The paper generalizes the direct method of moving planes to the Logarithmic Laplacian system.Firstly,some key ingredients of the method are discussed,for example,Narrow region principle and Decay at infinity.Then,the ...The paper generalizes the direct method of moving planes to the Logarithmic Laplacian system.Firstly,some key ingredients of the method are discussed,for example,Narrow region principle and Decay at infinity.Then,the radial symmetry of the solution of the Logarithmic Laplacian system is obtained.展开更多
This work presents a novel approach combining radial basis function(RBF)interpolation with Galerkin projection to efficiently solve general optimal control problems.The goal is to develop a highly flexible solution to...This work presents a novel approach combining radial basis function(RBF)interpolation with Galerkin projection to efficiently solve general optimal control problems.The goal is to develop a highly flexible solution to optimal control problems,especially nonsmooth problems involving discontinuities,while accounting for trajectory accuracy and computational efficiency simultaneously.The proposed solution,called the RBF-Galerkin method,offers a highly flexible framework for direct transcription by using any interpolant functions from the broad class of global RBFs and any arbitrary discretization points that do not necessarily need to be on a mesh of points.The RBF-Galerkin costate mapping theorem is developed that describes an exact equivalency between the Karush-Kuhn-Tucker(KKT)conditions of the nonlinear programming problem resulted from the RBF-Galerkin method and the discretized form of the first-order necessary conditions of the optimal control problem,if a set of discrete conditions holds.The efficacy of the proposed method along with the accuracy of the RBF-Galerkin costate mapping theorem is confirmed against an analytical solution for a bang-bang optimal control problem.In addition,the proposed approach is compared against both local and global polynomial methods for a robot motion planning problem to verify its accuracy and computational efficiency.展开更多
In this paper,we consider entire solutions of higher order homogeneous differential equations with the entire coefficients having the same order,and prove that the entire solutions are of infinite lower order.The prop...In this paper,we consider entire solutions of higher order homogeneous differential equations with the entire coefficients having the same order,and prove that the entire solutions are of infinite lower order.The properties on the radial distribution,the limit direction of the Julia set and the existence of a Baker wandering domain of the entire solutions are also discussed.展开更多
Neural networks require a lot of training to understand the model of a plant or a process. Issues such as learning speed, stability, and weight convergence remain as areas of research and comparison of many training a...Neural networks require a lot of training to understand the model of a plant or a process. Issues such as learning speed, stability, and weight convergence remain as areas of research and comparison of many training algorithms. The application of neural networks to control interior permanent magnet synchronous motor using direct torque control (DTC) is discussed. A neural network is used to emulate the state selector of the DTC. The neural networks used are the back-propagation and radial basis function. To reduce the training patterns and increase the execution speed of the training process, the inputs of switching table are converted to digital signals, i.e., one bit represent the flux error, one bit the torque error, and three bits the region of stator flux. Computer simulations of the motor and neural-network system using the two approaches are presented and compared. Discussions about the back-propagation and radial basis function as the most promising training techniques are presented, giving its advantages and disadvantages. The system using back-propagation and radial basis function networks controller has quick parallel speed and high torque response.展开更多
Within the framework of plane-wave angular spectrum analysis of the electromagnetic field structure, a solution valid for tightly focused radially polarized few-cycle laser pulses propagating in vacuum is presented. T...Within the framework of plane-wave angular spectrum analysis of the electromagnetic field structure, a solution valid for tightly focused radially polarized few-cycle laser pulses propagating in vacuum is presented. The resulting field distribution is significantly different from that based on the paraxial approximation for pulses with either small or large beam diameters. We compare the electron accelerations obtained with the two solutions and find that the energy gain obtained with our new solution is usually much larger than that with the paraxial approximation solution.展开更多
In this work, the reversal of radial glow distribution induced by reversed magnetic field is reported. Based on the Boswell antenna which is symmetric and insensitive to the magnetic field direction, it seems such a p...In this work, the reversal of radial glow distribution induced by reversed magnetic field is reported. Based on the Boswell antenna which is symmetric and insensitive to the magnetic field direction, it seems such a phenomenon in theory appears impossible. However, according to the diagnostic of the helicon waves by magnetic probe, it is found that the direction of magnetic field significantly affects the propagation characteristic of helicon waves, i.e., the interchange of the helicon waves at the upper and the lower half of tube was caused by reversing the direction of magnetic field. It is suggested that the variation of helicon wave against the direction of magnetic field causes the reversed radial glow distribution. The appearance of the traveling wave does not only improve the discharge strength, but also determines the transition of the discharge mode.展开更多
The effect of different scales thermoelectric magnetic convection(TEMC)on the radial solidification microstructure of hypereutectic Al alloy has been investigated under transverse static magnetic field during directio...The effect of different scales thermoelectric magnetic convection(TEMC)on the radial solidification microstructure of hypereutectic Al alloy has been investigated under transverse static magnetic field during directional solidification,focusing on the formation of freckle.Our experimental and numerical simulation results indicate that the TEMC circulation at sample scale under transverse static magnetic field leads to the enrichment of solute Al on one side of the sample.The TEMC and the solute enrichment degree increase with the increase of magnetic field when the magnetic field increases to 0.5 T.The enrichment degree of solute elements under magnetic field is affected by temperature gradient and growth rate.The non-uniform distribution of solute Al in the radial direction of the sample results in the non-uniform distribution of primary dendrite arm spacing(PDAS).Moreover,the applied magnetic field can lead to freckle formation and its number increases with the increase of magnetic field.The change of freckle is consistent with the anisotropy TEMC caused by the anisotropy of primary dendrite or primary dendrite network under magnetic field.Finally,the mechanism of synergism effect of the anisotropy TEMC,the distribution of solute Al and the PDAS on freckle formation and evolution is studied during directional solidification under magnetic field.展开更多
A test equipment was developed,which allows for real time observation of the deformation behav-ior of wood cellular structure under a compression load applied in radial direction.Compression tests were performed on ja...A test equipment was developed,which allows for real time observation of the deformation behav-ior of wood cellular structure under a compression load applied in radial direction.Compression tests were performed on jack pine(Pinus banksiana)and balsam poplar(Populus balsamifera)spec-imens to explore the relationship between the yield stress and the first failure occurring in wood cell layers during radial compression.The microstructural changes for P.banksiana and P.bal-samifera wood below and above the yield point were analyzed.The study results showed that for P.banksiana the first failure of wood cells occurred at the first earlywood layer,while for P.balsamifera it occurred at the layer with the largest vessels.The first failure of wood cell layer for each species tested was found to correspond to the yield point on the stress-strain curve.A new method of determining the yield stress for wood specimens under radial compression was developed.展开更多
This study investigated the influence of pressing temperature and moisture content on the me-chanical properties of wood compressed in radial direction.Jack pine(Pinus banksiana)and bal-sam poplar(Populus balsamifera)...This study investigated the influence of pressing temperature and moisture content on the me-chanical properties of wood compressed in radial direction.Jack pine(Pinus banksiana)and bal-sam poplar(Populus balsamifera)specimens were tested under a combination of pressing temper-ature(20℃,55℃,90℃,and 125℃)and wood moisture content(2%,7%,12%,and 17%).The yield stress(_(δ)y)and modulus of elasticity(MOE)of the specimens were determined from the stress-strain response.It was found that an increase in either pressing temperature or moisture content of wood generally caused a decrease in the mechanical properties for both species.The t-test results revealed that jack pine specimens are more sensitive to changes in pressing tem-perature and wood moisture content than balsam poplar.For jack pine specimens,at any of the pressing temperatures,the moisture content of 12%was found to be a crucial level to start a significant decrease in𝜎y and MOE,while at any of the moisture content,a change in temper-ature from 55℃to 90℃exhibited a significant change in𝜎y and MOE.The regression models developed can be used to predict𝜎y and MOE as a function of temperature and moisture content.展开更多
基金Supported by the National Natural Science Foundation of China(11501342,12001344)。
文摘The paper generalizes the direct method of moving planes to the Logarithmic Laplacian system.Firstly,some key ingredients of the method are discussed,for example,Narrow region principle and Decay at infinity.Then,the radial symmetry of the solution of the Logarithmic Laplacian system is obtained.
文摘This work presents a novel approach combining radial basis function(RBF)interpolation with Galerkin projection to efficiently solve general optimal control problems.The goal is to develop a highly flexible solution to optimal control problems,especially nonsmooth problems involving discontinuities,while accounting for trajectory accuracy and computational efficiency simultaneously.The proposed solution,called the RBF-Galerkin method,offers a highly flexible framework for direct transcription by using any interpolant functions from the broad class of global RBFs and any arbitrary discretization points that do not necessarily need to be on a mesh of points.The RBF-Galerkin costate mapping theorem is developed that describes an exact equivalency between the Karush-Kuhn-Tucker(KKT)conditions of the nonlinear programming problem resulted from the RBF-Galerkin method and the discretized form of the first-order necessary conditions of the optimal control problem,if a set of discrete conditions holds.The efficacy of the proposed method along with the accuracy of the RBF-Galerkin costate mapping theorem is confirmed against an analytical solution for a bang-bang optimal control problem.In addition,the proposed approach is compared against both local and global polynomial methods for a robot motion planning problem to verify its accuracy and computational efficiency.
基金supported partly by the National Natural Science Foundation of China(11926201,12171050)the National Science Foundation of Guangdong Province(2018A030313508)。
文摘In this paper,we consider entire solutions of higher order homogeneous differential equations with the entire coefficients having the same order,and prove that the entire solutions are of infinite lower order.The properties on the radial distribution,the limit direction of the Julia set and the existence of a Baker wandering domain of the entire solutions are also discussed.
基金the National Natural Science Foundation of China (60374032).
文摘Neural networks require a lot of training to understand the model of a plant or a process. Issues such as learning speed, stability, and weight convergence remain as areas of research and comparison of many training algorithms. The application of neural networks to control interior permanent magnet synchronous motor using direct torque control (DTC) is discussed. A neural network is used to emulate the state selector of the DTC. The neural networks used are the back-propagation and radial basis function. To reduce the training patterns and increase the execution speed of the training process, the inputs of switching table are converted to digital signals, i.e., one bit represent the flux error, one bit the torque error, and three bits the region of stator flux. Computer simulations of the motor and neural-network system using the two approaches are presented and compared. Discussions about the back-propagation and radial basis function as the most promising training techniques are presented, giving its advantages and disadvantages. The system using back-propagation and radial basis function networks controller has quick parallel speed and high torque response.
基金supported by the National Natural Science Foundation of China (Grant Nos.10734130,10935002,and 11075105)the National Basic Research Program of China (Grant No.2009GB105002)
文摘Within the framework of plane-wave angular spectrum analysis of the electromagnetic field structure, a solution valid for tightly focused radially polarized few-cycle laser pulses propagating in vacuum is presented. The resulting field distribution is significantly different from that based on the paraxial approximation for pulses with either small or large beam diameters. We compare the electron accelerations obtained with the two solutions and find that the energy gain obtained with our new solution is usually much larger than that with the paraxial approximation solution.
基金financially supported by National Natural Science Foundation of China(Nos.11175024,11375031,11505013)BJNSFC(No.KZ201510015014)+2 种基金Beijing Municipal Natural Science Foundation(No.4162024)State Key Laboratory of Electrical Insulation and Power Equipment(No.EIPE15208)Beijing municipal coordination innovation program 2011
文摘In this work, the reversal of radial glow distribution induced by reversed magnetic field is reported. Based on the Boswell antenna which is symmetric and insensitive to the magnetic field direction, it seems such a phenomenon in theory appears impossible. However, according to the diagnostic of the helicon waves by magnetic probe, it is found that the direction of magnetic field significantly affects the propagation characteristic of helicon waves, i.e., the interchange of the helicon waves at the upper and the lower half of tube was caused by reversing the direction of magnetic field. It is suggested that the variation of helicon wave against the direction of magnetic field causes the reversed radial glow distribution. The appearance of the traveling wave does not only improve the discharge strength, but also determines the transition of the discharge mode.
基金the National Natural Science Foundation of China(Nos.51571056,51690164 and 51904183)the Technological Innovation Projects of Universities in Guangdong Province(Nos.2017KTSCX177 and 2020KQNCX084)+2 种基金China Postdoctoral Science Foundation(No.2020M683463)Guangdong Basic and Applied Basic Research Foundation(No.2019A1515110135)the Natural Science Foundation of Guangdong Province(No.2018A030310024)。
文摘The effect of different scales thermoelectric magnetic convection(TEMC)on the radial solidification microstructure of hypereutectic Al alloy has been investigated under transverse static magnetic field during directional solidification,focusing on the formation of freckle.Our experimental and numerical simulation results indicate that the TEMC circulation at sample scale under transverse static magnetic field leads to the enrichment of solute Al on one side of the sample.The TEMC and the solute enrichment degree increase with the increase of magnetic field when the magnetic field increases to 0.5 T.The enrichment degree of solute elements under magnetic field is affected by temperature gradient and growth rate.The non-uniform distribution of solute Al in the radial direction of the sample results in the non-uniform distribution of primary dendrite arm spacing(PDAS).Moreover,the applied magnetic field can lead to freckle formation and its number increases with the increase of magnetic field.The change of freckle is consistent with the anisotropy TEMC caused by the anisotropy of primary dendrite or primary dendrite network under magnetic field.Finally,the mechanism of synergism effect of the anisotropy TEMC,the distribution of solute Al and the PDAS on freckle formation and evolution is studied during directional solidification under magnetic field.
基金Natural Sciences and Engineering Research Council of Canada(NSERC)New Brunswick Innovation Foundation(NBIF).
文摘A test equipment was developed,which allows for real time observation of the deformation behav-ior of wood cellular structure under a compression load applied in radial direction.Compression tests were performed on jack pine(Pinus banksiana)and balsam poplar(Populus balsamifera)spec-imens to explore the relationship between the yield stress and the first failure occurring in wood cell layers during radial compression.The microstructural changes for P.banksiana and P.bal-samifera wood below and above the yield point were analyzed.The study results showed that for P.banksiana the first failure of wood cells occurred at the first earlywood layer,while for P.balsamifera it occurred at the layer with the largest vessels.The first failure of wood cell layer for each species tested was found to correspond to the yield point on the stress-strain curve.A new method of determining the yield stress for wood specimens under radial compression was developed.
基金founded by a grant from the Natural Sciences and Engineering Research Council of Canada and New Brunswick Innovation Foundation.
文摘This study investigated the influence of pressing temperature and moisture content on the me-chanical properties of wood compressed in radial direction.Jack pine(Pinus banksiana)and bal-sam poplar(Populus balsamifera)specimens were tested under a combination of pressing temper-ature(20℃,55℃,90℃,and 125℃)and wood moisture content(2%,7%,12%,and 17%).The yield stress(_(δ)y)and modulus of elasticity(MOE)of the specimens were determined from the stress-strain response.It was found that an increase in either pressing temperature or moisture content of wood generally caused a decrease in the mechanical properties for both species.The t-test results revealed that jack pine specimens are more sensitive to changes in pressing tem-perature and wood moisture content than balsam poplar.For jack pine specimens,at any of the pressing temperatures,the moisture content of 12%was found to be a crucial level to start a significant decrease in𝜎y and MOE,while at any of the moisture content,a change in temper-ature from 55℃to 90℃exhibited a significant change in𝜎y and MOE.The regression models developed can be used to predict𝜎y and MOE as a function of temperature and moisture content.