In this paper, based on the invariant subspace theory and adjoint operator concept of linear operator, a new matrix representation method is proposed to calculate the normal forms of n order general nonlinear dyna...In this paper, based on the invariant subspace theory and adjoint operator concept of linear operator, a new matrix representation method is proposed to calculate the normal forms of n order general nonlinear dynamic systems. In the method, there is no need to determine the structure of the class of normal forms in advance. Because the subspace is not related to the dimensions of the system and the order of the normal forms directly, it is determined only by a given vector field. So the normal forms with high orders and dimensions can be calculated by the method without difficulties. In this paper, is used the method for selecting the minimal subspace and solving homological equations in the subspace, the examples show that the method is very effective.展开更多
Based on the Reynolds equation with Reynolds boundary conditions, the Castelli method was employed to solve the Reynolds equation for oil lubrication upon bearings. By doing so, a profile of nonlinear oil film force o...Based on the Reynolds equation with Reynolds boundary conditions, the Castelli method was employed to solve the Reynolds equation for oil lubrication upon bearings. By doing so, a profile of nonlinear oil film force of single-pad journal bearings is established. According to the structure of combination journal bearings, nonlinear oil film force of combination journal bearing is obtained by retrieval, interpolation and assembly techniques. As for symmetrical flexible Jeffcott rotor systems supported by combination journal bearings, the nonlinear motions of the center of the rotor are calculated by the self-adaptive Runge-Kutta method and Poincar6 mapping with different rotational speeds. The numerical results show that the system performance is slightly better when the pivot ratio changes from 0.5 to 0.6, and reveals nonlinear phenomena of periodic, period-doubing, quasi-periodic motion, etc.展开更多
The simplest normal form of resonant double Hopf bifurcation was studied based on Lie operator. The coefficients of the simplest normal forms of resonant double Hopf bifurcation and the nonlinear transformations in te...The simplest normal form of resonant double Hopf bifurcation was studied based on Lie operator. The coefficients of the simplest normal forms of resonant double Hopf bifurcation and the nonlinear transformations in terms of the original system coefficients were given explicitly. The nonlinear transformations were used for reducing the lower- and higher-order normal forms, and the rank of system matrix was used to determine the coefficient of normal form which could be reduced. These make the gained normal form simpler than the traditional one. A general program was compiled with Mathematica. This program can compute the simplest normal form of resonant double Hopf bifurcation and the non-resonant form up to the 7th order.展开更多
A discrete spectral problem is discussed, and a hierarchy of integrable nonlinear lattice equations related to this spectral problem is devised. The new integrable symplectic map and finite-dimensional integrable syst...A discrete spectral problem is discussed, and a hierarchy of integrable nonlinear lattice equations related to this spectral problem is devised. The new integrable symplectic map and finite-dimensional integrable systems are given by nonlinearization method. The binary Bargmann constraint gives rise to a B?cklund transformation for the resulting integrable lattice equations.展开更多
By combining the wavelet decomposition with kernel method, a practical approach of universal multiscale wavelet kernels constructed in reproducing kernel Hilbert space (RKHS) is discussed, and an identification sche...By combining the wavelet decomposition with kernel method, a practical approach of universal multiscale wavelet kernels constructed in reproducing kernel Hilbert space (RKHS) is discussed, and an identification scheme using wavelet support vector machines (WSVM) estimator is proposed for nordinear dynamic systems. The good approximating properties of wavelet kernel function enhance the generalization ability of the proposed method, and the comparison of some numerical experimental results between the novel approach and some existing methods is encouraging.展开更多
A new type of shear viscous damper for rotating machinery is designed. The new damper with good stability and reliability can inhibit all kinds of frequency multiplication vibration caused by misalignment in the condi...A new type of shear viscous damper for rotating machinery is designed. The new damper with good stability and reliability can inhibit all kinds of frequency multiplication vibration caused by misalignment in the condition of nonstop machine. It analyzes and discusses the use of the shear viscous damper for misalignment vibration response inhibition with a finite element method, and experi ments are extensively carried out with a laboratory test rig. Both the simulation and experimental re suits basically agree well in that, the damper can effectively control the misalignment vibration of the rotor system and improves the stability of the plitude of one time running speed component bration has been basically eliminated. entire rotor system. Experimental results show the am decreases by 30% , and the two time running speed vibration has been basically eliminated.展开更多
The active control of rotor vibration was studied while shape memory alloy (SMA) spring component was chosen as bearing of rotor system. The vibration of rotor system was controlled by the phase transformation of SM...The active control of rotor vibration was studied while shape memory alloy (SMA) spring component was chosen as bearing of rotor system. The vibration of rotor system was controlled by the phase transformation of SMA with electric heating method. The SMA spring component has nonlinear coupling problem of thermal stress and thermal elasticity,because thermal constants α,β and elasticity constants λ,G vary with temperature when temperature changes sharply. Because δ,ε were both small parameters, their square items could be ignored and approximate results were obtained by perturbation. The characters of α,β,λ,G changing with temperature were analyzed. Results show that the character of thermal diffusivity α changes with temperature, which cannot influence U,Ψ,So the nonlinearity of α can be ignored; the character of β changes with temperature, which cannot influence U, but influences Ψ at high temperature; the character of λ,G change with temperature, which cannot influence Ψ, but influences U with U(01) ε. The more λ,G, the more their influence on U; the nonlinearity of βTρcvεkk influences U and Ψ, which must be calculated.展开更多
The limit of rotational energy transfer in atom-diatomic systems due to inelastic collision was investigated over the wide range of collision energy, reduced mass and potential parameters of F2-He system. The IICS (i...The limit of rotational energy transfer in atom-diatomic systems due to inelastic collision was investigated over the wide range of collision energy, reduced mass and potential parameters of F2-He system. The IICS (integral inelastic cross-sections) is obtained by the IOSAM (infinite order sudden approximation method) and predicted by PG (power-gap) law in the variation of cross-sections. The investigation provided that the classical limit of angular momentum transfer is given by hard ellipsoid potential is meaningful even the cross-sections computed on the real potential, provided the classical turning point on the surface of soft potential is assumed as hard potential surface.展开更多
Based on the short-bearing model, the stability of a rigid Jeffcott rotor system is studied in a relatively wide parameter range by using Poincaré maps and the numerical integration method. The results of the cal...Based on the short-bearing model, the stability of a rigid Jeffcott rotor system is studied in a relatively wide parameter range by using Poincaré maps and the numerical integration method. The results of the calculation show that the period doubling bifurcation, quasi-periodic and chaotic motions may occur. In some typical parameter regions, the bifurcation diagrams, phase portrait, Poincaré maps and the frequency spectrums of the system are acquired with the numerical integration method. They demonstrate some motion state of the system. The fractal dimension concept is used to determine whether the system is in a state of chaotic motion. The analysis result of this paper provides the theoretical basis for qualitatively controlling the stable operating states of the rotors.展开更多
Nonlinear forces and moments caused by ball bearing were calculated based on relationship of displacement and deflection and quasi-dynamic model of bearing.Five-DOF dynamic equations of rotor supported by ball bearing...Nonlinear forces and moments caused by ball bearing were calculated based on relationship of displacement and deflection and quasi-dynamic model of bearing.Five-DOF dynamic equations of rotor supported by ball bearings were estimated.The Newmark-β method and Newton-Laphson method were used to solve the equations.The dynamic characteristics of rotor system were studied through the time response,the phase portrait,the Poincar?maps and the bifurcation diagrams.The results show that the system goes through the quasi-periodic bifurcation route to chaos as rotate speed increases and there are several quasi-periodic regions and chaos regions.The amplitude decreases and the dynamic behaviors change as the axial load of ball bearing increases;the initial contact angle of ball bearing affects dynamic behaviors of the system obviously.The system can avoid non-periodic vibration by choosing structural parameters and operating parameters reasonably.展开更多
As a typical implementation of the probability hypothesis density(PHD) filter, sequential Monte Carlo PHD(SMC-PHD) is widely employed in highly nonlinear systems. However, the particle impoverishment problem introduce...As a typical implementation of the probability hypothesis density(PHD) filter, sequential Monte Carlo PHD(SMC-PHD) is widely employed in highly nonlinear systems. However, the particle impoverishment problem introduced by the resampling step, together with the high computational burden problem, may lead to performance degradation and restrain the use of SMC-PHD filter in practical applications. In this work, a novel SMC-PHD filter based on particle compensation is proposed to solve above problems. Firstly, according to a comprehensive analysis on the particle impoverishment problem, a new particle generating mechanism is developed to compensate the particles. Then, all the particles are integrated into the SMC-PHD filter framework. Simulation results demonstrate that, in comparison with the SMC-PHD filter, proposed PC-SMC-PHD filter is capable of overcoming the particle impoverishment problem, as well as improving the processing rate for a certain tracking accuracy in different scenarios.展开更多
A 2D square lattice is studied. By using the continuum approximation, we set up the differential equations of motion for an arbitrary particle in the square lattice which subjects to an external periodic substrate pot...A 2D square lattice is studied. By using the continuum approximation, we set up the differential equations of motion for an arbitrary particle in the square lattice which subjects to an external periodic substrate potential. The exact solitary waves of the system are found for special cases. We conclude that the adhesive force f and the angle between propagation directions of upper and lower layers can affect these waves.展开更多
The adsorption state and catalytic properties of pepsin and acidic protease from microorganisms Asp. awamori and Asp. oryzae were studied in solid phase system (in presence of sorsilen, DEAE- and CM-cellulose). Acco...The adsorption state and catalytic properties of pepsin and acidic protease from microorganisms Asp. awamori and Asp. oryzae were studied in solid phase system (in presence of sorsilen, DEAE- and CM-cellulose). According to the results, adsorption capacity and catalytic activity of enzymes depend on the physical nature of surface groups of the solid phase. Changing the stability of enzymes in the system with solid phase is observed even the adsorption bond is less stable (in the case of DEAE- and CM-cellulose in acidic media). Injection to the medium ethanol, surfactants, sodium chloride and changing the temperature of the incubation medium could prevent the negative effects of the solid phases. When sorsilen is used as solid phase, pepsin and acidic protease from Asp. awamori suffer from high surface inactivation. Various surfactants influence adsorption state of enzymes differently. Non-ionic surfactants (Triton X-100) prevent adsorption and restore catalytic properties of enzymes.展开更多
A 3-dimensional Lie algebra sμ(3) is obtained with the help of the known Lie algebra. Based on the sμ(3), a new discrete 3 × 3 matrix spectral problem with three potentials is constructed. In virtue of disc...A 3-dimensional Lie algebra sμ(3) is obtained with the help of the known Lie algebra. Based on the sμ(3), a new discrete 3 × 3 matrix spectral problem with three potentials is constructed. In virtue of discrete zero curvature equations, a new matrix Lax representation for the hierarchy of the discrete lattice soliton equations is acquired. It is shown that the hierarchy possesses a Hamiltonian operator and a hereditary recursion operator, which implies that there exist infinitely many common commuting symmetries and infinitely many common commuting conserved functionals.展开更多
Lie group theoretical method and the equation of the Jacobi elliptic function are used to study the three wave system that couples two fundamental frequency (FF) and a single second harmonic (SH) one by competing...Lie group theoretical method and the equation of the Jacobi elliptic function are used to study the three wave system that couples two fundamental frequency (FF) and a single second harmonic (SH) one by competing X^(2) (quadratic) and X^(3) (cubic) nonlinearities and birefringence. This system shares some of the nice properties of soliton system. On the phase-locked condition; we obtain large families of analytical solutions as the soliton, kink and periodic solutions of this system.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
The identification of Wiener systems has been an active research topic for years. A Wiener system is a series connection of a linear dynamic system followed by a static nonlinearity. The difficulty in obtaining a repr...The identification of Wiener systems has been an active research topic for years. A Wiener system is a series connection of a linear dynamic system followed by a static nonlinearity. The difficulty in obtaining a representation of the Wiener model is the need to estimate the nonlinear function from the input and output data, without the intermediate signal availability. This paper presents a methodology for the nonlinear system identification of a Wiener type model, using methods for subspaces and polynomials of Chebyshev. The subspace methods used are MOESP (multivariable output-error state space) and N4SID (numerical algorithms for subspace state space system identification). A simulated example is presented to compare the performance of these algorithms.展开更多
In this paper, analytical and numerical studies are carried out on the full annular rub motions of a nonlinear Jeffcott rotor. Transition sets of the synchronous full annular rub are given with the help of averaging m...In this paper, analytical and numerical studies are carried out on the full annular rub motions of a nonlinear Jeffcott rotor. Transition sets of the synchronous full annular rub are given with the help of averaging method and constraint bifurcation theory to discuss the effects of system parameters on jump phenomena. Routh-Hurwitz criteria are employed to analyze the stability of synchronous full annular rub solution and determine the boundaries of static and Hopf bifurcations. Finally, the response and onset condition of reverse dry whip are investigated numerically, and at the same time, the influences of rotor parameters and rotation speed on the characteristics of the rotor response are investigated.展开更多
For the nonlinearity distortion problem of Mach-Zehnder modulator(MZM)applied in the on-board microwave photonics system,the situation for two input radio frequency(RF)signals with different frequencies and phases is ...For the nonlinearity distortion problem of Mach-Zehnder modulator(MZM)applied in the on-board microwave photonics system,the situation for two input radio frequency(RF)signals with different frequencies and phases is discussed,and an exact analytical solution is derived with the method of expanding Bessel series and Graf addition theory.According to the analytical expression,the nonlinearity characteristics of the modulator can be precisely predicted,and the system performance can be optimized.The correctness of the analytical solution is approved by simulation results.Analytical results indicate that the nonlinearity distortion is suppressed as the decrease of modulation index,the increase of direct current bias phase shift and phase difference between two input RF signals.When the phase difference equals zero orπand the direct current bias phase shift isπ/2,there are only odd-order distortion terms.When the phase difference equals zero orπand the direct current bias phase shift isπ,there are only even-order distortion terms.展开更多
文摘In this paper, based on the invariant subspace theory and adjoint operator concept of linear operator, a new matrix representation method is proposed to calculate the normal forms of n order general nonlinear dynamic systems. In the method, there is no need to determine the structure of the class of normal forms in advance. Because the subspace is not related to the dimensions of the system and the order of the normal forms directly, it is determined only by a given vector field. So the normal forms with high orders and dimensions can be calculated by the method without difficulties. In this paper, is used the method for selecting the minimal subspace and solving homological equations in the subspace, the examples show that the method is very effective.
基金Project(2007CB707706) supported by the National Basic Research Program of China Projects(51075327,10972179) supported by the National Natural Science Foundation of China+2 种基金 Project(SKLMT-KFKT-201011) supported by Open Foundation of State Key Laboratory of Mechanical Transmission,China Projects(2009JQ7006,2007E203) supported by the Natural Science Foundation of Shaanxi Province of China Projects(09JK680,07JK340) supported by the Natural Science Foundation of Department of Education of Shaanxi Province of China
文摘Based on the Reynolds equation with Reynolds boundary conditions, the Castelli method was employed to solve the Reynolds equation for oil lubrication upon bearings. By doing so, a profile of nonlinear oil film force of single-pad journal bearings is established. According to the structure of combination journal bearings, nonlinear oil film force of combination journal bearing is obtained by retrieval, interpolation and assembly techniques. As for symmetrical flexible Jeffcott rotor systems supported by combination journal bearings, the nonlinear motions of the center of the rotor are calculated by the self-adaptive Runge-Kutta method and Poincar6 mapping with different rotational speeds. The numerical results show that the system performance is slightly better when the pivot ratio changes from 0.5 to 0.6, and reveals nonlinear phenomena of periodic, period-doubing, quasi-periodic motion, etc.
基金Supported by National Natural Science Foundation of China(No. 10372068).
文摘The simplest normal form of resonant double Hopf bifurcation was studied based on Lie operator. The coefficients of the simplest normal forms of resonant double Hopf bifurcation and the nonlinear transformations in terms of the original system coefficients were given explicitly. The nonlinear transformations were used for reducing the lower- and higher-order normal forms, and the rank of system matrix was used to determine the coefficient of normal form which could be reduced. These make the gained normal form simpler than the traditional one. A general program was compiled with Mathematica. This program can compute the simplest normal form of resonant double Hopf bifurcation and the non-resonant form up to the 7th order.
文摘A discrete spectral problem is discussed, and a hierarchy of integrable nonlinear lattice equations related to this spectral problem is devised. The new integrable symplectic map and finite-dimensional integrable systems are given by nonlinearization method. The binary Bargmann constraint gives rise to a B?cklund transformation for the resulting integrable lattice equations.
基金the National 973 Key Fundamental Research Project of China (Grant No.2002CB312200)
文摘By combining the wavelet decomposition with kernel method, a practical approach of universal multiscale wavelet kernels constructed in reproducing kernel Hilbert space (RKHS) is discussed, and an identification scheme using wavelet support vector machines (WSVM) estimator is proposed for nordinear dynamic systems. The good approximating properties of wavelet kernel function enhance the generalization ability of the proposed method, and the comparison of some numerical experimental results between the novel approach and some existing methods is encouraging.
基金Supported by the National Basic Research Program of China(No.2012CB026000)the Joint Project Special Fund of Education Committee of Beijingthe Ph.D.Programs Foundation of Ministry of Education of China(No.20110010110009)
文摘A new type of shear viscous damper for rotating machinery is designed. The new damper with good stability and reliability can inhibit all kinds of frequency multiplication vibration caused by misalignment in the condition of nonstop machine. It analyzes and discusses the use of the shear viscous damper for misalignment vibration response inhibition with a finite element method, and experi ments are extensively carried out with a laboratory test rig. Both the simulation and experimental re suits basically agree well in that, the damper can effectively control the misalignment vibration of the rotor system and improves the stability of the plitude of one time running speed component bration has been basically eliminated. entire rotor system. Experimental results show the am decreases by 30% , and the two time running speed vibration has been basically eliminated.
文摘The active control of rotor vibration was studied while shape memory alloy (SMA) spring component was chosen as bearing of rotor system. The vibration of rotor system was controlled by the phase transformation of SMA with electric heating method. The SMA spring component has nonlinear coupling problem of thermal stress and thermal elasticity,because thermal constants α,β and elasticity constants λ,G vary with temperature when temperature changes sharply. Because δ,ε were both small parameters, their square items could be ignored and approximate results were obtained by perturbation. The characters of α,β,λ,G changing with temperature were analyzed. Results show that the character of thermal diffusivity α changes with temperature, which cannot influence U,Ψ,So the nonlinearity of α can be ignored; the character of β changes with temperature, which cannot influence U, but influences Ψ at high temperature; the character of λ,G change with temperature, which cannot influence Ψ, but influences U with U(01) ε. The more λ,G, the more their influence on U; the nonlinearity of βTρcvεkk influences U and Ψ, which must be calculated.
文摘The limit of rotational energy transfer in atom-diatomic systems due to inelastic collision was investigated over the wide range of collision energy, reduced mass and potential parameters of F2-He system. The IICS (integral inelastic cross-sections) is obtained by the IOSAM (infinite order sudden approximation method) and predicted by PG (power-gap) law in the variation of cross-sections. The investigation provided that the classical limit of angular momentum transfer is given by hard ellipsoid potential is meaningful even the cross-sections computed on the real potential, provided the classical turning point on the surface of soft potential is assumed as hard potential surface.
文摘Based on the short-bearing model, the stability of a rigid Jeffcott rotor system is studied in a relatively wide parameter range by using Poincaré maps and the numerical integration method. The results of the calculation show that the period doubling bifurcation, quasi-periodic and chaotic motions may occur. In some typical parameter regions, the bifurcation diagrams, phase portrait, Poincaré maps and the frequency spectrums of the system are acquired with the numerical integration method. They demonstrate some motion state of the system. The fractal dimension concept is used to determine whether the system is in a state of chaotic motion. The analysis result of this paper provides the theoretical basis for qualitatively controlling the stable operating states of the rotors.
基金Sponsored by the National Natural Science Foundation of China(Grant No. 50575054)
文摘Nonlinear forces and moments caused by ball bearing were calculated based on relationship of displacement and deflection and quasi-dynamic model of bearing.Five-DOF dynamic equations of rotor supported by ball bearings were estimated.The Newmark-β method and Newton-Laphson method were used to solve the equations.The dynamic characteristics of rotor system were studied through the time response,the phase portrait,the Poincar?maps and the bifurcation diagrams.The results show that the system goes through the quasi-periodic bifurcation route to chaos as rotate speed increases and there are several quasi-periodic regions and chaos regions.The amplitude decreases and the dynamic behaviors change as the axial load of ball bearing increases;the initial contact angle of ball bearing affects dynamic behaviors of the system obviously.The system can avoid non-periodic vibration by choosing structural parameters and operating parameters reasonably.
基金Projects(61671462,61471383,61671463,61304103)supported by the National Natural Science Foundation of ChinaProject(ZR2012FQ004)supported by the Natural Science Foundation of Shandong Province,China
文摘As a typical implementation of the probability hypothesis density(PHD) filter, sequential Monte Carlo PHD(SMC-PHD) is widely employed in highly nonlinear systems. However, the particle impoverishment problem introduced by the resampling step, together with the high computational burden problem, may lead to performance degradation and restrain the use of SMC-PHD filter in practical applications. In this work, a novel SMC-PHD filter based on particle compensation is proposed to solve above problems. Firstly, according to a comprehensive analysis on the particle impoverishment problem, a new particle generating mechanism is developed to compensate the particles. Then, all the particles are integrated into the SMC-PHD filter framework. Simulation results demonstrate that, in comparison with the SMC-PHD filter, proposed PC-SMC-PHD filter is capable of overcoming the particle impoverishment problem, as well as improving the processing rate for a certain tracking accuracy in different scenarios.
基金supported by National Natural Science Foundation of China under Grant No. 10575082the Natural Science Foundation of Gansu Province under Grant No. 3ZS061-A25-013the Natural Science Foundation of Northwest Normal University under Grant No. NWNU-KJCXGC-03-17
文摘A 2D square lattice is studied. By using the continuum approximation, we set up the differential equations of motion for an arbitrary particle in the square lattice which subjects to an external periodic substrate potential. The exact solitary waves of the system are found for special cases. We conclude that the adhesive force f and the angle between propagation directions of upper and lower layers can affect these waves.
文摘The adsorption state and catalytic properties of pepsin and acidic protease from microorganisms Asp. awamori and Asp. oryzae were studied in solid phase system (in presence of sorsilen, DEAE- and CM-cellulose). According to the results, adsorption capacity and catalytic activity of enzymes depend on the physical nature of surface groups of the solid phase. Changing the stability of enzymes in the system with solid phase is observed even the adsorption bond is less stable (in the case of DEAE- and CM-cellulose in acidic media). Injection to the medium ethanol, surfactants, sodium chloride and changing the temperature of the incubation medium could prevent the negative effects of the solid phases. When sorsilen is used as solid phase, pepsin and acidic protease from Asp. awamori suffer from high surface inactivation. Various surfactants influence adsorption state of enzymes differently. Non-ionic surfactants (Triton X-100) prevent adsorption and restore catalytic properties of enzymes.
基金Supported by the Science and Technology Plan project of the Educational Department of Shandong Province of China under Grant No. J09LA54the research project of "SUST Spring Bud" of Shandong university of science and technology of China under Grant No. 2009AZZ071
文摘A 3-dimensional Lie algebra sμ(3) is obtained with the help of the known Lie algebra. Based on the sμ(3), a new discrete 3 × 3 matrix spectral problem with three potentials is constructed. In virtue of discrete zero curvature equations, a new matrix Lax representation for the hierarchy of the discrete lattice soliton equations is acquired. It is shown that the hierarchy possesses a Hamiltonian operator and a hereditary recursion operator, which implies that there exist infinitely many common commuting symmetries and infinitely many common commuting conserved functionals.
基金Supported by the National Natural Science Foundation of China under Grant No.10875106
文摘Lie group theoretical method and the equation of the Jacobi elliptic function are used to study the three wave system that couples two fundamental frequency (FF) and a single second harmonic (SH) one by competing X^(2) (quadratic) and X^(3) (cubic) nonlinearities and birefringence. This system shares some of the nice properties of soliton system. On the phase-locked condition; we obtain large families of analytical solutions as the soliton, kink and periodic solutions of this system.
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.
文摘The identification of Wiener systems has been an active research topic for years. A Wiener system is a series connection of a linear dynamic system followed by a static nonlinearity. The difficulty in obtaining a representation of the Wiener model is the need to estimate the nonlinear function from the input and output data, without the intermediate signal availability. This paper presents a methodology for the nonlinear system identification of a Wiener type model, using methods for subspaces and polynomials of Chebyshev. The subspace methods used are MOESP (multivariable output-error state space) and N4SID (numerical algorithms for subspace state space system identification). A simulated example is presented to compare the performance of these algorithms.
基金supported by the National Natural Science Foundation of China (Grant No. 10632040)
文摘In this paper, analytical and numerical studies are carried out on the full annular rub motions of a nonlinear Jeffcott rotor. Transition sets of the synchronous full annular rub are given with the help of averaging method and constraint bifurcation theory to discuss the effects of system parameters on jump phenomena. Routh-Hurwitz criteria are employed to analyze the stability of synchronous full annular rub solution and determine the boundaries of static and Hopf bifurcations. Finally, the response and onset condition of reverse dry whip are investigated numerically, and at the same time, the influences of rotor parameters and rotation speed on the characteristics of the rotor response are investigated.
文摘For the nonlinearity distortion problem of Mach-Zehnder modulator(MZM)applied in the on-board microwave photonics system,the situation for two input radio frequency(RF)signals with different frequencies and phases is discussed,and an exact analytical solution is derived with the method of expanding Bessel series and Graf addition theory.According to the analytical expression,the nonlinearity characteristics of the modulator can be precisely predicted,and the system performance can be optimized.The correctness of the analytical solution is approved by simulation results.Analytical results indicate that the nonlinearity distortion is suppressed as the decrease of modulation index,the increase of direct current bias phase shift and phase difference between two input RF signals.When the phase difference equals zero orπand the direct current bias phase shift isπ/2,there are only odd-order distortion terms.When the phase difference equals zero orπand the direct current bias phase shift isπ,there are only even-order distortion terms.