In this paper, the conservation laws of generalized Birkhoff system in event space are studied by using the method of integrating factors. Firstly, the generalized Pfaff-Birkhoff principle and the generalized Birkhoff...In this paper, the conservation laws of generalized Birkhoff system in event space are studied by using the method of integrating factors. Firstly, the generalized Pfaff-Birkhoff principle and the generalized Birkhoff equations are established, and the definition of the integrating factors for the system is given. Secondly, based on the concept of integrating factors, the conservation theorems and their inverse for the generalized Birkhoff system in the event space are presented in detail, and the relation between the conservation laws and the integrating factors of the system is obtained and the generalized Killing equations for the determination of the integrating factors are given. Finally, an example is given to illustrate the application of the results.展开更多
A complete geometric nonlinear formulation for rigid-flexible coupling dynamics of a flexible beam undergoing large overall motion was proposed based on virtual work principle, in which all the high-order terms relate...A complete geometric nonlinear formulation for rigid-flexible coupling dynamics of a flexible beam undergoing large overall motion was proposed based on virtual work principle, in which all the high-order terms related to coupling deformation were included in dynamic equations. Simulation examples of the flexible beam with prescribed rotation and free rotation were investigated. Numerical results show that the use of the first-order approximation coupling (FOAC) model may lead to a significant error when the flexible beam experiences large deformation or large deformation velocity. However, the correct solutions can always be obtained by using the present complete model. The difference in essence between this model and the FOAC model is revealed. These coupling high-order terms, which are ignored in FOAC model, have a remarkable effect on the dynamic behavior of the flexible body. Therefore, these terms should be included for the rigid-flexible dynamic modeling and analysis of flexible body undergoing motions with high speed.展开更多
The controlling step and the extraction reaction rate equation of zinc extraction from Zn（II）-NH3 solution by using a newly synthesized organic compound, 2-acetyl-3-oxo-dithiobutyric acid-myristyl ester as the zinc ...The controlling step and the extraction reaction rate equation of zinc extraction from Zn（II）-NH3 solution by using a newly synthesized organic compound, 2-acetyl-3-oxo-dithiobutyric acid-myristyl ester as the zinc extractant, were clarified. The effects of agitation speed, specific interfacial area, temperature, extractant concentration and Zn ion concentration on the extraction rate are studied in constant interfacial area cell. The results show that the extraction rate depends on interfacial chemical reaction and diffusion by using this new extraetant to extract zinc, and the apparent activation energy of this extraction reaction is measured as 28.2 kJ/mol, which demonstrates that the extraction reaction is controlled by the mixed-controlled reaction rate. The apparent reaction orders a and b are measured as 1 and 0.38, and the constant k0 is 138.70. So, when extraction conditions are controlled as [HR]=20%-50%, T=0-30℃, N=120-177 r/min and S=72.6-127.5 m-1, the solvent extraction reaction rate can be depicted as v/（mol . m-2 . s-1 ） = 138.7. exp（ - 28 206/8.314T ）. [Zn 2＋ ]r ·[HR ]o0.38.展开更多
Based on a dynamical Langevin equation coupled with a statistical decay model, we calculate the variation of the post-saddle giant dipole resonance （GDR） q-ray multiplicity of the heavy nuclei 24^240Cf, ^246Cf, ^252...Based on a dynamical Langevin equation coupled with a statistical decay model, we calculate the variation of the post-saddle giant dipole resonance （GDR） q-ray multiplicity of the heavy nuclei 24^240Cf, ^246Cf, ^252Cf and ^240U with the post-saddle friction strength （13）. We find that the sensitivity of the post-saddle γ emission to β decreases considerably with increasing the neutron-to-proton ratio （N/Z） of the system. Moreover, for 240 U, the γ emission is no longer sensitive to 13. We suggest that to accurately obtain information of the post-saddle friction strength by measuring pre-scission GDR γ-ray multiplicities, it is optimal to choose among the various compound systems those with low N/Z.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
Noether symmetry of Nielsen equation and Noether conserved quantity deduced directly from Noether symmetry for dynamical systems of the relative motion are studied. The definition and criteria of Noether symmetry of a...Noether symmetry of Nielsen equation and Noether conserved quantity deduced directly from Noether symmetry for dynamical systems of the relative motion are studied. The definition and criteria of Noether symmetry of a Nielsen equation under the infinitesimal transformations of groups are given. Expression of Noether conserved quantity deduced directly from Noether symmetry of Nielsen equation for the system are obtained. Finally, an example is given to illustrate the application of the results.展开更多
We perform langevin dynamics simulation for envelope solitons in an FPU-β lattice,with the nearestneighborinteraction and quartic anharmonicity.We get the motion equations of our discrete system by adding noiseand da...We perform langevin dynamics simulation for envelope solitons in an FPU-β lattice,with the nearestneighborinteraction and quartic anharmonicity.We get the motion equations of our discrete system by adding noiseand damping to the set of deterministic motion equations.We define'half-time'as the time when the amplitude of theenvelope soliton decreases by half due to damping.And then the mass,center and half-time of the perturbed envelopesoliton are numerically simulated,beginning with the discrete envelope soliton at rest.Results show successfully hownoise affects behavior of the envelope soliton.展开更多
Perturbation theory is an important tool in quantum mechanics. In this paper, we extend the traditional perturbation theory to open nonlinear two-level systems, treating decoherence parameter γ as a perturbation. By ...Perturbation theory is an important tool in quantum mechanics. In this paper, we extend the traditional perturbation theory to open nonlinear two-level systems, treating decoherence parameter γ as a perturbation. By this virtue, we give a perturbative solution to the master equation, which describes a nonlinear open quantum system. The results show that for small decoherence rate γ the ratio of the nonlinear rate C to the tunneling coefficient V （i.e., r = O/V） determines the validity of the perturbation theory. For small ratio r, the perturbation theory is valid, otherwise it yields wrong results.展开更多
Since Gibbs synthesized a general equilibrium statistical ensemble theory, many theorists have attempted to generalized the Gibbsian theory to non-equilibrium phenomena domain, however the status of the theory of non-...Since Gibbs synthesized a general equilibrium statistical ensemble theory, many theorists have attempted to generalized the Gibbsian theory to non-equilibrium phenomena domain, however the status of the theory of non-equilibrium phenomena can not be said as firm as well established as the Gibbsian ensemble theory. In this work, we present a framework for the non-equilibrium statistical ensemble formalism based on a subdynamic kinetic equation (SKE) rooted from the Brussels-Austin school and followed by some up-to-date works. The constructed key is to use a similarity transformation between Gibbsian ensembles formalism based on Liouville equation and the subdynamic ensemble formalism based on the SKE. Using this formalism, we study the spin-Boson system, as cases of weak coupling or strongly coupling, and obtain the reduced density operators for the Canonical ensembles easily.展开更多
A dynamic model to describe the torsional vibration behaviors of a spur gear system is presented in this paper.Differential equations of nonlinear dynamics for the gear system exhibiting combined nonlinearity influenc...A dynamic model to describe the torsional vibration behaviors of a spur gear system is presented in this paper.Differential equations of nonlinear dynamics for the gear system exhibiting combined nonlinearity influence such as time-varying mesh stiffness,backlash and dynamic transmission error(DTE) were obtained.The method of multiple scales was employed to solve the nonlinear differential equations with parametric excitation in gear systems,by which both the frequency-response curves of the primary resonance caused by internal excitation and the analytical periodic solutions of nonlinear differential equations were obtained.The nonlinear influence of stiffness variation,the damping and the internal excitation on the system response was shown by frequency-response curves.Compared with numerical examples,the approximate analytical solutions are in good agreement with exact solutions,which proves that the method of multiple scales is effective for solving nonlinear problems in gear systems.展开更多
Efficient, precise dynamic modeling and analysis for complex weapon systems have become more and more important in their dynamic design and performance optimizing. As a new method developed in recent years, the discre...Efficient, precise dynamic modeling and analysis for complex weapon systems have become more and more important in their dynamic design and performance optimizing. As a new method developed in recent years, the discrete time transfer matrix method of multibody system is highly efficient for multibody system dynamics. In this paper, taking a shipboard gun system as an example, by deducing some new transfer equations of elements, the discrete time transfer matrix method of multibody sys- tem is used to solve the dynamics problems of complex rigid-flexible coupling weapon systems successfully. This method does not need the global dynamic equations of system and has the low order of system matrix, high computational efficiency. The proposed method has advantages for dynamic design of complex weapon systems, and can be carried over straightforwardly to other complex mechanical systems.展开更多
基金supported by National Natural Science Foundation of China under Grant No. 10572021
文摘In this paper, the conservation laws of generalized Birkhoff system in event space are studied by using the method of integrating factors. Firstly, the generalized Pfaff-Birkhoff principle and the generalized Birkhoff equations are established, and the definition of the integrating factors for the system is given. Secondly, based on the concept of integrating factors, the conservation theorems and their inverse for the generalized Birkhoff system in the event space are presented in detail, and the relation between the conservation laws and the integrating factors of the system is obtained and the generalized Killing equations for the determination of the integrating factors are given. Finally, an example is given to illustrate the application of the results.
基金Project(10772113) supported by the National Natural Science Foundation of China
文摘A complete geometric nonlinear formulation for rigid-flexible coupling dynamics of a flexible beam undergoing large overall motion was proposed based on virtual work principle, in which all the high-order terms related to coupling deformation were included in dynamic equations. Simulation examples of the flexible beam with prescribed rotation and free rotation were investigated. Numerical results show that the use of the first-order approximation coupling (FOAC) model may lead to a significant error when the flexible beam experiences large deformation or large deformation velocity. However, the correct solutions can always be obtained by using the present complete model. The difference in essence between this model and the FOAC model is revealed. These coupling high-order terms, which are ignored in FOAC model, have a remarkable effect on the dynamic behavior of the flexible body. Therefore, these terms should be included for the rigid-flexible dynamic modeling and analysis of flexible body undergoing motions with high speed.
基金Foundation item： Project（51174240） supported by the National Natural Science Foundation of China Project（2006BA02B04-4-2） supported by the National Eleventh Five-Year Research Program of China Project（20100908） supported by Scientific and Industrial Research Organisation of Guangdong Province, China
文摘The controlling step and the extraction reaction rate equation of zinc extraction from Zn（II）-NH3 solution by using a newly synthesized organic compound, 2-acetyl-3-oxo-dithiobutyric acid-myristyl ester as the zinc extractant, were clarified. The effects of agitation speed, specific interfacial area, temperature, extractant concentration and Zn ion concentration on the extraction rate are studied in constant interfacial area cell. The results show that the extraction rate depends on interfacial chemical reaction and diffusion by using this new extraetant to extract zinc, and the apparent activation energy of this extraction reaction is measured as 28.2 kJ/mol, which demonstrates that the extraction reaction is controlled by the mixed-controlled reaction rate. The apparent reaction orders a and b are measured as 1 and 0.38, and the constant k0 is 138.70. So, when extraction conditions are controlled as [HR]=20%-50%, T=0-30℃, N=120-177 r/min and S=72.6-127.5 m-1, the solvent extraction reaction rate can be depicted as v/（mol . m-2 . s-1 ） = 138.7. exp（ - 28 206/8.314T ）. [Zn 2＋ ]r ·[HR ]o0.38.
基金Supported by the Foundation of Nanjing University of Finance & Economics under Grant No. JGY1030
文摘Based on a dynamical Langevin equation coupled with a statistical decay model, we calculate the variation of the post-saddle giant dipole resonance （GDR） q-ray multiplicity of the heavy nuclei 24^240Cf, ^246Cf, ^252Cf and ^240U with the post-saddle friction strength （13）. We find that the sensitivity of the post-saddle γ emission to β decreases considerably with increasing the neutron-to-proton ratio （N/Z） of the system. Moreover, for 240 U, the γ emission is no longer sensitive to 13. We suggest that to accurately obtain information of the post-saddle friction strength by measuring pre-scission GDR γ-ray multiplicities, it is optimal to choose among the various compound systems those with low N/Z.
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Supported by the National Natural Science Foundation of China under Grant No.10572021the Preparatory Research Foundation of Jiangnan University under Grant No.2008LYY011
文摘Noether symmetry of Nielsen equation and Noether conserved quantity deduced directly from Noether symmetry for dynamical systems of the relative motion are studied. The definition and criteria of Noether symmetry of a Nielsen equation under the infinitesimal transformations of groups are given. Expression of Noether conserved quantity deduced directly from Noether symmetry of Nielsen equation for the system are obtained. Finally, an example is given to illustrate the application of the results.
基金Supported by Scientific Research Fund of Hunan Provincial Education Department under Grant No.07B075Interactive Project Fund of Xiangtan University under Grant No.061ND09Initial Scientific Research Fund of Xiangtan University
文摘We perform langevin dynamics simulation for envelope solitons in an FPU-β lattice,with the nearestneighborinteraction and quartic anharmonicity.We get the motion equations of our discrete system by adding noiseand damping to the set of deterministic motion equations.We define'half-time'as the time when the amplitude of theenvelope soliton decreases by half due to damping.And then the mass,center and half-time of the perturbed envelopesoliton are numerically simulated,beginning with the discrete envelope soliton at rest.Results show successfully hownoise affects behavior of the envelope soliton.
基金Supported by National Natural Science Foundation of China under Grant No. 61078011
文摘Perturbation theory is an important tool in quantum mechanics. In this paper, we extend the traditional perturbation theory to open nonlinear two-level systems, treating decoherence parameter γ as a perturbation. By this virtue, we give a perturbative solution to the master equation, which describes a nonlinear open quantum system. The results show that for small decoherence rate γ the ratio of the nonlinear rate C to the tunneling coefficient V （i.e., r = O/V） determines the validity of the perturbation theory. For small ratio r, the perturbation theory is valid, otherwise it yields wrong results.
基金Supported by the National Natural Science Foundation of China under Grant No. 60874087the Grants from Wuhan University of Technology,in Canada by NSERC, MITACS, CIPI, MMO, and CITO
文摘Since Gibbs synthesized a general equilibrium statistical ensemble theory, many theorists have attempted to generalized the Gibbsian theory to non-equilibrium phenomena domain, however the status of the theory of non-equilibrium phenomena can not be said as firm as well established as the Gibbsian ensemble theory. In this work, we present a framework for the non-equilibrium statistical ensemble formalism based on a subdynamic kinetic equation (SKE) rooted from the Brussels-Austin school and followed by some up-to-date works. The constructed key is to use a similarity transformation between Gibbsian ensembles formalism based on Liouville equation and the subdynamic ensemble formalism based on the SKE. Using this formalism, we study the spin-Boson system, as cases of weak coupling or strongly coupling, and obtain the reduced density operators for the Canonical ensembles easily.
文摘A dynamic model to describe the torsional vibration behaviors of a spur gear system is presented in this paper.Differential equations of nonlinear dynamics for the gear system exhibiting combined nonlinearity influence such as time-varying mesh stiffness,backlash and dynamic transmission error(DTE) were obtained.The method of multiple scales was employed to solve the nonlinear differential equations with parametric excitation in gear systems,by which both the frequency-response curves of the primary resonance caused by internal excitation and the analytical periodic solutions of nonlinear differential equations were obtained.The nonlinear influence of stiffness variation,the damping and the internal excitation on the system response was shown by frequency-response curves.Compared with numerical examples,the approximate analytical solutions are in good agreement with exact solutions,which proves that the method of multiple scales is effective for solving nonlinear problems in gear systems.
基金supported by the National Natural Science Foundation of China (Grant No: 10902051)the Natural Science Foundation of Jiangsu Province (Grant No: BK2008046)
文摘Efficient, precise dynamic modeling and analysis for complex weapon systems have become more and more important in their dynamic design and performance optimizing. As a new method developed in recent years, the discrete time transfer matrix method of multibody system is highly efficient for multibody system dynamics. In this paper, taking a shipboard gun system as an example, by deducing some new transfer equations of elements, the discrete time transfer matrix method of multibody sys- tem is used to solve the dynamics problems of complex rigid-flexible coupling weapon systems successfully. This method does not need the global dynamic equations of system and has the low order of system matrix, high computational efficiency. The proposed method has advantages for dynamic design of complex weapon systems, and can be carried over straightforwardly to other complex mechanical systems.
