In this paper, the Non-Commutative phase space and Dirac equation, time-dependent Dirac oscillator are introduced. After presenting the desire general form of a two-dimensional linear dependency on the coordinate time...In this paper, the Non-Commutative phase space and Dirac equation, time-dependent Dirac oscillator are introduced. After presenting the desire general form of a two-dimensional linear dependency on the coordinate timedependent potential, the Dirac equation is written in terms of Non-Commutative phase space parameters and solved in a general form by using Lewis–Riesenfield invariant method and the time-dependent invariant of Dirac equation with two-dimensional linear dependency on the coordinate time-dependent potential in Non-Commutative phase space has been constructed, then such latter operations are done for time-dependent Dirac oscillator. In order to solve the differential equation of wave function time evolution for Dirac equation and time-dependent Dirac oscillator which are partial differential equation some appropriate ordinary physical problems have been studied and at the end the interesting result has been achieved.展开更多
In [1] the boundedness of one dimensional maximal operator of dyadic derivative is discussed. In this paper, we consider the two-dimensional maximal operator of dyadic derivative on Vilenkin martingale spaces. With th...In [1] the boundedness of one dimensional maximal operator of dyadic derivative is discussed. In this paper, we consider the two-dimensional maximal operator of dyadic derivative on Vilenkin martingale spaces. With the help of countcr-example we prove that the maximal operator is not bounded from the Hardy spacc Hq to the Hardy space Hq for 0 ≤ q ≤1 and is bounded from p∑a, Da to La for some a.展开更多
Under some assumptions and dividing the combustion space into several isothermal zones and isothermal surface elements, a two-dimensional mathematical model for combustion space in cross-fired glass melting furnaces w...Under some assumptions and dividing the combustion space into several isothermal zones and isothermal surface elements, a two-dimensional mathematical model for combustion space in cross-fired glass melting furnaces was constructed. The finite element method and the Gauss integration were used to calculate direct ex-change areas, and a inverse matrix was used to obtained the total ex-change areas. The temperature distributions were obtained by itera-tions. Some results were presented to show the effects of the fire tem-perature distribution, the convective -heat transfer coefficients and the heat losses through crown surfaces on the temperature distributions.展开更多
Some estimates on 2-D Euler equations are given when initia l vorticity ω0 belongs to a Lorentz space L(2,1). Then based on these estimates, it is proved that there exist global weak solutions of two dim ensional...Some estimates on 2-D Euler equations are given when initia l vorticity ω0 belongs to a Lorentz space L(2,1). Then based on these estimates, it is proved that there exist global weak solutions of two dim ensional Euler equations when ω0∈L(2,1).展开更多
In this article, we consider a two-dimensional symmetric space-fractional diffusion equation in which the space fractional derivatives are defined in Riesz potential sense. The well-posed feature is guaranteed by ener...In this article, we consider a two-dimensional symmetric space-fractional diffusion equation in which the space fractional derivatives are defined in Riesz potential sense. The well-posed feature is guaranteed by energy inequality. To solve the diffusion equation, a fully discrete form is established by employing Crank-Nicolson technique in time and Galerkin finite element method in space. The stability and convergence are proved and the stiffness matrix is given analytically. Three numerical examples are given to confirm our theoretical analysis in which we find that even with the same initial condition, the classical and fractional diffusion equations perform differently but tend to be uniform diffusion at last.展开更多
In this paper, decoherence of a damped anisotropic harmonic oscillator in the presence of a magnetic field is studied in the framework of the Lindblad theory of open quantum systems in noncommutative phase-space. Gene...In this paper, decoherence of a damped anisotropic harmonic oscillator in the presence of a magnetic field is studied in the framework of the Lindblad theory of open quantum systems in noncommutative phase-space. General fundamental conditions that should follow our quantum mechanical diffusion coefficients appearing in the master equation are kindly derived. From the master equation, the expressions of density operator, the Wigner distribution function, the expectation and variance with respect to coordinates and momenta are obtained. Based on these quantities, the total energy of the system is evaluated and simulations show its dependency to phase-space structure and its improvement due to noncommutativity effects and the environmental temperature as well. In addition, we also evaluate the decoherence time scale and show that it increases with noncommutativity phase-space effects as compared to the commutative case. It turns out from simulations that this time scale is significantly improved under magnetic field effects.展开更多
随着全球供应链的日益复杂化和不确定性增加,提升供应链韧性成为我国面临的重要挑战。本文基于Web of Science数据库和知网数据库,结合可视化分析方法,对2013—2024年国内外供应链韧性领域相关文献进行对比分析,研究结果表明:(1)国内研...随着全球供应链的日益复杂化和不确定性增加,提升供应链韧性成为我国面临的重要挑战。本文基于Web of Science数据库和知网数据库,结合可视化分析方法,对2013—2024年国内外供应链韧性领域相关文献进行对比分析,研究结果表明:(1)国内研究起步晚于国外,且发文量少于国外。国外整体合作密切程度强于国内,国内、国外均未形成核心作者群。(2)国内相关研究主要集中在技术创新对供应链韧性的影响、供应链韧性战略以及供应链韧性评价等方面;国外相关研究主要集中在供应链韧性内涵、供应链韧性作用机制、供应链韧性评估模型等方面。(3)国内研究演进脉络分为两个阶段,国外研究演进脉络分为三个阶段。(4)在研究前沿方面,国内现阶段聚焦数字化方面,反映了产业升级需求;国外现阶段侧重于数字化与地缘政治方面。展开更多
Some theorems of compactly supported non-tensor product form two-dimension Daubechies wavelet were analysed carefully. Compactly supported non-tensor product form two-dimension wavelet was constructed, then non-tensor...Some theorems of compactly supported non-tensor product form two-dimension Daubechies wavelet were analysed carefully. Compactly supported non-tensor product form two-dimension wavelet was constructed, then non-tensor product form two dimension wavelet finite element was used to solve the deflection problem of elastic thin plate. The error order was researched. A numerical example was given at last.展开更多
The adaptive mesh refinement （AMR） method is applied in the 2-D Euler multi-component elasticplastic hydrodynamics code （MEPH2Y）. It is applied on detonation. Firstly, the AMR method is described, including a cons...The adaptive mesh refinement （AMR） method is applied in the 2-D Euler multi-component elasticplastic hydrodynamics code （MEPH2Y）. It is applied on detonation. Firstly, the AMR method is described, including a conservative spatial interpolation, the time integration methodology with the adapitve time increment and an adaptive computational region method. The advantage of AMR technique is exhibited by numerical examples, including the 1-D C-J detonation and the 2-D implosion ignited from a single point. Results show that AMR can promote the computational efficiency, keeping the accuracy in interesting regions.展开更多
A viscoelastic beam in a two-dimensional space is considered with nonlinear tension. A boundary feedback is applied at the right boundary of the beam to suppress the undesirable vibration. The well-posedness of the pr...A viscoelastic beam in a two-dimensional space is considered with nonlinear tension. A boundary feedback is applied at the right boundary of the beam to suppress the undesirable vibration. The well-posedness of the problem is established. With the multiplier method, a uniform decay result is proven.展开更多
In the two-dimensional positioning method of pulsars, the grid method is used to provide non-sensitive direction and positional estimates. However, the grid method has a high computational load and low accuracy due to...In the two-dimensional positioning method of pulsars, the grid method is used to provide non-sensitive direction and positional estimates. However, the grid method has a high computational load and low accuracy due to the interval of the grid. To improve estimation accuracy and reduce the computational load, we propose a fast twodimensional positioning method for the crab pulsar based on multiple optimization algorithms(FTPCO). The FTPCO uses the Levenberg–Marquardt(LM) algorithm, three-point orientation(TPO) method, particle swarm optimization(PSO) and Newton–Raphson-based optimizer(NRBO) to substitute the grid method. First, to avoid the influence of the non-sensitive direction on positioning, we take an orbital error and the distortion of the pulsar profile as optimization objectives and combine the grid method with the LM algorithm or PSO to search for the non-sensitive direction. Then, on the sensitive plane perpendicular to the non-sensitive direction, the TPO method is proposed to fast search the sensitive direction and sub-sensitive direction. Finally, the NRBO is employed on the sensitive and sub-sensitive directions to achieve two-dimensional positioning of the Crab pulsar. The simulation results show that the computational load of the FTPCO is reduced by 89.4% and the positioning accuracy of the FTPCO is improved by approximately 38% compared with the grid method. The FTPCO has the advantage of high real-time accuracy and does not fall into the local optimum.展开更多
A two-dimensional model of a weakly-ionized hydrogen direct-current （DC） discharge at low pressure is simulated. In the model, the metal electron overflow and secondary electron emission coefficient at the cathode s...A two-dimensional model of a weakly-ionized hydrogen direct-current （DC） discharge at low pressure is simulated. In the model, the metal electron overflow and secondary electron emission coefficient at the cathode spot axe introduced to represent the relationship between the electron and ion density, and the electron energy distribution function is expressed by kinetic theory. The electron current density and reaction constant reasonably set on the boundary are discussed. It is determined that 11 collision reactions play a major role in low pressure and weakly ionized hydrogen discharge. On this basis, the relationship between mobility, electrode spacing, and breakdown voltage is verified. Good agreement is achieved between the simulation curve and Paschen curve.展开更多
By considering the effect of suspended solid particles in the ordinary equations for two-dimension inviscid incompressible mixing layer, the Rayleigh equation and the modified Rayleigh equation are obtained. And then,...By considering the effect of suspended solid particles in the ordinary equations for two-dimension inviscid incompressible mixing layer, the Rayleigh equation and the modified Rayleigh equation are obtained. And then, by solving the corresponding eigen-value equations with numerical computational method, the relation curves between perturbation frequency and spacial growth rate of the mixing layer for the varying particle loading, ratio of particle velocity to fluid velocity and Stokes number are got. Sever al important conclusions on the effect of suspended solid particles on unstability of the mixing layer are presented in the end by analyzing all the relation curves.展开更多
Classical-quantum correspondence has been an intriguing issue ever since quantum theory was proposed. The search- ing for signatures of classically nonintegrable dynamics in quantum systems comprises the interesting f...Classical-quantum correspondence has been an intriguing issue ever since quantum theory was proposed. The search- ing for signatures of classically nonintegrable dynamics in quantum systems comprises the interesting field of quantum chaos. In this short review, we shall go over recent efforts of extending the understanding of quantum chaos to relativistic cases. We shall focus on the level spacing statistics for two-dimensional massless Dirac billiards, i.e., particles confined in a closed region. We shall discuss the works for both the particle described by the massless Dirac equation （or Weyl equation） and the quasiparticle from graphene. Although the equations are the same, the boundary conditions are typically different, rendering distinct level spacing statistics.展开更多
文摘In this paper, the Non-Commutative phase space and Dirac equation, time-dependent Dirac oscillator are introduced. After presenting the desire general form of a two-dimensional linear dependency on the coordinate timedependent potential, the Dirac equation is written in terms of Non-Commutative phase space parameters and solved in a general form by using Lewis–Riesenfield invariant method and the time-dependent invariant of Dirac equation with two-dimensional linear dependency on the coordinate time-dependent potential in Non-Commutative phase space has been constructed, then such latter operations are done for time-dependent Dirac oscillator. In order to solve the differential equation of wave function time evolution for Dirac equation and time-dependent Dirac oscillator which are partial differential equation some appropriate ordinary physical problems have been studied and at the end the interesting result has been achieved.
基金supported by National Natural Science Foundation of China (11201354)Hubei Province Key Laboratory of Systems Science in Metallurgical Process (Wuhan University of Science and Technology) (Y201121)+3 种基金National Natural Science Foundation of Pre-Research Project (2011XG005)supported by Natural Science Fund of Hubei Province (2010CDB03305)Wuhan Chenguang Program (201150431096)Open Fund of State Key Laboratory of Information Engineeringin Surveying Mapping and Remote Sensing (11R01)
文摘In [1] the boundedness of one dimensional maximal operator of dyadic derivative is discussed. In this paper, we consider the two-dimensional maximal operator of dyadic derivative on Vilenkin martingale spaces. With the help of countcr-example we prove that the maximal operator is not bounded from the Hardy spacc Hq to the Hardy space Hq for 0 ≤ q ≤1 and is bounded from p∑a, Da to La for some a.
文摘Under some assumptions and dividing the combustion space into several isothermal zones and isothermal surface elements, a two-dimensional mathematical model for combustion space in cross-fired glass melting furnaces was constructed. The finite element method and the Gauss integration were used to calculate direct ex-change areas, and a inverse matrix was used to obtained the total ex-change areas. The temperature distributions were obtained by itera-tions. Some results were presented to show the effects of the fire tem-perature distribution, the convective -heat transfer coefficients and the heat losses through crown surfaces on the temperature distributions.
基金The Beijing Natural Science Foundation (1992002) and Beijing Education Committee Foundation.
文摘Some estimates on 2-D Euler equations are given when initia l vorticity ω0 belongs to a Lorentz space L(2,1). Then based on these estimates, it is proved that there exist global weak solutions of two dim ensional Euler equations when ω0∈L(2,1).
文摘In this article, we consider a two-dimensional symmetric space-fractional diffusion equation in which the space fractional derivatives are defined in Riesz potential sense. The well-posed feature is guaranteed by energy inequality. To solve the diffusion equation, a fully discrete form is established by employing Crank-Nicolson technique in time and Galerkin finite element method in space. The stability and convergence are proved and the stiffness matrix is given analytically. Three numerical examples are given to confirm our theoretical analysis in which we find that even with the same initial condition, the classical and fractional diffusion equations perform differently but tend to be uniform diffusion at last.
文摘In this paper, decoherence of a damped anisotropic harmonic oscillator in the presence of a magnetic field is studied in the framework of the Lindblad theory of open quantum systems in noncommutative phase-space. General fundamental conditions that should follow our quantum mechanical diffusion coefficients appearing in the master equation are kindly derived. From the master equation, the expressions of density operator, the Wigner distribution function, the expectation and variance with respect to coordinates and momenta are obtained. Based on these quantities, the total energy of the system is evaluated and simulations show its dependency to phase-space structure and its improvement due to noncommutativity effects and the environmental temperature as well. In addition, we also evaluate the decoherence time scale and show that it increases with noncommutativity phase-space effects as compared to the commutative case. It turns out from simulations that this time scale is significantly improved under magnetic field effects.
文摘随着全球供应链的日益复杂化和不确定性增加,提升供应链韧性成为我国面临的重要挑战。本文基于Web of Science数据库和知网数据库,结合可视化分析方法,对2013—2024年国内外供应链韧性领域相关文献进行对比分析,研究结果表明:(1)国内研究起步晚于国外,且发文量少于国外。国外整体合作密切程度强于国内,国内、国外均未形成核心作者群。(2)国内相关研究主要集中在技术创新对供应链韧性的影响、供应链韧性战略以及供应链韧性评价等方面;国外相关研究主要集中在供应链韧性内涵、供应链韧性作用机制、供应链韧性评估模型等方面。(3)国内研究演进脉络分为两个阶段,国外研究演进脉络分为三个阶段。(4)在研究前沿方面,国内现阶段聚焦数字化方面,反映了产业升级需求;国外现阶段侧重于数字化与地缘政治方面。
文摘Some theorems of compactly supported non-tensor product form two-dimension Daubechies wavelet were analysed carefully. Compactly supported non-tensor product form two-dimension wavelet was constructed, then non-tensor product form two dimension wavelet finite element was used to solve the deflection problem of elastic thin plate. The error order was researched. A numerical example was given at last.
基金Sponsored by the National Natural Science Foundation of China(10676120)Laboratory of Computational Physics Foundation(9140C690101070C69)
文摘The adaptive mesh refinement （AMR） method is applied in the 2-D Euler multi-component elasticplastic hydrodynamics code （MEPH2Y）. It is applied on detonation. Firstly, the AMR method is described, including a conservative spatial interpolation, the time integration methodology with the adapitve time increment and an adaptive computational region method. The advantage of AMR technique is exhibited by numerical examples, including the 1-D C-J detonation and the 2-D implosion ignited from a single point. Results show that AMR can promote the computational efficiency, keeping the accuracy in interesting regions.
文摘A viscoelastic beam in a two-dimensional space is considered with nonlinear tension. A boundary feedback is applied at the right boundary of the beam to suppress the undesirable vibration. The well-posedness of the problem is established. With the multiplier method, a uniform decay result is proven.
基金supported by the National Natural Science Foundation of China (Nos. 61873196 and 62373030)the Innovation Program for Quantum Science and Technology(No. 2021ZD0303400)。
文摘In the two-dimensional positioning method of pulsars, the grid method is used to provide non-sensitive direction and positional estimates. However, the grid method has a high computational load and low accuracy due to the interval of the grid. To improve estimation accuracy and reduce the computational load, we propose a fast twodimensional positioning method for the crab pulsar based on multiple optimization algorithms(FTPCO). The FTPCO uses the Levenberg–Marquardt(LM) algorithm, three-point orientation(TPO) method, particle swarm optimization(PSO) and Newton–Raphson-based optimizer(NRBO) to substitute the grid method. First, to avoid the influence of the non-sensitive direction on positioning, we take an orbital error and the distortion of the pulsar profile as optimization objectives and combine the grid method with the LM algorithm or PSO to search for the non-sensitive direction. Then, on the sensitive plane perpendicular to the non-sensitive direction, the TPO method is proposed to fast search the sensitive direction and sub-sensitive direction. Finally, the NRBO is employed on the sensitive and sub-sensitive directions to achieve two-dimensional positioning of the Crab pulsar. The simulation results show that the computational load of the FTPCO is reduced by 89.4% and the positioning accuracy of the FTPCO is improved by approximately 38% compared with the grid method. The FTPCO has the advantage of high real-time accuracy and does not fall into the local optimum.
基金supported by National Natural Science Foundation of China(No.50877003)
文摘A two-dimensional model of a weakly-ionized hydrogen direct-current （DC） discharge at low pressure is simulated. In the model, the metal electron overflow and secondary electron emission coefficient at the cathode spot axe introduced to represent the relationship between the electron and ion density, and the electron energy distribution function is expressed by kinetic theory. The electron current density and reaction constant reasonably set on the boundary are discussed. It is determined that 11 collision reactions play a major role in low pressure and weakly ionized hydrogen discharge. On this basis, the relationship between mobility, electrode spacing, and breakdown voltage is verified. Good agreement is achieved between the simulation curve and Paschen curve.
文摘By considering the effect of suspended solid particles in the ordinary equations for two-dimension inviscid incompressible mixing layer, the Rayleigh equation and the modified Rayleigh equation are obtained. And then, by solving the corresponding eigen-value equations with numerical computational method, the relation curves between perturbation frequency and spacial growth rate of the mixing layer for the varying particle loading, ratio of particle velocity to fluid velocity and Stokes number are got. Sever al important conclusions on the effect of suspended solid particles on unstability of the mixing layer are presented in the end by analyzing all the relation curves.
基金supported by the National Natural Science Foundation of China (Grant Nos. 11005053,11135001,and 11375074)the Air Force Office of Scientific Research (Grant No. FA9550-12-1-0095)the Office of Naval Research (Grant No. N00014-08-1-0627)
文摘Classical-quantum correspondence has been an intriguing issue ever since quantum theory was proposed. The search- ing for signatures of classically nonintegrable dynamics in quantum systems comprises the interesting field of quantum chaos. In this short review, we shall go over recent efforts of extending the understanding of quantum chaos to relativistic cases. We shall focus on the level spacing statistics for two-dimensional massless Dirac billiards, i.e., particles confined in a closed region. We shall discuss the works for both the particle described by the massless Dirac equation （or Weyl equation） and the quasiparticle from graphene. Although the equations are the same, the boundary conditions are typically different, rendering distinct level spacing statistics.
