Investigating the combined effects of mining damage and creep damage on slope stability is crucial,as it can comprehensively reveal the non-linear deformation characteristics of rock under their joint influence.This s...Investigating the combined effects of mining damage and creep damage on slope stability is crucial,as it can comprehensively reveal the non-linear deformation characteristics of rock under their joint influence.This study develops a fractional-order nonlinear creep constitutive model that incorporates the double damage effect and implements a non-linear creep subroutine for soft rock using the threedimensional finite difference method on the FLAC3D platform.Comparative analysis of the theoretical,numerical,and experimental results reveals that the fractional-order constitutive model,which incorporates the double damage effect,accurately reflects the distinct deformation stages of green mudstone during creep failure and effectively captures the non-linear deformation in the accelerated creep phase.The numerical results show a fitting accuracy exceeding 97%with the creep test curves,significantly outperforming the 61%accuracy of traditional creep models.展开更多
In this paper, the fractional-order mathematical model and the fractional-order state-space averaging model of the Buck-Boost converter in continuous conduction mode （CCM） are established based on the fractional cal...In this paper, the fractional-order mathematical model and the fractional-order state-space averaging model of the Buck-Boost converter in continuous conduction mode （CCM） are established based on the fractional calculus and the Adomian decomposition method. Some dynamical properties of the current-mode controlled fractional-order Buck- Boost converter are analysed. The simulation is accomplished by using SIMULINK. Numerical simulations are presented to verify the analytical results and we find that bifurcation points will be moved backward as α and β vary. At the same time, the simulation results show that the converter goes through different routes to chaos.展开更多
This paper proposes a novel unified visco-plastic constitutive model for uniaxial ratcheting behaviors. The cyclic deformation of the material presents remarkable time-dependence and history memory phenomena. The frac...This paper proposes a novel unified visco-plastic constitutive model for uniaxial ratcheting behaviors. The cyclic deformation of the material presents remarkable time-dependence and history memory phenomena. The fractional(fractional-order)derivative is an efficient tool for modeling these phenomena. Therefore, we develop a cyclic fractional-order unified visco-plastic(FVP) constitutive model. Specifically, within the framework of the cyclic elasto-plastic theory, the fractional derivative is used to describe the accumulated plastic strain rate and nonlinear kinematic hardening rule based on the Ohno-Abdel-Karim model. Moreover, a new radial return method for the back stress is developed to describe the unclosed hysteresis loops of the stress-strain properly.The capacity of the FVP model used to predict the cyclic deformation of the SS304 stainless steel is verified through a comparison with the corresponding experimental data found in the literature(KANG, G. Z., KAN, Q. H., ZHANG, J., and SUN, Y. F. Timedependent ratcheting experiments of SS304 stainless steel. International Journal of Plasticity, 22(5), 858–894(2006)). The FVP model is shown to be successful in predicting the rate-dependent ratcheting behaviors of the SS304 stainless steel.展开更多
The major advantage of grey system theory is that both incomplete information and unclear problems can be processed precisely. Considering that the modeling of grey model(GM) depends on the preprocessing of the origin...The major advantage of grey system theory is that both incomplete information and unclear problems can be processed precisely. Considering that the modeling of grey model(GM) depends on the preprocessing of the original data,the fractional-order accumulation calculus could be used to do preprocessing. In this paper, the residual sequence represented by Fourier series is used to ameliorate performance of the fractionalorder accumulation GM(1,1) and improve the accuracy of predictor. The state space model of optimally modified GM(1,1)predictor is given and genetic algorithm(GA) is used to find the smallest relative error during the modeling step. Furthermore,the fractional form of continuous GM(1,1) is given to enlarge the content of prediction model. The simulation results illustrated that the fractional-order calculus could be used to depict the GM precisely with more degrees of freedom. Meanwhile, the ranges of the parameters and model application could be enlarged with better performance. The method of modified GM predictor using optimal fractional-order accumulation calculus is expected to be widely used in data processing, model theory, prediction control and related fields.展开更多
A fractional-order Maxwell model is used to describe the viscoelastic seabed mud. The experimental data of the real mud well fit the results of the fractional-order Maxwell model that has fewer parameters than the tra...A fractional-order Maxwell model is used to describe the viscoelastic seabed mud. The experimental data of the real mud well fit the results of the fractional-order Maxwell model that has fewer parameters than the traditional model. The model is then used to investigate the effect of the mud on the surface-wave damping. The damping rate of a linear monochromatic wave is obtained. The elastic resonance of the mud layer is observed, which leads to the peaks in the damping rate. The damping rate is a sum of the modal damping rates, which indicates the wave damping induced by the mud motion of particular modes. The analysis shows that near the resonance, the total damping rate is dominated by the damping rate of the corresponding mode.展开更多
The purpose of this paper is to present a numerical approach based on the artificial neural networks(ANNs)for solving a novel fractional chaotic financial model that represents the effect of memory and chaos in the pr...The purpose of this paper is to present a numerical approach based on the artificial neural networks(ANNs)for solving a novel fractional chaotic financial model that represents the effect of memory and chaos in the presented system.The method is constructed with the combination of the ANNs along with the Levenberg-Marquardt backpropagation(LMB),named the ANNs-LMB.This technique is tested for solving the novel problem for three cases of the fractional-order values and the obtained results are compared with the reference solution.Fifteen numbers neurons have been used to solve the fractional-order chaotic financial model.The selection of the data to solve the fractional-order chaotic financial model are selected as 75%for training,10%for testing,and 15%for certification.The results indicate that the presented approximate solutions fit exactly with the reference solution and the method is effective and precise.The obtained results are testified to reduce the mean square error(MSE)for solving the fractional model and verified through the various measures including correlation,MSE,regression histogram of the errors,and state transition(ST).展开更多
In this paper,we formulate and analyze a new fractional-order Logistic model with feedback control,which is different from a recognized mathematical model proposed in our very recent work.Asymptotic stability of the p...In this paper,we formulate and analyze a new fractional-order Logistic model with feedback control,which is different from a recognized mathematical model proposed in our very recent work.Asymptotic stability of the proposed model and its numerical solutions are studied rigorously.By using the Lyapunov direct method for fractional dynamical systems and a suitable Lyapunov function,we show that a unique positive equilibrium point of the new model is asymptotically stable.As an important consequence of this,we obtain a new mathematical model in which the feedback control variables only change the position of the unique positive equilibrium point of the original model but retain its asymptotic stability.Furthermore,we construct unconditionally positive nonstandard finite difference(NSFD)schemes for the proposed model using the Mickens’methodology.It is worth noting that the constructed NSFD schemes not only preserve the positivity but also provide reliable numerical solutions that correctly reflect the dynamics of the new fractional-order model.Finally,we report some numerical examples to support and illustrate the theoretical results.The results indicate that there is a good agreement between the theoretical results and numerical ones.展开更多
The outbreak of COVID-19 in 2019 resulted in numerous infections and deaths. In order to better study the transmission of COVID-19, this article adopts an improved fractional-order SIR model. Firstly, the properties o...The outbreak of COVID-19 in 2019 resulted in numerous infections and deaths. In order to better study the transmission of COVID-19, this article adopts an improved fractional-order SIR model. Firstly, the properties of the model are studied, including the feasible domain and bounded solutions of the system. Secondly, the stability of the system is discussed, among other things. Then, the GMMP method is introduced to obtain numerical solutions for the COVID-19 system and combined with the improved MH-NMSS-PSO parameter estimation method to fit the real data of Delhi, India from April 1, 2020 to June 30, 2020. The results show that the fitting effect is quite ideal. Finally, long-term predictions were made on the number of infections. We accurately estimate that the peak number of infections in Delhi, India, can reach around 2.1 million. This paper also compares the fitting performance of the integer-order COVID-19 model and the fractional-order COVID-19 model using the real data from Delhi. The results indicate that the fractional-order model with different orders, as we proposed, performs the best.展开更多
A molten salt reactor(MSR) is one of the six advanced reactor concepts selected by the generation Ⅳ international forum because of its advantages of inherent safety, and the promising capabilities of Th-U breeding an...A molten salt reactor(MSR) is one of the six advanced reactor concepts selected by the generation Ⅳ international forum because of its advantages of inherent safety, and the promising capabilities of Th-U breeding and transuranics transmutation. A dynamics model for the channel-type MSR is developed in this work based on a three-dimensional thermal–hydraulic model(3DTH) and a point reactor model. The 3DTH couples a three-dimensional heat conduction model and a one-dimensional single-phase flow model that can accurately consider the heat conduction between different assemblies. The 3DTH is validated by the RELAP5 code in terms of the temperature and mass flow distribution calculation. A point reactor model considering the drift of delayed neutron precursors is adopted in the dynamics model. To verify the dynamics model, three experiments from the molten salt reactor experiment are simulated. The agreement of the experimental data and simulation results was excellent.With the aid of this model, the unprotected step reactivity addition and unprotected loss of flow of the 2 MWt experimental MSR are modeled, and the reactor power and temperature evolution are analyzed.展开更多
The crystal structure evolution of the Cu-rich nano precipitates from bcc to 9R during thermal aging was studied in nuclear reactor pressure vessel （RPV） model steels. The specimens, contained higher copper and nick...The crystal structure evolution of the Cu-rich nano precipitates from bcc to 9R during thermal aging was studied in nuclear reactor pressure vessel （RPV） model steels. The specimens, contained higher copper and nickel contents than commercially available one, were heated at 890 ~C for 0.5 h and then water quenched followed by tempering at 0（50 ~C for I0 h and aging at 400 ~C for 1000 h. It was observed that bcc and 9R orthogonal structure, as well as 9R orthogonal and 9R monoclinic structure, coexist in a single Cu-rich nano precipitate. Further analyses pointed out that Cu-rich nano precipitates of bcc structure were not stable, it may preferentially transform to 9R orthogonal structure and then to 9R monoclinic structure. This results showed that the crystal structure evolution of the Cu-rich nano precipitates was complex.展开更多
treatability of synthetic sago wastewater was investigated in a laboratory anaerobic tapered fluidized bed reactor （ATFBR） with a mesoporous granular activated carbon （GAC） as a support material. The experimental ...treatability of synthetic sago wastewater was investigated in a laboratory anaerobic tapered fluidized bed reactor （ATFBR） with a mesoporous granular activated carbon （GAC） as a support material. The experimental protocol was defined to examine the effect of the maximum organic loading rate （OLR）, hydraulic retention time （HRT）, the efficiency of the reactor and to report on its steady- state performance. The reactor was subjected to a steady-state operation over a range of OLR up to 85.44 kg COD/（m^3·d）. The COD removal efficiency was found to be 92% in the reactor while the biogas produced in the digester reached 25.38 m^3/（m^3·d） of the reactor. With the increase of OLR from 83.7 kg COD/（m^3·d）, the COD removal efficiency decreased. Also an artificial neural network （ANN） model using multilayer perceptron （MLP） has been developed for a system of two input variable and five output dependent variables. For the training of the input-output data, the experimental values obtained have been used. The output parameters predicted have been found to be much closer to the corresponding experimental ones and the model was validated for 30% of the untrained data. The mean square error （MSE） was found to be only 0.0146.展开更多
This work aims at comparing surface tension models in VOF(Volume of Fluid) modeling and investigating the effects of gas distributor and gas velocity. Hydrodynamics of a continuous chain of bubbles inside a bubble col...This work aims at comparing surface tension models in VOF(Volume of Fluid) modeling and investigating the effects of gas distributor and gas velocity. Hydrodynamics of a continuous chain of bubbles inside a bubble column reactor was simulated. The grid independence study was first conducted and a grid size of 1.0 mm was adopted in order to minimize the computing time without compromising the accuracy of the results. The predictions were validated by comparing the experimental studies reported in the literature. It was found that all surface tension models can describe the bubble rise and bubble plume in a column with slight deviations.展开更多
Gas-solid two-phase turbulent flows,mass transfer,heat transfer and catalytic cracking reactions areknown to exert interrelated influences in commercial fluid catalytic cracking(FCC)riser reactors.In the presentpaper,...Gas-solid two-phase turbulent flows,mass transfer,heat transfer and catalytic cracking reactions areknown to exert interrelated influences in commercial fluid catalytic cracking(FCC)riser reactors.In the presentpaper,a three-dimensional turbulent gas-solid two-phase flow-reaction model for FCC riser reactors was devel-oped.The model took into account the gas-solid two-phase turbulent flows,inter-phase heat transfer,masstransfer,catalytic cracking reactions and their interrelated influence.The k-V-k_P two-phase turbulence modelwas employed and modified for the two-phase turbulent flow patterns with relatively high particle concentration.Boundary conditions for the flow-reaction model were given.Related numerical algorithm was formed and a nu-merical code was drawn up.Numerical modeling for commercial FCC riser reactors could be carried out with thepresented model.展开更多
The simulation was made based on the model of pipe-shell reactor that was established by the model of global kinetics of synthesis of dimethyl ether from syngas over a bifunctional catalyst. The results of simulation ...The simulation was made based on the model of pipe-shell reactor that was established by the model of global kinetics of synthesis of dimethyl ether from syngas over a bifunctional catalyst. The results of simulation showed that the selectivity for dimethyl ether （DME） and the conversion of CO were higher but the hot spot was kept below the temperature limit of the pipe-shell reactor. The suitable diameter of the pipe was φ38×2 mm, and the length of the pipe was 5.8 m. The optimal process conditions of the reactor were that the pressure was 5 MPa, the temperature of the cooling water was 240 ℃, and the temperature of the raw gas at inlet of the reactor was 220 ℃. The production of this reactor was 102800 t/y （ton per year） under these conditions.展开更多
On the basis of the analysis of the process of treating low concentrations of sulfur dioxide （SO2） gas in a fixed bed reactor, a kinetic model is proposed for this process after taking into consideration the effects...On the basis of the analysis of the process of treating low concentrations of sulfur dioxide （SO2） gas in a fixed bed reactor, a kinetic model is proposed for this process after taking into consideration the effects of internal diffusion, cell concentration, and production yield of microorganisms but ignoring the effect of external diffusion. The results obtained from the model simulation show that this model can indicate the influence of the process factors, Cin, η μmax, Cx, A, h, Kin, and Q, on the removal of SO2 and that the prediction of the results by this model is also satisfactory. This kinetic model can also provide some very important indications regarding the preparation of immobilized microorganisms, selection and domestication of proper species of microorganisms, as well as the design of bioreactors.展开更多
Flow characteristics, such as flow pattern, gas holdup, and bubble size distribution, in an internal loop reactor with external liquid circulation, are simulated to investigate the influence of reactor internals by us...Flow characteristics, such as flow pattern, gas holdup, and bubble size distribution, in an internal loop reactor with external liquid circulation, are simulated to investigate the influence of reactor internals by using the computational fluid dynamics （CFD）-population balance equations （PBE） coupled model. Numerical results reveal that introducing a downcomer tube and a draft tube can help to improve the mass and heat transfer of the reactor through enhanced liquid circulation, increased gas holdup and reduced bubble diameter. The hydrodynamic behavior in the internal loop reactor with external liquid circulation can be managed effectively by adjusting the diameter and axial position of the draft tube.展开更多
New modified combination mathematical models including the pores blocking models and the cake layer models were developed to describe the continuous cross-flow microfiltration in an airlift external loop slurry reacto...New modified combination mathematical models including the pores blocking models and the cake layer models were developed to describe the continuous cross-flow microfiltration in an airlift external loop slurry reactor. The pores blocking models were created based on the standard blocking law and the intermediate blocking law, and then the cake layer models were developed based on the hydrodynamic theory in which the calculation method of porosity of cake layer was newly corrected. The Air-Water-FCC equilibrium catalysts cold model experiment was used to verify the relevant models.Results showed that the calculated values fitted well with experimental data with a relative error of less than 10%.展开更多
A dynamic mass transfer model of isobutane/butene alkylation over solid acid catalysts in a fixed bed reactor was established. In the model, a modified equation for the relationship between point activity and effectiv...A dynamic mass transfer model of isobutane/butene alkylation over solid acid catalysts in a fixed bed reactor was established. In the model, a modified equation for the relationship between point activity and effective diffusion coefficient was proposed. It is found that the simulation results fit the experimental data well and the breakthrough time of the bed layer is predicted accurately. By modeling the alkylation process, the time-space distribution of butene and point activity profiles of catalysts can be obtained. Furthermore, the reasons for the deactivation of solid acid catalysts were investigated. It indicates that the main reason for the deactivation of catalysts is the site coverage near the inlet of the reactor, while it is ascribed to the steric effect in the region far away from the inlet.展开更多
A novel control strategy for a continuous stirred tank reactor(CSTR)system,which has the typical characteristic of strongly pronounced nonlinearity,multiple operating points,and a wide operating range,is initiated fro...A novel control strategy for a continuous stirred tank reactor(CSTR)system,which has the typical characteristic of strongly pronounced nonlinearity,multiple operating points,and a wide operating range,is initiated from the point of hybrid systems.The proposed scheme makes full use of the modeling power of mixed logical dy- namical(MLD)systems to describe the highly nonlinear dynamics and multiple operating points in a unified framework as a hybrid system,and takes advantage of the good control quality of model predictive control(MPC) to design a controller.Thus,this approach avoids oscillation during switching between sub-systems,helps to relieve shaking in transition,and augments the stability robustness of the whole system,and finally achieves optimal(i.e. fast and smooth)transition between operating points.The simulation results demonstrate that the presented ap- proach has a satisfactory performance.展开更多
Two identical full-scale biogas-lift reactors treating brewery wastewater were inoculated with different types of sludge to compare their operational conditions, sludge characteristics, and kinetic models at a mesophi...Two identical full-scale biogas-lift reactors treating brewery wastewater were inoculated with different types of sludge to compare their operational conditions, sludge characteristics, and kinetic models at a mesophilic temperature. One reactor （R1） started up with anaerobic granular sludge in 12 weeks and obtained a continuously average organic loading rate （OLR） of 7.4 kg chemical oxygen demand （COD）/（m3.day）, COD removal efficiency of 80%, and effluent COD of 450 mg/L. The other reactor （R2） started up with residual activated sludge in 30 weeks and granulation accomplished when the reactor reached an average OLR of 8.3 kg COD/（m^3·day）, COD removal efficiency of 90%, and effluent COD of 240 mg/L. Differences in sludge characteristics,biogas compositions, and biogas- lift processes may be accounted for the superior efficiency of the treatment performance of R2 over R1. Grau second-order and modified StoverKincannon models based on influent and effluent concentrations as well as hydraulic retention time were successfully used to develop kinetic parameters of the experimental data with high correlation coefficients （R2 〉 0.95）, which further showed that R2 had higher treatment performance than R1. These results demonstrated that residual activated sludge could be used effectively instead of anaerobic granular sludge despite the need for a longer time.展开更多
基金support from the National Natural Science Foundation of China(No.52308316)the Scientific Research Foundation of Weifang University(Grant No.2024BS42)+2 种基金China Postdoctoral Science Foundation(No.2022M721885)the Key Laboratory of Rock Mechanics and Geohazards of Zhejiang Province(No.ZJRMG-2022-01)supported by Open Research Fund of State Key Laboratory of Geomechanics and Geotechnical Engineering,Institute of Rock and Soil Mechanics,Chinese Academy of Sciences(NO.SKLGME023017).
文摘Investigating the combined effects of mining damage and creep damage on slope stability is crucial,as it can comprehensively reveal the non-linear deformation characteristics of rock under their joint influence.This study develops a fractional-order nonlinear creep constitutive model that incorporates the double damage effect and implements a non-linear creep subroutine for soft rock using the threedimensional finite difference method on the FLAC3D platform.Comparative analysis of the theoretical,numerical,and experimental results reveals that the fractional-order constitutive model,which incorporates the double damage effect,accurately reflects the distinct deformation stages of green mudstone during creep failure and effectively captures the non-linear deformation in the accelerated creep phase.The numerical results show a fitting accuracy exceeding 97%with the creep test curves,significantly outperforming the 61%accuracy of traditional creep models.
基金Project supported by the National Natural Science Foundation of China (Grant No. 51177117)the Specialized Research Fund for the Doctoral Program of Higher Education,China (Grant No. 20100201110023)
文摘In this paper, the fractional-order mathematical model and the fractional-order state-space averaging model of the Buck-Boost converter in continuous conduction mode （CCM） are established based on the fractional calculus and the Adomian decomposition method. Some dynamical properties of the current-mode controlled fractional-order Buck- Boost converter are analysed. The simulation is accomplished by using SIMULINK. Numerical simulations are presented to verify the analytical results and we find that bifurcation points will be moved backward as α and β vary. At the same time, the simulation results show that the converter goes through different routes to chaos.
基金Project supported by the National Natural Science Foundation of China(Nos.11790282,U1534204,and 11472179)the Natural Science Foundation of Hebei Province of China(No.A2016210099)
文摘This paper proposes a novel unified visco-plastic constitutive model for uniaxial ratcheting behaviors. The cyclic deformation of the material presents remarkable time-dependence and history memory phenomena. The fractional(fractional-order)derivative is an efficient tool for modeling these phenomena. Therefore, we develop a cyclic fractional-order unified visco-plastic(FVP) constitutive model. Specifically, within the framework of the cyclic elasto-plastic theory, the fractional derivative is used to describe the accumulated plastic strain rate and nonlinear kinematic hardening rule based on the Ohno-Abdel-Karim model. Moreover, a new radial return method for the back stress is developed to describe the unclosed hysteresis loops of the stress-strain properly.The capacity of the FVP model used to predict the cyclic deformation of the SS304 stainless steel is verified through a comparison with the corresponding experimental data found in the literature(KANG, G. Z., KAN, Q. H., ZHANG, J., and SUN, Y. F. Timedependent ratcheting experiments of SS304 stainless steel. International Journal of Plasticity, 22(5), 858–894(2006)). The FVP model is shown to be successful in predicting the rate-dependent ratcheting behaviors of the SS304 stainless steel.
基金supported by the National Natural Science Foundation of China(61174145)
文摘The major advantage of grey system theory is that both incomplete information and unclear problems can be processed precisely. Considering that the modeling of grey model(GM) depends on the preprocessing of the original data,the fractional-order accumulation calculus could be used to do preprocessing. In this paper, the residual sequence represented by Fourier series is used to ameliorate performance of the fractionalorder accumulation GM(1,1) and improve the accuracy of predictor. The state space model of optimally modified GM(1,1)predictor is given and genetic algorithm(GA) is used to find the smallest relative error during the modeling step. Furthermore,the fractional form of continuous GM(1,1) is given to enlarge the content of prediction model. The simulation results illustrated that the fractional-order calculus could be used to depict the GM precisely with more degrees of freedom. Meanwhile, the ranges of the parameters and model application could be enlarged with better performance. The method of modified GM predictor using optimal fractional-order accumulation calculus is expected to be widely used in data processing, model theory, prediction control and related fields.
基金Project supported by the National Natural Science Foundation of China(No.10972117)
文摘A fractional-order Maxwell model is used to describe the viscoelastic seabed mud. The experimental data of the real mud well fit the results of the fractional-order Maxwell model that has fewer parameters than the traditional model. The model is then used to investigate the effect of the mud on the surface-wave damping. The damping rate of a linear monochromatic wave is obtained. The elastic resonance of the mud layer is observed, which leads to the peaks in the damping rate. The damping rate is a sum of the modal damping rates, which indicates the wave damping induced by the mud motion of particular modes. The analysis shows that near the resonance, the total damping rate is dominated by the damping rate of the corresponding mode.
基金This research received funding support from the NSRF via the Program Management Unit for Human Resources&Institutional Development,Research and Innovation(Grant Number B05F640088).
文摘The purpose of this paper is to present a numerical approach based on the artificial neural networks(ANNs)for solving a novel fractional chaotic financial model that represents the effect of memory and chaos in the presented system.The method is constructed with the combination of the ANNs along with the Levenberg-Marquardt backpropagation(LMB),named the ANNs-LMB.This technique is tested for solving the novel problem for three cases of the fractional-order values and the obtained results are compared with the reference solution.Fifteen numbers neurons have been used to solve the fractional-order chaotic financial model.The selection of the data to solve the fractional-order chaotic financial model are selected as 75%for training,10%for testing,and 15%for certification.The results indicate that the presented approximate solutions fit exactly with the reference solution and the method is effective and precise.The obtained results are testified to reduce the mean square error(MSE)for solving the fractional model and verified through the various measures including correlation,MSE,regression histogram of the errors,and state transition(ST).
文摘In this paper,we formulate and analyze a new fractional-order Logistic model with feedback control,which is different from a recognized mathematical model proposed in our very recent work.Asymptotic stability of the proposed model and its numerical solutions are studied rigorously.By using the Lyapunov direct method for fractional dynamical systems and a suitable Lyapunov function,we show that a unique positive equilibrium point of the new model is asymptotically stable.As an important consequence of this,we obtain a new mathematical model in which the feedback control variables only change the position of the unique positive equilibrium point of the original model but retain its asymptotic stability.Furthermore,we construct unconditionally positive nonstandard finite difference(NSFD)schemes for the proposed model using the Mickens’methodology.It is worth noting that the constructed NSFD schemes not only preserve the positivity but also provide reliable numerical solutions that correctly reflect the dynamics of the new fractional-order model.Finally,we report some numerical examples to support and illustrate the theoretical results.The results indicate that there is a good agreement between the theoretical results and numerical ones.
文摘The outbreak of COVID-19 in 2019 resulted in numerous infections and deaths. In order to better study the transmission of COVID-19, this article adopts an improved fractional-order SIR model. Firstly, the properties of the model are studied, including the feasible domain and bounded solutions of the system. Secondly, the stability of the system is discussed, among other things. Then, the GMMP method is introduced to obtain numerical solutions for the COVID-19 system and combined with the improved MH-NMSS-PSO parameter estimation method to fit the real data of Delhi, India from April 1, 2020 to June 30, 2020. The results show that the fitting effect is quite ideal. Finally, long-term predictions were made on the number of infections. We accurately estimate that the peak number of infections in Delhi, India, can reach around 2.1 million. This paper also compares the fitting performance of the integer-order COVID-19 model and the fractional-order COVID-19 model using the real data from Delhi. The results indicate that the fractional-order model with different orders, as we proposed, performs the best.
基金supported by the Chinese TMSR Strategic Pioneer Science and Technology Project(No.XDA02010000)the Frontier Science Key Program of the Chinese Academy of Sciences(No.QYZDY-SSW-JSC016)the National Natural Science Foundation of China Key Program(No.91326201)
文摘A molten salt reactor(MSR) is one of the six advanced reactor concepts selected by the generation Ⅳ international forum because of its advantages of inherent safety, and the promising capabilities of Th-U breeding and transuranics transmutation. A dynamics model for the channel-type MSR is developed in this work based on a three-dimensional thermal–hydraulic model(3DTH) and a point reactor model. The 3DTH couples a three-dimensional heat conduction model and a one-dimensional single-phase flow model that can accurately consider the heat conduction between different assemblies. The 3DTH is validated by the RELAP5 code in terms of the temperature and mass flow distribution calculation. A point reactor model considering the drift of delayed neutron precursors is adopted in the dynamics model. To verify the dynamics model, three experiments from the molten salt reactor experiment are simulated. The agreement of the experimental data and simulation results was excellent.With the aid of this model, the unprotected step reactivity addition and unprotected loss of flow of the 2 MWt experimental MSR are modeled, and the reactor power and temperature evolution are analyzed.
基金financially supported by the National Basic Research Program of China(No.2011CB610503)National Natural Science Foundation of China(No.50931003)Ministry of Major Subject of Shanghai(No.S30107)
文摘The crystal structure evolution of the Cu-rich nano precipitates from bcc to 9R during thermal aging was studied in nuclear reactor pressure vessel （RPV） model steels. The specimens, contained higher copper and nickel contents than commercially available one, were heated at 890 ~C for 0.5 h and then water quenched followed by tempering at 0（50 ~C for I0 h and aging at 400 ~C for 1000 h. It was observed that bcc and 9R orthogonal structure, as well as 9R orthogonal and 9R monoclinic structure, coexist in a single Cu-rich nano precipitate. Further analyses pointed out that Cu-rich nano precipitates of bcc structure were not stable, it may preferentially transform to 9R orthogonal structure and then to 9R monoclinic structure. This results showed that the crystal structure evolution of the Cu-rich nano precipitates was complex.
文摘treatability of synthetic sago wastewater was investigated in a laboratory anaerobic tapered fluidized bed reactor （ATFBR） with a mesoporous granular activated carbon （GAC） as a support material. The experimental protocol was defined to examine the effect of the maximum organic loading rate （OLR）, hydraulic retention time （HRT）, the efficiency of the reactor and to report on its steady- state performance. The reactor was subjected to a steady-state operation over a range of OLR up to 85.44 kg COD/（m^3·d）. The COD removal efficiency was found to be 92% in the reactor while the biogas produced in the digester reached 25.38 m^3/（m^3·d） of the reactor. With the increase of OLR from 83.7 kg COD/（m^3·d）, the COD removal efficiency decreased. Also an artificial neural network （ANN） model using multilayer perceptron （MLP） has been developed for a system of two input variable and five output dependent variables. For the training of the input-output data, the experimental values obtained have been used. The output parameters predicted have been found to be much closer to the corresponding experimental ones and the model was validated for 30% of the untrained data. The mean square error （MSE） was found to be only 0.0146.
基金Supported by the National Ministry of Science and Technology of China(2017YFB0602401)the National Natural Science Foundation of China(21776173,91834303,U1862201,21625603)the Program of Shanghai Subject Chief Scientists(18XD1402000).
文摘This work aims at comparing surface tension models in VOF(Volume of Fluid) modeling and investigating the effects of gas distributor and gas velocity. Hydrodynamics of a continuous chain of bubbles inside a bubble column reactor was simulated. The grid independence study was first conducted and a grid size of 1.0 mm was adopted in order to minimize the computing time without compromising the accuracy of the results. The predictions were validated by comparing the experimental studies reported in the literature. It was found that all surface tension models can describe the bubble rise and bubble plume in a column with slight deviations.
文摘Gas-solid two-phase turbulent flows,mass transfer,heat transfer and catalytic cracking reactions areknown to exert interrelated influences in commercial fluid catalytic cracking(FCC)riser reactors.In the presentpaper,a three-dimensional turbulent gas-solid two-phase flow-reaction model for FCC riser reactors was devel-oped.The model took into account the gas-solid two-phase turbulent flows,inter-phase heat transfer,masstransfer,catalytic cracking reactions and their interrelated influence.The k-V-k_P two-phase turbulence modelwas employed and modified for the two-phase turbulent flow patterns with relatively high particle concentration.Boundary conditions for the flow-reaction model were given.Related numerical algorithm was formed and a nu-merical code was drawn up.Numerical modeling for commercial FCC riser reactors could be carried out with thepresented model.
基金Development Project of Shanghai Priority Academic Discipline and Development of Research Projects of China Petroleum and Natural Gas Corporation (No.03js-079)
文摘The simulation was made based on the model of pipe-shell reactor that was established by the model of global kinetics of synthesis of dimethyl ether from syngas over a bifunctional catalyst. The results of simulation showed that the selectivity for dimethyl ether （DME） and the conversion of CO were higher but the hot spot was kept below the temperature limit of the pipe-shell reactor. The suitable diameter of the pipe was φ38×2 mm, and the length of the pipe was 5.8 m. The optimal process conditions of the reactor were that the pressure was 5 MPa, the temperature of the cooling water was 240 ℃, and the temperature of the raw gas at inlet of the reactor was 220 ℃. The production of this reactor was 102800 t/y （ton per year） under these conditions.
基金This project was supported by the National Natural Science Foundation of China (2003E0027M)
文摘On the basis of the analysis of the process of treating low concentrations of sulfur dioxide （SO2） gas in a fixed bed reactor, a kinetic model is proposed for this process after taking into consideration the effects of internal diffusion, cell concentration, and production yield of microorganisms but ignoring the effect of external diffusion. The results obtained from the model simulation show that this model can indicate the influence of the process factors, Cin, η μmax, Cx, A, h, Kin, and Q, on the removal of SO2 and that the prediction of the results by this model is also satisfactory. This kinetic model can also provide some very important indications regarding the preparation of immobilized microorganisms, selection and domestication of proper species of microorganisms, as well as the design of bioreactors.
基金Financial support from the Central Universities (12QN02)National Natural Science Foundation of China (51025624and 51076043)111 Project (B12034)
文摘Flow characteristics, such as flow pattern, gas holdup, and bubble size distribution, in an internal loop reactor with external liquid circulation, are simulated to investigate the influence of reactor internals by using the computational fluid dynamics （CFD）-population balance equations （PBE） coupled model. Numerical results reveal that introducing a downcomer tube and a draft tube can help to improve the mass and heat transfer of the reactor through enhanced liquid circulation, increased gas holdup and reduced bubble diameter. The hydrodynamic behavior in the internal loop reactor with external liquid circulation can be managed effectively by adjusting the diameter and axial position of the draft tube.
基金financially supported by the National Key Research & Development Program of China (2016YFB0301600)
文摘New modified combination mathematical models including the pores blocking models and the cake layer models were developed to describe the continuous cross-flow microfiltration in an airlift external loop slurry reactor. The pores blocking models were created based on the standard blocking law and the intermediate blocking law, and then the cake layer models were developed based on the hydrodynamic theory in which the calculation method of porosity of cake layer was newly corrected. The Air-Water-FCC equilibrium catalysts cold model experiment was used to verify the relevant models.Results showed that the calculated values fitted well with experimental data with a relative error of less than 10%.
文摘A dynamic mass transfer model of isobutane/butene alkylation over solid acid catalysts in a fixed bed reactor was established. In the model, a modified equation for the relationship between point activity and effective diffusion coefficient was proposed. It is found that the simulation results fit the experimental data well and the breakthrough time of the bed layer is predicted accurately. By modeling the alkylation process, the time-space distribution of butene and point activity profiles of catalysts can be obtained. Furthermore, the reasons for the deactivation of solid acid catalysts were investigated. It indicates that the main reason for the deactivation of catalysts is the site coverage near the inlet of the reactor, while it is ascribed to the steric effect in the region far away from the inlet.
基金Supported by the National Natural Science Foundation of China （No.60404018） and the State Key Development Program for Basic Research of China （No.2002CB312200）.
文摘A novel control strategy for a continuous stirred tank reactor(CSTR)system,which has the typical characteristic of strongly pronounced nonlinearity,multiple operating points,and a wide operating range,is initiated from the point of hybrid systems.The proposed scheme makes full use of the modeling power of mixed logical dy- namical(MLD)systems to describe the highly nonlinear dynamics and multiple operating points in a unified framework as a hybrid system,and takes advantage of the good control quality of model predictive control(MPC) to design a controller.Thus,this approach avoids oscillation during switching between sub-systems,helps to relieve shaking in transition,and augments the stability robustness of the whole system,and finally achieves optimal(i.e. fast and smooth)transition between operating points.The simulation results demonstrate that the presented ap- proach has a satisfactory performance.
基金supported by the National Natural Science Foundation of China (No.NSFC20976069)the Fundamental Research Funds for the Central Universities,China (No.JUSRP111A12)+1 种基金the Higher School Science and Technology Innovation Project of Cultivating the Capital Project,China (No.708048)the Selfdetermined Research Program of Jiangnan University (No.JUSRP11006)
文摘Two identical full-scale biogas-lift reactors treating brewery wastewater were inoculated with different types of sludge to compare their operational conditions, sludge characteristics, and kinetic models at a mesophilic temperature. One reactor （R1） started up with anaerobic granular sludge in 12 weeks and obtained a continuously average organic loading rate （OLR） of 7.4 kg chemical oxygen demand （COD）/（m3.day）, COD removal efficiency of 80%, and effluent COD of 450 mg/L. The other reactor （R2） started up with residual activated sludge in 30 weeks and granulation accomplished when the reactor reached an average OLR of 8.3 kg COD/（m^3·day）, COD removal efficiency of 90%, and effluent COD of 240 mg/L. Differences in sludge characteristics,biogas compositions, and biogas- lift processes may be accounted for the superior efficiency of the treatment performance of R2 over R1. Grau second-order and modified StoverKincannon models based on influent and effluent concentrations as well as hydraulic retention time were successfully used to develop kinetic parameters of the experimental data with high correlation coefficients （R2 〉 0.95）, which further showed that R2 had higher treatment performance than R1. These results demonstrated that residual activated sludge could be used effectively instead of anaerobic granular sludge despite the need for a longer time.
