Algorithm Selection Method Based on Coupling Strength for Partitioned Analysis of Structure-Piezoelectric-Circuit Coupling

In this study, we propose an algorithm selection method based on coupling strength for the partitioned analysis ofstructure-piezoelectric-circuit coupling, which includes two types of coupling or inverse and direct piezoelectriccoupling and direct piezoelectric and circuit coupling. In the proposed method, implicit and explicit formulationsare used for strong and weak coupling, respectively. Three feasible partitioned algorithms are generated, namely(1) a strongly coupled algorithm that uses a fully implicit formulation for both types of coupling, (2) a weaklycoupled algorithm that uses a fully explicit formulation for both types of coupling, and (3) a partially stronglycoupled and partially weakly coupled algorithm that uses an implicit formulation and an explicit formulation forthe two types of coupling, respectively.Numerical examples using a piezoelectric energy harvester,which is a typicalstructure-piezoelectric-circuit coupling problem, demonstrate that the proposed method selects the most costeffectivealgorithm.

A review on electrocatalytic CO_(2) conversion via C-C and C-N coupling

Electrochemical C-C and C-N coupling reactions with the conversion of abundant and inexpensive small molecules,such as CO_(2) and nitrogencontaining species,are considered a promising route for increasing the value of CO_(2) reduction products.The development of high-performance catalysts is the key to the both electrocatalytic reactions.In this review,we present a systematic summary of the reaction systems for electrocatalytic CO_(2) reduction,along with the coupling mechanisms of C-C and C-N bonds over outstanding electrocatalytic materials recently developed.The key intermediate species and reaction pathways related to the coupling as well as the catalyst-structure relationship will be also discussed,aiming to provide insights and guidance for designing efficient CO_(2) reduction systems.

Study on synergistic leaching of potassium and phosphorus from potassium feldspar and solid waste phosphogypsum via coupling reactions

To achieve the resource utilization of solid waste phosphogypsum(PG)and tackle the problem of utilizing potassium feldspar(PF),a coupled synergistic process between PG and PF is proposed in this paper.The study investigates the features of P and F in PG,and explores the decomposition of PF using hydrofluoric acid(HF)in the sulfuric acid system for K leaching and leaching of P and F in PG.The impact factors such as sulfuric acid concentration,reaction temperature,reaction time,material ratio(PG/PF),liquid–solid ratio,PF particle size,and PF calcination temperature on the leaching of P and K is systematically investigated in this paper.The results show that under optimal conditions,the leaching rate of K and P reach more than 93%and 96%,respectively.Kinetics study using shrinking core model(SCM)indicates two significant stages with internal diffusion predominantly controlling the leaching of K.The apparent activation energies of these two stages are 11.92 kJ·mol^(-1)and 11.55 kJ·mol^(-1),respectively.

Dynamic impact properties of deep sandstone under thermal-hydraulicmechanical coupling loads

The deep rock mass within coal mines situated in a challenging environment are characterized by high ground stress,high geotemperature,high osmotic water pressure,and dynamic disturbances from mechanical excavation.To investigate the impact of this complex mechanical environment on the dynamic characteristics of roof sandstone in self-formed roadways without coal pillars,standard specimens of deep sandstone from the 2611 upper tunnel working face of the Yongmei Company within the Henan Coal Chemical Industry Group in Henan,China were prepared,and an orthogonal test was designed.Using a self-developed geotechnical dynamic impact mechanics test system,triaxial dynamic impact tests under thermal-hydraulicmechanical coupling conditions were conducted on deep sandstone.The results indicate that under high confining pressure,deep sandstone exhibits pronounced brittle failure at low temperatures,with peak strength gradually decreasing as temperature and osmotic water pressure increase.Conversely,under low confining pressure and low temperature,the brittleness of deep sandstone weakens gradually,while ductility increases.Moreover,sandstone demonstrates higher peak strength at low temperatures under high axial pressure conditions,lower peak strength at high temperatures,and greater strain under low axial pressure and high osmotic water pressure.Increases in impact air pressure and osmotic water pressure have proportionally greater effects on peak stress and peak strain.Approximately 50%of the input strain energy is utilized as effective energy driving the sandstone fracture process.Polar analysis identifies the optimal combination of factors affecting the peak stress and peak strain of sandstone.Under the coupling effect,intergranular and transgranular fractures occur within the sandstone.SEM images illustrate that the damage forms range from minor damage with multiple fissures to extensive fractures and severe fragmentation.This study elucidates the varied dynamic impact mechanical properties of deep sandstones under thermal-hydraulic-mechanical coupling,along with multifactor analysis methods and their optimal factor combinations.

Optimization Control of Multi-Mode Coupling All-Wheel Drive System for Hybrid Vehicle

The all-wheel drive(AWD)hybrid system is a research focus on high-performance new energy vehicles that can meet the demands of dynamic performance and passing ability.Simultaneous optimization of the power and economy of hybrid vehicles becomes an issue.A unique multi-mode coupling(MMC)AWD hybrid system is presented to realize the distributed and centralized driving of the front and rear axles to achieve vectored distribution and full utilization of the system power between the axles of vehicles.Based on the parameters of the benchmarking model of a hybrid vehicle,the best model-predictive control-based energy management strategy is proposed.First,the drive system model was built after the analysis of the MMC-AWD’s drive modes.Next,three fundamental strategies were established to address power distribution adjustment and battery SOC maintenance when the SOC changed,which was followed by the design of a road driving force observer.Then,the energy consumption rate in the average time domain was processed before designing the minimum fuel consumption controller based on the equivalent fuel consumption coefficient.Finally,the advantage of the MMC-AWD was confirmed by comparison with the dynamic performance and economy of the BYD Song PLUS DMI-AWD.The findings indicate that,in comparison to the comparative hybrid system at road adhesion coefficients of 0.8 and 0.6,the MMC-AWD’s capacity to accelerate increases by 5.26%and 7.92%,respectively.When the road adhesion coefficient is 0.8,0.6,and 0.4,the maximum climbing ability increases by 14.22%,12.88%,and 4.55%,respectively.As a result,the dynamic performance is greatly enhanced,and the fuel savings rate per 100 km of mileage reaches 12.06%,which is also very economical.The proposed control strategies for the new hybrid AWD vehicle can optimize the power and economy simultaneously.

Evolution and Application of Sealing Ability of Gypsum Caprocks under Temperature-Pressure Coupling:An Example of the ZS5 Well in the Tazhong Area of the Tarim Basin

Gypsum caprocks'sealing ability is affected by temperature-pressure coupling.Due to the limitations of experimental conditions,there is still a lack of triaxial stress-strain experiments that simultaneously consider changes in temperature and pressure conditions,which limits the accuracy of the comprehensive evaluation of the brittle plastic evolution and sealing ability of gypsum rocks using temperature pressure coupling.Triaxial stress-strain tests were utilized to investigate the differences in the evolution of the confinement capacity of gypsum rocks under coupled temperaturepressure action and isothermal-variable pressure action on the basis of sample feasibility analysis.According to research,the gypsum rock's peak and residual strengths decrease under simultaneous increases in temperature and pressure over isothermal pressurization experimental conditions,and it becomes more ductile.This reduces the amount of time it takes for the rock to transition from brittle to plastic.When temperature is taken into account,both the brittle–plastic transformation's depth limit and the lithological transformation of gypsum rocks become shallower,and the evolution of gypsum rocks under variable temperature and pressure conditions is more complicated than that under isothermal pressurization.The sealing ability under the temperature-pressure coupling is more in line with the actual geological context when the application results of the Well#ZS5 are compared.This provides a theoretical basis for precisely determining the process of hydrocarbon accumulation and explains why the early hydrocarbon were not well preserved.

Dynamic Coupling Analysis of Semisubmersible Platform Float-over Method for Docking Case

In this paper,the multi-body coupled dynamic characteristics of a semisubmersible platform and an HYSY 229 barge were investigated.First,coupled hydrodynamic analysis of the HYSY 229 barge and the semisubmersible platform was performed.Relevant hydrodynamic parameters were obtained using the retardation function method of three-dimensional frequency-domain potential flow theory.The results of the hydrodynamic analysis were highly consistent with the test findings,verifying the accuracy of the multifloating hydrodynamic coupling analysis,and key hydrodynamic parameters were solved for different water depths and the coupling effect.According to the obtained results,the hydrodynamic influence was the largest in shallow waters when the coupling effect was considered.Furthermore,the coupled motion equation combined with viscous damping,fender system,and mooring system was established,and the hydrodynamics,floating body motion,and dynamic response of the fender system were analyzed.Motion analysis revealed good agreement among the surge,sway,and yaw motions of the two floating bodies.However,when the wave period reached 10 s,the motion of the two floating bodies showed severe shock,and a relative motion was also observed.Therefore,excessive constraints should be added between the two floating bodies during construction to ensure construction safety.The numerical analysis and model test results of the semisubmersible platform and HYSY 229 barge at a water depth of 42 m and sea conditions of 0°,45°,and 90° were in good agreement,and the error was less than 5%.The maximum movement of the HYSY 229 barge reached 2.61 m in the sway direction,whereas that of the semisubmersible platform was 2.11 m.During construction,excessive constraints should be added between the two floating bodies to limit their relative movement and ensure construction safety.

Research on modeling and self-excited vibration mechanism in magnetic levitation-collision interface coupling system

The modeling and self-excited vibration mechanism in the magnetic levitation-collision interface coupling system are investigated.The effects of the control and interface parameters on the system's stability are analyzed.The frequency range of self-excited vibrations is investigated from the energy point of view.The phenomenon of self-excited vibrations is elaborated with the phase trajectory.The corresponding control strategies are briefly analyzed with respect to the vibration mechanism.The results show that when the levitation objects collide with the mechanical interface,the system's vibration frequency becomes larger with the decrease in the collision gap;when the vibration frequency exceeds the critical frequency,the electromagnetic system continues to provide energy to the system,and the collision interface continuously dissipates energy so that the system enters the self-excited vibration state.

Application of CFD and FEA Coupling to Predict Structural Dynamic Responses of A Trimaran in Uni-and Bi-Directional Waves

To predict the wave loads of a flexible trimaran in different wave fields,a one-way interaction numerical simulation method is proposed by integrating the fluid solver(Star-CCM+)and structural solver(Abaqus).Differing from the existing coupled CFD-FEA method for monohull ships in head waves,the presented method equates the mass and stiffness of the whole ship to the hull shell so that any transverse and longitudinal section stress of the hull in oblique waves can be obtained.Firstly,verification study and sensitivity analysis are carried out by comparing the trimaran motions using different mesh sizes and time step schemes.Discussion on the wave elevation of uni-and bi-directional waves is also carried out.Then a comprehensive analysis on the structural responses of the trimaran in different uni-directional regular wave and bi-directional cross sea conditions is carried out,respectively.Finally,the differences in structural response characteristics of trimaran in different wave fields are studied.The results show that the present method can reduce the computational burden of the two-way fluid-structure interaction simulations.

Efficient C-N coupling in electrocatalytic urea generation on copper carbonate hydroxide electrocatalysts

Urea generation through electrochemical CO_(2) and NO_(3)~-co-reduction reaction(CO_(2)NO_(3)RR)is still limited by either the low selectivity or yield rate of urea.Herein,we report copper carbonate hydroxide(Cu_2(OH)_2CO_(3))as an efficient CO_(2)NO_(3)RR electrocatalyst with an impressive urea Faradaic efficiency of45.2%±2.1%and a high yield rate of 1564.5±145.2μg h~(-1)mg_(cat)~(-1).More importantly,H_(2) evolution is fully inhibited on this electrocatalyst over a wide potential range between-0.3 and-0.8 V versus reversible hydrogen electrode.Our thermodynamic simulation reveals that the first C-N coupling follows a unique pathway on Cu_2(OH)_2CO_(3) by combining the two intermediates,~*COOH and~*NHO.This work demonstrates that high selectivity and yield rate of urea can be simultaneously achieved on simple Cu-based electrocatalysts in CO_(2)NO_(3)RR,and provide guidance for rational design of more advanced catalysts.

Mass transfer enhancement and hydrodynamic performance with wire mesh coupling solid particles in bubble column reactor

It is of vital significance to investigate mass transfer enhancements for chemical engineering processes.This work focuses on investigating the coupling influence of embedding wire mesh and adding solid particles on bubble motion and gas-liquid mass transfer process in a bubble column.Particle image velocimetry(PIV)technology was employed to analyze the flow field and bubble motion behavior,and dynamic oxygen absorption technology was used to measure the gas-liquid volumetric mass transfer coefficient(kLa).The effect of embedding wire mesh,adding solid particles,and wire mesh coupling solid particles on the flow characteristic and kLa were analyzed and compared.The results show that the gas-liquid interface area increases by 33%-72%when using the wire mesh coupling solid particles strategy compared to the gas-liquid two-phase flow,which is superior to the other two strengthening methods.Compared with the system without reinforcement,kLa in the bubble column increased by 0.5-1.8 times with wire mesh coupling solid particles method,which is higher than the sum of kLa increases with inserting wire mesh and adding particles,and the coupling reinforcement mechanism for affecting gas-liquid mass transfer process was discussed to provide a new idea for enhancing gas-liquid mass transfer.

Seismic performance evaluation of hybrid coupled shear wall system with shear and flexural fuse-type steel coupling beams

Replaceable flexural and shear fuse-type coupling beams are used in hybrid coupled shear wall(HCSW)systems,enabling concrete buildings to be promptly recovered after severe earthquakes.This study aimed to analytically evaluate the seismic behavior of flexural and shear fuse beams situated in short-,medium-and high-rise RC buildings that have HCSWs.Three building groups hypothetically located in a high seismic hazard zone were studied.A series of 2D nonlinear time history analyses was accomplished in OpenSees,using the ground motion records scaled at the design basis earthquake level.It was found that the effectiveness of fuses in HCSWs depends on various factors such as size and scale of the building,allowable rotation value,inter-story drift ratio,residual drift quantity,energy dissipation value of the fuses,etc.The results show that shear fuses better meet the requirements of rotations and drifts.In contrast,flexural fuses dissipate more energy,but their sectional stiffness should increase to meet other requirements.It was concluded that adoption of proper fuses depends on the overall scale of the building and on how associated factors are considered.

d-d Orbital coupling induced by crystal-phase engineering assists acetonitrile electroreduction to ethylamine

The d-d orbital coupling induced by crystal-phase engineering can effectively adjust the electronic structure of electrocatalysts,thus showing significant catalytic performance,while it has been rarely explored in electrochemical acetonitrile reduction reaction(ARR)to date.Herein,we successfully realize the structural transformation of Pd Cu metallic aerogels(MAs)from face-centered cubic(FCC)to body-centered cubic(BCC)through annealing treatment.Specifically,the BCC Pd Cu MAs exhibit excellent ARR performance with high ethylamine selectivity of 90.91%,Faradaic efficiency of 88.60%,yield rate of 316.0 mmol h^(-1)g^(-1)_(Pd+Cu)and long-term stability for consecutive electrolysis within 20 h at-0.55 V vs.reversible hydrogen electrode,outperforming than those of FCC Pd Cu MAs.Under the membrane electrode assembly system,BCC Pd Cu MAs also demonstrate excellent ethylamine yield rate of 389.5 mmol h^(-1)g^(-1)_(Pd+Cu).Density functional theory calculation reveals that the d-d orbital coupling in BCC Pd Cu MAs results in an evident correlation effect for the interaction of Pd and Cu sites,which boosts up the Cu sites electronic activities to enhance ARR performance.Our work opens a new route to develop efficient ARR electrocatalysts from the perspective of crystalline structure transformation.

Rheological properties and concentration evolution of thickened tailings under the coupling effect of compression and shear

Cemented paste backfill(CPB)is a key technology for green mining in metal mines,in which tailings thickening comprises the primary link of CPB technology.However,difficult flocculation and substandard concentrations of thickened tailings often occur.The rheological properties and concentration evolution in the thickened tailings remain unclear.Moreover,traditional indoor thickening experiments have yet to quantitatively characterize their rheological properties.An experiment of flocculation condition optimization based on the Box-Behnken design(BBD)was performed in the study,and the two response values were investigated:concentration and the mean weighted chord length(MWCL)of flocs.Thus,optimal flocculation conditions were obtained.In addition,the rheological properties and concentration evolution of different flocculant dosages and ultrafine tailing contents under shear,compression,and compression-shear coupling experimental conditions were tested and compared.The results show that the shear yield stress under compression and compression-shear coupling increases with the growth of compressive yield stress,while the shear yield stress increases slightly under shear.The order of shear yield stress from low to high under different thickening conditions is shear,compression,and compression-shear coupling.Under compression and compression-shear coupling,the concentration first rapidly increases with the growth of compressive yield stress and then slowly increases,while concentration increases slightly under shear.The order of concentration from low to high under different thickening conditions is shear,compression,and compression-shear coupling.Finally,the evolution mechanism of the flocs and drainage channels during the thickening of the thickened tailings under different experimental conditions was revealed.

Time-dependent behavior and permeability evolution of limestone under hydro-mechanical coupling

Excessively high pore water pressure presents unpredictable risks to the safety of rock tunnels in mountainous regions that are predominantly composed of limestone. Investigating the creep characteristics and permeability evolution of limestone under varying hydrated conditions is crucial for a better understanding of the delayed deformation mechanisms of limestone rock tunnels. To this end, this paper initially conducts a series of multi-stage triaxial creep tests on limestone samples under varying pore water pressures. The experiment examines how pore water pressure affects limestone’s creep strain, strain rate, long-term strength, lifespan, and permeability, all within the context of hydraulicmechanical(HM) coupling. To better describe the creep behavior associated with pore water pressure, this paper proposes a new nonlinear fractional creep constitutive model. This constitutive model depicts the initial, steady-state, and accelerated phases of limestone’s creep behavior. Finally, the proposed model is applied to the numerical realization of deformation in limestone tunnel, validating the effectiveness of the proposed constitutive model in predicting tunnel’s creep deformation. This research enhances our understanding of limestone’s creep characteristics and permeability evolution under HM coupling, laying a foundation for assessing the longterm stability of mountain tunnels.

Mechanical behaviours of bedded sandstone under hydromechanical coupling

The combination of the dipping effect and hydromechanical(H-M)coupling effect can easily lead to water inrush disasters in water-rich roadways with different dip angles in coal mines.Therefore,H-M coupling tests of bedded sandstones under identical osmotic pressure and various confining pressures were conducted.Then,the evolution curves of stress-strain,permeability and damage,macro-and mesoscopic failure characteristics were obtained.Subsequently,the mechanical behaviour was characterized,and finally the failure mechanism was revealed.The results showed that:(1)The failure of the sandstone with the bedding angle of 45°or 60°was the structure-dominant type,while that with the bedding angle of 0°,30°or 90°was the force-dominant type.(2)When the bedding angle was in the range of(0°,30°)or(45°,90°),the confining pressure played a dominant role in influencing the peak strength.However,withinβ∈(30°,45°),the bedding effect played a dominant role in the peak strength.(3)With the increase in bedding angle,the cohesion increased first,then decreased and finally increased,while the internal friction angle was the opposite.(4)When the bedding angle was 0°or 30°,the“water wedging”effect and the“bedding buckling”effect would lead to the forking or converging shear failure.When the bedding angle was 45°or 60°,the sliding friction effect would lead to the shear slipping failure.When the bedding angle was 90°,the combination of the“bedding buckling”effect and shear effect would lead to the mixed tension-shear failure.The above conclusions obtained are helpful for the prevention of water inrush disasters in water-rich roadways with different dips in coal mines.

Photothermal catalytic C-C coupling to ethylene from CO_(2) with high efficiency by synergistic cooperation of oxygen vacancy and half-metallic WTe_(2)

Photothermal catalytic CO_(2) conversion provides an effective solution targeting carbon neutrality by synergistic utilization of photon and heat.However,the C-C coupling initiated by photothermal catalysis is still a big challenge.Herein,a three-dimensional(3D)hierarchical W_(18)O_(49)/WTe_(2) hollow nanosphere is constructed through in-situ embodying of oxygen vacancy and tellurium on the scaffold of WO_(3).The light absorption towards near-infrared spectral region and CO_(2) adsorption are enhanced by the formation of half-metal WTe_(2) and the unique hierarchical hollow architecture.Combining with the generation of oxygen vacancy with strengthened CO_(2) capture,the photothermal effect on the samples can be sufficiently exploited for activating the CO_(2) molecules.In particular,the close contact between W_(18)O_(49)and WTe_(2) largely promotes the photoinduced charge separation and mass transfer,and thus the~*CHO intermediate formation and fixedness are facilitated.As a result,the C-C coupling can be evoked between tungsten and tellurium atoms on WTe_(2).The ethylene production by optimized W_(18)O_(49)/WTe_(2) reaches 147.6μmol g^(-1)with the selectivity of 80%.The in-situ diffuse reflectance infrared Fourier transform spectroscopy(DRIFTS)and density functional theory(DFT)calculations are performed to unveil the presence and significance of aldehyde intermediate groups in C-C coupling.The half-metallic WTe_(2) cocatalyst proposes a new approach for efficient CO_(2) conversion with solar energy,and may especially create a new platform for the generation of multi-carbon products.

Metal–Organic Gel Leading to Customized Magnetic‑Coupling Engineering in Carbon Aerogels for Excellent Radar Stealth and Thermal Insulation Performances

Metal–organic gel(MOG)derived composites are promising multi-functional materials due to their alterable composition,identifiable chemical homogeneity,tunable shape,and porous structure.Herein,stable metal–organic hydrogels are prepared by regulating the complexation effect,solution polarity and curing speed.Meanwhile,collagen peptide is used to facilitate the fabrication of a porous aerogel with excellent physical properties as well as the homogeneous dispersion of magnetic particles during calcination.Subsequently,two kinds of heterometallic magnetic coupling systems are obtained through the application of Kirkendall effect.FeCo/nitrogen-doped carbon(NC)aerogel demonstrates an ultra-strong microwave absorption of−85 dB at an ultra-low loading of 5%.After reducing the time taken by atom shifting,a FeCo/Fe3O4/NC aerogel containing virus-shaped particles is obtained,which achieves an ultra-broad absorption of 7.44 GHz at an ultra-thin thickness of 1.59 mm due to the coupling effect offered by dual-soft-magnetic particles.Furthermore,both aerogels show excellent thermal insulation property,and their outstanding radar stealth performances in J-20 aircraft are confirmed by computer simulation technology.The formation mechanism of MOG is also discussed along with the thermal insulation and electromagnetic wave absorption mechanism of the aerogels,which will enable the development and application of novel and lightweight stealth coatings.

Development of multi-functional anchorage support dynamic-static coupling performance test system and its application

In underground engineering with complex conditions,the bolt(cable)anchorage support system is in an environment where static and dynamic stresses coexist,under the action of geological conditions such as high stresses and strong disturbances and construction conditions such as the application of high prestress.It is essential to study the support components performance under dynamic-static coupling conditions.Based on this,a multi-functional anchorage support dynamic-static coupling performance test system(MAC system)is developed,which can achieve 7 types of testing functions,including single component performance,anchored net performance,anchored rock performance and so on.The bolt and cable mechanical tests are conducted by MAC system under different prestress levels.The results showed that compared to the non-prestress condition,the impact resistance performance of prestressed bolts(cables)is significantly reduced.In the prestress range of 50–160 k N,the maximum reduction rate of impact energy resisted by different types of bolts is 53.9%–61.5%compared to non-prestress condition.In the prestress range of 150–300 k N,the impact energy resisted by high-strength cable is reduced by76.8%–84.6%compared to non-prestress condition.The MAC system achieves dynamic-static coupling performance test,which provide an effective means for the design of anchorage support system.

Coupling Coordination Analysis of Cropland Intensification and Agroecosystem Services:Evidence from Loess Plateau in Shaanxi Province,China

One of the greatest challenges in the agroecosystem is to improve cropland intensification while preserving agroecosystem services.While many studies have investigated the effect of cropland intensification on agroecosystem service,the interactive coupling and coordination among these factors remain largely unexplored.In view of this,this study performed a case study of the Loess Plateau in Shaanxi Province,China and constructed comprehensive evaluation models to quantify the cropland intensification and agroecosystem service in this area.Balance analysis and the coupling coordination degree model were used to evaluate the interactive relationship between cropland intensification and agroecosystem service,and statistical analysis and spatial autocorrelation were used to analyze the spatial characteristics and potential mechanism of the coupling coordination.Results show that both the cropland intensification and agroecosystem service in the study area were relatively low yet gradually increased from 2000 to 2020.Agroecosystem service lag was identified as the dominant unbalanced development type.Improving the supply capacity of agroecosystem services plays a key role in the balanced development of cropland in the Loess Plateau.The coupling coordination degree between cropland intensification and agroecosystem service ranges from basic coordination to serious incoordination.Therefore,cropland intensification practices in the area should be optimized to enhance this coordination degree.An upward trend was also observed in the coupling coordination degree from2000 to 2020.The withdrawal of marginal cropland in the Grain for Green program is one of the most important reasons for this trend,especially for the northern region.Around 83.6%of the high-high clusters are concentrated in the southern region of the Loess Plateau,whereas 70.5%of the low-low clusters are distributed in the northern region.These clustering characteristics are mainly attributed to the environmental suitability of these areas for agriculture and their degree of economic development.