A 3D finite element vibration model of water turbine generator set is constructed considering the coupling with hydropower house foundation. The method of determining guide bearing dynamic characteristic coefficients ...A 3D finite element vibration model of water turbine generator set is constructed considering the coupling with hydropower house foundation. The method of determining guide bearing dynamic characteristic coefficients according to the swing of the shaft is proposed, which can be used for studying the self-vibration characteristic and stability of the water turbine generator set. The method fully considers the complex supporting boundary and loading conditions; especially the nonlinear variation of guide bearing dynamic characteristic coefficients and the coupling effect of the whole power-house foundation. The swing and critical rotating speed of an actual generator set shaft system are calculated. The simulated results of the generator set indicate that the coupling vibration model and calculation method presented in this paper are suitable for stability analysis of the water turbine generator set.展开更多
The C-C method was adopted to analyze the nonlinear characteristics of masseter electromyography （EMG） signals and the chaotic degree by the largest Lyapunov exponent （LLE） of different genders and sides. First, t...The C-C method was adopted to analyze the nonlinear characteristics of masseter electromyography （EMG） signals and the chaotic degree by the largest Lyapunov exponent （LLE） of different genders and sides. First, the embedding dimension and the delay time were obtained through this method, then the phase space was reconstructed to resume the chaotie attractor and determine the LLE. The result shows that the trajectory of attractor is denser than Chen＇s attractor, and the LLE is positive, which means that not only the signal has the character of chaos, but also the chaotic degree of masseter EMG is relatively high. According to the value of the LLE, the chaotic degree of men＇s masseter EMG is higher than that of women＇s; when the dentition is normal, the chaotic degree of two sides is almost the same. Then, a conclusion can be deduced that if the LLE of both sides are in great difference, the unilateral mastication is likely to exist, which means that the nonlinear characteristics of masseter EMG can be applied to predict the unilateral mastication.展开更多
The nonlinear static characteristic of a piezoelectric unimorph cantilever micro actuator driven by a strong applied electric field is studied based on the couple stress theory.The cantilever actuator consists of a pi...The nonlinear static characteristic of a piezoelectric unimorph cantilever micro actuator driven by a strong applied electric field is studied based on the couple stress theory.The cantilever actuator consists of a piezoelectric layer,a passive（elastic）layer and two electrode layers.First,the nonlinear static characteristic of the actuator caused by the electrostriction of the piezoelectric layer under a strong applied electric field is analyzed using the Rayleigh-Ritz method.Secondly,since the thickness of the cantilever beam is in micro scale and there exists a size effect,the size dependence of the deformation behavior is evaluated using the couple stress theory.The results show that the nonlinearities of the beam deflection increase along with the increase of the applied electric field which means that softening of the micro beam rigidity exists when a strong external electric field is applied.Meanwhile,the optimal value of the thickness ratio for the passive layer and the piezoelectric layer is not around 1.0 which is usually adopted by some previous researchers.Since there exists a size effect of the micro beam deflection,the optimal value of this thickness ratio should be greater than 1.0 in micro scale.展开更多
In this paper, we generalize the method of mechanical theorem proving in curves to prove theorems about surfaces in differential geometry with a mechanical procedure. We improve the classical result on Wronskian deter...In this paper, we generalize the method of mechanical theorem proving in curves to prove theorems about surfaces in differential geometry with a mechanical procedure. We improve the classical result on Wronskian determinant, which can be used to decide whether the elements in a partial differential field are linearly dependent over its constant field. Based on Wronskian determinant, we can describe the geometry statements in the surfaces by an algebraic language and then prove them by the characteristic set method.展开更多
This paper presents a characteristic more efficient and has better properties than the set method for solving Boolean equations, which is general characteristic set method. In particular, the authors give a disjoint a...This paper presents a characteristic more efficient and has better properties than the set method for solving Boolean equations, which is general characteristic set method. In particular, the authors give a disjoint and monic zero decomposition algorithm for the zero set of a Boolean equation system and an explicit formula for the number of solutions of a Boolean equation system. The authors also prove that a characteristic set can be computed with a polynomial number of multiplications of Boolean polynomials in terms of the number of variables. As experiments, the proposed method is used to solve equations from cryptanalysis of a class of stream ciphers based on nonlinear filter generators. Extensive experiments show that the method is quite effective.展开更多
This paper presents an algorithm to reduce a nonlinear algebraic partial differential equation system into the involutive characteristic set with respect to an abstract involutive prolongation direction, which covers ...This paper presents an algorithm to reduce a nonlinear algebraic partial differential equation system into the involutive characteristic set with respect to an abstract involutive prolongation direction, which covers the existing algorithms based on Riquier method, Thomas method, and Pommaret method. It also provides new algorithms for computing involutive characteristic sets due to the existence of new involutive directions. Experiments show that these new algorithms may be used to significantly reduce the computational steps in Wu-Ritt's characteristic set method for algebraic partial differential equations.展开更多
A brief introduction to the characteristic set method is given for solving algebraic equation systems and then the method is extended to algebraic difference systems. The method can be used to decompose the zero set f...A brief introduction to the characteristic set method is given for solving algebraic equation systems and then the method is extended to algebraic difference systems. The method can be used to decompose the zero set for a difference polynomial set in general form to the union of difference polynomial sets in triangular form. Based on the characteristic set method, a decision procedure for the first order theory over an algebraically closed field and a procedure to prove certain difference identities are proposed.展开更多
For a parametric algebraic system in finite fields, this paper presents a method for computing the cover and the refined cover based on the characteristic set method. From the cover, the author knows for what parametr...For a parametric algebraic system in finite fields, this paper presents a method for computing the cover and the refined cover based on the characteristic set method. From the cover, the author knows for what parametric values the system has solutions and at the same time presents the solutions in the form of proper chains. By the refined cover, the author gives a complete classification of the number of solutions for this system, that is, the author divides the parameter space into several disjoint components, and on every component the system has a fix number of solutions. Moreover, the author develops a method of quantifier elimination for first order formulas in finite fields.展开更多
Level set methods are widely used for predicting evolutions of complex free surface topologies,such as the crystal and crack growth,bubbles and droplets deformation,spilling and breaking waves,and two-phase flow pheno...Level set methods are widely used for predicting evolutions of complex free surface topologies,such as the crystal and crack growth,bubbles and droplets deformation,spilling and breaking waves,and two-phase flow phenomena.This paper presents a characteristic level set equation which is derived from the two-dimensional level set equation by using the characteristic-based scheme.An explicit finite volume element method is developed to discretize the equation on triangular grids.Several examples are presented to demonstrate the performance of the proposed method for calculating interface evolutions in time.The proposed level set method is also coupled with the Navier-Stokes equations for two-phase immiscible incompressible flow analysis with surface tension.The Rayleigh-Taylor instability problem is used to test and evaluate the effectiveness of the proposed scheme.展开更多
Wu’s Characteristic Set Method is a theory that can compute, analyze thestructure of the zeros of a polynomial system. In the past two decades, the practice applications of Wu’s method have proved that it is a power...Wu’s Characteristic Set Method is a theory that can compute, analyze thestructure of the zeros of a polynomial system. In the past two decades, the practice applications of Wu’s method have proved that it is a powerful tool for many problems encountered in mathematics, science, engineering, and industrial/ social applications. Focusingon the implementation of Characteristic Set method, ELIMINO is a computer mathematics research system designed for researchers to perform sophisticated mathematicalcomputations. It has very general capabilities for treating integers, it has an interactiveprogramming capability which allow users to create new facilities.展开更多
Aim To eliminate the influences of backlash nonlinear characteristics generally existing in servo systems, a nonlinear compensation method using backpropagation neural networks(BPNN) is presented. Methods Based on s...Aim To eliminate the influences of backlash nonlinear characteristics generally existing in servo systems, a nonlinear compensation method using backpropagation neural networks(BPNN) is presented. Methods Based on some weapon tracking servo system, a three layer BPNN was used to off line identify the backlash characteristics, then a nonlinear compensator was designed according to the identification results. Results The simulation results show that the method can effectively get rid of the sustained oscillation(limit cycle) of the system caused by the backlash characteristics, and can improve the system accuracy. Conclusion The method is effective on sloving the problems produced by the backlash characteristics in servo systems, and it can be easily accomplished in engineering.展开更多
By virtue of the invariant eigen-operator method we search for the invariant eigen-operators for someHamiltonians describing nonlinear processes in particle physics.In this way the energy-gap of the Hamiltonians can b...By virtue of the invariant eigen-operator method we search for the invariant eigen-operators for someHamiltonians describing nonlinear processes in particle physics.In this way the energy-gap of the Hamiltonians can benaturally obtained.The characteristic polynomial theory has been fully employed in our derivation.展开更多
In this work, two-grid characteristic finite volume schemes for the nonlinear parabolic problem are considered. In our algorithms, the diffusion term is discretized by the finite volume method, while the temporal diff...In this work, two-grid characteristic finite volume schemes for the nonlinear parabolic problem are considered. In our algorithms, the diffusion term is discretized by the finite volume method, while the temporal differentiation and advection terms are treated by the characteristic scheme. Under some conditions about the coefficients and exact solution, optimal error estimates for the numerical solution are obtained. Furthermore, the two- grid characteristic finite volume methods involve solving a nonlinear equation on coarse mesh with mesh size H, a large linear problem for the Oseen two-grid characteristic finite volume method on a fine mesh with mesh size h = O（H2） or a large linear problem for the Newton two-grid characteristic finite volume method on a fine mesh with mesh size h = 0（I log hll/2H3）. These methods we studied provide the same convergence rate as that of the characteristic finite volume method, which involves solving one large nonlinear problem on a fine mesh with mesh size h. Some numerical results are presented to demonstrate the efficiency of the proposed methods.展开更多
基金supported by National Natural Science Foundation of China (Grant No. 50679009)
文摘A 3D finite element vibration model of water turbine generator set is constructed considering the coupling with hydropower house foundation. The method of determining guide bearing dynamic characteristic coefficients according to the swing of the shaft is proposed, which can be used for studying the self-vibration characteristic and stability of the water turbine generator set. The method fully considers the complex supporting boundary and loading conditions; especially the nonlinear variation of guide bearing dynamic characteristic coefficients and the coupling effect of the whole power-house foundation. The swing and critical rotating speed of an actual generator set shaft system are calculated. The simulated results of the generator set indicate that the coupling vibration model and calculation method presented in this paper are suitable for stability analysis of the water turbine generator set.
文摘The C-C method was adopted to analyze the nonlinear characteristics of masseter electromyography （EMG） signals and the chaotic degree by the largest Lyapunov exponent （LLE） of different genders and sides. First, the embedding dimension and the delay time were obtained through this method, then the phase space was reconstructed to resume the chaotie attractor and determine the LLE. The result shows that the trajectory of attractor is denser than Chen＇s attractor, and the LLE is positive, which means that not only the signal has the character of chaos, but also the chaotic degree of masseter EMG is relatively high. According to the value of the LLE, the chaotic degree of men＇s masseter EMG is higher than that of women＇s; when the dentition is normal, the chaotic degree of two sides is almost the same. Then, a conclusion can be deduced that if the LLE of both sides are in great difference, the unilateral mastication is likely to exist, which means that the nonlinear characteristics of masseter EMG can be applied to predict the unilateral mastication.
基金The National Natural Science Foundation of China(No.10772086,10772085)
文摘The nonlinear static characteristic of a piezoelectric unimorph cantilever micro actuator driven by a strong applied electric field is studied based on the couple stress theory.The cantilever actuator consists of a piezoelectric layer,a passive（elastic）layer and two electrode layers.First,the nonlinear static characteristic of the actuator caused by the electrostriction of the piezoelectric layer under a strong applied electric field is analyzed using the Rayleigh-Ritz method.Secondly,since the thickness of the cantilever beam is in micro scale and there exists a size effect,the size dependence of the deformation behavior is evaluated using the couple stress theory.The results show that the nonlinearities of the beam deflection increase along with the increase of the applied electric field which means that softening of the micro beam rigidity exists when a strong external electric field is applied.Meanwhile,the optimal value of the thickness ratio for the passive layer and the piezoelectric layer is not around 1.0 which is usually adopted by some previous researchers.Since there exists a size effect of the micro beam deflection,the optimal value of this thickness ratio should be greater than 1.0 in micro scale.
基金the National Key Basic Research Project of China (Grant No.2004CB318000)
文摘In this paper, we generalize the method of mechanical theorem proving in curves to prove theorems about surfaces in differential geometry with a mechanical procedure. We improve the classical result on Wronskian determinant, which can be used to decide whether the elements in a partial differential field are linearly dependent over its constant field. Based on Wronskian determinant, we can describe the geometry statements in the surfaces by an algebraic language and then prove them by the characteristic set method.
基金This research is partially supported by a National Key Basic Research Project of China under Grant No.2004CB318000.
文摘This paper presents a characteristic more efficient and has better properties than the set method for solving Boolean equations, which is general characteristic set method. In particular, the authors give a disjoint and monic zero decomposition algorithm for the zero set of a Boolean equation system and an explicit formula for the number of solutions of a Boolean equation system. The authors also prove that a characteristic set can be computed with a polynomial number of multiplications of Boolean polynomials in terms of the number of variables. As experiments, the proposed method is used to solve equations from cryptanalysis of a class of stream ciphers based on nonlinear filter generators. Extensive experiments show that the method is quite effective.
基金This work was supported in part by a National Key Basic Research Project of China(No.G19980306)the National Natural Science Foundation of China(Grant No.69725002).
文摘This paper presents an algorithm to reduce a nonlinear algebraic partial differential equation system into the involutive characteristic set with respect to an abstract involutive prolongation direction, which covers the existing algorithms based on Riquier method, Thomas method, and Pommaret method. It also provides new algorithms for computing involutive characteristic sets due to the existence of new involutive directions. Experiments show that these new algorithms may be used to significantly reduce the computational steps in Wu-Ritt's characteristic set method for algebraic partial differential equations.
基金This work is supported by the National Grand Fundamental Research 973 Program of China under Grant No. 2004CB318000. Acknowledgement We would like to take this opportunity to express our deep gratitude to the National Natural Science Foundation of China （NSFC） for its support during the past twenty years. Without the support from NSFC, mathematics mechanization is impossible to be so prosperous today. The second author would like, in particular, to thank NSFC for an 0utstanding Young Investigator Award for the period 1998 to 2001.
文摘A brief introduction to the characteristic set method is given for solving algebraic equation systems and then the method is extended to algebraic difference systems. The method can be used to decompose the zero set for a difference polynomial set in general form to the union of difference polynomial sets in triangular form. Based on the characteristic set method, a decision procedure for the first order theory over an algebraically closed field and a procedure to prove certain difference identities are proposed.
基金supported by the National 973 Program of China under Grant No.2011CB302400the National Natural Science Foundation of China under Grant No.60970152
文摘For a parametric algebraic system in finite fields, this paper presents a method for computing the cover and the refined cover based on the characteristic set method. From the cover, the author knows for what parametric values the system has solutions and at the same time presents the solutions in the form of proper chains. By the refined cover, the author gives a complete classification of the number of solutions for this system, that is, the author divides the parameter space into several disjoint components, and on every component the system has a fix number of solutions. Moreover, the author develops a method of quantifier elimination for first order formulas in finite fields.
基金King Mongkut’s University of Technology North Bangkok (KMUTNB)the Office of the Higher Education Commission (OHEC)the National Metal and Materials Technology Center (MTEC) for supporting this research work
文摘Level set methods are widely used for predicting evolutions of complex free surface topologies,such as the crystal and crack growth,bubbles and droplets deformation,spilling and breaking waves,and two-phase flow phenomena.This paper presents a characteristic level set equation which is derived from the two-dimensional level set equation by using the characteristic-based scheme.An explicit finite volume element method is developed to discretize the equation on triangular grids.Several examples are presented to demonstrate the performance of the proposed method for calculating interface evolutions in time.The proposed level set method is also coupled with the Navier-Stokes equations for two-phase immiscible incompressible flow analysis with surface tension.The Rayleigh-Taylor instability problem is used to test and evaluate the effectiveness of the proposed scheme.
文摘Wu’s Characteristic Set Method is a theory that can compute, analyze thestructure of the zeros of a polynomial system. In the past two decades, the practice applications of Wu’s method have proved that it is a powerful tool for many problems encountered in mathematics, science, engineering, and industrial/ social applications. Focusingon the implementation of Characteristic Set method, ELIMINO is a computer mathematics research system designed for researchers to perform sophisticated mathematicalcomputations. It has very general capabilities for treating integers, it has an interactiveprogramming capability which allow users to create new facilities.
文摘Aim To eliminate the influences of backlash nonlinear characteristics generally existing in servo systems, a nonlinear compensation method using backpropagation neural networks(BPNN) is presented. Methods Based on some weapon tracking servo system, a three layer BPNN was used to off line identify the backlash characteristics, then a nonlinear compensator was designed according to the identification results. Results The simulation results show that the method can effectively get rid of the sustained oscillation(limit cycle) of the system caused by the backlash characteristics, and can improve the system accuracy. Conclusion The method is effective on sloving the problems produced by the backlash characteristics in servo systems, and it can be easily accomplished in engineering.
基金National Natural Science Foundation of China under grant No.10775097the President Foundation of the Chinese Academy of Sciences
文摘By virtue of the invariant eigen-operator method we search for the invariant eigen-operators for someHamiltonians describing nonlinear processes in particle physics.In this way the energy-gap of the Hamiltonians can benaturally obtained.The characteristic polynomial theory has been fully employed in our derivation.
基金Acknowledgments. The work was supported by the Natural Science Foundation of China （No.11126117）, CAPES and CNPq of Brazil, and the Doctor Fund of Henan Polytechnic Univer- sity （B2012-098）. The author is very grateful to Professor JinYun Yuan for his kind invitation to visit the Universidade Federal do Paran, Brazil.
文摘In this work, two-grid characteristic finite volume schemes for the nonlinear parabolic problem are considered. In our algorithms, the diffusion term is discretized by the finite volume method, while the temporal differentiation and advection terms are treated by the characteristic scheme. Under some conditions about the coefficients and exact solution, optimal error estimates for the numerical solution are obtained. Furthermore, the two- grid characteristic finite volume methods involve solving a nonlinear equation on coarse mesh with mesh size H, a large linear problem for the Oseen two-grid characteristic finite volume method on a fine mesh with mesh size h = O（H2） or a large linear problem for the Newton two-grid characteristic finite volume method on a fine mesh with mesh size h = 0（I log hll/2H3）. These methods we studied provide the same convergence rate as that of the characteristic finite volume method, which involves solving one large nonlinear problem on a fine mesh with mesh size h. Some numerical results are presented to demonstrate the efficiency of the proposed methods.
