correlation between gravity anomaly and faults is particularly significant from 4 to 12 km depth. The residual gravity with small amplitude in each layer indicates weak tectonic activity in the crust. In the upper layers, positive anomalies along most of faults reveal the upwelling of high-density materials during the past tectonic movements. The multilayer residual anomalies also yield important information about the faults, such as the vertical extension and the dip direction. The maximum depth of the faults is about 20 km. In general, NE-striking faults extend deeper than NW-striking faults and have a larger dip angle.
文摘This paper deals with modeling of the phenomenon of fretting fatigue in heterogeneous materials using the multi-scale computational homogenization technique and finite element analysis(FEA).The heterogeneous material for the specimens consists of a single hole model(25% void/cell,16% void/cell and 10% void/cell)and a four-hole model(25%void/cell).Using a representative volume element(RVE),we try to produce the equivalent homogenized properties and work on a homogeneous specimen for the study of fretting fatigue.Next,the fretting fatigue contact problem is performed for 3 new cases of models that consist of a homogeneous and a heterogeneous part(single hole cell)in the contact area.The aim is to analyze the normal and shear stresses of these models and compare them with the results of the corresponding heterogeneous models based on the Direct Numerical Simulation(DNS)method.Finally,by comparing the computational time and%deviations,we draw conclusions about the reliability and effectiveness of the proposed method.
基金Chinese Joint Seismological Science Foundation and the Chinese-Greece Cooperation Project.
文摘Identifying the active and inactive period of earthquakes in Chinese mainland is of great importance for guiding mid-short term, especially short term, earthquake forecast.……
基金This work is supported by National KeyR&D Program of China(Gran Nt oS.2016YFB0300400 and 2016YFB0300404).
文摘The void evolution of large-section plastic mold steel during multi-directional forging(MDF)was investigated using multiscale analysis.To simulate the forging process of the plastic mold steel(SDP1 steel)and realize micro-void reconstruction in a representative volume element(RVE),MDF experiment and void-characteristic evaluation of the SDP1 steel were carried out.Traditional upsetting and stretching forging(TUSF)and MDF were simulated to comparatively analyze the evolution of temperature,effective stress,and effective strain.By embedding RVE with a micro-void and using boundary condition by point tracking into the forging process,the single-void evolution in TUSF and MDF was studied.The effect of void orientation on single-void evolution was also investigated.The multi-scale analysis revealed the following results.(1)Compared with TUSF,MDF achieved a higher efficiency in void closure.(2)The closing efficiency of the void increased with the increase in angle h(the angle between the Z and long axes of the void).(3)The closing efficiency increased with the increase in the orientation angle during the forging process.On the basis of the important role of the main stress in each forging step on the void closure,an integral formula of the main stress was proposed.When main compressive-stress integration reached-0.4,the closed state of the void could be accurately determined.
基金supported by the National Natural Science Foundation of China (51109029,51178081,51138001,and 51009020)the State Key Development Program for Basic Research of China (2013CB035905)
文摘A new finite element method （FEM） of B-spline wavelet on the interval （BSWI） is proposed. Through analyzing the scaling functions of BSWI in one dimension, the basic formula for 2D FEM of BSWI is deduced. The 2D FEM of 7 nodes and 10 nodes are constructed based on the basic formula. Using these proposed elements, the multiscale numerical model for foundation subjected to harmonic periodic load, the foundation model excited by external and internal dynamic load are studied. The results show the pro- posed finite elements have higher precision than the tradi- tional elements with 4 nodes. The proposed finite elements can describe the propagation of stress waves well whenever the foundation model excited by extemal or intemal dynamic load. The proposed finite elements can be also used to con- nect the multi-scale elements. And the proposed finite elements also have high precision to make multi-scale analysis for structure.
基金National Natural Science Foundation of China,No.41630644Innovative Think-tank Foundation for Young Scientists of China Association for Science and Technology,No.DXB-ZKQN-2017-048。
文摘The spatial structures of China’s Major Function Zoning are important constraining indicators in all types of spatial planning and key parameters for accurately downscaling major functions.Taking the proportion of urbanization zones,agricultural development zones and ecological security zones as the basic parameter,this paper explores the spatial structures of major function zoning at different scales using spatial statistics,spatial modeling and landscape metrics methods.The results show:First,major function zones have spatial gradient structures,which are prominently represented by latitudinal and longitudinal gradients,a coastal distance gradient,and an eastern-central-western gradient.Second,the pole-axis system structure and core-periphery structure exist at provincial scales.The general principle of the pole-axis structure is that as one moves along the distance axis,the proportion of urbanization zones decreases and the proportion of ecological security zones increases.This also means that the proportion of different function zones has a ring-shaped spatial differentiation principle with distance from the core.Third,there is a spatial mosaic structure at the city and county scale.This spatial mosaic structure has features of both spatial heterogeneity,such as agglomeration and dispersion,as well as of mutual,adjacent topological correlation and spatial proximity.The results of this study contribute to scientific knowledge on major function zones and the principles of spatial organization,and it acts as an important reference for China’s integrated geographical zoning.
基金Project supported by the National Natural Science Foundation of China(Nos.21076180and20736011)the National High-Tech R&D Program(863)of China(No.2007AA04Z182)
文摘Particle size distribution(PSD) is an important parameter in the process of fluidization,and it always plays a crucial role in a gas-solid fluidized system.A PSD model for on-line PSD determination based on acoustic emission(AE) measurement was developed according to the mechanism of particle collision with the inner wall of the cylinder and multi-scale wavelet decomposition analysis.This PSD model illuminates the quantitative relationship between the energy percentage of AE signals for different scales and the PSD,which indicates the feasibility of the application of the PSD model.Experiments were undertaken both in lab and plant gas-solid fluidized setup with polyethylene particles,and the parameters of the PSD model were calibrated and revised.The experimental conditions and results proved that the PSD model was suitable for on-line measurement and was sufficiently sensible and accurate.Concerning agglomeration,the PSD model also showed exact serviceability on detecting the onset of agglomeration by abnormal PSD,and the result agreed with that from the radiation method.Ultimately,AE measurement was found to be a reliable and credible means for understanding the PSD information that affects the behavior of a system,which can provide valuable guidance for practical applications.
基金supported by the National Natural Science Foundation of China(10472053 and 10772098)
文摘In present study, the subgrid scale （SGS） stress and dissipation for multiscale formulation of large eddy simulation are analyzed using the data of turbulent channel flow at Ret = 180 obtained by direct numerical simulation. It is found that the small scale SGS stress is much smaller than the large scale SGS stress for all the stress components. The dominant contributor to large scale SGS stress is the cross stress between small scale and subgrid scale motions, while the cross stress between large scale and subgrid scale motions make major contributions to small scale SGS stress. The energy transfer from resolved large scales to subgrid scales is mainly caused by SGS Reynolds stress, while that between resolved small scales and subgrid scales are mainly due to the cross stress. The multiscale formulation of SGS models are evaluated a priori, and it is found that the small- small model is superior to other variants in terms of SGS dissipation.
基金Opening Foundation of Key Laboratory of Explosive Energy Utilization and Control,Anhui Province(BP20240104)Graduate Innovation Program of China University of Mining and Technology(2024WLJCRCZL049)Postgraduate Research&Practice Innovation Program of Jiangsu Province(KYCX24_2701)。
文摘Because of the challenge of compounding lightweight,high-strength Ti/Al alloys due to their considerable disparity in properties,Al 6063 as intermediate layer was proposed to fabricate TC4/Al 6063/Al 7075 three-layer composite plate by explosive welding.The microscopic properties of each bonding interface were elucidated through field emission scanning electron microscope and electron backscattered diffraction(EBSD).A methodology combining finite element method-smoothed particle hydrodynamics(FEM-SPH)and molecular dynamics(MD)was proposed for the analysis of the forming and evolution characteristics of explosive welding interfaces at multi-scale.The results demonstrate that the bonding interface morphologies of TC4/Al 6063 and Al 6063/Al 7075 exhibit a flat and wavy configuration,without discernible defects or cracks.The phenomenon of grain refinement is observed in the vicinity of the two bonding interfaces.Furthermore,the degree of plastic deformation of TC4 and Al 7075 is more pronounced than that of Al 6063 in the intermediate layer.The interface morphology characteristics obtained by FEM-SPH simulation exhibit a high degree of similarity to the experimental results.MD simulations reveal that the diffusion of interfacial elements predominantly occurs during the unloading phase,and the simulated thickness of interfacial diffusion aligns well with experimental outcomes.The introduction of intermediate layer in the explosive welding process can effectively produce high-quality titanium/aluminum alloy composite plates.Furthermore,this approach offers a multi-scale simulation strategy for the study of explosive welding bonding interfaces.
基金support from the National Natural Science Foundation of China(12202042)the Fundamental Research Funds for the Central Universities(QNXM20220011,FRF-TP-22-119A1,FRF-IDRY-22-001)+2 种基金the Open Fund Project of Sinopec State Key Laboratory of Shale Oil and Gas Enrichment Mechanisms and Effective Development(33550000-22-ZC0613-0269)China Postdoctoral Science Foundations(2021M700391)High-end Foreign Expert Introduction Program(G2023105006L).
文摘Shale gas, as a clean, low-carbon, and abundant unconventional natural gas resource, plays a crucial role in achieving clean energy transformation and carbon neutrality. The Fuling shale gas reservoir in Sichuan Basin stands out as China's most promising area for shale gas exploration and recovery. However, the continuous recovery of shale gas in the southern Sichuan Basin has led to well interference events in hundreds of wells, with the furthest well distance reaching over 2000 m. This study introduces a multi-scale approach for transient analysis of a multi-well horizontal pad with well interference in shale gas reservoirs. The approach utilizes Laplace transform technology, boundary element theory, and the finite difference method to address the complexities of the system. Well interference is managed using the pressure superposition principle. To validate the proposed multi-scale method, a commercial numerical simulator is employed. The comprehensive pressure behavior of a multi-well horizontal pad in a shale gas reservoir is analyzed, encompassing wellbore storage effect, skin effect, bilinear flow, linear flow, pseudo-radial flow of primary fractures, well interference period, dual-porosity flow, pseudo-radial flow of the total system, and boundary-dominated flow. A case study is conducted on the typical well, the well with the longest production history in the Fuling shale gas reservoir. The rate transient analysis is conducted to integrate up to 229 days of shale gas production daily data and wellhead pressure data, enabling the generation of pressure behavior under unit flow rate. The results indicate that the linear flow, transitional flow, and boundary-dominated flow are more likely to be observed in the actual data. Secondary fractures are considered to be the primary pathways for fluid migration during well interference events. The evaluated formation permeability is 2.58 × 10^(-2) mD, the well spacing is 227.8 m, the diffusion coefficient is 1.49 × 10^(-4), and the skin factor is 0.09.
基金the research project funded by the Fundamental Research Funds for the Central Universities(No.HIT.OCEP.2024038)the National Natural Science Foundation of China(No.52372351)the State Key Laboratory of Micro-Spacecraft Rapid Design and Intelligent Cluster,China(No.MS02240107)。
文摘To improve design accuracy and reliability of structures,this study solves the uncertain natural frequencies with consideration for geometric nonlinearity and structural uncertainty.Frequencies of the laminated plate with all four edges clamped(CCCC)are derived based on Navier's method and Galerkin's method.The novelty of the current work is that the number of unknowns in the displacement field model of a CCCC plate with free midsurface(CCCC-2 plate)is only three compared with four or five in cases of other exposed methods.The present analytical method is proved to be accurate and reliable by comparing linear natural frequencies and nonlinear natural frequencies with other models available in the open literature.Furthermore,a novel method for analyzing effects of mean values and tolerance zones of uncertain structural parameters on random frequencies is proposed based on a self-developed Multiscale Feature Extraction and Fusion Network(MFEFN)system.Compared with a direct Monte Carlo Simulation(MCS),the MFEFNbased procedure significantly reduces the calculation burden with a guarantee of accuracy.Our research provides a method to calculate nonlinear natural frequencies under two boundary conditions and presentes a surrogate model to predict frequencies for accuracy analysis and optimization design.
基金supported in part by the major scientific and technological project of Shenzhen Municipal Science,Technology and Innovation Bureau(KJZD20230923114259049)National Key R&D Program of China(2023YFB2504605).
文摘In high-performance electric sports vehicles,the application of woven composite materials with the purpose of lightweight has become an inevitable choice.It is considerably difference between traditional metal materials and composites for the lightweight design strategy of electric vehicle structures,due to the multi-scale and anisotropic characteristics of fiber reinforced composites.Nevertheless,most of scholars are focus on the meso-scale mechanical responses of woven composites,and few studies are involved in their multi-scale mechanical behaviors and hierarchical design strategy of composite structures in electric vehicles.In this work,a multiscale analysis strategy was proposed to investigate mechanical behaviors of composite front firewall.Subsequently,a hierarchical optimization strategy with the objective of lightweight design of composite front firewall was carried out.Finally,a reasonable layout scheme of composite front firewall was quantitatively obtained.The maximum errors between the predicted and theoretical/experimental results in terms of equivalent engineering constants of fiber yarns and 2D twill woven composites(2DTWCs)were 8.8 GPa and 7%,respectively.It indicates that the multi-scale models can be used to evaluate the mechanical properties of 2DTWCs.Additionally,the total weight of optimized composite front firewall was reduced by 36%in comparison with the reference,and simultaneously the total stiffness was improved by 26%.Hence,it is an effective strategy to design lightweight composite structures of electric vehicles.We hope the proposed multi-scale and hierarchical design strategy could promote the further development of composite structures in high-performance electric sports vehicles.
基金Project supported by the National Natural Science Foundation of China(Nos.11932008 and 12272156)the Fundamental Research Funds for the Central Universities(No.lzujbky-2022-kb06)+1 种基金the Gansu Science and Technology ProgramLanzhou City’s Scientific Research Funding Subsidy to Lanzhou University of China。
文摘Second-generation high-temperature superconducting(HTS)conductors,specifically rare earth-barium-copper-oxide(REBCO)coated conductor(CC)tapes,are promising candidates for high-energy and high-field superconducting applications.With respect to epoxy-impregnated REBCO composite magnets that comprise multilayer components,the thermomechanical characteristics of each component differ considerably under extremely low temperatures and strong electromagnetic fields.Traditional numerical models include homogenized orthotropic models,which simplify overall field calculation but miss detailed multi-physics aspects,and full refinement(FR)ones that are thorough but computationally demanding.Herein,we propose an extended multi-scale approach for analyzing the multi-field characteristics of an epoxy-impregnated composite magnet assembled by HTS pancake coils.This approach combines a global homogenization(GH)scheme based on the homogenized electromagnetic T-A model,a method for solving Maxwell's equations for superconducting materials based on the current vector potential T and the magnetic field vector potential A,and a homogenized orthotropic thermoelastic model to assess the electromagnetic and thermoelastic properties at the macroscopic scale.We then identify“dangerous regions”at the macroscopic scale and obtain finer details using a local refinement(LR)scheme to capture the responses of each component material in the HTS composite tapes at the mesoscopic scale.The results of the present GH-LR multi-scale approach agree well with those of the FR scheme and the experimental data in the literature,indicating that the present approach is accurate and efficient.The proposed GH-LR multi-scale approach can serve as a valuable tool for evaluating the risk of failure in large-scale HTS composite magnets.
基金The National Key Research and Development Program of China under contract No.2023YFC3107701the National Natural Science Foundation of China under contract No.42375143.
文摘To effectively extract multi-scale information from observation data and improve computational efficiency,a multi-scale second-order autoregressive recursive filter(MSRF)method is designed.The second-order autoregressive filter used in this study has been attempted to replace the traditional first-order recursive filter used in spatial multi-scale recursive filter(SMRF)method.The experimental results indicate that the MSRF scheme successfully extracts various scale information resolved by observations.Moreover,compared with the SMRF scheme,the MSRF scheme improves computational accuracy and efficiency to some extent.The MSRF scheme can not only propagate to a longer distance without the attenuation of innovation,but also reduce the mean absolute deviation between the reconstructed sea ice concentration results and observations reduced by about 3.2%compared to the SMRF scheme.On the other hand,compared with traditional first-order recursive filters using in the SMRF scheme that multiple filters are executed,the MSRF scheme only needs to perform two filter processes in one iteration,greatly improving filtering efficiency.In the two-dimensional experiment of sea ice concentration,the calculation time of the MSRF scheme is only 1/7 of that of SMRF scheme.This means that the MSRF scheme can achieve better performance with less computational cost,which is of great significance for further application in real-time ocean or sea ice data assimilation systems in the future.
基金This work is supported by the National Natural Science Foundation Program of China(Grant No.10972009).Help from Simon Skraatz is acknowledged.
文摘Distinct from the case with width-dominated shallow wetland flows,the longitudinal evolution of contaminant concentration in the most-typical pattern of wetland as dominated by free-water-surface-effect is characterized by a multi-scale analysis in the present study.An environmental dispersion model for the evolution of the mean concentration is deduced as an extension of Taylor's classical formulation by Mei’s multi-scale analysis.Corresponding environmental dispersivity is found identical to that determined by the method of concentration moments.
基金supported by grants from the National Natural Science Foundation of China(Grant No.31960585)Science and Technology Major Project of Guangxi(Grant No.Guike AA22068092)+1 种基金Guangxi Science and Technology Vanguard Special Action Project(Grant No.202204)State Key Laboratory for Conservation and Utilization of Subtropical Agro-bioresources(Grant Nos.SKLCUSA-a201906,SKLCU-SA-c201901)。
文摘The SKP1 gene is an important component of the SCF(SKP1-Cullin1-F-box)complex and serves as a bridge connecting the F-box and Cullin1genes(F-box-SKP1-Cullin1).The pattern of S-RNase being ubiquitously labelled by the SCF complex and degraded by the 26S protease accounts for the bulk of the available self-incompatibility studies.In this study,15 ClSKP1s from the‘Xiangshui'lemon genome and ubiquitome exist in the same SKP1 conserved domain(CD)as SKP1s in other species.The q PCR results showed that SKP1-6 and SKP1-14 have tissue expression patterns specific for expression in pollen.In addition,SKP1-6 and SKP1-14 in the stigma,style and ovary were significantly upregulated after self-pollination compared to those after cross-pollination.A subcellular location showed that SKP1-6 and SKP1-14 were located in the nucleus.In addition,yeast two-hybrid(Y2H)assays,bimolecular fluorescence complementation(BiFC)and luciferase complementation imaging(LCI)assays showed that SKP1-6 interacted with F-box1,F-box33,F-box34,F-box17,F-box19,Cullin1-2 and 26S proteasome subunit 4 homolog A(26S PS4HA).SKP1-14 interacted with F-box17,F-box19,F-box35,Cullin1-2 and 26S PS4HA.The interaction of Cullin1-2 and the F-box with SKP1 as a bridge was verified by a yeast three-hybrid experiment.The ability of S3-RNase to inhibit pollen and pollen tube growth and development was assessed using in vitro pollen co-culture experiments with recombinant S3-RNase proteins.Overall,this study provides important experimental evidence and theoretical basis for understanding the mechanism of self-incompatibility in plants by revealing the key role of the SCF complex in‘Xiangshui'lemon,which is bridged by ClSKP1-6,in self-incompatibility.The results of this study are of great significance for the future indepth exploration of the molecular mechanism of the SCF complex and its wide application in the self-incompatibility of plants.
