Dear Editor,This letter proposes a novel Nash bargaining solution-based multiobjective model predictive control(MPC)scheme to deal with the interaction force control and the path-following problem of the constrained i...Dear Editor,This letter proposes a novel Nash bargaining solution-based multiobjective model predictive control(MPC)scheme to deal with the interaction force control and the path-following problem of the constrained interactive robot.Considering the elastic interaction force model,a mechanical trade-off always exists between the interaction force and position,which means that neither force nor path following can satisfy their desired demands completely.Based on this consideration,two irreconcilable control specifications,the force object function and the position track object function,are proposed,and a new multi-objective MPC scheme is then designed.展开更多
The authors of this article are interested in characterization of efficient solutions for special classes of problems. These classes consider semi-strong E-convexity of involved functions. Sufficient and necessary con...The authors of this article are interested in characterization of efficient solutions for special classes of problems. These classes consider semi-strong E-convexity of involved functions. Sufficient and necessary conditions for a feasible solution to be an efficient or properly efficient solution are obtained.展开更多
Using the homogeneous balance method introduced by Wang Mingliang, the multi- solitary wave solutions are obtained for the variant Boussinesq equation and Kupershmidt equation. The Wang's result is a special case ...Using the homogeneous balance method introduced by Wang Mingliang, the multi- solitary wave solutions are obtained for the variant Boussinesq equation and Kupershmidt equation. The Wang's result is a special case of above results for the variant Boussinesq equation.展开更多
This study investigates the multi-solution search of the optimized quantum random-walk search algorithm on the hypercube. Through generalizing the abstract search algorithm which is a general tool for analyzing the se...This study investigates the multi-solution search of the optimized quantum random-walk search algorithm on the hypercube. Through generalizing the abstract search algorithm which is a general tool for analyzing the search on the graph to the multi-solution case, it can be applied to analyze the multi-solution case of quantum random-walk search on the graph directly. Thus, the computational complexity of the optimized quantum random-walk search algorithm for the multi-solution search is obtained. Through numerical simulations and analysis, we obtain a critical value of the proportion of solutions q. For a given q, we derive the relationship between the success rate of the algorithm and the number of iterations when q is no longer than the critical value.展开更多
An initial value problem was considered for a coupled differential system with multi-term Caputo type fractional derivatives. By means of nonlinear alternative of Leray-Schauder and Banach contraction principle,the ex...An initial value problem was considered for a coupled differential system with multi-term Caputo type fractional derivatives. By means of nonlinear alternative of Leray-Schauder and Banach contraction principle,the existence and uniqueness of solutions for the system were derived. Using a fractional predictorcorrector method, a numerical method was presented for the specified system. An example was given to illustrate the obtained results.展开更多
Arrhenius formula was applied to calculate the apparent activation energy of zincate reaction. The standard electrode potential of all the metal coordinating ions and the order of galvanic couple of different metals i...Arrhenius formula was applied to calculate the apparent activation energy of zincate reaction. The standard electrode potential of all the metal coordinating ions and the order of galvanic couple of different metals in zincate solution were also calculated. Electrochemical behavior of zincate process was studied by Tafel polarization curves, E—t curves, and electrochemical impedance spectroscopy(EIS). The results show that the apparent activation energy of zincate reaction in non-cyanide multi-metal zincate solution is smaller than that in simple zincate solution, and precipitation sequence of all the metals in zincate solution is Cu, Ni, Fe and Zn. Relationship between the potential at 30 s before zincate and coverage was attained according to the change of potential of zincate. EIS shows that inductive reactance is produced during zincate.展开更多
For complementarity and redundancy of multi-sensor data fusion (MSDF) system,it is an effective approach for multiple components measurement.In order to measure nutrient solution on-line,a dynamic and complex system ...For complementarity and redundancy of multi-sensor data fusion (MSDF) system,it is an effective approach for multiple components measurement.In order to measure nutrient solution on-line,a dynamic and complex system under greenhouse environment,sensors should have intelligent properties including self-calibration and self-compensation. Meanwhile,it is necessary for multiple sensors to cooperate and interact for enhancing reliability of multi-sensor system. Because of the properties of multi-agent system (MAS),it is an appropriate tool to study MSDF system.This paper proposed an architecture of MSDF system based on MAS for the multiple components measurement of nutrient solution.The sensor agent's structure and function modules are analyzed and described in detail,the formal definitions are given,too.The relations of the sensors are modeled to implement reliability diagnosis of the multi-sensor system,so that the reliability of nutrient control system is enhanced.This study offers an effective approach for the study of MSDF.展开更多
Morphology of zinc alloy layer,from zincate solution with zinc sulfate and zinc oxide respectively,together with the consequent deposit was observed with SEM and back scattering electron image.EDS was applied to analy...Morphology of zinc alloy layer,from zincate solution with zinc sulfate and zinc oxide respectively,together with the consequent deposit was observed with SEM and back scattering electron image.EDS was applied to analyze the components of zinc alloy layer and the interface of high-Si aluminum alloy substrate-zinc alloy-deposit.Besides,the surface morphology of the zincated aluminum alloy after immersing in 3.5% NaCl solution for 7 d,is observed and the corrosion rate was calculate.Finally,tension test is conducted to quantify the adhesion between high-Si aluminum cast substrate and the deposit.The results show that,the zinc oxide contained zincating solution with sodium potassium tartrate and sodium citrate is a better one in multi-metal zincating solutions.The zinc alloy layer from this one gets stable performance,perfect adhesion with deposit,and good corrosion resistance.展开更多
In this paper we proposed an AMH Supply Chain model to obtain optimal solutions for Two-, Three- and Four-Stage for deterministic models. Besides deriving its algebraic solutions, a simple searching method is successf...In this paper we proposed an AMH Supply Chain model to obtain optimal solutions for Two-, Three- and Four-Stage for deterministic models. Besides deriving its algebraic solutions, a simple searching method is successfully applied in obtaining optimal total costs and its integer multipliers. Our model has shown promising results in comparison to Equal Cycle Time and other existing ones. The tests focused on obtaining optimal total annual costs and other related details of Two-, Three- and Four-Stage for deterministic models. The results are run under Visual Basic Programming platform using Intel? CoreTM2 Duo T6500 Processor.展开更多
In this paper, we address bilevel multi-objective programming problems (BMPP) in which the decision maker at each level has multiple objective functions conflicting with each other. Given a BMPP, we show how to constr...In this paper, we address bilevel multi-objective programming problems (BMPP) in which the decision maker at each level has multiple objective functions conflicting with each other. Given a BMPP, we show how to construct two artificial multiobjective programming problems such that any point that is efficient for both the two problems is an efficient solution of the BMPP. Some necessary and sufficient conditions for which the obtained result is applicable are provided. A complete procedure of the implementation of an algorithm for generating efficient solutions for the linear case of BMPP is presented. A numerical example is provided to illustrate how the algorithm operates.展开更多
The Hartree-Fock equation is non-linear and has, in principle, multiple solutions. The ωth HF extreme and its associated virtual spin-orbitals furnish an orthogonal base Bω of the full configuration interaction spac...The Hartree-Fock equation is non-linear and has, in principle, multiple solutions. The ωth HF extreme and its associated virtual spin-orbitals furnish an orthogonal base Bω of the full configuration interaction space. Although all Bω bases generate the same CI space, the corresponding configurations of each Bω base have distinct quantum-mechanical information contents. In previous works, we have introduced a multi-reference configuration interaction method, based on the multiple extremes of the Hartree-Fock problem. This method was applied to calculate the permanent electrical dipole and quadrupole moments of some small molecules using minimal and double, triple and polarized double-zeta bases. In all cases were possible, using a reduced number of configurations, to obtain dipole and quadrupole moments in close agreement with the experimental values and energies without compromising the energy of the state function. These results show the positive effect of the use of the multi-reference Hartree-Fock bases that allowed a better extraction of quantum mechanical information from the several Bω bases. But to extend these ideas for larger systems and atomic bases, it is necessary to develop criteria to build the multireference Hartree-Fock bases. In this project, we are beginning a study of the non-uniform distribution of quantum-mechanical information content of the Bω bases, searching identify the factors that allowed obtain the good results cited展开更多
Based on the teaching video of middle school English teachers, through observation and analysis, it puts forward the problem of less use, wrong use and abuse in the use of teachers' teaching gestures in middle sch...Based on the teaching video of middle school English teachers, through observation and analysis, it puts forward the problem of less use, wrong use and abuse in the use of teachers' teaching gestures in middle school English teaching. And then it puts forward corresponding solutions from three aspects: concept, theory and practice. Hoping to provide further reference to the complementary role of teaching gesture and teaching discourse.展开更多
The functional equation f(z)^n+g(z)^n=1 can be interpreted as the Fermat-type equations over function field.In this paper,by using Nevanlinna theory of meromorphic functions,we investigate the existence of meromorphic...The functional equation f(z)^n+g(z)^n=1 can be interpreted as the Fermat-type equations over function field.In this paper,by using Nevanlinna theory of meromorphic functions,we investigate the existence of meromorphic solutions of hyper-order strictly less than 1 to the Fermat-type functional equation(a0f(z)+a1f(z+c))^(3)+(b0f(z)+b1f(z+c))3=e^(αz+β),where a0,a1,b0,b1,α,β,c are complex constants and c≠0.展开更多
During reservoir operation,the erosion effects of groundwater change the porosity and permeability of the dam curtain,causing changes to the seepage field.To understand where the changes take place and to what degree ...During reservoir operation,the erosion effects of groundwater change the porosity and permeability of the dam curtain,causing changes to the seepage field.To understand where the changes take place and to what degree the porosity and permeability change,a multi-field coupling model was built and solved.The model takes into account seepage,solution concentration,and solid structure.The model was validated using uplift pressure monitoring data.Then,the variations in curtain porosity,seepage flow,and loss quantity of Ca(OH)2 were calculated.The key time nodes were obtained through curve fitting of the variation of seepage flow with the BiDoseResp function.The results showed that the model could reflect the attenuation trend of curtain performance well.The process and position of the erosion were not homogeneous.Although erosion mainly occurred at the top and bottom of the curtain,it was most developed at the top.The erosion effects developed slowly during the early stage,much fast during the middle and late stages,and culminated in complete dissolution.The model results and the daily monitoring data can provide a scientific basis for the safe operation and management of reservoirs.展开更多
The nonlinear Schrodinger （NLS） equation and Boussinesq equation are two very important integrable equations. They have widely physical applications. In this paper, we investigate a nonlinear system, which is the tw...The nonlinear Schrodinger （NLS） equation and Boussinesq equation are two very important integrable equations. They have widely physical applications. In this paper, we investigate a nonlinear system, which is the two-component NLS equation coupled to the Boussinesq equation. We obtain the bright-bright, bright-dark, and dark-dark soliton solutions to the nonlinear system. We discuss the collision between two solitons. We observe that the collision of bright-bright soliton is inelastic and two solitons oscillating periodically can happen in the two parallel-traveling bright-bright or bright-dark soliton solution. The general breather and rogue wave solutions are also given. Our results show again that there are more abundant dynamical properties for multi-component nonlinear systems.展开更多
This paper demonstrated our discovery of the movement effect of BiFeO_3 nanoparticles in solution by strong electrical polarization. First, BiFeO_3 nanoparticles were prepared by ball milling and characterized by SEM....This paper demonstrated our discovery of the movement effect of BiFeO_3 nanoparticles in solution by strong electrical polarization. First, BiFeO_3 nanoparticles were prepared by ball milling and characterized by SEM. Then, the preparation of BiFeO_3 solution was finished. BiFeO_3 nanoparticles are found to move in solution due to electrical field. The movement velocity of BiFeO_3 nanoparticles, which is about 10 μm·s^-1 , is influenced and controlled by the applied electrical field. The concentration of BiFeO_3 solution and the nanoparticle sizes also have effects on its movement properties. The movement of BiFeO_3 nanoparticles in solution is induced by strong polarization, and BiFeO_3 nanoparticles have net negative electric charges because of the electrostatic force between BiFeO_3 nanoparticles and the negative ions in water resolver.展开更多
A modified multi-component solute diffusion equation described with diffusion flux was derived in detail based on the classical MaxwellStefan diffusion theory. The friction between the solute species and the soil skel...A modified multi-component solute diffusion equation described with diffusion flux was derived in detail based on the classical MaxwellStefan diffusion theory. The friction between the solute species and the soil skeleton wall, which is proportional to the relative velocity between the solute species and the soil skeleton, is introduced. The chemical potential gradient is considered the driving force. A one-dimensional model for transport of multi-component solute in saturated soil was developed based on the modified diffusion equation and the modified competitive Langmuir adsorption equation. Numerical calculation of a case of two heavy metal ion species, which was chosen as an example, was carried out using the finite element software COMSOL Multiphysics. A comparative analysis was performed between the multi-component solute transport model developed in this study and the convection-diffusion transport model of single-component solute based on Fick's law. Simulation results show that the transport behavior of each species in a multi-component solute system is different from that in a single-component system, and the friction characteristics considered in the developed model contribute to obstructing the movement of each solute component. At the same time,the influence of modified competitive Langmuir adsorption on solute transport was investigated. These research results can provide strong theoretical support for the design of antifouling barriers in landfills and the maintenance of operation stability.展开更多
Sufficient conditions for the existence of at least two positive solutions of a nonlinear m -points boundary value problems are established. The results are obtained by using a new fixed point theorem in cones. An exa...Sufficient conditions for the existence of at least two positive solutions of a nonlinear m -points boundary value problems are established. The results are obtained by using a new fixed point theorem in cones. An example is provided to illustrate the theory.展开更多
The existence of positive solutions for second order m-point boundary value problemx″-q(t)f(x,x′)x′=0, x(0)= m i=2 b ix(ξ i),x′(1)=αx′(0)are investigated,where ξ i,b i and α are constants satisfying...The existence of positive solutions for second order m-point boundary value problemx″-q(t)f(x,x′)x′=0, x(0)= m i=2 b ix(ξ i),x′(1)=αx′(0)are investigated,where ξ i,b i and α are constants satisfying 0=ξ 1<ξ 2<...<ξ m-1 <ξ m=1,b i≥0 for i=2,...,m with β∶= m i=2 b i∈[0,1), and α>1. Our approach is based on the fixed point theorem in cones.展开更多
基金supported by the National Natural Science Foundation of China(62303095)the Natural Science Foundation of Sichuan Province(2023NSFSC0872).
文摘Dear Editor,This letter proposes a novel Nash bargaining solution-based multiobjective model predictive control(MPC)scheme to deal with the interaction force control and the path-following problem of the constrained interactive robot.Considering the elastic interaction force model,a mechanical trade-off always exists between the interaction force and position,which means that neither force nor path following can satisfy their desired demands completely.Based on this consideration,two irreconcilable control specifications,the force object function and the position track object function,are proposed,and a new multi-objective MPC scheme is then designed.
文摘The authors of this article are interested in characterization of efficient solutions for special classes of problems. These classes consider semi-strong E-convexity of involved functions. Sufficient and necessary conditions for a feasible solution to be an efficient or properly efficient solution are obtained.
文摘Using the homogeneous balance method introduced by Wang Mingliang, the multi- solitary wave solutions are obtained for the variant Boussinesq equation and Kupershmidt equation. The Wang's result is a special case of above results for the variant Boussinesq equation.
基金supported by the National Basic Research Program of China(Grant No.2013CB338002)
文摘This study investigates the multi-solution search of the optimized quantum random-walk search algorithm on the hypercube. Through generalizing the abstract search algorithm which is a general tool for analyzing the search on the graph to the multi-solution case, it can be applied to analyze the multi-solution case of quantum random-walk search on the graph directly. Thus, the computational complexity of the optimized quantum random-walk search algorithm for the multi-solution search is obtained. Through numerical simulations and analysis, we obtain a critical value of the proportion of solutions q. For a given q, we derive the relationship between the success rate of the algorithm and the number of iterations when q is no longer than the critical value.
基金National Natural Science Foundation of China(No.11371087)
文摘An initial value problem was considered for a coupled differential system with multi-term Caputo type fractional derivatives. By means of nonlinear alternative of Leray-Schauder and Banach contraction principle,the existence and uniqueness of solutions for the system were derived. Using a fractional predictorcorrector method, a numerical method was presented for the specified system. An example was given to illustrate the obtained results.
文摘Arrhenius formula was applied to calculate the apparent activation energy of zincate reaction. The standard electrode potential of all the metal coordinating ions and the order of galvanic couple of different metals in zincate solution were also calculated. Electrochemical behavior of zincate process was studied by Tafel polarization curves, E—t curves, and electrochemical impedance spectroscopy(EIS). The results show that the apparent activation energy of zincate reaction in non-cyanide multi-metal zincate solution is smaller than that in simple zincate solution, and precipitation sequence of all the metals in zincate solution is Cu, Ni, Fe and Zn. Relationship between the potential at 30 s before zincate and coverage was attained according to the change of potential of zincate. EIS shows that inductive reactance is produced during zincate.
文摘For complementarity and redundancy of multi-sensor data fusion (MSDF) system,it is an effective approach for multiple components measurement.In order to measure nutrient solution on-line,a dynamic and complex system under greenhouse environment,sensors should have intelligent properties including self-calibration and self-compensation. Meanwhile,it is necessary for multiple sensors to cooperate and interact for enhancing reliability of multi-sensor system. Because of the properties of multi-agent system (MAS),it is an appropriate tool to study MSDF system.This paper proposed an architecture of MSDF system based on MAS for the multiple components measurement of nutrient solution.The sensor agent's structure and function modules are analyzed and described in detail,the formal definitions are given,too.The relations of the sensors are modeled to implement reliability diagnosis of the multi-sensor system,so that the reliability of nutrient control system is enhanced.This study offers an effective approach for the study of MSDF.
基金This work is financially supported by the Foundation of Basic Research of Harbin Engineering Universi-ty( HEUFT06030)
文摘Morphology of zinc alloy layer,from zincate solution with zinc sulfate and zinc oxide respectively,together with the consequent deposit was observed with SEM and back scattering electron image.EDS was applied to analyze the components of zinc alloy layer and the interface of high-Si aluminum alloy substrate-zinc alloy-deposit.Besides,the surface morphology of the zincated aluminum alloy after immersing in 3.5% NaCl solution for 7 d,is observed and the corrosion rate was calculate.Finally,tension test is conducted to quantify the adhesion between high-Si aluminum cast substrate and the deposit.The results show that,the zinc oxide contained zincating solution with sodium potassium tartrate and sodium citrate is a better one in multi-metal zincating solutions.The zinc alloy layer from this one gets stable performance,perfect adhesion with deposit,and good corrosion resistance.
文摘In this paper we proposed an AMH Supply Chain model to obtain optimal solutions for Two-, Three- and Four-Stage for deterministic models. Besides deriving its algebraic solutions, a simple searching method is successfully applied in obtaining optimal total costs and its integer multipliers. Our model has shown promising results in comparison to Equal Cycle Time and other existing ones. The tests focused on obtaining optimal total annual costs and other related details of Two-, Three- and Four-Stage for deterministic models. The results are run under Visual Basic Programming platform using Intel? CoreTM2 Duo T6500 Processor.
文摘In this paper, we address bilevel multi-objective programming problems (BMPP) in which the decision maker at each level has multiple objective functions conflicting with each other. Given a BMPP, we show how to construct two artificial multiobjective programming problems such that any point that is efficient for both the two problems is an efficient solution of the BMPP. Some necessary and sufficient conditions for which the obtained result is applicable are provided. A complete procedure of the implementation of an algorithm for generating efficient solutions for the linear case of BMPP is presented. A numerical example is provided to illustrate how the algorithm operates.
文摘The Hartree-Fock equation is non-linear and has, in principle, multiple solutions. The ωth HF extreme and its associated virtual spin-orbitals furnish an orthogonal base Bω of the full configuration interaction space. Although all Bω bases generate the same CI space, the corresponding configurations of each Bω base have distinct quantum-mechanical information contents. In previous works, we have introduced a multi-reference configuration interaction method, based on the multiple extremes of the Hartree-Fock problem. This method was applied to calculate the permanent electrical dipole and quadrupole moments of some small molecules using minimal and double, triple and polarized double-zeta bases. In all cases were possible, using a reduced number of configurations, to obtain dipole and quadrupole moments in close agreement with the experimental values and energies without compromising the energy of the state function. These results show the positive effect of the use of the multi-reference Hartree-Fock bases that allowed a better extraction of quantum mechanical information from the several Bω bases. But to extend these ideas for larger systems and atomic bases, it is necessary to develop criteria to build the multireference Hartree-Fock bases. In this project, we are beginning a study of the non-uniform distribution of quantum-mechanical information content of the Bω bases, searching identify the factors that allowed obtain the good results cited
文摘Based on the teaching video of middle school English teachers, through observation and analysis, it puts forward the problem of less use, wrong use and abuse in the use of teachers' teaching gestures in middle school English teaching. And then it puts forward corresponding solutions from three aspects: concept, theory and practice. Hoping to provide further reference to the complementary role of teaching gesture and teaching discourse.
基金Supported by the National Natural Science Foundation of China(Grant No.11971344)。
文摘The functional equation f(z)^n+g(z)^n=1 can be interpreted as the Fermat-type equations over function field.In this paper,by using Nevanlinna theory of meromorphic functions,we investigate the existence of meromorphic solutions of hyper-order strictly less than 1 to the Fermat-type functional equation(a0f(z)+a1f(z+c))^(3)+(b0f(z)+b1f(z+c))3=e^(αz+β),where a0,a1,b0,b1,α,β,c are complex constants and c≠0.
基金supported by the Young Scientists Fund of the National Natural Science Foundation of China(Grant No.51609150)the National Key Research and Development Program of China(Grant No.2018YFC0407103)the National Natural Science Foundation of China(Grant No.51779155)
文摘During reservoir operation,the erosion effects of groundwater change the porosity and permeability of the dam curtain,causing changes to the seepage field.To understand where the changes take place and to what degree the porosity and permeability change,a multi-field coupling model was built and solved.The model takes into account seepage,solution concentration,and solid structure.The model was validated using uplift pressure monitoring data.Then,the variations in curtain porosity,seepage flow,and loss quantity of Ca(OH)2 were calculated.The key time nodes were obtained through curve fitting of the variation of seepage flow with the BiDoseResp function.The results showed that the model could reflect the attenuation trend of curtain performance well.The process and position of the erosion were not homogeneous.Although erosion mainly occurred at the top and bottom of the curtain,it was most developed at the top.The erosion effects developed slowly during the early stage,much fast during the middle and late stages,and culminated in complete dissolution.The model results and the daily monitoring data can provide a scientific basis for the safe operation and management of reservoirs.
基金supported by the National Natural Science Foundation of China(Grant Nos.11371248,11431008,11271254,11428102,and 11671255)the Fund from the Ministry of Economy and Competitiveness of Spain(Grant Nos.MTM2012-37070 and MTM2016-80276-P(AEI/FEDER,EU))
文摘The nonlinear Schrodinger （NLS） equation and Boussinesq equation are two very important integrable equations. They have widely physical applications. In this paper, we investigate a nonlinear system, which is the two-component NLS equation coupled to the Boussinesq equation. We obtain the bright-bright, bright-dark, and dark-dark soliton solutions to the nonlinear system. We discuss the collision between two solitons. We observe that the collision of bright-bright soliton is inelastic and two solitons oscillating periodically can happen in the two parallel-traveling bright-bright or bright-dark soliton solution. The general breather and rogue wave solutions are also given. Our results show again that there are more abundant dynamical properties for multi-component nonlinear systems.
基金supported by the National Natural Science Foundation of China(No.50807042)the Research Fund for the Doctoral Program of Higher Education of China(No.200806981043)+1 种基金the Fundamental Research Fund for the Central Universities(No.xjj2012088)the fund of StateKey Laboratory of Electrical Insulation and Power Equipment(Xi'an Jiaotong University No.EIPE12305)
文摘This paper demonstrated our discovery of the movement effect of BiFeO_3 nanoparticles in solution by strong electrical polarization. First, BiFeO_3 nanoparticles were prepared by ball milling and characterized by SEM. Then, the preparation of BiFeO_3 solution was finished. BiFeO_3 nanoparticles are found to move in solution due to electrical field. The movement velocity of BiFeO_3 nanoparticles, which is about 10 μm·s^-1 , is influenced and controlled by the applied electrical field. The concentration of BiFeO_3 solution and the nanoparticle sizes also have effects on its movement properties. The movement of BiFeO_3 nanoparticles in solution is induced by strong polarization, and BiFeO_3 nanoparticles have net negative electric charges because of the electrostatic force between BiFeO_3 nanoparticles and the negative ions in water resolver.
基金supported by the National Basic Research Program of China(Grant No.2014CB744702)the Beijing Natural Science Foundation Key Projects(Grant No.8171001)the National Natural Science Foundation of China(Grant No.51678012)
文摘A modified multi-component solute diffusion equation described with diffusion flux was derived in detail based on the classical MaxwellStefan diffusion theory. The friction between the solute species and the soil skeleton wall, which is proportional to the relative velocity between the solute species and the soil skeleton, is introduced. The chemical potential gradient is considered the driving force. A one-dimensional model for transport of multi-component solute in saturated soil was developed based on the modified diffusion equation and the modified competitive Langmuir adsorption equation. Numerical calculation of a case of two heavy metal ion species, which was chosen as an example, was carried out using the finite element software COMSOL Multiphysics. A comparative analysis was performed between the multi-component solute transport model developed in this study and the convection-diffusion transport model of single-component solute based on Fick's law. Simulation results show that the transport behavior of each species in a multi-component solute system is different from that in a single-component system, and the friction characteristics considered in the developed model contribute to obstructing the movement of each solute component. At the same time,the influence of modified competitive Langmuir adsorption on solute transport was investigated. These research results can provide strong theoretical support for the design of antifouling barriers in landfills and the maintenance of operation stability.
文摘Sufficient conditions for the existence of at least two positive solutions of a nonlinear m -points boundary value problems are established. The results are obtained by using a new fixed point theorem in cones. An example is provided to illustrate the theory.
基金Natural Scince Foundation of China and Foundation for University Key Teacher by the Ministry of Education
文摘The existence of positive solutions for second order m-point boundary value problemx″-q(t)f(x,x′)x′=0, x(0)= m i=2 b ix(ξ i),x′(1)=αx′(0)are investigated,where ξ i,b i and α are constants satisfying 0=ξ 1<ξ 2<...<ξ m-1 <ξ m=1,b i≥0 for i=2,...,m with β∶= m i=2 b i∈[0,1), and α>1. Our approach is based on the fixed point theorem in cones.
