共查询到19条相似文献,搜索用时 203 毫秒
1.
YANG Xu-Dong RUAN Hang-Yu LOU Sen-Yue 《理论物理通讯》2008,50(7):23-30
An improved algorithm for symbolic computations of polynomial-type conservation laws (PCLaws) of a general polynomial nonlinear system is presented. The algorithm is implemented in Maple and can be successfully used for high-dimensional models. Furthermore, the algorithm discards the restriction to evolution equations. The program can also be used to determine the preferences for a given parameterized nonlinear systems. The code is tested on several known nonlinear equations from the soliton theory. 相似文献
2.
LIU XiaoMei ZHOU Gang ZHU Shuai WANG YongHong SUN WeiRong WENG ShiLie 《中国科学:物理学 力学 天文学(英文版)》2014,57(7):1382-1389
It is always a bottleneck to design an effective algorithm for linear time-varying systems in engineering applications.For a class of systems,whose coefficients matrix is based on time-varying polynomial,a modified highly precise direct integration(VHPD-T method)was presented.Through introducing new variables and expanding dimensions,the system can be transformed into a timeinvariant system,in which the transfer matrix can be computed for once and used forever with a highly precise direct integration method.The method attains higher precision than the common methods(e.g.RK4 and power series)and high efficiency in computation.Some numerical examples demonstrate the validity and efficiency of the method proposed. 相似文献
3.
In this paper, the Faddeev--Jackiw approach is improved by the Wu
elimination method, so a great many complicated computations in
solving constraints for the finite-dimensional polynomial-type
constrained dynamics can be executed easily by using computers.
Moreover, based on the Faddeev--Jackiw approach, a new algorithm of
solving the constrained dynamics is presented. The new algorithm is
simpler and stricter than the Faddeev--Jackiw approach. Using the new
algorithm, the second Cawley counterexample is solved. 相似文献
4.
In this paper the energy diffusion controlled reaction rate in dissipative Hamiltonian
systems is investigated by using the stochastic averaging method for quasi
Hamiltonian systems. The boundary value problem of mean first-passage time
(MFPT) of averaged system is formulated and the energy diffusion controlled
reaction rate is obtained as the inverse of MFPT. The energy diffusion
controlled reaction rate in the classical Kramers bistable potential and in
a two-dimensional bistable potential with a heat bath are obtained by using
the proposed approach respectively. The obtained results are then compared
with those from Monte Carlo simulation of original systems and from the
classical Kramers theory. It is shown that the reaction rate obtained by
using the proposed approach agrees well with that from Monte Carlo
simulation and is more accurate than the classical Kramers rate. 相似文献
5.
The static and dynamic properties of the two-dimensional classic system of two-species interacting charged particles in a parabolic trap are studied. The ground state energy and configuration for different kinds of binary systems are obtained by Monte Carlo simulation and Newton optimization. The spectrum and normal modes vectors can be gained by diagonalizing the dynamical matrix of the system. It is found that the total particle number, particle number and mass-to-charge ratio of each species are decisive factors for the system structure and spectrum. The three intrinsic normal modes of single species Coulomb clusters are inherent, concluded from our numerical simulations and analytical results. 相似文献
6.
Parameter estimation for chaotic systems using the cuckoo search algorithm with an orthogonal learning method 下载免费PDF全文
We study the parameter estimation of a nonlinear chaotic system,which can be essentially formulated as a multidimensional optimization problem.In this paper,an orthogonal learning cuckoo search algorithm is used to estimate the parameters of chaotic systems.This algorithm can combine the stochastic exploration of the cuckoo search and the exploitation capability of the orthogonal learning strategy.Experiments are conducted on the Lorenz system and the Chen system.The proposed algorithm is used to estimate the parameters for these two systems.Simulation results and comparisons demonstrate that the proposed algorithm is better or at least comparable to the particle swarm optimization and the genetic algorithm when considering the quality of the solutions obtained. 相似文献
7.
To determine whether a given deterministic nonlinear dynamic system is chaotic or periodic,a novel test approach named zero-one (0-1) test has been proposed recently.In this approach,the regular and chaotic motions can be decided by calculating the parameter K approaching asymptotically to zero or one.In this study,we focus on the 0-1 test algorithm and illustrate the selection of parameters of this algorithm by numerical experiments.To validate the reliability and the universality of this algorithm,it is applied to typical nonlinear dynamic systems,including fractional-order dynamic system. 相似文献
8.
A synchronization method is proposed for a class of chaotic systems which can be translated into the strictfeedback form.This approach needs only a single controller and turns out to be globally exponentially asymptotically stable.The effectiveness of this approach has been demonstrated with the Rossler chaotic system. 相似文献
9.
We apply the algebraic Bethe technique to the nuclear pairing problem with certain limits. We obtain the exact energies and eigenstates, and find the symmetry between the states corresponding to less and more than half full shell. We also proved that the problem of solving BAE can be transformed into the problem of finding the roots of a hypergeometric polynomial, which is much 相似文献
10.
11.
讨论简谐激励作用下含有界随机参数的双势阱Duffing-van der Pol系统的倍周期分岔现象.首先用Chebyshev 多项式逼近法将随机Duffing-van der Pol系统化成与其等价的确定性系统,然后通过等价确定性系统来探索该系统的倍周期分岔现象.数值模拟显示随机Duffing-van der Pol 系统与均值参数系统有着类似的倍周期分岔行为,同时指出,随机参数系统的倍周期分岔有其自身独有的特点.文中的主要数值结果表明Chebyshev 多项式逼近法是研究非线性随机参数系统动力学问题的一种有效方法.
关键词:
Chebyshev多项式
随机Duffing-van der Pol系统
倍周期分岔 相似文献
12.
使用中子密度一阶泰劳多项式分段近似技术,给出一个新的求解点堆中子动力学方程组的数值方法并采用全隐格式以克服方程组的刚性,同时确保解的必要精度。数值结果表明:在隐式一阶多项式近似下,对合适的反应性输入能够取得足够精确的结果。当反应性给定时,对于求解反应堆动力学问题,能给出一个简法的计算过程。 相似文献
13.
Aeroheating-induced intensity nonuniformity effects severely influence the effective performance of an infrared (IR) imaging system in high-speed flight. In this paper, we propose a new approach to the correction of intensity nonuniformity in IR images. The basic assumption is that the low-frequency intensity bias is additive and smoothly varying so that it can be modeled as a bivariate polynomial and estimated by using an isotropic total variation (TV) model. A half quadratic penalty method is applied to the isotropic form of TV discretization. And an alternating minimization algorithm is adopted for solving the optimization model. The experimental results of simulated and real aerothermal images show that the proposed correction method can effectively improve IR image quality. 相似文献
14.
We apply the algebraic Bethe technique to the nuclear pairing problem with certain limits. We obtain the exact energies and eigenstates, and find the symmetry between the states corresponding to less and more than half full shell. We also proved that the problem of solving BAE can be transformed into the problem of finding the roots of a hypergeometric polynomial, which is much simpler. 相似文献
15.
Conservation Quantities of the Explicit Symplectic Scheme for Time-evolution of Quantum System 总被引:2,自引:0,他引:2
Zhou Zhongyuan Ding Peizhu Institute of Atomic Molecular Physics Jilin University Changchun P R China Supported by National Natural Science Foundation of China State Commission of Science Technology Chinese Research Asso 《原子与分子物理学报》1997,(2)
ConservationQuantitiesoftheExplicitSymplecticSchemeforTime-evolutionofQuantumSystemZhouZhongyuanDingPeizhuInstituteofAtomican... 相似文献
16.
In this article, an extended Taylor expansion method is proposed to estimate the solution of linear singular Volterra integral equations systems. The method is based on combining the m-th order Taylor polynomial of unknown functions at an arbitrary point and integration method, such that the given system of singular integral equations is converted into a system of linear equations with respect to unknown functions and their derivatives. The required solutions are obtained by solving the resulting linear system. The proposed method gives a very satisfactory solution, which can be performed by any symbolic mathematical packages such as Maple, Mathematica, etc. Our proposed approach provides a significant advantage that the m-th order approximate solutions are equal to exact solutions if the exact solutions are polynomial functions of degree less than or equal to m. We present an error analysis for the proposed method to emphasize its reliability. Six numerical examples are provided to show the accuracy and the efficiency of the suggested scheme for which the exact solutions are known in advance. 相似文献
17.
In this article, an extended Taylor expansion method is proposed to estimate the solution of linear singular Volterra integral equations systems. The method is based on combining the m-th order Taylor polynomial of unknown functions at an arbitrary point and integration method, such that the given system of singular integral equations is converted into a system of linear equations with respect to unknown functions and their derivatives. The required solutions are obtained by solving the resulting linear system. The proposed method gives a very satisfactory solution,which can be performed by any symbolic mathematical packages such as Maple, Mathematica, etc. Our proposed approach provides a significant advantage that the m-th order approximate solutions are equal to exact solutions if the exact solutions are polynomial functions of degree less than or equal to m. We present an error analysis for the proposed method to emphasize its reliability. Six numerical examples are provided to show the accuracy and the efficiency of the suggested scheme for which the exact solutions are known in advance. 相似文献
18.
As one of the most adopted sequential data assimilation methods in many areas, especially those involving complex nonlinear dynamics, the ensemble Kalman filter (EnKF) has been under extensive investigation regarding its properties and efficiency. Compared to other variants of the Kalman filter (KF), EnKF is straightforward to implement, as it employs random ensembles to represent solution states. This, however, introduces sampling errors that affect the accuracy of EnKF in a negative manner. Though sampling errors can be easily reduced by using a large number of samples, in practice this is undesirable as each ensemble member is a solution of the system of state equations and can be time consuming to compute for large-scale problems. In this paper we present an efficient EnKF implementation via generalized polynomial chaos (gPC) expansion. The key ingredients of the proposed approach involve (1) solving the system of stochastic state equations via the gPC methodology to gain efficiency; and (2) sampling the gPC approximation of the stochastic solution with an arbitrarily large number of samples, at virtually no additional computational cost, to drastically reduce the sampling errors. The resulting algorithm thus achieves a high accuracy at reduced computational cost, compared to the classical implementations of EnKF. Numerical examples are provided to verify the convergence property and accuracy improvement of the new algorithm. We also prove that for linear systems with Gaussian noise, the first-order gPC Kalman filter method is equivalent to the exact Kalman filter. 相似文献
19.
James Lu 《advances in applied mathematics and mechanics.》2009,1(6):711-728
This paper describes inverse eigenvalue problems that arise in
studying qualitative dynamics in systems biology models.
An
algorithm based on lift-and-project iterations is proposed, where the lifting step entails solving a constrained matrix inverse
eigenvalue problem. In particular, prior to carrying out the iterative steps, $a$-$priori$ bounds on
the entries of the Jacobian matrix are computed by relying on the reaction network structure as well as the form of
the rate law expressions for the model under consideration. Numerical results on a number of models show that the proposed
algorithm can be used to computationally explore the possible dynamical scenarios while identifying the important
mechanisms via the use of sparsity-promoting regularization. 相似文献