A modified alternating direction implicit algorithm is proposed to solve the full-vectorial finite-difference beam propagation method formulation based on H fields. The cross-coupling terms are neglected in the first ...A modified alternating direction implicit algorithm is proposed to solve the full-vectorial finite-difference beam propagation method formulation based on H fields. The cross-coupling terms are neglected in the first sub-step, but evaluated and doubly used in the second sub-step. The order of two sub-steps is reversed for each transverse magnetic field component so that the cross-coupling terms are always expressed in implicit form, thus the calculation is very efficient and stable. Moreover, an improved six-point finite-difference scheme with high accuracy independent of specific structures of waveguide is also constructed to approximate the cross-coupling terms along the transverse directions. The imaginary-distance procedure is used to assess the validity and utility of the present method. The field patterns and the normalized propagation constants of the fundamental mode for a buried rectangular waveguide and a rib waveguide are presented. Solutions are in excellent agreement with the benchmark results from the modal transverse resonance method.展开更多
Let {(D n, FFFn),n/->1} be a sequence of martingale differences and {a ni, 1≤i≤n,n≥1} be an array of real constants. Almost sure convergence for the row sums ?i = 1n ani D1\sum\limits_{i = 1}^n {a_{ni} D_1 } are...Let {(D n, FFFn),n/->1} be a sequence of martingale differences and {a ni, 1≤i≤n,n≥1} be an array of real constants. Almost sure convergence for the row sums ?i = 1n ani D1\sum\limits_{i = 1}^n {a_{ni} D_1 } are discussed. We also discuss complete convergence for the moving average processes underB-valued martingale differences assumption.展开更多
The sets of Minkowski algebraic sum and geometric difference are considered. The purpose of the research in this paper is to apply the properties of Minkowski sum and geometric difference to fractional differential ga...The sets of Minkowski algebraic sum and geometric difference are considered. The purpose of the research in this paper is to apply the properties of Minkowski sum and geometric difference to fractional differential games. This paper investigates the geometric properties of the Minkowski algebraic sum and the geometric difference of sets. Various examples are considered that calculate the geometric differences of sets. The results of the research are presented and proved as a theorem. At the end of the article, the results were applied to fractional differential games.展开更多
This paper presents a study on the motion response of a tension-leg platform(TLP) under first-and second-order wave forces, including the mean-drift force, difference and sum-frequency forces. The second-order wave fo...This paper presents a study on the motion response of a tension-leg platform(TLP) under first-and second-order wave forces, including the mean-drift force, difference and sum-frequency forces. The second-order wave force is calculated using the full-field quadratic transfer function(QTF). The coupled effect of the horizontal motions, such as surge, sway and yaw motions, and the set-down motion are taken into consideration by the nonlinear restoring matrix. The time-domain analysis with 50-yr random sea state is performed. A comparison of the results of different case studies is made to assess the influence of second-order wave force on the motions of the platform. The analysis shows that the second-order wave force has a major impact on motions of the TLP. The second-order difference-frequency wave force has an obvious influence on the low-frequency motions of surge and sway, and also will induce a large set-down motion which is an important part of heave motion. Besides, the second-order sum-frequency force will induce a set of high-frequency motions of roll and pitch. However, little influence of second-order wave force is found on the yaw motion.展开更多
Let {Xn, n≥1} be a martingale difference sequence and {a nk , 1?k?n,n?1} an array of constant real numbers. The limiting behavior of weighted partial sums ∑ k=1 n a nk X k is investigated and some new results are ob...Let {Xn, n≥1} be a martingale difference sequence and {a nk , 1?k?n,n?1} an array of constant real numbers. The limiting behavior of weighted partial sums ∑ k=1 n a nk X k is investigated and some new results are obtained.展开更多
This paper presents a simple method of forming sum and difference patterns with adaptivenulls. The effects on the sidelobe level and the pointing null of difference pattern by adaptive null areanalyzed. The result tha...This paper presents a simple method of forming sum and difference patterns with adaptivenulls. The effects on the sidelobe level and the pointing null of difference pattern by adaptive null areanalyzed. The result that the increment value of the envelope of the sidelobe level under the effect ofa null is less than l.6dB is proved. The formula about shift value of the pointing null which is thefunction of the jammer direction and array parameters is given in the paper.展开更多
Chaotic vibrations of flexible non-linear Euler-Bernoulli beams subjected to harmonic load and with various boundary conditions（symmetric and non-symmetric）are studied in this work.Reliability of the obtained result...Chaotic vibrations of flexible non-linear Euler-Bernoulli beams subjected to harmonic load and with various boundary conditions（symmetric and non-symmetric）are studied in this work.Reliability of the obtained results is verified by the finite difference method（FDM）and the finite element method（FEM）with the Bubnov-Galerkin approximation for various boundary conditions and various dynamic regimes（regular and non-regular）.The influence of boundary conditions on the Euler-Bernoulli beams dynamics is studied mainly,dynamic behavior vs.control parameters { ωp,q0 } is reported,and scenarios of the system transition into chaos are illustrated.展开更多
In this paper, we investigate a two electronic level system with vibrational modes coupled to a Brownian oscillator bath. The difference frequency generation （DFG） signals and sum frequency generation （SFG） signal...In this paper, we investigate a two electronic level system with vibrational modes coupled to a Brownian oscillator bath. The difference frequency generation （DFG） signals and sum frequency generation （SFG） signals are calculated. It is shown that, for the same model, the SFG signals are more sensitive than the DFG signals to the changes of the vibrational modes of the electronic two-level system. Because the SFG conversion efficiency can be improved by using the time-delay method, the findings in this paper predict that the SFG spectrum may probe the changes of the microstructure more effectively.展开更多
As is well known,the definitions of fractional sum and fractional difference of f(z)on non-uniform lattices x(z)=c1z^(2)+c2z+c3 or x(z)=c1q^(z)+c2q^(-z)+c3 are more difficult and complicated.In this article,for the fi...As is well known,the definitions of fractional sum and fractional difference of f(z)on non-uniform lattices x(z)=c1z^(2)+c2z+c3 or x(z)=c1q^(z)+c2q^(-z)+c3 are more difficult and complicated.In this article,for the first time we propose the definitions of the fractional sum and fractional difference on non-uniform lattices by two different ways.The analogue of Euler’s Beta formula,Cauchy’Beta formula on non-uniform lattices are established,and some fundamental theorems of fractional calculas,the solution of the generalized Abel equation on non-uniform lattices are obtained etc.展开更多
<div style="text-align:justify;"> Transceiver module and two-dimensional sum difference network are important components of phased array antenna. In this paper, multilayer printed board is used to inte...<div style="text-align:justify;"> Transceiver module and two-dimensional sum difference network are important components of phased array antenna. In this paper, multilayer printed board is used to integrate millimeter wave multi-channel transceiver circuit and sum difference network. The interconnection between them is realized through RF coaxial vertical transition. At the same time, the heat dissipation design and inter channel shielding design of the module are carried out. The RF and low frequency required by the module are completed through the wiring between and within the dielectric plate layers. Finally, 128 arrays are fabricated and verified by multi-channel passive test. The results show that the type transceiver module integrating with two-dimensional sum difference network has good performance, and 128 channels have excellent amplitude and phase characteristics. The integration technology has the characteristics of lightweight, miniaturization, high integration and low manufacturing cost. It can be widely used in miniaturized phased array antennas. </div>展开更多
The difference discrete system of Euler-beam with arbitrary supports was constructed by using the two order central difference formulas. This system is equivalent to the spring-mass-rigidrod model. By using the theory...The difference discrete system of Euler-beam with arbitrary supports was constructed by using the two order central difference formulas. This system is equivalent to the spring-mass-rigidrod model. By using the theory of oscillatory matrix, the signoscillatory property of stiffness matrices of this system was proved, and the necessary and sufficient condition for the system to be positive was obtained completely.展开更多
We present the application of differential quadrature（DQ） method for the buckling analysis of nanobeams with exponentially varying stiffness based on four different beam theories of Euler-Bernoulli, Timoshenko, Redd...We present the application of differential quadrature（DQ） method for the buckling analysis of nanobeams with exponentially varying stiffness based on four different beam theories of Euler-Bernoulli, Timoshenko, Reddy, and Levison.The formulation is based on the nonlocal elasticity theory of Eringen. New results are presented for the guided and simply supported guided boundary conditions. Numerical results are obtained to investigate the effects of the nonlocal parameter,length-to-height ratio, boundary condition, and nonuniform parameter on the critical buckling load parameter. It is observed that the critical buckling load decreases with increase in the nonlocal parameter while the critical buckling load parameter increases with increase in the length-to-height ratio.展开更多
With the diversification of manufacture methods, joining the same materials with different states becomes indispensable in practical application. In present work, 6061 aluminum alloys with different states were welded...With the diversification of manufacture methods, joining the same materials with different states becomes indispensable in practical application. In present work, 6061 aluminum alloys with different states were welded by laser beam welding （LBW）. The microstructures of welded joint, before and after heat treating, were investigated. The mechanical properties, such as the tensile properties and microhardness , were tested. And the fracture characteristic was observed by means of scanning electron microscope （SEM）. The results show that the 6061 aluminum alloys have superior weldability and the microstructures are different significantly in different states. Besides, the grain boundaries of the joint microstructures become unclear after the heat treating. The strength and the elongations of welded joints could reach to those of the base metal. The tensile fracture occurs in the fusion zone and near 6061-0 alloy. And the fracture presents ductile rupture. Therefore, the LBW is an effective method for 6061 aluminum alloy.展开更多
A bending beam,subjected to state of plane stress,was chosen to investigate.The determination of the neutral surface of the structure was made,and the calculating formulas of neutral axis,normal stress,shear stress a...A bending beam,subjected to state of plane stress,was chosen to investigate.The determination of the neutral surface of the structure was made,and the calculating formulas of neutral axis,normal stress,shear stress and displacement were derived.It is concluded that, for the elastic bending beam with different tension-compression modulus in the condition of complex stress, the position of the neutral axis is not related with the shear stress, and the analytical solution can be derived by normal stress used as a criterion, improving the multiple cyclic method which determines the position of neutral point by the principal stress. Meanwhile, a comparison is made between the results of the analytical solution and those calculated from the classic mechanics theory, assuming the tension modulus is equal to the compression modulus, and those from the finite element method (FEM) numerical solution. The comparison shows that the analytical solution considers well the effects caused by the condition of different tension and compression modulus. Finally, a calculation correction of the structure with different modulus is proposed to optimize the structure.展开更多
Fusion power output is proportional not only to the fuel particle number densities participating in reaction but also to the fusion reaction rate coefficient （or reactivity）, which is dependent on reactant velocity ...Fusion power output is proportional not only to the fuel particle number densities participating in reaction but also to the fusion reaction rate coefficient （or reactivity）, which is dependent on reactant velocity distribution functions. They are usuMly assumed to be dual Maxwellian distribution functions with the same temperature for thermal nuclear fusion circumstances. However, if high power neutral beam injection and minority ion species ICRF plasma heating, or multi-pinched plasma beam head-on collision, in a converging region are required and investigated in future large scale fusion reactors, then the fractions of the injected energetic fast ion tail resulting from ionization or charge exchange will be large enough and their contribution to the non-Maxwellian distribution functions is not negligible, hence to the fusion reaction rate coefficient or calculation of fusion power. In such cases, beam-target, and beam-beam reaction enhancement effect contributions should play very important roles. In this paper, several useful formulae to calculate the fusion reaction rate coefticient for different beam and target combination scenarios are derived in detail展开更多
Here some steady-state experiments on oxidation of CO on Pd were performed on a molecular beam apparatus. It is found that the characteristics of the rate of CO_2 formation r versus substrate temperature T are depende...Here some steady-state experiments on oxidation of CO on Pd were performed on a molecular beam apparatus. It is found that the characteristics of the rate of CO_2 formation r versus substrate temperature T are dependent on the ratio P=P_(CO)/P_(O2) in the mixed beam. These characteristics are related to the complicated interactions of co-adsorbed CO and O particles on Pd surface.展开更多
文摘A modified alternating direction implicit algorithm is proposed to solve the full-vectorial finite-difference beam propagation method formulation based on H fields. The cross-coupling terms are neglected in the first sub-step, but evaluated and doubly used in the second sub-step. The order of two sub-steps is reversed for each transverse magnetic field component so that the cross-coupling terms are always expressed in implicit form, thus the calculation is very efficient and stable. Moreover, an improved six-point finite-difference scheme with high accuracy independent of specific structures of waveguide is also constructed to approximate the cross-coupling terms along the transverse directions. The imaginary-distance procedure is used to assess the validity and utility of the present method. The field patterns and the normalized propagation constants of the fundamental mode for a buried rectangular waveguide and a rib waveguide are presented. Solutions are in excellent agreement with the benchmark results from the modal transverse resonance method.
文摘Let {(D n, FFFn),n/->1} be a sequence of martingale differences and {a ni, 1≤i≤n,n≥1} be an array of real constants. Almost sure convergence for the row sums ?i = 1n ani D1\sum\limits_{i = 1}^n {a_{ni} D_1 } are discussed. We also discuss complete convergence for the moving average processes underB-valued martingale differences assumption.
文摘The sets of Minkowski algebraic sum and geometric difference are considered. The purpose of the research in this paper is to apply the properties of Minkowski sum and geometric difference to fractional differential games. This paper investigates the geometric properties of the Minkowski algebraic sum and the geometric difference of sets. Various examples are considered that calculate the geometric differences of sets. The results of the research are presented and proved as a theorem. At the end of the article, the results were applied to fractional differential games.
基金supported by the National Natural Science Foundation of China(Nos.51239008 and 51279130)
文摘This paper presents a study on the motion response of a tension-leg platform(TLP) under first-and second-order wave forces, including the mean-drift force, difference and sum-frequency forces. The second-order wave force is calculated using the full-field quadratic transfer function(QTF). The coupled effect of the horizontal motions, such as surge, sway and yaw motions, and the set-down motion are taken into consideration by the nonlinear restoring matrix. The time-domain analysis with 50-yr random sea state is performed. A comparison of the results of different case studies is made to assess the influence of second-order wave force on the motions of the platform. The analysis shows that the second-order wave force has a major impact on motions of the TLP. The second-order difference-frequency wave force has an obvious influence on the low-frequency motions of surge and sway, and also will induce a large set-down motion which is an important part of heave motion. Besides, the second-order sum-frequency force will induce a set of high-frequency motions of roll and pitch. However, little influence of second-order wave force is found on the yaw motion.
基金SupportedbytheNationalNaturalScienceFoundationofChina (No .10 0 710 5 8)and (No .10 0 710 19)
文摘Let {Xn, n≥1} be a martingale difference sequence and {a nk , 1?k?n,n?1} an array of constant real numbers. The limiting behavior of weighted partial sums ∑ k=1 n a nk X k is investigated and some new results are obtained.
文摘This paper presents a simple method of forming sum and difference patterns with adaptivenulls. The effects on the sidelobe level and the pointing null of difference pattern by adaptive null areanalyzed. The result that the increment value of the envelope of the sidelobe level under the effect ofa null is less than l.6dB is proved. The formula about shift value of the pointing null which is thefunction of the jammer direction and array parameters is given in the paper.
文摘Chaotic vibrations of flexible non-linear Euler-Bernoulli beams subjected to harmonic load and with various boundary conditions（symmetric and non-symmetric）are studied in this work.Reliability of the obtained results is verified by the finite difference method（FDM）and the finite element method（FEM）with the Bubnov-Galerkin approximation for various boundary conditions and various dynamic regimes（regular and non-regular）.The influence of boundary conditions on the Euler-Bernoulli beams dynamics is studied mainly,dynamic behavior vs.control parameters { ωp,q0 } is reported,and scenarios of the system transition into chaos are illustrated.
基金Supported by the National Natural Science Foundation of China under Grant No. 61078065, Natural Science Foundation of Ningbo City under Grant No. 2008A61009, and K.C. Wong Magna Foundation in Ningbo University
文摘In this paper, we investigate a two electronic level system with vibrational modes coupled to a Brownian oscillator bath. The difference frequency generation （DFG） signals and sum frequency generation （SFG） signals are calculated. It is shown that, for the same model, the SFG signals are more sensitive than the DFG signals to the changes of the vibrational modes of the electronic two-level system. Because the SFG conversion efficiency can be improved by using the time-delay method, the findings in this paper predict that the SFG spectrum may probe the changes of the microstructure more effectively.
基金Supported by the National Natural Science Foundation Fujian province of China(2016J01032).
文摘As is well known,the definitions of fractional sum and fractional difference of f(z)on non-uniform lattices x(z)=c1z^(2)+c2z+c3 or x(z)=c1q^(z)+c2q^(-z)+c3 are more difficult and complicated.In this article,for the first time we propose the definitions of the fractional sum and fractional difference on non-uniform lattices by two different ways.The analogue of Euler’s Beta formula,Cauchy’Beta formula on non-uniform lattices are established,and some fundamental theorems of fractional calculas,the solution of the generalized Abel equation on non-uniform lattices are obtained etc.
文摘<div style="text-align:justify;"> Transceiver module and two-dimensional sum difference network are important components of phased array antenna. In this paper, multilayer printed board is used to integrate millimeter wave multi-channel transceiver circuit and sum difference network. The interconnection between them is realized through RF coaxial vertical transition. At the same time, the heat dissipation design and inter channel shielding design of the module are carried out. The RF and low frequency required by the module are completed through the wiring between and within the dielectric plate layers. Finally, 128 arrays are fabricated and verified by multi-channel passive test. The results show that the type transceiver module integrating with two-dimensional sum difference network has good performance, and 128 channels have excellent amplitude and phase characteristics. The integration technology has the characteristics of lightweight, miniaturization, high integration and low manufacturing cost. It can be widely used in miniaturized phased array antennas. </div>
基金Project supported by the National Natural Science Foundation of China (No.60034010)
文摘The difference discrete system of Euler-beam with arbitrary supports was constructed by using the two order central difference formulas. This system is equivalent to the spring-mass-rigidrod model. By using the theory of oscillatory matrix, the signoscillatory property of stiffness matrices of this system was proved, and the necessary and sufficient condition for the system to be positive was obtained completely.
文摘We present the application of differential quadrature（DQ） method for the buckling analysis of nanobeams with exponentially varying stiffness based on four different beam theories of Euler-Bernoulli, Timoshenko, Reddy, and Levison.The formulation is based on the nonlocal elasticity theory of Eringen. New results are presented for the guided and simply supported guided boundary conditions. Numerical results are obtained to investigate the effects of the nonlocal parameter,length-to-height ratio, boundary condition, and nonuniform parameter on the critical buckling load parameter. It is observed that the critical buckling load decreases with increase in the nonlocal parameter while the critical buckling load parameter increases with increase in the length-to-height ratio.
文摘With the diversification of manufacture methods, joining the same materials with different states becomes indispensable in practical application. In present work, 6061 aluminum alloys with different states were welded by laser beam welding （LBW）. The microstructures of welded joint, before and after heat treating, were investigated. The mechanical properties, such as the tensile properties and microhardness , were tested. And the fracture characteristic was observed by means of scanning electron microscope （SEM）. The results show that the 6061 aluminum alloys have superior weldability and the microstructures are different significantly in different states. Besides, the grain boundaries of the joint microstructures become unclear after the heat treating. The strength and the elongations of welded joints could reach to those of the base metal. The tensile fracture occurs in the fusion zone and near 6061-0 alloy. And the fracture presents ductile rupture. Therefore, the LBW is an effective method for 6061 aluminum alloy.
文摘A bending beam,subjected to state of plane stress,was chosen to investigate.The determination of the neutral surface of the structure was made,and the calculating formulas of neutral axis,normal stress,shear stress and displacement were derived.It is concluded that, for the elastic bending beam with different tension-compression modulus in the condition of complex stress, the position of the neutral axis is not related with the shear stress, and the analytical solution can be derived by normal stress used as a criterion, improving the multiple cyclic method which determines the position of neutral point by the principal stress. Meanwhile, a comparison is made between the results of the analytical solution and those calculated from the classic mechanics theory, assuming the tension modulus is equal to the compression modulus, and those from the finite element method (FEM) numerical solution. The comparison shows that the analytical solution considers well the effects caused by the condition of different tension and compression modulus. Finally, a calculation correction of the structure with different modulus is proposed to optimize the structure.
基金Supported by the International Thermonuclear Experimental Reactor Project of China under Grant No 2013GB114003the National Natural Science Foundation of China under Grant No 11275135
文摘Fusion power output is proportional not only to the fuel particle number densities participating in reaction but also to the fusion reaction rate coefficient （or reactivity）, which is dependent on reactant velocity distribution functions. They are usuMly assumed to be dual Maxwellian distribution functions with the same temperature for thermal nuclear fusion circumstances. However, if high power neutral beam injection and minority ion species ICRF plasma heating, or multi-pinched plasma beam head-on collision, in a converging region are required and investigated in future large scale fusion reactors, then the fractions of the injected energetic fast ion tail resulting from ionization or charge exchange will be large enough and their contribution to the non-Maxwellian distribution functions is not negligible, hence to the fusion reaction rate coefficient or calculation of fusion power. In such cases, beam-target, and beam-beam reaction enhancement effect contributions should play very important roles. In this paper, several useful formulae to calculate the fusion reaction rate coefticient for different beam and target combination scenarios are derived in detail
基金Project supported by National Natural Science Foundation of China
文摘Here some steady-state experiments on oxidation of CO on Pd were performed on a molecular beam apparatus. It is found that the characteristics of the rate of CO_2 formation r versus substrate temperature T are dependent on the ratio P=P_(CO)/P_(O2) in the mixed beam. These characteristics are related to the complicated interactions of co-adsorbed CO and O particles on Pd surface.
