As a new structure of solid matter quasicrystal brings profound new ideas to the traditional condensed matter physics, its elastic equations are more complicated than that of traditional crystal. A contact problem of ...As a new structure of solid matter quasicrystal brings profound new ideas to the traditional condensed matter physics, its elastic equations are more complicated than that of traditional crystal. A contact problem of decagonal two? dimensional quasicrystal material under the action of a rigid flat die is solved satisfactorily by introducing displacement function and using Fourier analysis and dual integral equations theory, and the analytical expressions of stress and displacement fields of the contact problem are achieved. The results show that if the contact displacement is a constant in the contact zone, the vertical contact stress has order -1/2 singularity on the edge of contact zone, which provides the important mechanics parameter for contact deformation of the quasicrystal.展开更多
In this paper we survey the authors＇ and related work on two-dimensional Riemann problems for hyperbolic conservation laws, mainly those related to the compressible Euler equations in gas dynamics. It contains four s...In this paper we survey the authors＇ and related work on two-dimensional Riemann problems for hyperbolic conservation laws, mainly those related to the compressible Euler equations in gas dynamics. It contains four sections： 1. Historical review. 2. Scalar conservation laws. 3. Euler equations. 4. Simplified models.展开更多
This paper proposes an eigenfunction expansion method to solve twodimensional （2D） elasticity problems based on stress formulation. By introducing appropriate state functions, the fundamental system of partial diffe...This paper proposes an eigenfunction expansion method to solve twodimensional （2D） elasticity problems based on stress formulation. By introducing appropriate state functions, the fundamental system of partial differential equations of the above 2D problems is rewritten as an upper triangular differential system. For the associated operator matrix, the existence and the completeness of two normed orthogonal eigenfunction systems in some space are obtained, which belong to the two block operators arising in the operator matrix. Moreover, the general solution to the above 2D problem is given by the eigenfunction expansion method.展开更多
Using a polarization method, the scattering problem for a two-dimensional inclusion embedded in infinite piezoelectric/piezomagnetic matrices is investigated. To achieve the purpose, the polarization method for a two-...Using a polarization method, the scattering problem for a two-dimensional inclusion embedded in infinite piezoelectric/piezomagnetic matrices is investigated. To achieve the purpose, the polarization method for a two-dimensional piezoelectric/piezomagnetic ＂comparison body＂ is formulated. For simple harmonic motion, kernel of the polarization method reduces to a 2-D time-harmonic Green＇s function, which is obtained using the Radon transform. The expression is further simplified under conditions of low frequency of the incident wave and small diameter of the inclusion. Some analytical expressions are obtained. The analytical solutions for generalized piezoelectric/piezomagnetic anisotropic composites are given followed by simplified results for piezoelectric composites. Based on the latter results, two numerical results are provided for an elliptical cylindrical inclusion in a PZT-5H-matrix, showing the effect of different factors including size, shape, material properties, and piezoelectricity on the scattering cross-section.展开更多
We are concerned with global solutions of multidimensional(M-D)Riemann problems for nonlinear hyperbolic systems of conservation laws,focusing on their global configurations and structures.We present some recent devel...We are concerned with global solutions of multidimensional(M-D)Riemann problems for nonlinear hyperbolic systems of conservation laws,focusing on their global configurations and structures.We present some recent developments in the rigorous analysis of two-dimensional(2-D)Riemann problems involving transonic shock waves through several prototypes of hyperbolic systems of conservation laws and discuss some further M-D Riemann problems and related problems for nonlinear partial differential equations.In particular,we present four different 2-D Riemann problems through these prototypes of hyperbolic systems and show how these Riemann problems can be reformulated/solved as free boundary problems with transonic shock waves as free boundaries for the corresponding nonlinear conservation laws of mixed elliptic-hyperbolic type and related nonlinear partial differential equations.展开更多
This paper studies the eigenfunction expansion method to solve the two dimensional （2D） elasticity problems based on the stress formulation. The fundamental system of partial differential equations of the 2D problem...This paper studies the eigenfunction expansion method to solve the two dimensional （2D） elasticity problems based on the stress formulation. The fundamental system of partial differential equations of the 2D problems is rewritten as an upper tri angular differential system based on the known results, and then the associated upper triangular operator matrix matrix is obtained. By further research, the two simpler com plete orthogonal systems of eigenfunctions in some space are obtained, which belong to the two block operators arising in the operator matrix. Then, a more simple and conve nient general solution to the 2D problem is given by the eigenfunction expansion method. Furthermore, the boundary conditions for the 2D problem, which can be solved by this method, are indicated. Finally, the validity of the obtained results is verified by a specific example.展开更多
The Riemann problem for a two-dimensional 2 x 2 nonstrictly hyperbolic system of nonlinear conservation laws has been solved thoroughly for any given initial data which are constant in each quadrant. The non-classical...The Riemann problem for a two-dimensional 2 x 2 nonstrictly hyperbolic system of nonlinear conservation laws has been solved thoroughly for any given initial data which are constant in each quadrant. The non-classical shockwaves, which are labelled as delta-shock waves, appear in some solutions. The solutions have been obtained are not unique. Due to the specific property of the system considered, there are no rarefaction waves in solution. This paper is divided into three parts. The first part constructs Riemann solutions for initial data involving two contact discontinuities while the second considers the case for other initial data. The last part briefly discusses the non-uniqueness of the solutions.展开更多
To improve the mainlainability design efficiency and quality, a layout optimization method for maintainability of multi-component systems was proposed. The impact of the component layout design on system maintainabili...To improve the mainlainability design efficiency and quality, a layout optimization method for maintainability of multi-component systems was proposed. The impact of the component layout design on system maintainability was analyzed, and the layout problem for maintainability was presented. It was formulated as an optimization problem, where maintainability, layout space and distance requirement were formulated as objective functions. A multi-objective particle swarm optimization algorithm, in which the constrained-domination relationship and the update strategy of the global best were simply modified, was then used to obtain Pareto optimal solutions for the maintainability layout design problem. Finally, application in oxygen generation system of a spacecraft was studied in detail to illustrate the effectiveness and usefulness of the proposed method. The results show that the concurrent maintainability design can be carried out during the layout design process by solving the layout optimization problem for maintainability.展开更多
We extended an improved version of the discrete particle swarm optimization (DPSO) algorithm proposed by Liao et al.(2007) to solve the dynamic facility layout problem (DFLP). A computational study was performed with ...We extended an improved version of the discrete particle swarm optimization (DPSO) algorithm proposed by Liao et al.(2007) to solve the dynamic facility layout problem (DFLP). A computational study was performed with the existing heuristic algorithms, including the dynamic programming (DP), genetic algorithm (GA), simulated annealing (SA), hybrid ant system (HAS), hybrid simulated annealing (SA-EG), hybrid genetic algorithms (NLGA and CONGA). The proposed DPSO algorithm, SA, HAS, GA, DP, SA-EG, NLGA, and CONGA obtained the best solutions for 33, 24, 20, 10, 12, 20, 5, and 2 of the 48 problems from (Balakrishnan and Cheng, 2000), respectively. These results show that the DPSO is very effective in dealing with the DFLP. The extended DPSO also has very good computational efficiency when the problem size increases.展开更多
A warehouse layout problem where the warehouse has more than one level and both the distance from the cell to the receive/exit bay and demand of item types are fuzzy variables is proposed. The problem is to find a lay...A warehouse layout problem where the warehouse has more than one level and both the distance from the cell to the receive/exit bay and demand of item types are fuzzy variables is proposed. The problem is to find a layout with the minimum transportation cost subject to adjacency and other constraints. A fuzzy expected value model is given and an ant colony system is designed to solve the problem. Computational results indicate the efficiency and effectiveness of the method.展开更多
Based on the dynamical theory of multi-body systems with nonholonomic constraints and an algorithm for complementarity problems, a numerical method for the multi-body systems with two-dimensional Coulomb dry friction ...Based on the dynamical theory of multi-body systems with nonholonomic constraints and an algorithm for complementarity problems, a numerical method for the multi-body systems with two-dimensional Coulomb dry friction and nonholonomic constraints is presented. In particular, a wheeled multi-body system is considered. Here, the state transition of stick-slip between wheel and ground is transformed into a nonlinear complementarity problem （NCP）. An iterative algorithm for solving the NCP is then presented using an event-driven method. Dynamical equations of the multi-body system with holonomic and nonholonomic constraints are given using Routh equations and a con- straint stabilization method. Finally, an example is used to test the proposed numerical method. The results show some dynamical behaviors of the wheeled multi-body system and its constraint stabilization effects.展开更多
The double row layout problem(DRLP)is to assign facilities on two rows in parallel so that the total cost of material handling among facilities is minimized.Since it is vital to save cost and enhance productivity,the ...The double row layout problem(DRLP)is to assign facilities on two rows in parallel so that the total cost of material handling among facilities is minimized.Since it is vital to save cost and enhance productivity,the DRLP plays an important role in many application fields.Nevertheless,it is very hard to handle the DRLP because of its complex model.In this paper,we consider a new simplified model for the DRLP(SM-DRLP)and provide a mixed integer programming(MIP)formulation for it.The continuous decision variables of the DRLP are divided into two parts:start points of double rows and adjustable clearances between adjacent facilities.The former one is considered in the new simplified model for the DRLP with the purpose of maintaining solution quality,while the latter one is not taken into account with the purpose of reducing computational time.To evaluate its performance,our SM-DRLP is compared with the model of a general DRLP and the model of another simplified DRLP.The experimental results show the efficiency of our proposed model.展开更多
We calculate the energy spectrum of three identical fermionic ultracold atoms in two different internal states confined in a two-dimensional anisotropic harmonic trap.Using the solutions of the corresponding two-body ...We calculate the energy spectrum of three identical fermionic ultracold atoms in two different internal states confined in a two-dimensional anisotropic harmonic trap.Using the solutions of the corresponding two-body problems obtained in our previous work(Chen et al 2020 Phys.Rev.A 101,053624),we derive the explicit transcendental equation for the eigen-energies,from which the energy spectrum is derived.Our results can be used for the calculation of the 3rd Virial coefficients or the studies of few-body dynamics.展开更多
This article studies the pod layout problem in the Kiva mobile fulfillment system which adopts the synchronized zoning strategy. An integer programming model for the pod layout problem is formulated under the premise ...This article studies the pod layout problem in the Kiva mobile fulfillment system which adopts the synchronized zoning strategy. An integer programming model for the pod layout problem is formulated under the premise of knowing the relationship of the pods and items. A three-stage algorithm is proposed based on the Spectral Clustering algorithm. Firstly, the pod similarity matrix and the Laplacian matrix are constructed according to the relationship of the pods and items. Secondly, the pods are clustered by the Spectral Clustering algorithm and assigned to each zone based on the cluster results. Finally, the exact locations of pods in each zone are determined by the historical retrieval frequency of items, using the real data of a large-scale Kiva mobile fulfillment system to simulate and calculate the order picking efficiency before and after the adjustment of the pod layout. The results showed that the pod layout using synchronized zoning strategy can effectively improve the picking efficiency.展开更多
With the rapid development of the individualized demand market,the demand for manufacturing flexibility has increased over time.As a result,a cell manufacturing system suitable for many varieties and small batches has...With the rapid development of the individualized demand market,the demand for manufacturing flexibility has increased over time.As a result,a cell manufacturing system suitable for many varieties and small batches has been produced.With the goal of minimizing the area and logistics handling volume,and considering the arrangement order of facilities and channel constraints,a mathematical model was established,and the problem was solved by improved NSGA-II.After non-dominated sorting,traditional NSGA-II will cross-operate the individuals with the best sorting to generate new individuals.Such a selection strategy is extremely easy to fall into the local optimal solution.The improved NSGA-II is to improve the original selection operation,which is to select the first half of the excellent individuals in the non-dominated sorting into the cross operation,and then select the last sorted ones of the remaining individuals into the cross operation,and combine the best and the worst ones into the cross operation.Finally,an example is given to simulate and improve the solution of NSGA-II and NSGA-II.The simulation results indicate that the improved NSGA-II population shows more obvious diversity,it is easier to jump out of the local optimal solution than NSGA-II,and the satisfactory layout scheme of manufacturing cells is obtained.Therefore,it is more effective to use improved NSGA-II to solve the problem of manufacturing cell layout.展开更多
In this paper,the approximate solutions for two different type of two-dimensional nonlinear integral equations:two-dimensional nonlinear Volterra-Fredholm integral equations and the nonlinear mixed Volterra-Fredholm i...In this paper,the approximate solutions for two different type of two-dimensional nonlinear integral equations:two-dimensional nonlinear Volterra-Fredholm integral equations and the nonlinear mixed Volterra-Fredholm integral equations are obtained using the Laguerre wavelet method.To do this,these two-dimensional nonlinear integral equations are transformed into a system of nonlinear algebraic equations in matrix form.By solving these systems,unknown coefficients are obtained.Also,some theorems are proved for convergence analysis.Some numerical examples are presented and results are compared with the analytical solution to demonstrate the validity and applicability of the proposed method.展开更多
To adapt to the complex and changeable market environment,the cell formation problems(CFPs) and the cell layout problems(CLPs) with fuzzy demands were optimized simultaneously. Firstly,CFPs and CLPs were described for...To adapt to the complex and changeable market environment,the cell formation problems(CFPs) and the cell layout problems(CLPs) with fuzzy demands were optimized simultaneously. Firstly,CFPs and CLPs were described formally. To deal with the uncertainty fuzzy parameters brought,a chance constraint was introduced. A mathematical model was established with an objective function of minimizing intra-cell and inter-cell material handling cost. As the chance constraint of this problem could not be converted into its crisp equivalent,a hybrid simulated annealing(HSA) based on fuzzy simulation was put forward. Finally,simulation experiments were conducted under different confidence levels. Results indicated that the proposed hybrid algorithm was feasible and effective.展开更多
We are concerned with the global existence of entropy solutions of the two-dimensional steady Euler equations for an ideal gas, which undergoes a one-step exothermic chemical reaction under the Arrhenius-type kinetics...We are concerned with the global existence of entropy solutions of the two-dimensional steady Euler equations for an ideal gas, which undergoes a one-step exothermic chemical reaction under the Arrhenius-type kinetics. The reaction rate function φ（T ） is assumed to have a positive lower bound. We first consider the Cauchy problem （the initial value problem）, that is, seek a supersonic downstream reacting flow when the incoming flow is supersonic, and establish the global existence of entropy solutions when the total variation of the initial data is sufficiently small. Then we analyze the problem of steady supersonic, exothermically reacting Euler flow past a Lipschitz wedge, generating an ad-ditional detonation wave attached to the wedge vertex, which can be then formulated as an initial-boundary value problem. We establish the global existence of entropy solutions containing the additional detonation wave （weak or strong, determined by the wedge angle at the wedge vertex） when the total variation of both the slope of the wedge boundary and the incoming flow is suitably small. The downstream asymptotic behavior of the global solutions is also obtained.展开更多
Layout design problem is to determine a suitable arrangement for the departments so that the total costs associated with the flow among departments become least. Single Row Facility Layout Problem, SRFLP, is one of &l...Layout design problem is to determine a suitable arrangement for the departments so that the total costs associated with the flow among departments become least. Single Row Facility Layout Problem, SRFLP, is one of </span></span><span style="font-family:Verdana;"><span style="font-family:Verdana;"><span style="font-family:Verdana;">the </span></span></span><span><span><span style="font-family:""><span style="font-family:Verdana;">layout problems that have many practical applications. This problem and its specific scenarios are often used to model many of the raised issues in the field of facility location. SRFLP is an arrangement of </span><i><span style="font-family:Verdana;">n</span></i><span style="font-family:Verdana;"> departments with a specified length in a straight line so that the sum of the weighted distances between the pairs of departments is minimized. This problem is NP-hard. In this paper, first, a lower bound for a special case of SRFLP is presented. Then, a general </span><span style="font-family:Verdana;">case of SRFLP is presented in which some new and real assumptions are added to generate more practical model. Then a lower bound, as well as an algorithm, is proposed for solving the model. Experimental results on some instances in literature show the efficiency of our algorithm.展开更多
Land is the foundation for human survival and development,and all human social and economic activities are inseparable from the land as a space carrier.With the continuous development of China's social economy,Chi...Land is the foundation for human survival and development,and all human social and economic activities are inseparable from the land as a space carrier.With the continuous development of China's social economy,China is facing new social development needs such as urban-rural integration and rural revitalization.At the same time,China starts to attach great importance to ecology and has proposed the concept that lucid waters and lush mountains are invaluable assets.In this situation,the rational use of land resources,the optimization of land use structure and layout are also facing new challenges and problems,and more comprehensive consideration is required to make relevant optimization.Using the method of literature comparative analysis,from the conceptual connotation,basic theory,method model,and specific practice of land use structure and layout optimization,this paper analyzed and summarized the current research situations and problems,and finally came up with recommendations for the future research.展开更多
文摘As a new structure of solid matter quasicrystal brings profound new ideas to the traditional condensed matter physics, its elastic equations are more complicated than that of traditional crystal. A contact problem of decagonal two? dimensional quasicrystal material under the action of a rigid flat die is solved satisfactorily by introducing displacement function and using Fourier analysis and dual integral equations theory, and the analytical expressions of stress and displacement fields of the contact problem are achieved. The results show that if the contact displacement is a constant in the contact zone, the vertical contact stress has order -1/2 singularity on the edge of contact zone, which provides the important mechanics parameter for contact deformation of the quasicrystal.
基金supported by 973 Key program and the Key Program from Beijing Educational Commission with No. KZ200910028002Program for New Century Excellent Talents in University (NCET)+4 种基金Funding Project for Academic Human Resources Development in Institutions of Higher Learning Under the Jurisdiction of Beijing Municipality (PHR-IHLB)The research of Sheng partially supported by NSFC (10671120)Shanghai Leading Academic Discipline Project: J50101The research of Zhang partially supported by NSFC (10671120)The research of Zheng partially supported by NSF-DMS-0603859
文摘In this paper we survey the authors＇ and related work on two-dimensional Riemann problems for hyperbolic conservation laws, mainly those related to the compressible Euler equations in gas dynamics. It contains four sections： 1. Historical review. 2. Scalar conservation laws. 3. Euler equations. 4. Simplified models.
基金Project supported by the National Natural Science Foundation of China (No. 10962004)the Special-ized Research Fund for the Doctoral Program of Higher Education of China (No. 20070126002)+1 种基金the Chunhui Program of Ministry of Education of China (No. Z2009-1-01010)the Natural Science Foundation of Inner Mongolia (No. 2009BS0101)
文摘This paper proposes an eigenfunction expansion method to solve twodimensional （2D） elasticity problems based on stress formulation. By introducing appropriate state functions, the fundamental system of partial differential equations of the above 2D problems is rewritten as an upper triangular differential system. For the associated operator matrix, the existence and the completeness of two normed orthogonal eigenfunction systems in some space are obtained, which belong to the two block operators arising in the operator matrix. Moreover, the general solution to the above 2D problem is given by the eigenfunction expansion method.
基金supported by the National Natural Science Foundation of China (Nos. 10732100, 10572155)the Science and Technology Planning Project of Guangdong Province of China (No. 2006A11001002)the Ph. D. Programs Foundation of Ministry of Education of China (No. 2006300004111179)
文摘Using a polarization method, the scattering problem for a two-dimensional inclusion embedded in infinite piezoelectric/piezomagnetic matrices is investigated. To achieve the purpose, the polarization method for a two-dimensional piezoelectric/piezomagnetic ＂comparison body＂ is formulated. For simple harmonic motion, kernel of the polarization method reduces to a 2-D time-harmonic Green＇s function, which is obtained using the Radon transform. The expression is further simplified under conditions of low frequency of the incident wave and small diameter of the inclusion. Some analytical expressions are obtained. The analytical solutions for generalized piezoelectric/piezomagnetic anisotropic composites are given followed by simplified results for piezoelectric composites. Based on the latter results, two numerical results are provided for an elliptical cylindrical inclusion in a PZT-5H-matrix, showing the effect of different factors including size, shape, material properties, and piezoelectricity on the scattering cross-section.
基金The research of Gui-Qiang G.Chen was supported in part by the UK Engineering and Physical Sciences Research Council Awards EP/L015811/1,EP/V008854/1,EP/V051121/1the Royal Society-Wolfson Research Merit Award WM090014.
文摘We are concerned with global solutions of multidimensional(M-D)Riemann problems for nonlinear hyperbolic systems of conservation laws,focusing on their global configurations and structures.We present some recent developments in the rigorous analysis of two-dimensional(2-D)Riemann problems involving transonic shock waves through several prototypes of hyperbolic systems of conservation laws and discuss some further M-D Riemann problems and related problems for nonlinear partial differential equations.In particular,we present four different 2-D Riemann problems through these prototypes of hyperbolic systems and show how these Riemann problems can be reformulated/solved as free boundary problems with transonic shock waves as free boundaries for the corresponding nonlinear conservation laws of mixed elliptic-hyperbolic type and related nonlinear partial differential equations.
基金supported by the Specialized Research Fund for the Doctoral Program of Higher Education of China (No. 20070126002)the National Natural Science Foundation of China (No. 10962004)
文摘This paper studies the eigenfunction expansion method to solve the two dimensional （2D） elasticity problems based on the stress formulation. The fundamental system of partial differential equations of the 2D problems is rewritten as an upper tri angular differential system based on the known results, and then the associated upper triangular operator matrix matrix is obtained. By further research, the two simpler com plete orthogonal systems of eigenfunctions in some space are obtained, which belong to the two block operators arising in the operator matrix. Then, a more simple and conve nient general solution to the 2D problem is given by the eigenfunction expansion method. Furthermore, the boundary conditions for the 2D problem, which can be solved by this method, are indicated. Finally, the validity of the obtained results is verified by a specific example.
文摘The Riemann problem for a two-dimensional 2 x 2 nonstrictly hyperbolic system of nonlinear conservation laws has been solved thoroughly for any given initial data which are constant in each quadrant. The non-classical shockwaves, which are labelled as delta-shock waves, appear in some solutions. The solutions have been obtained are not unique. Due to the specific property of the system considered, there are no rarefaction waves in solution. This paper is divided into three parts. The first part constructs Riemann solutions for initial data involving two contact discontinuities while the second considers the case for other initial data. The last part briefly discusses the non-uniqueness of the solutions.
基金Project(51005238)supported by the National Natural Science Foundation of China
文摘To improve the mainlainability design efficiency and quality, a layout optimization method for maintainability of multi-component systems was proposed. The impact of the component layout design on system maintainability was analyzed, and the layout problem for maintainability was presented. It was formulated as an optimization problem, where maintainability, layout space and distance requirement were formulated as objective functions. A multi-objective particle swarm optimization algorithm, in which the constrained-domination relationship and the update strategy of the global best were simply modified, was then used to obtain Pareto optimal solutions for the maintainability layout design problem. Finally, application in oxygen generation system of a spacecraft was studied in detail to illustrate the effectiveness and usefulness of the proposed method. The results show that the concurrent maintainability design can be carried out during the layout design process by solving the layout optimization problem for maintainability.
文摘We extended an improved version of the discrete particle swarm optimization (DPSO) algorithm proposed by Liao et al.(2007) to solve the dynamic facility layout problem (DFLP). A computational study was performed with the existing heuristic algorithms, including the dynamic programming (DP), genetic algorithm (GA), simulated annealing (SA), hybrid ant system (HAS), hybrid simulated annealing (SA-EG), hybrid genetic algorithms (NLGA and CONGA). The proposed DPSO algorithm, SA, HAS, GA, DP, SA-EG, NLGA, and CONGA obtained the best solutions for 33, 24, 20, 10, 12, 20, 5, and 2 of the 48 problems from (Balakrishnan and Cheng, 2000), respectively. These results show that the DPSO is very effective in dealing with the DFLP. The extended DPSO also has very good computational efficiency when the problem size increases.
基金the National Natural Science Foundation of China (70471063 ,70171036)
文摘A warehouse layout problem where the warehouse has more than one level and both the distance from the cell to the receive/exit bay and demand of item types are fuzzy variables is proposed. The problem is to find a layout with the minimum transportation cost subject to adjacency and other constraints. A fuzzy expected value model is given and an ant colony system is designed to solve the problem. Computational results indicate the efficiency and effectiveness of the method.
基金Project supported by the National Natural Science Foundation of China(Nos.11372018 and 11572018)
文摘Based on the dynamical theory of multi-body systems with nonholonomic constraints and an algorithm for complementarity problems, a numerical method for the multi-body systems with two-dimensional Coulomb dry friction and nonholonomic constraints is presented. In particular, a wheeled multi-body system is considered. Here, the state transition of stick-slip between wheel and ground is transformed into a nonlinear complementarity problem （NCP）. An iterative algorithm for solving the NCP is then presented using an event-driven method. Dynamical equations of the multi-body system with holonomic and nonholonomic constraints are given using Routh equations and a con- straint stabilization method. Finally, an example is used to test the proposed numerical method. The results show some dynamical behaviors of the wheeled multi-body system and its constraint stabilization effects.
基金Supported by the National Natural Science Foundation of China(61871204,62174033)the Natural Science Foundation of Fujian Province(2017J01767,2020J01843)+1 种基金the Program for New Century Excellent Talents in Fujian Province Universitythe Science and Technology Project of Minjiang University(MYK19017)。
文摘The double row layout problem(DRLP)is to assign facilities on two rows in parallel so that the total cost of material handling among facilities is minimized.Since it is vital to save cost and enhance productivity,the DRLP plays an important role in many application fields.Nevertheless,it is very hard to handle the DRLP because of its complex model.In this paper,we consider a new simplified model for the DRLP(SM-DRLP)and provide a mixed integer programming(MIP)formulation for it.The continuous decision variables of the DRLP are divided into two parts:start points of double rows and adjustable clearances between adjacent facilities.The former one is considered in the new simplified model for the DRLP with the purpose of maintaining solution quality,while the latter one is not taken into account with the purpose of reducing computational time.To evaluate its performance,our SM-DRLP is compared with the model of a general DRLP and the model of another simplified DRLP.The experimental results show the efficiency of our proposed model.
基金supported in part by the National Key Research and Development Program of China Grant No.2018YFA0306502NSAF(Grant No.U1930201)+1 种基金supported by the Fundamental Research Funds for the Central Universitiesthe Research Funds of Renmin University of China under Grant No.21XNH088。
文摘We calculate the energy spectrum of three identical fermionic ultracold atoms in two different internal states confined in a two-dimensional anisotropic harmonic trap.Using the solutions of the corresponding two-body problems obtained in our previous work(Chen et al 2020 Phys.Rev.A 101,053624),we derive the explicit transcendental equation for the eigen-energies,from which the energy spectrum is derived.Our results can be used for the calculation of the 3rd Virial coefficients or the studies of few-body dynamics.
文摘This article studies the pod layout problem in the Kiva mobile fulfillment system which adopts the synchronized zoning strategy. An integer programming model for the pod layout problem is formulated under the premise of knowing the relationship of the pods and items. A three-stage algorithm is proposed based on the Spectral Clustering algorithm. Firstly, the pod similarity matrix and the Laplacian matrix are constructed according to the relationship of the pods and items. Secondly, the pods are clustered by the Spectral Clustering algorithm and assigned to each zone based on the cluster results. Finally, the exact locations of pods in each zone are determined by the historical retrieval frequency of items, using the real data of a large-scale Kiva mobile fulfillment system to simulate and calculate the order picking efficiency before and after the adjustment of the pod layout. The results showed that the pod layout using synchronized zoning strategy can effectively improve the picking efficiency.
文摘With the rapid development of the individualized demand market,the demand for manufacturing flexibility has increased over time.As a result,a cell manufacturing system suitable for many varieties and small batches has been produced.With the goal of minimizing the area and logistics handling volume,and considering the arrangement order of facilities and channel constraints,a mathematical model was established,and the problem was solved by improved NSGA-II.After non-dominated sorting,traditional NSGA-II will cross-operate the individuals with the best sorting to generate new individuals.Such a selection strategy is extremely easy to fall into the local optimal solution.The improved NSGA-II is to improve the original selection operation,which is to select the first half of the excellent individuals in the non-dominated sorting into the cross operation,and then select the last sorted ones of the remaining individuals into the cross operation,and combine the best and the worst ones into the cross operation.Finally,an example is given to simulate and improve the solution of NSGA-II and NSGA-II.The simulation results indicate that the improved NSGA-II population shows more obvious diversity,it is easier to jump out of the local optimal solution than NSGA-II,and the satisfactory layout scheme of manufacturing cells is obtained.Therefore,it is more effective to use improved NSGA-II to solve the problem of manufacturing cell layout.
文摘In this paper,the approximate solutions for two different type of two-dimensional nonlinear integral equations:two-dimensional nonlinear Volterra-Fredholm integral equations and the nonlinear mixed Volterra-Fredholm integral equations are obtained using the Laguerre wavelet method.To do this,these two-dimensional nonlinear integral equations are transformed into a system of nonlinear algebraic equations in matrix form.By solving these systems,unknown coefficients are obtained.Also,some theorems are proved for convergence analysis.Some numerical examples are presented and results are compared with the analytical solution to demonstrate the validity and applicability of the proposed method.
基金Supported by the National Natural Science Foundation of China(No.61273035,71471135)
文摘To adapt to the complex and changeable market environment,the cell formation problems(CFPs) and the cell layout problems(CLPs) with fuzzy demands were optimized simultaneously. Firstly,CFPs and CLPs were described formally. To deal with the uncertainty fuzzy parameters brought,a chance constraint was introduced. A mathematical model was established with an objective function of minimizing intra-cell and inter-cell material handling cost. As the chance constraint of this problem could not be converted into its crisp equivalent,a hybrid simulated annealing(HSA) based on fuzzy simulation was put forward. Finally,simulation experiments were conducted under different confidence levels. Results indicated that the proposed hybrid algorithm was feasible and effective.
基金Gui-Qiang CHEN was supported in part by the UK EPSRC Science and Innovation Award to the Oxford Centre for Nonlinear PDE(EP/E035027/1)the NSFC under a joint project Grant 10728101+4 种基金the Royal Society-Wolfson Research Merit Award(UK)Changguo XIAO was supported in part by the NSFC under a joint project Grant 10728101Yongqian ZHANG was supported in part by NSFC Project 11031001NSFC Project 11121101the 111 Project B08018(China)
文摘We are concerned with the global existence of entropy solutions of the two-dimensional steady Euler equations for an ideal gas, which undergoes a one-step exothermic chemical reaction under the Arrhenius-type kinetics. The reaction rate function φ（T ） is assumed to have a positive lower bound. We first consider the Cauchy problem （the initial value problem）, that is, seek a supersonic downstream reacting flow when the incoming flow is supersonic, and establish the global existence of entropy solutions when the total variation of the initial data is sufficiently small. Then we analyze the problem of steady supersonic, exothermically reacting Euler flow past a Lipschitz wedge, generating an ad-ditional detonation wave attached to the wedge vertex, which can be then formulated as an initial-boundary value problem. We establish the global existence of entropy solutions containing the additional detonation wave （weak or strong, determined by the wedge angle at the wedge vertex） when the total variation of both the slope of the wedge boundary and the incoming flow is suitably small. The downstream asymptotic behavior of the global solutions is also obtained.
文摘Layout design problem is to determine a suitable arrangement for the departments so that the total costs associated with the flow among departments become least. Single Row Facility Layout Problem, SRFLP, is one of </span></span><span style="font-family:Verdana;"><span style="font-family:Verdana;"><span style="font-family:Verdana;">the </span></span></span><span><span><span style="font-family:""><span style="font-family:Verdana;">layout problems that have many practical applications. This problem and its specific scenarios are often used to model many of the raised issues in the field of facility location. SRFLP is an arrangement of </span><i><span style="font-family:Verdana;">n</span></i><span style="font-family:Verdana;"> departments with a specified length in a straight line so that the sum of the weighted distances between the pairs of departments is minimized. This problem is NP-hard. In this paper, first, a lower bound for a special case of SRFLP is presented. Then, a general </span><span style="font-family:Verdana;">case of SRFLP is presented in which some new and real assumptions are added to generate more practical model. Then a lower bound, as well as an algorithm, is proposed for solving the model. Experimental results on some instances in literature show the efficiency of our algorithm.
文摘Land is the foundation for human survival and development,and all human social and economic activities are inseparable from the land as a space carrier.With the continuous development of China's social economy,China is facing new social development needs such as urban-rural integration and rural revitalization.At the same time,China starts to attach great importance to ecology and has proposed the concept that lucid waters and lush mountains are invaluable assets.In this situation,the rational use of land resources,the optimization of land use structure and layout are also facing new challenges and problems,and more comprehensive consideration is required to make relevant optimization.Using the method of literature comparative analysis,from the conceptual connotation,basic theory,method model,and specific practice of land use structure and layout optimization,this paper analyzed and summarized the current research situations and problems,and finally came up with recommendations for the future research.
