The microstructure evolution and properties of an Al-Zn-Mg-Cu alloy were investigated under different non-linear cooling processes from the solution temperature, combined with in-situ electrical resistivity measuremen...The microstructure evolution and properties of an Al-Zn-Mg-Cu alloy were investigated under different non-linear cooling processes from the solution temperature, combined with in-situ electrical resistivity measurements, selected area diffraction patterns （SADPs）, transmission electron microscopy （TEM）, and tensile tests. The relative resistivity was calculated to characterize the phase transformation of the experimental alloy during different cooling processes. The results show that at high temperatures, the microstructure evolutions change from the directional diffusion of Zn and Mg atoms to the precipitation of S phase, depending on the cooling rate. At medium temperatures, q phase nucleates on A13Zr dispersoids and grain boundaries under fast cooling conditions, while S phase precipitates under the slow cooling conditions. The strength and ductility of the aged alloy suffer a significant deterioration due to the heterogeneous precipitation in medium temperature range. At low temperatures, homogeneously nucleated GP zone, η′ and η phases precipitate.展开更多
In this paper, based on the Lame function and Jacobi emptic function, the perturbation method is appliedto some nonlinear evolution equations to derive their multi-order solutions.
This paper introduces a robust global nonlinear optimizer—differential evolution(DE),which is a simple evolution algorithm to search for an optimal transformation that makes the best alignment of two sets of feature ...This paper introduces a robust global nonlinear optimizer—differential evolution(DE),which is a simple evolution algorithm to search for an optimal transformation that makes the best alignment of two sets of feature points.To map the problem of matching into the framework of DE,the objective function is proportional to the registration error which is measured by Hausdorff distance,while the parameters of transformation are encoded in floating-point as the functional variables.Three termination criteria are proposed for DE.A simulation of 2-dimensional point sets and a similarity transformation are presented to compare the robustness and convergence properties of DE with genetic algorithm’s (GA).And the registration of an object and its contour model have been demonstrated by using of DE to natural images.展开更多
We give the generalized definitions of variable separable solutions to nonlinear evolution equations, and characterize the relation between the functional separable solution and the derivative-dependent functional sep...We give the generalized definitions of variable separable solutions to nonlinear evolution equations, and characterize the relation between the functional separable solution and the derivative-dependent functional separable solution. The new definitions can unify various kinds of variable separable solutions appearing in references. As application, we classify the generalized nonlinear diffusion equations that admit special functional separable solutions and obtain some exact solutions to the resulting equations.展开更多
To seek new infinite sequence soliton-like exact solutions to nonlinear evolution equations （NEE（s））, by developing two characteristics of construction and mechanization on auxiliary equation method, the second ki...To seek new infinite sequence soliton-like exact solutions to nonlinear evolution equations （NEE（s））, by developing two characteristics of construction and mechanization on auxiliary equation method, the second kind of elliptie equation is highly studied and new type solutions and Backlund transformation are obtained. Then （2＋ l ）-dimensional breaking soliton equation is chosen as an example and its infinite sequence soliton-like exact solutions are constructed with the help of symbolic computation system Mathematica, which include infinite sequence smooth soliton-like solutions of Jacobi elliptic type, infinite sequence compact soliton solutions of Jacobi elliptic type and infinite sequence peak soliton solutions of exponential function type and triangular function type.展开更多
In this letter, by means of the Lax pair, Darboux transformation, and variable separation approach, a new exact solution of a sixth-order (1+ 1)-dimensional nonlinear evolution equation, which includes some arbitrary ...In this letter, by means of the Lax pair, Darboux transformation, and variable separation approach, a new exact solution of a sixth-order (1+ 1)-dimensional nonlinear evolution equation, which includes some arbitrary functions,is obtained. Abundant new localized excitations can be found by selecting appropriate functions and they are illustrated both analytically and graphically.展开更多
By means of the variable separation method, new exact solutions of some （1 ＋ 1）-dimensionaJ nonlinear evolution equations are obtained. Abundant localized excitations can be found by selecting corresponding arbitra...By means of the variable separation method, new exact solutions of some （1 ＋ 1）-dimensionaJ nonlinear evolution equations are obtained. Abundant localized excitations can be found by selecting corresponding arbitrary functions appropriately. Namely, the new soliton-like localized excitations and instanton-like localized excitations are presented.展开更多
Sensing structure of grid strip capacitors can be used in the design of capacitive micro-electromechanical system （MEMS） resonators, accelerometers etc. A grid strip structure consists of nonentirely overlap plates ...Sensing structure of grid strip capacitors can be used in the design of capacitive micro-electromechanical system （MEMS） resonators, accelerometers etc. A grid strip structure consists of nonentirely overlap plates so that the capacitor fringe effect cannot be neglected in the design. Electricmagnetic Finite Element Method （FEM） software ANSOFF-Maxwell is employed to analyze the fringe effect of a grid strip capacitor. The analysis includes capacitance changes with change of overlap length, overlap width, plate thickness, grid strip density etc. The results show that fringe effect leads to non-linear change of grid strip capacitance with the change of overlap length and width, that the capacitance increases with the increase of grid strip width and plate thickness, and that sensitivity can be improved through the increase of grid strip density in the condition of identical total overlap area, but linearity is reduced.展开更多
By using the variable separation approach, which is based on the corresponding Backlund transformation, new exact solutions of a （1＋1）-dimensional nonlinear evolution equation are obtained. Abundant new soliton mot...By using the variable separation approach, which is based on the corresponding Backlund transformation, new exact solutions of a （1＋1）-dimensional nonlinear evolution equation are obtained. Abundant new soliton motions of the potential field can be found by selecting appropriate functions.展开更多
This paper applies the exp-function method, which was originally proposed to find new exact travelling wave solutions of nonlinear evolution equations, to the Riccati equation, and some exact solutions of this equatio...This paper applies the exp-function method, which was originally proposed to find new exact travelling wave solutions of nonlinear evolution equations, to the Riccati equation, and some exact solutions of this equation are obtained. Based on the Riccati equation and its exact solutions, we find new and more general variable separation solutions with two arbitrary functions of （1＋1）-dimensional coupled integrable dispersionless system. As some special examples, some new solutions can degenerate into variable separation solutions reported in open literatures. By choosing suitably two independent variables p（x） and q（t） in our solutions, the annihilation phenomena of the fiat-basin soliton, arch-basin soliton, and fiat-top soliton are discussed.展开更多
We have set up a new reduced model Hamiltonian for the polariton system, in which the nonlinear interaction contains the rotating term k l （ a ＋ b ＋ ab＋） and the attractive two-mode squeezed coupling - k2 （ a ...We have set up a new reduced model Hamiltonian for the polariton system, in which the nonlinear interaction contains the rotating term k l （ a ＋ b ＋ ab＋） and the attractive two-mode squeezed coupling - k2 （ a ＋ b＋ ＋ ab ） . The dynamical evolution of this system has been solved and the nonclassical features relevant to the second-order and high-order squeezing have been obtained in an analytical form. For the first time, in contrast to the existing result, we have confirmed for the phonon field that the attractive two-mode squeezed interaction will not only result in the second-order and high-order squeezing in X-component with the time evolution, but also in time average. Furthermore, the phenomena of collapse and revival of inversion will occur as well in the time evolution of the average number of photon and phonon, as also in the second-order and high-order squeezing of photon field, particularly, in the high-order squeezing of phonon field.展开更多
Based on characteristic functions of variants, we developed an unconventional phase field modeling for investigating domains formation and evolution in tetragonal ferroelectrics. In order to develop this computational...Based on characteristic functions of variants, we developed an unconventional phase field modeling for investigating domains formation and evolution in tetragonal ferroelectrics. In order to develop this computational approach, we constructed the anisotropy energy of tetragonal variants, which is used instead of Landau-Devonshire potential in the conventional phase field method, resulting in that much fewer parameters are needed for simulations. This approach is advantageous in simulations of emerging ferroelectric materials. We employ it to study the formation and evolution of domains in tetragonal barium titanate single crystal, as well as the nonlinear behaviors under cyclical stress and electric field loading. A multi-rank laminated ferroelectric domain pattern, 90° domain switching accompanied by polarization rotation, and 180° domain switching accompanied by move of domain wall are predicted. It is found that the speed of 90° domain switching is slower than that of 180° domain switching, due to both polarization and transformation strain changed in 90° domain switching. It also suggests that large strain actuation can be generated in single crystal ferroelectrics via combined electromechanical loading inducing 90° domain switching. The good agreement between simulation results and experimental measurements is observed.展开更多
基金Project(2014GK2013)supported by the Science and Technology Program of Hunan Province,China
文摘The microstructure evolution and properties of an Al-Zn-Mg-Cu alloy were investigated under different non-linear cooling processes from the solution temperature, combined with in-situ electrical resistivity measurements, selected area diffraction patterns （SADPs）, transmission electron microscopy （TEM）, and tensile tests. The relative resistivity was calculated to characterize the phase transformation of the experimental alloy during different cooling processes. The results show that at high temperatures, the microstructure evolutions change from the directional diffusion of Zn and Mg atoms to the precipitation of S phase, depending on the cooling rate. At medium temperatures, q phase nucleates on A13Zr dispersoids and grain boundaries under fast cooling conditions, while S phase precipitates under the slow cooling conditions. The strength and ductility of the aged alloy suffer a significant deterioration due to the heterogeneous precipitation in medium temperature range. At low temperatures, homogeneously nucleated GP zone, η′ and η phases precipitate.
文摘In this paper, based on the Lame function and Jacobi emptic function, the perturbation method is appliedto some nonlinear evolution equations to derive their multi-order solutions.
文摘This paper introduces a robust global nonlinear optimizer—differential evolution(DE),which is a simple evolution algorithm to search for an optimal transformation that makes the best alignment of two sets of feature points.To map the problem of matching into the framework of DE,the objective function is proportional to the registration error which is measured by Hausdorff distance,while the parameters of transformation are encoded in floating-point as the functional variables.Three termination criteria are proposed for DE.A simulation of 2-dimensional point sets and a similarity transformation are presented to compare the robustness and convergence properties of DE with genetic algorithm’s (GA).And the registration of an object and its contour model have been demonstrated by using of DE to natural images.
基金The project supported by National Natural Science Foundation of China under Grant Nos.10447007 and 10671156the Natural Science Foundation of Shaanxi Province of China under Grant No.2005A13
文摘We give the generalized definitions of variable separable solutions to nonlinear evolution equations, and characterize the relation between the functional separable solution and the derivative-dependent functional separable solution. The new definitions can unify various kinds of variable separable solutions appearing in references. As application, we classify the generalized nonlinear diffusion equations that admit special functional separable solutions and obtain some exact solutions to the resulting equations.
基金Supported by the Natural Natural Science Foundation of China under Grant No.10461006the Science Research Foundation of Institution of Higher Education of Inner Mongolia Autonomous Region,China under Grant No.NJZZ07031the Natural Science Foundation of Inner Mongolia Autonomous Region,China under Grant No.2010MS0111
文摘To seek new infinite sequence soliton-like exact solutions to nonlinear evolution equations （NEE（s））, by developing two characteristics of construction and mechanization on auxiliary equation method, the second kind of elliptie equation is highly studied and new type solutions and Backlund transformation are obtained. Then （2＋ l ）-dimensional breaking soliton equation is chosen as an example and its infinite sequence soliton-like exact solutions are constructed with the help of symbolic computation system Mathematica, which include infinite sequence smooth soliton-like solutions of Jacobi elliptic type, infinite sequence compact soliton solutions of Jacobi elliptic type and infinite sequence peak soliton solutions of exponential function type and triangular function type.
文摘In this letter, by means of the Lax pair, Darboux transformation, and variable separation approach, a new exact solution of a sixth-order (1+ 1)-dimensional nonlinear evolution equation, which includes some arbitrary functions,is obtained. Abundant new localized excitations can be found by selecting appropriate functions and they are illustrated both analytically and graphically.
文摘By means of the variable separation method, new exact solutions of some （1 ＋ 1）-dimensionaJ nonlinear evolution equations are obtained. Abundant localized excitations can be found by selecting corresponding arbitrary functions appropriately. Namely, the new soliton-like localized excitations and instanton-like localized excitations are presented.
基金Supported by the National Natural Science Foundation of China （ No. 60903195 ） and the Key Technological Problems Tackling Project of Wuhan （No. 200750499172）.
文摘Sensing structure of grid strip capacitors can be used in the design of capacitive micro-electromechanical system （MEMS） resonators, accelerometers etc. A grid strip structure consists of nonentirely overlap plates so that the capacitor fringe effect cannot be neglected in the design. Electricmagnetic Finite Element Method （FEM） software ANSOFF-Maxwell is employed to analyze the fringe effect of a grid strip capacitor. The analysis includes capacitance changes with change of overlap length, overlap width, plate thickness, grid strip density etc. The results show that fringe effect leads to non-linear change of grid strip capacitance with the change of overlap length and width, that the capacitance increases with the increase of grid strip width and plate thickness, and that sensitivity can be improved through the increase of grid strip density in the condition of identical total overlap area, but linearity is reduced.
基金The project supported by National Natural Science Foundation of China under Grant No. 10501040
文摘By using the variable separation approach, which is based on the corresponding Backlund transformation, new exact solutions of a （1＋1）-dimensional nonlinear evolution equation are obtained. Abundant new soliton motions of the potential field can be found by selecting appropriate functions.
基金Supported by the National Natural Science Foundation of China under Grant No.11005092the Program for Innovative Research Team of Young Teachers under Grant No.2009RC01Scientific Research,and Developed Fund under Grant No.2009FK42 of Zhejiang A&F University
文摘This paper applies the exp-function method, which was originally proposed to find new exact travelling wave solutions of nonlinear evolution equations, to the Riccati equation, and some exact solutions of this equation are obtained. Based on the Riccati equation and its exact solutions, we find new and more general variable separation solutions with two arbitrary functions of （1＋1）-dimensional coupled integrable dispersionless system. As some special examples, some new solutions can degenerate into variable separation solutions reported in open literatures. By choosing suitably two independent variables p（x） and q（t） in our solutions, the annihilation phenomena of the fiat-basin soliton, arch-basin soliton, and fiat-top soliton are discussed.
基金Supported by the Foundation of Scientific Research Education and Innovations under Grant No.11609506,Jinan University
文摘We have set up a new reduced model Hamiltonian for the polariton system, in which the nonlinear interaction contains the rotating term k l （ a ＋ b ＋ ab＋） and the attractive two-mode squeezed coupling - k2 （ a ＋ b＋ ＋ ab ） . The dynamical evolution of this system has been solved and the nonclassical features relevant to the second-order and high-order squeezing have been obtained in an analytical form. For the first time, in contrast to the existing result, we have confirmed for the phonon field that the attractive two-mode squeezed interaction will not only result in the second-order and high-order squeezing in X-component with the time evolution, but also in time average. Furthermore, the phenomena of collapse and revival of inversion will occur as well in the time evolution of the average number of photon and phonon, as also in the second-order and high-order squeezing of photon field, particularly, in the high-order squeezing of phonon field.
基金supported by the National Natural Science Foundation of China(Grant Nos.11572276&11502225)Hunan Provincial Natural Science Foundation of China(Grant No.14JJ6015)
文摘Based on characteristic functions of variants, we developed an unconventional phase field modeling for investigating domains formation and evolution in tetragonal ferroelectrics. In order to develop this computational approach, we constructed the anisotropy energy of tetragonal variants, which is used instead of Landau-Devonshire potential in the conventional phase field method, resulting in that much fewer parameters are needed for simulations. This approach is advantageous in simulations of emerging ferroelectric materials. We employ it to study the formation and evolution of domains in tetragonal barium titanate single crystal, as well as the nonlinear behaviors under cyclical stress and electric field loading. A multi-rank laminated ferroelectric domain pattern, 90° domain switching accompanied by polarization rotation, and 180° domain switching accompanied by move of domain wall are predicted. It is found that the speed of 90° domain switching is slower than that of 180° domain switching, due to both polarization and transformation strain changed in 90° domain switching. It also suggests that large strain actuation can be generated in single crystal ferroelectrics via combined electromechanical loading inducing 90° domain switching. The good agreement between simulation results and experimental measurements is observed.
