This paper extends the one-dimensional(1D)nonlocal strain gradient integral model(NStraGIM)to the two-dimensional(2D)Kirchhoff axisymmetric nanoplates,based on nonlocal strain gradient integral relations formulated al...This paper extends the one-dimensional(1D)nonlocal strain gradient integral model(NStraGIM)to the two-dimensional(2D)Kirchhoff axisymmetric nanoplates,based on nonlocal strain gradient integral relations formulated along both the radial and circumferential directions.By transforming the proposed integral constitutive equations into the equivalent differential forms,complemented by the corresponding constitutive boundary conditions(CBCs),a well-posed mathematical formulation is established for analyzing the axisymmetric bending and buckling of annular/circular functionally graded(FG)sandwich nanoplates.The boundary conditions at the inner edge of a solid nanoplate are derived by L'H?spital's rule.The numerical solution is obtained by the generalized differential quadrature method(GDQM).The accuracy of the proposed model is validated through comparison with the data from the existing literature.A parameter study is conducted to demonstrate the effects of FG sandwich parameters,size parameters,and nonlocal gradient parameters.展开更多
In this work,the static tensile and free vibration of nanorods are studied via both the strain-driven(Strain D)and stress-driven(Stress D)two-phase nonlocal models with a bi-Helmholtz averaging kernel.Merely adjusting...In this work,the static tensile and free vibration of nanorods are studied via both the strain-driven(Strain D)and stress-driven(Stress D)two-phase nonlocal models with a bi-Helmholtz averaging kernel.Merely adjusting the limits of integration,the integral constitutive equation of the Fredholm type is converted to that of the Volterra type and then solved directly via the Laplace transform technique.The unknown constants can be uniquely determined through the standard boundary conditions and two constrained conditions accompanying the Laplace transform process.In the numerical examples,the bi-Helmholtz kernel-based Strain D(or Stress D)two-phase model shows consistently softening(or stiffening)effects on both the tension and the free vibration of nanorods with different boundary edges.The effects of the two nonlocal parameters of the bi-Helmholtz kernel-based two-phase nonlocal models are studied and compared with those of the Helmholtz kernel-based models.展开更多
A torsional static and free vibration analysis of the functionally graded nanotube(FGNT)composed of two materials varying continuously according to the power-law along the radial direction is performed using the bi-He...A torsional static and free vibration analysis of the functionally graded nanotube(FGNT)composed of two materials varying continuously according to the power-law along the radial direction is performed using the bi-Helmholtz kernel based stress-driven nonlocal integral model.The differential governing equation and boundary conditions are deduced on the basis of Hamilton’s principle,and the constitutive relationship is expressed as an integral equation with the bi-Helmholtz kernel.Several nominal variables are introduced to simplify the differential governing equation,integral constitutive equation,and boundary conditions.Rather than transforming the constitutive equation from integral to differential forms,the Laplace transformation is used directly to solve the integro-differential equations.The explicit expression for nominal torsional rotation and torque contains four unknown constants,which can be determined with the help of two boundary conditions and two extra constraints from the integral constitutive relation.A few benchmarked examples are solved to illustrate the nonlocal influence on the static torsion of a clamped-clamped(CC)FGNT under torsional constraints and a clamped-free(CF)FGNT under concentrated and uniformly distributed torques as well as the torsional free vibration of an FGNT under different boundary conditions.展开更多
We present a study on the dynamic stability of porous functionally graded(PFG)beams under hygro-thermal loading.The variations of the properties of the beams across the beam thicknesses are described by the power-law ...We present a study on the dynamic stability of porous functionally graded(PFG)beams under hygro-thermal loading.The variations of the properties of the beams across the beam thicknesses are described by the power-law model.Unlike most studies on this topic,we consider both the bending deformation of the beams and the hygro-thermal load as size-dependent,simultaneously,by adopting the equivalent differential forms of the well-posed nonlocal strain gradient integral theory(NSGIT)which are strictly equipped with a set of constitutive boundary conditions(CBCs),and through which both the stiffness-hardening and stiffness-softening effects of the structures can be observed with the length-scale parameters changed.All the variables presented in the differential problem formulation are discretized.The numerical solution of the dynamic instability region(DIR)of various bounded beams is then developed via the generalized differential quadrature method(GDQM).After verifying the present formulation and results,we examine the effects of different parameters such as the nonlocal/gradient length-scale parameters,the static force factor,the functionally graded(FG)parameter,and the porosity parameter on the DIR.Furthermore,the influence of considering the size-dependent hygro-thermal load is also presented.展开更多
In this paper,we propose general strain-and stress-driven two-phase local/nonlocal piezoelectric integral models,which can distinguish the difference of nonlocal effects on the elastic and piezoelectric behaviors of n...In this paper,we propose general strain-and stress-driven two-phase local/nonlocal piezoelectric integral models,which can distinguish the difference of nonlocal effects on the elastic and piezoelectric behaviors of nanostructures.The nonlocal piezoelectric model is transformed from integral to an equivalent differential form with four constitutive boundary conditions due to the difficulty in solving intergro-differential equations directly.The nonlocal piezoelectric integral models are used to model the static bending of the Euler-Bernoulli piezoelectric beam on the assumption that the nonlocal elastic and piezoelectric parameters are coincident with each other.The governing differential equations as well as constitutive and standard boundary conditions are deduced.It is found that purely strain-and stress-driven nonlocal piezoelectric integral models are ill-posed,because the total number of differential orders for governing equations is less than that of boundary conditions.Meanwhile,the traditional nonlocal piezoelectric differential model would lead to inconsistent bending response for Euler-Bernoulli piezoelectric beam under different boundary and loading conditions.Several nominal variables are introduced to normalize the governing equations and boundary conditions,and the general differential quadrature method(GDQM)is used to obtain the numerical solutions.The results from current models are validated against results in the literature.It is clearly established that a consistent softening and toughening effects can be obtained for static bending of the Euler-Bernoulli beam based on the general strain-and stress-driven local/nonlocal piezoelectric integral models,respectively.展开更多
We prove a local existence of a strong solution v ：Ω×T→R^3 for a system of nonlinear integrodifferential equations describing motion of an incompressible viscoelastic fluid using standard mathematical tools. T...We prove a local existence of a strong solution v ：Ω×T→R^3 for a system of nonlinear integrodifferential equations describing motion of an incompressible viscoelastic fluid using standard mathematical tools. The problem is considered in a bounded, smooth domain ΩСR^3 with a Dirichlet boundary condition and a standard initial condition.展开更多
Submarine landslides can cause severe damage to marine engineering structures. Their sliding velocity and runout distance are two major parameters for quantifying and analyzing the risk of submarine landslides.Current...Submarine landslides can cause severe damage to marine engineering structures. Their sliding velocity and runout distance are two major parameters for quantifying and analyzing the risk of submarine landslides.Currently, commercial calculation programs such as BING have limitations in simulating underwater soil movements. All of these processes can be consistently simulated through a smoothed particle hydrodynamics（SPH） depth integrated model. The basis of the model is a control equation that was developed to take into account the effects of soil consolidation and erosion. In this work, the frictional rheological mode has been used to perform a simulation study of submarine landslides. Time-history curves of the sliding body＇s velocity, height,and length under various conditions of water depth, slope gradient, contact friction coefficient, and erosion rate are compared; the maximum sliding distance and velocity are calculated; and patterns of variation are discussed.The findings of this study can provide a reference for disaster warnings and pipeline route selection.展开更多
To address the issue of disturbance compensation deviation in linear active disturbance rejection control(LADRC),a linear active disturbance rejection control method with reference to the integral chain model(LADRC-R)...To address the issue of disturbance compensation deviation in linear active disturbance rejection control(LADRC),a linear active disturbance rejection control method with reference to the integral chain model(LADRC-R)is proposed.By constructing an ideal control reference model,a dynamic correlation between output deviation and uncompensated disturbances is established,and a dual-loop compensation mechanism is designed.Based on theoretical analysis and frequency-domain characteristics of typical first/second-order systems,this method maintains the parameter-tuning advantages of LADRC while reducing disturbance effects by 50%and introducing no phase lag during low-frequency disturbance suppression.Simulations on second-order systems verify its robustness under parameter perturbations,gain mismatch,and complex disturbances,and an optimized design scheme for the deviation compensator is proposed to suppress discontinuous measurement noise interference.Finally,the engineering effectiveness of this method in precision motion control is validated on an electromagnetic suspension platform,providing a new approach to improving the control performance of LADRC in environments with uncertain disturbances.展开更多
Previous studies have shown that Eringen’s differential nonlocal model would lead to the ill-posed mathematical formulation for axisymmetric bending of circular microplates.Based on the nonlocal integral models along...Previous studies have shown that Eringen’s differential nonlocal model would lead to the ill-posed mathematical formulation for axisymmetric bending of circular microplates.Based on the nonlocal integral models along the radial and circumferential directions,we propose nonlocal integral polar models in this work.The proposed strainand stress-driven two-phase nonlocal integral polar models are applied to model the axisymmetric bending of circular microplates.The governing differential equations and boundary conditions(BCs)as well as constitutive constraints are deduced.It is found that the purely strain-driven nonlocal integral polar model turns to a traditional nonlocal differential polar model if the constitutive constraints are neglected.Meanwhile,the purely strain-and stress-driven nonlocal integral polar models are ill-posed,because the total number of the differential orders of the governing equations is less than that of the BCs plus constitutive constraints.Several nominal variables are introduced to simplify the mathematical expression,and the general differential quadrature method(GDQM)is applied to obtain the numerical solutions.The results from the current models(CMs)are compared with the data in the literature.It is clearly established that the consistent softening and toughening effects can be obtained for the strain-and stress-driven local/nonlocal integral polar models,respectively.The proposed two-phase local/nonlocal integral polar models(TPNIPMs)may provide an efficient method to design and optimize the plate-like structures for microelectro-mechanical systems.展开更多
This paper addresses an integral model of development a large electric power system using the example of the Unified Energy System of Russia.The model takes account of the age structure of the plants main equipment.Be...This paper addresses an integral model of development a large electric power system using the example of the Unified Energy System of Russia.The model takes account of the age structure of the plants main equipment.Besides,generating equipment is divided into components depending on the types of energy resources used.The mathematical model is presented by a system of nonclassical Volterra integral equations of the first kind.One of the equations describes the balance between the total available capacity of the electric power system,commissioning of new equipment,and dismantling of obsolete one.The other equations define the shares of different types of power plants in the total composition of the electric power system equipment.Based on the considered model,we set a problem that searches the optimal lifetimes of electric power system capacities for a given demand for electricity.The optimality criterion is a functional reflecting cost of commissioning and operating the capacities.The specifics of the optimization problem are that the optimization parameter is in the lower limit of integration.An algorithm for solving of this optimal control problem numerically is developed.The influence of economic indices on the solution to the optimal control problem is studied.Calculations of the optimal development of the Unified Energy System of Russia until 2050 are carried out using real-life data.展开更多
To evaluate the lateral sealing mechanism of extensional fault based on the pressure difference between fault and reservoir, an integral mathematical-geological model of diagenetic time on diagenetic pressure consider...To evaluate the lateral sealing mechanism of extensional fault based on the pressure difference between fault and reservoir, an integral mathematical-geological model of diagenetic time on diagenetic pressure considering the influence of diagenetic time on the diagenetic pressure and diagenetic degree of fault rock has been established to quantitatively calculate the lateral sealing ability of extensional fault. By calculating the time integral of the vertical stress and horizontal in-situ stress on the fault rock and surrounding rock, the burial depth of the surrounding rock with the same clay content and diagenesis degree as the target fault rock was worked out. In combination with the statistical correlation of clay content, burial depth and displacement pressure of rock in the study area, the displacement pressure of target fault rock was calculated quantitatively. The calculated displacement pressure was compared with that of the target reservoir to quantitatively evaluate lateral sealing state and ability of the extensional fault. The method presented in this work was used to evaluate the sealing of F_(1), F_(2) and F_(3) faults in No.1 structure of Nanpu Sag, and the results were compared with those from fault-reservoir displacement pressure differential methods without considering the diagenetic time and simple considering the diagenetic time. It is found that the results calculated by the integral mathematical-geological model are the closest to the actual underground situation, the errors between the hydrocarbon column height predicted by this method and the actual column height were 0–8 m only, proving that this model is more feasible and credible.展开更多
Background As information technology has advanced and been popularized,open pit mining has rapidly developed toward integration and digitization.The three-dimensional reconstruction technology has been successfully ap...Background As information technology has advanced and been popularized,open pit mining has rapidly developed toward integration and digitization.The three-dimensional reconstruction technology has been successfully applied to geological reconstruction and modeling of surface scenes in open pit mines.However,an integrated modeling method for surface and underground mine sites has not been reported.Methods In this study,we propose an integrated modeling method for open pit mines that fuses a real scene on the surface with an underground geological model.Based on oblique photography,a real-scene model was established on the surface.Based on the surface-stitching method proposed,the upper and lower surfaces and sides of the model were constructed in stages to construct a complete underground three-dimensional geological model,and the aboveground and underground models were registered together to build an integrated open pit mine model.Results The oblique photography method used reconstructed a surface model of an open pit mine using a real scene.The surface-stitching algorithm proposed was compared with the ball-pivoting and Poisson algorithms,and the integrity of the reconstructed model was markedly superior to that of the other two reconstruction methods.In addition,the surface-stitching algorithm was applied to the reconstruction of different formation models and showed good stability and reconstruction efficiency.Finally,the aboveground and underground models were accurately fitted after registration to form an integrated model.Conclusions The proposed method can efficiently establish an integrated open pit model.Based on the integrated model,an open pit auxiliary planning system was designed and realized.It supports the functions of mining planning and output calculation,assists users in mining planning and operation management,and improves production efficiency and management levels.展开更多
We investigate the integrability of the Rabi model,which is traditionally viewed as not Yang–Baxter-integrable despite its solvability.Building on efforts by Bogoliubov and Kulish(2013 J.Math.Sci.19214–30),Amico et ...We investigate the integrability of the Rabi model,which is traditionally viewed as not Yang–Baxter-integrable despite its solvability.Building on efforts by Bogoliubov and Kulish(2013 J.Math.Sci.19214–30),Amico et al(2007 Nucl.Phys.B 787283–300),and Batchelor and Zhou(2015 Phys.Rev.A 91053808),who explored special limiting cases of the model,we develop a spin–boson interaction Hamiltonian under more general boundary conditions,particularly focusing on open boundary conditions with off-diagonal terms.Our approach maintains the direction of the spin in the z direction and also preserves the boson particle number operator a^(†)a,marking a progression beyond previous efforts that have primarily explored reduced forms of the Rabi model from Yang–Baxter algebra.We also address the presence of‘unwanted’quadratic boson terms a^(2) and a^(†2),which share coefficients with the boson particle number operator.Interestingly,these terms vanish when spectral parameter u=±θ_(s),simplifying the model to a limiting case of operator-valued twists,a scenario previously discussed by Batchelor and Zhou(2015 Phys.Rev.A 91053808).展开更多
Quantification of river flood risks is a prerequisite for floodplain management and development.The lower Yellow River(LYR)is characterized by a complex channel–floodplain system,which is prone to flooding but inhabi...Quantification of river flood risks is a prerequisite for floodplain management and development.The lower Yellow River(LYR)is characterized by a complex channel–floodplain system,which is prone to flooding but inhabits a large population on the floodplains.Many floodplain management modes have been presented,but implementation effects of these management modes have not been evaluated correctly.An integrated model was first proposed to evaluate the flood risks to people’s life and property,covering an improved module of two-dimensional(2D)morphodynamic processes and a module of flood risk evaluation for people,buildings and crops on the floodplains.Two simulation cases were then conducted to validate the model accuracy,including the hyperconcentrated flood event and dike-breach induced flood event occurring in the LYR.Finally,the integrated model was applied to key floodplains in the LYR,and the effects of different floodplain management modes were quantified on the risks to people’s life and property under an extreme flood event.Results indicate that:①Satisfactory accuracy was achieved in the simulation of these two flood events.The maximum sediment concentration was just underestimated by 9%,and the simulated inundation depth agreed well with the field record;②severe inundation was predicted to occur in most domains under the current topography(SchemeⅠ),which would be alleviated after implementing different floodplain management modes,with the area in slight inundation degree accounting for a large proportion under the mode of“construction of protection embankment”(SchemeⅡ)and the area in medium inundation degree occupying a high ratio under the mode of“floodplain partition harnessing”(SchemeⅢ);and③compared with SchemeⅠ,the high-risk area for people’s life and property would reduce by 21%–49%under SchemeⅡ,and by 35%–93%under SchemeⅢ.展开更多
As a prominent mode of variability in the tropical stratosphere on the interannual timescale,the Quasi-Biennial Oscillation(QBO)can significantly influence global atmospheric circulation and weather patterns.This stud...As a prominent mode of variability in the tropical stratosphere on the interannual timescale,the Quasi-Biennial Oscillation(QBO)can significantly influence global atmospheric circulation and weather patterns.This study explores the dynamic processes of QBO disruptions using the integrated climate model of the China Meteorological Administration(CMA)by nudging the tropical zonal winds toward observations.A comparative analysis with ERA5 reanalysis data shows that the nudged runs accurately replicate the general characteristics of the QBO,including the alternating QBO wind regimes and QBO disruption events.The evolution of the QBO winds is diagnosed using empirical orthogonal function and root-mean-square difference analyses,and the rarity of the disruption events is confirmed in the CMA model.Different aspects of the QBO disruptions and the relevant dynamics are present in the model.Firstly,the momentum budget analysis highlights the crucial roles of extratropical Rossby waves and non-orographic gravity waves in the transition from westerly to easterly winds during a disruption.Secondly,Kelvin waves and non-orographic gravity waves explain much of the transition from easterly to westerly winds near 40 hPa.Thirdly,the positive tendency from enhanced vertical advection further accelerates westerly momentum development via secondary meridional circulation.These findings underscore the importance of nudging techniques in understanding QBO dynamics,which provides valuable insights for future climate model improvements toward better forecasting QBO-related climate variability.Notably,due to model limitations,no QBO disruptions were simulated in the free-run experiments.展开更多
Objective:To explore the connotation of the integrated medical-care-rehabilitation nursing model and its application effect in elderly patients with chronic diseases.Methods:A total of 122 elderly patients with chroni...Objective:To explore the connotation of the integrated medical-care-rehabilitation nursing model and its application effect in elderly patients with chronic diseases.Methods:A total of 122 elderly patients with chronic diseases admitted to our hospital from January 2023 to June 2023 were selected and randomly divided into an observation group(62 cases)and a control group(60 cases).Both groups received routine nursing during hospitalization.After discharge,the control group received conventional continuous nursing,while the observation group was given the integrated medical-care-rehabilitation nursing model.The psychological status of the elderly patients in the two groups was compared before nursing and 6 months after nursing.Assessments were made on their clinical symptoms of mental health,self-care ability,health behaviors,and mastery of knowledge about elderly chronic diseases.Results:Six months after nursing,the scores of self-rated clinical symptoms of mental health and negative coping in both groups were lower than those before nursing(P<0.05).Meanwhile,the scores of negative coping,self-care ability,and health behaviors in both groups were higher than those before nursing(P<0.05).Conclusion:The integrated medical-care-rehabilitation nursing model can not only improve the nursing quality for elderly patients with chronic diseases but also foster their positive mentality,help them understand knowledge about diet and health care related to chronic diseases,enhance their self-care ability and health awareness,and assist them in achieving better recovery[1].展开更多
Firstly,based on the data of air quality and the meteorological data in Baoding City from 2017 to 2021,the correlations of meteorological elements and pollutants with O_(3)concentration were explored to determine the ...Firstly,based on the data of air quality and the meteorological data in Baoding City from 2017 to 2021,the correlations of meteorological elements and pollutants with O_(3)concentration were explored to determine the forecast factors of forecast models.Secondly,the O_(3)-8h concentration in Baoding City in 2021 was predicted based on the constructed models of multiple linear regression(MLR),backward propagation neural network(BPNN),and auto regressive integrated moving average(ARIMA),and the predicted values were compared with the observed values to test their prediction effects.The results show that overall,the MLR,BPNN and ARIMA models were able to forecast the changing trend of O_(3)-8h concentration in Baoding in 2021,but the BPNN model gave better forecast results than the ARIMA and MLR models,especially for the prediction of the high values of O_(3)-8h concentration,and the correlation coefficients between the predicted values and the observed values were all higher than 0.9 during June-September.The mean error(ME),mean absolute error(MAE),and root mean square error(RMSE)of the predicted values and the observed values of daily O_(3)-8h concentration based on the BPNN model were 0.45,19.11 and 24.41μg/m 3,respectively,which were significantly better than those of the MLR and ARIMA models.The prediction effects of the MLR,BPNN and ARIMA models were the best at the pollution level,followed by the excellent level,and it was the worst at the good level.In comparison,the prediction effect of BPNN model was better than that of the MLR and ARIMA models as a whole,especially for the pollution and excellent levels.The TS scores of the BPNN model were all above 66%,and the PC values were above 86%.The BPNN model can forecast the changing trend of O_(3)concentration more accurately,and has a good practical application value,but at the same time,the predicted high values of O_(3)concentration should be appropriately increased according to error characteristics of the model.展开更多
Transpiration element is included in the integrated stomatal conductance photosynthesis model by considering gaseous transfer processes, so the present model is capable to simulate the influence of boundary layer con...Transpiration element is included in the integrated stomatal conductance photosynthesis model by considering gaseous transfer processes, so the present model is capable to simulate the influence of boundary layer conductance. Leuning in his revised Ball's model replaced relative humidity with VPD s (the vapor pressure deficit from stomatal pore to leaf surface) and thereby made the relation with transpiration more straightforward, and made it possible for the regulation of transpiration and the influence of boundary layer conductance to be integrated into the combined model. If the differences in water vapor and CO 2 concentration between leaf and ambient air are considered, VPD s , the evaporative demand, is influenced by stomatal and boundary layer conductance. The physiological responses of photosynthesis, transpiration, and stomatal function, and the changes of intercellular CO 2 and water use efficiency to environmental factors, such as wind speed, photon flux density, leaf temperature and ambient CO 2, are analyzed. It is shown that if the boundary layer conductance drops to a level comparable with stomatal conductance, the results of simulation by the model presented here differ significantly from those by the previous model, and, in some cases, are more realistic than the latter.展开更多
The dynamic ground subsidence due to underground mining is a complicated time-dependent and rate- dependent process. Based. on the theory of rock rheology and probability integral method, this study developed the supe...The dynamic ground subsidence due to underground mining is a complicated time-dependent and rate- dependent process. Based. on the theory of rock rheology and probability integral method, this study developed the superposltlOn model for the prediction and analysis of the ground dynamic subsidence in mining area of thick !oose layer. The model consists of two parts （the prediction of overlying bedrock and the prediction of thick loose layer）. The overlying bedrock is regarded as visco-elastic beam, of which the dynamic subsidence is predicted by the Kelvin visco-elastic rheological model. The thick loose layer is regarded as random medium, and the ground dynamic subsidence, is predicted by the probability integral model. At last, the two prediction models are vertically stacked in the same coordinate system, and the bedrock dynamic subsidence is regarded as a variable mining thickness input into the prediction model of ground dynamic subsidence. The prediction results obtained were compared w^th actual movement and deformation data from Zhao I and Zhao II mine, central China. The agreement of the prediction results with the. field measurements.show that the superposition model （SM） is more satisfactory and the formulae obtained are more effective than the classical single probability Integral model（SPIM）, and thus can be effectively used for predicting the ground dynamic subsidence in mining area of thick loose layer.展开更多
A novel simulation program with an integrated circuit emphasis（SPICE） model developed for trench-gate metal-oxide-semiconductor field-effect transistor（M OSFET）devices is proposed. The drift region resistance was ...A novel simulation program with an integrated circuit emphasis（SPICE） model developed for trench-gate metal-oxide-semiconductor field-effect transistor（M OSFET）devices is proposed. The drift region resistance was modeled according to the physical characteristics and the specific structure of the trench-gate MOSFET device. For the accurate simulation of dynamic characteristics, three important capacitances, gate-to-drain capacitance Cgd, gate-to-source capacitance Cgsand drain-to-source capacitance Cds, were modeled, respectively, in the proposed model. Furthermore,the self-heating effect, temperature effect and breakdown characteristic were taken into account; the self-heating model and breakdown model were built in the proposed model; and the temperature parameters of the model were revised. The proposed model is verified by experimental results, and the errors between measured data and simulation results of the novel model are less than 5%. Therefore, the model can give an accurate description for both the static and dynamic characteristics of the trench-gate MOSFET device.展开更多
基金Project supported by the National Natural Science Foundation of China(No.12172169)the Priority Academic Program Development of Jiangsu Higher Education Institutions。
文摘This paper extends the one-dimensional(1D)nonlocal strain gradient integral model(NStraGIM)to the two-dimensional(2D)Kirchhoff axisymmetric nanoplates,based on nonlocal strain gradient integral relations formulated along both the radial and circumferential directions.By transforming the proposed integral constitutive equations into the equivalent differential forms,complemented by the corresponding constitutive boundary conditions(CBCs),a well-posed mathematical formulation is established for analyzing the axisymmetric bending and buckling of annular/circular functionally graded(FG)sandwich nanoplates.The boundary conditions at the inner edge of a solid nanoplate are derived by L'H?spital's rule.The numerical solution is obtained by the generalized differential quadrature method(GDQM).The accuracy of the proposed model is validated through comparison with the data from the existing literature.A parameter study is conducted to demonstrate the effects of FG sandwich parameters,size parameters,and nonlocal gradient parameters.
基金the National Natural Science Foundation of China(No.12172169)the China Scholarship Council(CSC)(No.202006830038)。
文摘In this work,the static tensile and free vibration of nanorods are studied via both the strain-driven(Strain D)and stress-driven(Stress D)two-phase nonlocal models with a bi-Helmholtz averaging kernel.Merely adjusting the limits of integration,the integral constitutive equation of the Fredholm type is converted to that of the Volterra type and then solved directly via the Laplace transform technique.The unknown constants can be uniquely determined through the standard boundary conditions and two constrained conditions accompanying the Laplace transform process.In the numerical examples,the bi-Helmholtz kernel-based Strain D(or Stress D)two-phase model shows consistently softening(or stiffening)effects on both the tension and the free vibration of nanorods with different boundary edges.The effects of the two nonlocal parameters of the bi-Helmholtz kernel-based two-phase nonlocal models are studied and compared with those of the Helmholtz kernel-based models.
基金Project supported by the National Natural Science Foundation of China(No.11672131)the Priority Academic Program Development of Jiangsu Higher Education Institutions。
文摘A torsional static and free vibration analysis of the functionally graded nanotube(FGNT)composed of two materials varying continuously according to the power-law along the radial direction is performed using the bi-Helmholtz kernel based stress-driven nonlocal integral model.The differential governing equation and boundary conditions are deduced on the basis of Hamilton’s principle,and the constitutive relationship is expressed as an integral equation with the bi-Helmholtz kernel.Several nominal variables are introduced to simplify the differential governing equation,integral constitutive equation,and boundary conditions.Rather than transforming the constitutive equation from integral to differential forms,the Laplace transformation is used directly to solve the integro-differential equations.The explicit expression for nominal torsional rotation and torque contains four unknown constants,which can be determined with the help of two boundary conditions and two extra constraints from the integral constitutive relation.A few benchmarked examples are solved to illustrate the nonlocal influence on the static torsion of a clamped-clamped(CC)FGNT under torsional constraints and a clamped-free(CF)FGNT under concentrated and uniformly distributed torques as well as the torsional free vibration of an FGNT under different boundary conditions.
基金Project supported by the National Natural Science Foundation of China(No.12172169)the Natural Sciences and Engineering Research Council of Canada(No.NSERC RGPIN-2023-03227)。
文摘We present a study on the dynamic stability of porous functionally graded(PFG)beams under hygro-thermal loading.The variations of the properties of the beams across the beam thicknesses are described by the power-law model.Unlike most studies on this topic,we consider both the bending deformation of the beams and the hygro-thermal load as size-dependent,simultaneously,by adopting the equivalent differential forms of the well-posed nonlocal strain gradient integral theory(NSGIT)which are strictly equipped with a set of constitutive boundary conditions(CBCs),and through which both the stiffness-hardening and stiffness-softening effects of the structures can be observed with the length-scale parameters changed.All the variables presented in the differential problem formulation are discretized.The numerical solution of the dynamic instability region(DIR)of various bounded beams is then developed via the generalized differential quadrature method(GDQM).After verifying the present formulation and results,we examine the effects of different parameters such as the nonlocal/gradient length-scale parameters,the static force factor,the functionally graded(FG)parameter,and the porosity parameter on the DIR.Furthermore,the influence of considering the size-dependent hygro-thermal load is also presented.
基金the National Natural Science Foundation of China(No.12172169)the Scholarship of the China Scholarship Council(No.202106830093)。
文摘In this paper,we propose general strain-and stress-driven two-phase local/nonlocal piezoelectric integral models,which can distinguish the difference of nonlocal effects on the elastic and piezoelectric behaviors of nanostructures.The nonlocal piezoelectric model is transformed from integral to an equivalent differential form with four constitutive boundary conditions due to the difficulty in solving intergro-differential equations directly.The nonlocal piezoelectric integral models are used to model the static bending of the Euler-Bernoulli piezoelectric beam on the assumption that the nonlocal elastic and piezoelectric parameters are coincident with each other.The governing differential equations as well as constitutive and standard boundary conditions are deduced.It is found that purely strain-and stress-driven nonlocal piezoelectric integral models are ill-posed,because the total number of differential orders for governing equations is less than that of boundary conditions.Meanwhile,the traditional nonlocal piezoelectric differential model would lead to inconsistent bending response for Euler-Bernoulli piezoelectric beam under different boundary and loading conditions.Several nominal variables are introduced to normalize the governing equations and boundary conditions,and the general differential quadrature method(GDQM)is used to obtain the numerical solutions.The results from current models are validated against results in the literature.It is clearly established that a consistent softening and toughening effects can be obtained for static bending of the Euler-Bernoulli beam based on the general strain-and stress-driven local/nonlocal piezoelectric integral models,respectively.
基金supported by Grant Agency of the Charles University(454213)
文摘We prove a local existence of a strong solution v ：Ω×T→R^3 for a system of nonlinear integrodifferential equations describing motion of an incompressible viscoelastic fluid using standard mathematical tools. The problem is considered in a bounded, smooth domain ΩСR^3 with a Dirichlet boundary condition and a standard initial condition.
基金The Specialized Research Fund for the Doctoral Program of Higher Education under contract No.20120041130002the National Key Project of Science and Technology under contract No.2011ZX 05056-001-02the Fundamental Research Funds for the Central Universities under contract No.DUT14ZD220
文摘Submarine landslides can cause severe damage to marine engineering structures. Their sliding velocity and runout distance are two major parameters for quantifying and analyzing the risk of submarine landslides.Currently, commercial calculation programs such as BING have limitations in simulating underwater soil movements. All of these processes can be consistently simulated through a smoothed particle hydrodynamics（SPH） depth integrated model. The basis of the model is a control equation that was developed to take into account the effects of soil consolidation and erosion. In this work, the frictional rheological mode has been used to perform a simulation study of submarine landslides. Time-history curves of the sliding body＇s velocity, height,and length under various conditions of water depth, slope gradient, contact friction coefficient, and erosion rate are compared; the maximum sliding distance and velocity are calculated; and patterns of variation are discussed.The findings of this study can provide a reference for disaster warnings and pipeline route selection.
基金supported by the National Natural Science Foundation of China(Nos.62063009,52262050)the National Key Research and Development Program during the 14th 5-Year Plan(No.2023YFB4302100)the Major Science and Technology Research and Development Special Project in Jiangxi Province(No.20232ACE01011).
文摘To address the issue of disturbance compensation deviation in linear active disturbance rejection control(LADRC),a linear active disturbance rejection control method with reference to the integral chain model(LADRC-R)is proposed.By constructing an ideal control reference model,a dynamic correlation between output deviation and uncompensated disturbances is established,and a dual-loop compensation mechanism is designed.Based on theoretical analysis and frequency-domain characteristics of typical first/second-order systems,this method maintains the parameter-tuning advantages of LADRC while reducing disturbance effects by 50%and introducing no phase lag during low-frequency disturbance suppression.Simulations on second-order systems verify its robustness under parameter perturbations,gain mismatch,and complex disturbances,and an optimized design scheme for the deviation compensator is proposed to suppress discontinuous measurement noise interference.Finally,the engineering effectiveness of this method in precision motion control is validated on an electromagnetic suspension platform,providing a new approach to improving the control performance of LADRC in environments with uncertain disturbances.
基金Project supported by the National Natural Science Foundation of China(No.12172169)the Research Fund of State Key Laboratory of Mechanicsthe Priority Academic Program Development of Jiangsu Higher Education Institutions of China。
文摘Previous studies have shown that Eringen’s differential nonlocal model would lead to the ill-posed mathematical formulation for axisymmetric bending of circular microplates.Based on the nonlocal integral models along the radial and circumferential directions,we propose nonlocal integral polar models in this work.The proposed strainand stress-driven two-phase nonlocal integral polar models are applied to model the axisymmetric bending of circular microplates.The governing differential equations and boundary conditions(BCs)as well as constitutive constraints are deduced.It is found that the purely strain-driven nonlocal integral polar model turns to a traditional nonlocal differential polar model if the constitutive constraints are neglected.Meanwhile,the purely strain-and stress-driven nonlocal integral polar models are ill-posed,because the total number of the differential orders of the governing equations is less than that of the BCs plus constitutive constraints.Several nominal variables are introduced to simplify the mathematical expression,and the general differential quadrature method(GDQM)is applied to obtain the numerical solutions.The results from the current models(CMs)are compared with the data in the literature.It is clearly established that the consistent softening and toughening effects can be obtained for the strain-and stress-driven local/nonlocal integral polar models,respectively.The proposed two-phase local/nonlocal integral polar models(TPNIPMs)may provide an efficient method to design and optimize the plate-like structures for microelectro-mechanical systems.
基金The research was carried out under State Assignment,Project 17.3.1(Reg.No.AAAA-A17-117030310442-8)Project 17.4.2(Reg.No.AAAA-A17-117030310438-1)of the Fundamental Research of Siberian Branch of the Russian Academy of Sciences.
文摘This paper addresses an integral model of development a large electric power system using the example of the Unified Energy System of Russia.The model takes account of the age structure of the plants main equipment.Besides,generating equipment is divided into components depending on the types of energy resources used.The mathematical model is presented by a system of nonclassical Volterra integral equations of the first kind.One of the equations describes the balance between the total available capacity of the electric power system,commissioning of new equipment,and dismantling of obsolete one.The other equations define the shares of different types of power plants in the total composition of the electric power system equipment.Based on the considered model,we set a problem that searches the optimal lifetimes of electric power system capacities for a given demand for electricity.The optimality criterion is a functional reflecting cost of commissioning and operating the capacities.The specifics of the optimization problem are that the optimization parameter is in the lower limit of integration.An algorithm for solving of this optimal control problem numerically is developed.The influence of economic indices on the solution to the optimal control problem is studied.Calculations of the optimal development of the Unified Energy System of Russia until 2050 are carried out using real-life data.
基金Supported by the China National Science and Technology Major Project(41872153)Northeast Petroleum University Research Startup Fund(1305021839)。
文摘To evaluate the lateral sealing mechanism of extensional fault based on the pressure difference between fault and reservoir, an integral mathematical-geological model of diagenetic time on diagenetic pressure considering the influence of diagenetic time on the diagenetic pressure and diagenetic degree of fault rock has been established to quantitatively calculate the lateral sealing ability of extensional fault. By calculating the time integral of the vertical stress and horizontal in-situ stress on the fault rock and surrounding rock, the burial depth of the surrounding rock with the same clay content and diagenesis degree as the target fault rock was worked out. In combination with the statistical correlation of clay content, burial depth and displacement pressure of rock in the study area, the displacement pressure of target fault rock was calculated quantitatively. The calculated displacement pressure was compared with that of the target reservoir to quantitatively evaluate lateral sealing state and ability of the extensional fault. The method presented in this work was used to evaluate the sealing of F_(1), F_(2) and F_(3) faults in No.1 structure of Nanpu Sag, and the results were compared with those from fault-reservoir displacement pressure differential methods without considering the diagenetic time and simple considering the diagenetic time. It is found that the results calculated by the integral mathematical-geological model are the closest to the actual underground situation, the errors between the hydrocarbon column height predicted by this method and the actual column height were 0–8 m only, proving that this model is more feasible and credible.
基金Supported by Liaoning Province Science and Technology Research Project(2021JH1/10400011)National Natural Science Foundation of China(61971118).
文摘Background As information technology has advanced and been popularized,open pit mining has rapidly developed toward integration and digitization.The three-dimensional reconstruction technology has been successfully applied to geological reconstruction and modeling of surface scenes in open pit mines.However,an integrated modeling method for surface and underground mine sites has not been reported.Methods In this study,we propose an integrated modeling method for open pit mines that fuses a real scene on the surface with an underground geological model.Based on oblique photography,a real-scene model was established on the surface.Based on the surface-stitching method proposed,the upper and lower surfaces and sides of the model were constructed in stages to construct a complete underground three-dimensional geological model,and the aboveground and underground models were registered together to build an integrated open pit mine model.Results The oblique photography method used reconstructed a surface model of an open pit mine using a real scene.The surface-stitching algorithm proposed was compared with the ball-pivoting and Poisson algorithms,and the integrity of the reconstructed model was markedly superior to that of the other two reconstruction methods.In addition,the surface-stitching algorithm was applied to the reconstruction of different formation models and showed good stability and reconstruction efficiency.Finally,the aboveground and underground models were accurately fitted after registration to form an integrated model.Conclusions The proposed method can efficiently establish an integrated open pit model.Based on the integrated model,an open pit auxiliary planning system was designed and realized.It supports the functions of mining planning and output calculation,assists users in mining planning and operation management,and improves production efficiency and management levels.
基金supported by the National Natural Science Foundation of China(Grant Nos.12275214,12247103,12047502)the Natural Science Basic Research Program of Shaanxi Province Grant Nos.2021JCW-19 and 2019JQ-107Shaanxi Key Laboratory for Theoretical Physics Frontiers in China.
文摘We investigate the integrability of the Rabi model,which is traditionally viewed as not Yang–Baxter-integrable despite its solvability.Building on efforts by Bogoliubov and Kulish(2013 J.Math.Sci.19214–30),Amico et al(2007 Nucl.Phys.B 787283–300),and Batchelor and Zhou(2015 Phys.Rev.A 91053808),who explored special limiting cases of the model,we develop a spin–boson interaction Hamiltonian under more general boundary conditions,particularly focusing on open boundary conditions with off-diagonal terms.Our approach maintains the direction of the spin in the z direction and also preserves the boson particle number operator a^(†)a,marking a progression beyond previous efforts that have primarily explored reduced forms of the Rabi model from Yang–Baxter algebra.We also address the presence of‘unwanted’quadratic boson terms a^(2) and a^(†2),which share coefficients with the boson particle number operator.Interestingly,these terms vanish when spectral parameter u=±θ_(s),simplifying the model to a limiting case of operator-valued twists,a scenario previously discussed by Batchelor and Zhou(2015 Phys.Rev.A 91053808).
基金supported by the National Natural Science Foundation of China(U2243238)the Program of the National Key Research and Development Plan(2023YFC3209304).
文摘Quantification of river flood risks is a prerequisite for floodplain management and development.The lower Yellow River(LYR)is characterized by a complex channel–floodplain system,which is prone to flooding but inhabits a large population on the floodplains.Many floodplain management modes have been presented,but implementation effects of these management modes have not been evaluated correctly.An integrated model was first proposed to evaluate the flood risks to people’s life and property,covering an improved module of two-dimensional(2D)morphodynamic processes and a module of flood risk evaluation for people,buildings and crops on the floodplains.Two simulation cases were then conducted to validate the model accuracy,including the hyperconcentrated flood event and dike-breach induced flood event occurring in the LYR.Finally,the integrated model was applied to key floodplains in the LYR,and the effects of different floodplain management modes were quantified on the risks to people’s life and property under an extreme flood event.Results indicate that:①Satisfactory accuracy was achieved in the simulation of these two flood events.The maximum sediment concentration was just underestimated by 9%,and the simulated inundation depth agreed well with the field record;②severe inundation was predicted to occur in most domains under the current topography(SchemeⅠ),which would be alleviated after implementing different floodplain management modes,with the area in slight inundation degree accounting for a large proportion under the mode of“construction of protection embankment”(SchemeⅡ)and the area in medium inundation degree occupying a high ratio under the mode of“floodplain partition harnessing”(SchemeⅢ);and③compared with SchemeⅠ,the high-risk area for people’s life and property would reduce by 21%–49%under SchemeⅡ,and by 35%–93%under SchemeⅢ.
基金funded by the National Natural Science Foundation of China(Grant No.42275056).
文摘As a prominent mode of variability in the tropical stratosphere on the interannual timescale,the Quasi-Biennial Oscillation(QBO)can significantly influence global atmospheric circulation and weather patterns.This study explores the dynamic processes of QBO disruptions using the integrated climate model of the China Meteorological Administration(CMA)by nudging the tropical zonal winds toward observations.A comparative analysis with ERA5 reanalysis data shows that the nudged runs accurately replicate the general characteristics of the QBO,including the alternating QBO wind regimes and QBO disruption events.The evolution of the QBO winds is diagnosed using empirical orthogonal function and root-mean-square difference analyses,and the rarity of the disruption events is confirmed in the CMA model.Different aspects of the QBO disruptions and the relevant dynamics are present in the model.Firstly,the momentum budget analysis highlights the crucial roles of extratropical Rossby waves and non-orographic gravity waves in the transition from westerly to easterly winds during a disruption.Secondly,Kelvin waves and non-orographic gravity waves explain much of the transition from easterly to westerly winds near 40 hPa.Thirdly,the positive tendency from enhanced vertical advection further accelerates westerly momentum development via secondary meridional circulation.These findings underscore the importance of nudging techniques in understanding QBO dynamics,which provides valuable insights for future climate model improvements toward better forecasting QBO-related climate variability.Notably,due to model limitations,no QBO disruptions were simulated in the free-run experiments.
文摘Objective:To explore the connotation of the integrated medical-care-rehabilitation nursing model and its application effect in elderly patients with chronic diseases.Methods:A total of 122 elderly patients with chronic diseases admitted to our hospital from January 2023 to June 2023 were selected and randomly divided into an observation group(62 cases)and a control group(60 cases).Both groups received routine nursing during hospitalization.After discharge,the control group received conventional continuous nursing,while the observation group was given the integrated medical-care-rehabilitation nursing model.The psychological status of the elderly patients in the two groups was compared before nursing and 6 months after nursing.Assessments were made on their clinical symptoms of mental health,self-care ability,health behaviors,and mastery of knowledge about elderly chronic diseases.Results:Six months after nursing,the scores of self-rated clinical symptoms of mental health and negative coping in both groups were lower than those before nursing(P<0.05).Meanwhile,the scores of negative coping,self-care ability,and health behaviors in both groups were higher than those before nursing(P<0.05).Conclusion:The integrated medical-care-rehabilitation nursing model can not only improve the nursing quality for elderly patients with chronic diseases but also foster their positive mentality,help them understand knowledge about diet and health care related to chronic diseases,enhance their self-care ability and health awareness,and assist them in achieving better recovery[1].
基金the Project of the Key Open Laboratory of Atmospheric Detection,China Meteorological Administration(2023KLAS02M)the Second Batch of Science and Technology Project of China Meteorological Administration("Jiebangguashuai"):the Research and Development of Short-term and Near-term Warning Products for Severe Convective Weather in Beijing-Tianjin-Hebei Region(CMAJBGS202307).
文摘Firstly,based on the data of air quality and the meteorological data in Baoding City from 2017 to 2021,the correlations of meteorological elements and pollutants with O_(3)concentration were explored to determine the forecast factors of forecast models.Secondly,the O_(3)-8h concentration in Baoding City in 2021 was predicted based on the constructed models of multiple linear regression(MLR),backward propagation neural network(BPNN),and auto regressive integrated moving average(ARIMA),and the predicted values were compared with the observed values to test their prediction effects.The results show that overall,the MLR,BPNN and ARIMA models were able to forecast the changing trend of O_(3)-8h concentration in Baoding in 2021,but the BPNN model gave better forecast results than the ARIMA and MLR models,especially for the prediction of the high values of O_(3)-8h concentration,and the correlation coefficients between the predicted values and the observed values were all higher than 0.9 during June-September.The mean error(ME),mean absolute error(MAE),and root mean square error(RMSE)of the predicted values and the observed values of daily O_(3)-8h concentration based on the BPNN model were 0.45,19.11 and 24.41μg/m 3,respectively,which were significantly better than those of the MLR and ARIMA models.The prediction effects of the MLR,BPNN and ARIMA models were the best at the pollution level,followed by the excellent level,and it was the worst at the good level.In comparison,the prediction effect of BPNN model was better than that of the MLR and ARIMA models as a whole,especially for the pollution and excellent levels.The TS scores of the BPNN model were all above 66%,and the PC values were above 86%.The BPNN model can forecast the changing trend of O_(3)concentration more accurately,and has a good practical application value,but at the same time,the predicted high values of O_(3)concentration should be appropriately increased according to error characteristics of the model.
文摘Transpiration element is included in the integrated stomatal conductance photosynthesis model by considering gaseous transfer processes, so the present model is capable to simulate the influence of boundary layer conductance. Leuning in his revised Ball's model replaced relative humidity with VPD s (the vapor pressure deficit from stomatal pore to leaf surface) and thereby made the relation with transpiration more straightforward, and made it possible for the regulation of transpiration and the influence of boundary layer conductance to be integrated into the combined model. If the differences in water vapor and CO 2 concentration between leaf and ambient air are considered, VPD s , the evaporative demand, is influenced by stomatal and boundary layer conductance. The physiological responses of photosynthesis, transpiration, and stomatal function, and the changes of intercellular CO 2 and water use efficiency to environmental factors, such as wind speed, photon flux density, leaf temperature and ambient CO 2, are analyzed. It is shown that if the boundary layer conductance drops to a level comparable with stomatal conductance, the results of simulation by the model presented here differ significantly from those by the previous model, and, in some cases, are more realistic than the latter.
基金provided by the National Natural Science Foundation of China Youth Found of China (No.41102169)the doctoral foundation of Henan Polytechnic University of China (No. B2014-056)
文摘The dynamic ground subsidence due to underground mining is a complicated time-dependent and rate- dependent process. Based. on the theory of rock rheology and probability integral method, this study developed the superposltlOn model for the prediction and analysis of the ground dynamic subsidence in mining area of thick !oose layer. The model consists of two parts （the prediction of overlying bedrock and the prediction of thick loose layer）. The overlying bedrock is regarded as visco-elastic beam, of which the dynamic subsidence is predicted by the Kelvin visco-elastic rheological model. The thick loose layer is regarded as random medium, and the ground dynamic subsidence, is predicted by the probability integral model. At last, the two prediction models are vertically stacked in the same coordinate system, and the bedrock dynamic subsidence is regarded as a variable mining thickness input into the prediction model of ground dynamic subsidence. The prediction results obtained were compared w^th actual movement and deformation data from Zhao I and Zhao II mine, central China. The agreement of the prediction results with the. field measurements.show that the superposition model （SM） is more satisfactory and the formulae obtained are more effective than the classical single probability Integral model（SPIM）, and thus can be effectively used for predicting the ground dynamic subsidence in mining area of thick loose layer.
基金The National Natural Science Foundation of China(No.61604038)China Postdoctoral Science Foundation(No.2015M580376)+1 种基金the Natural Science Foundation of Jiangsu Province(No.BK20160691)Jiangsu Postdoctoral Science Foundation(No.1501010A)
文摘A novel simulation program with an integrated circuit emphasis（SPICE） model developed for trench-gate metal-oxide-semiconductor field-effect transistor（M OSFET）devices is proposed. The drift region resistance was modeled according to the physical characteristics and the specific structure of the trench-gate MOSFET device. For the accurate simulation of dynamic characteristics, three important capacitances, gate-to-drain capacitance Cgd, gate-to-source capacitance Cgsand drain-to-source capacitance Cds, were modeled, respectively, in the proposed model. Furthermore,the self-heating effect, temperature effect and breakdown characteristic were taken into account; the self-heating model and breakdown model were built in the proposed model; and the temperature parameters of the model were revised. The proposed model is verified by experimental results, and the errors between measured data and simulation results of the novel model are less than 5%. Therefore, the model can give an accurate description for both the static and dynamic characteristics of the trench-gate MOSFET device.
