共查询到19条相似文献,搜索用时 468 毫秒
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本文研究离散差分序列变质量Hamilton系统的Lie对称性与Noether守恒量. 构建了离散差分序列变质量Hamilton系统的差分动力学方程, 给出了离散差分序列变质量Hamilton系统差分动力学方程在无限小变 换群下的Lie对称性的确定方程和定义, 得到了离散力学系统Lie对称性导致Noether守恒量的条件及形式, 举例说明结果的应用.
关键词:
离散力学
Hamilton系统
Lie对称性
Noether守恒量 相似文献
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为拓广离散忆阻器的研究与应用,基于差分算子,构建了具有平方非线性的离散忆阻模型,并实现了Simulink仿真.仿真结果表明,设计的忆阻器满足广义忆阻定义.将得到的离散忆阻引入三维混沌映射中,设计了一种新型四维忆阻混沌映射,并建立了该混沌映射的Simulink模型.通过平衡点、分岔图、Lyapunov指数谱、复杂度、多稳态分析了系统复杂动力学特性.本文从系统建模角度出发,构建离散忆阻与离散忆阻混沌映射,进一步验证了离散忆阻的可实现性,为离散忆阻应用研究奠定了基础. 相似文献
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H定理直接联系着动力学方法的稳定性,一直是各种简化求解Boltzmann方程方法的重要研究方向之一。本文证明了离散速度方向模型在平衡态和非平衡态下以及全部流动领域内都存在H定理,表明离散速度方向模型具有内在的稳定性。为了提高离散速度方向模型的数值稳定性,本文找到了一组该模型满足H定理的充分条件,该条件具有清晰的物理意义和简单的数学形式,可以方便地应用在数值计算中。 相似文献
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换热器集箱管组流动和换热分析 总被引:1,自引:0,他引:1
本文通过实验研究和理论分析,提出准确计算换热器集箱管组中流量分配的离散模型.应用离散模型对某台锅炉再热器的爆管原因进行分析,指出蒸汽侧流量偏差太大是造成超温爆管的主要原因之一. 相似文献
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This paper shows that first integrals of discrete equation of motion for
Birkhoff systems can be determined explicitly by investigating the invariance properties of
the discrete Pfaffian. The result obtained is a discrete
analogue of theorem of Noether in the
calculus of variations. An example is given to illustrate
the application of the results. 相似文献
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In this paper we show that the first integrals of the discrete equation of motion for nonconservative and nonholonomic mechanical systems can be determined explicitly by investigating the invariance properties of the discrete Lagrangian. The result obtained is a discrete analogue of the generalized theorem of Noether in the Calculus of variations. 相似文献
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Christopher Chong Dmitry E. Pelinovsky Guido Schneider 《Physica D: Nonlinear Phenomena》2012,241(2):115-124
The variational approximation is a well known tool to approximate localized states in nonlinear systems. In the context of a discrete nonlinear Schrödinger equation with a small coupling constant, we prove error estimates for the variational approximations of site-symmetric, bond-symmetric, and twisted discrete solitons. This is shown for various trial configurations, which become increasingly more accurate as more parameters are taken. It is also shown that the variational approximation yields the correct spectral stability result and controls the oscillatory dynamics of stable discrete solitons for long but finite time intervals. 相似文献
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用离散的位置基矢作为连续位置基矢的近似,构建分立位置表象.在分立位置表象中,哈密顿算符矩阵具有对角占优、带状稀疏的特点,矩阵元不用做积分运算,具有特别简单的解析表达式.分别对双原子分子在Morse势、Murrell-Sorbie势和双阱势中运动情形,进行了数值计算.结果表明,在分立位置表象中计算双原子分子振动能级,方法简便,稳定性好,计算精度高. 相似文献
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Discrete solitons of the discrete nonlinear Schrödinger (dNLS) equation are compactly supported in the anti-continuum limit of the zero coupling between lattice sites. Eigenvalues of the linearization of the dNLS equation at the discrete soliton determine its spectral stability. Small eigenvalues bifurcating from the zero eigenvalue near the anti-continuum limit were characterized earlier for this model. Here we analyze the resolvent operator and prove that it is bounded in the neighborhood of the continuous spectrum if the discrete soliton is simply connected in the anti-continuum limit. This result rules out the existence of internal modes (neutrally stable eigenvalues of the discrete spectrum) near the anti-continuum limit. 相似文献
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This paper sets the scene for discrete variational problems on an abstract cellular complex that serves as discrete model of Rp and for the discrete theory of partial differential operators that are common in the Calculus of Variations. A central result is the construction of a unique decomposition of certain partial difference operators into two components, one that is a vector bundle morphism and other one that leads to boundary terms. Application of this result to the differential of the discrete Lagrangian leads to unique discrete Euler and momentum forms not depending either on the choice of reference on the base lattice or on the choice of coordinates on the configuration manifold, and satisfying the corresponding discrete first variation formula. This formula leads to discrete Euler equations for critical points and to exact discrete conservation laws for infinitesimal symmetries of the Lagrangian density, with a clear physical interpretation. 相似文献
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Y. Wang J.F. Jiang Q.Y. Cai 《Physica E: Low-dimensional Systems and Nanostructures》2006,31(2):196-199
In the nanometer structure, the island with discrete energy spectrum should be considered. The transport characteristics of an electromechanical quantum dots device at zero temperature are investigated by using Monte Carlo method. An indirect and effective method is applied to estimate the trend of the current curves, by analyzing the average electrostatic forces. The current–voltage curves show the Coulomb blockade phenomena, which is the result of the interaction between discrete levels and the island vibration. 相似文献
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《Journal of computational physics》2008,227(1):797-819
This paper establishes a link between the stability of a first order, explicit discrete event integration scheme and the stability criteria for the explicit Euler method. The paper begins by constructing a time-varying linear system with bounded inputs that is equivalent to the first order discrete event integration scheme. The stability of the discrete event system is shown to result from the fact that it automatically adjusts its time advance to lie below the limit set by the explicit Euler stability criteria. Moreover, because it is not necessary to update all integrators at this rate, a significant performance advantage is possible. Our results confirm and explain previously reported studies where it is demonstrated that a reduced number of updates can provide a significant performance advantage compared to fixed step methods. These results also throw some light on stability requirements for discrete event simulation of spatially extended systems. 相似文献
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Fajun Yu 《Physics letters. A》2008,372(24):4353-4360
In [W.X. Ma, J. Phys. A: Math. Theor. 40 (2007) 15055], Prof. Ma gave a beautiful result (a discrete variational identity). In this Letter, based on a discrete block matrix spectral problem, a new hierarchy of Lax integrable lattice equations with four potentials is derived. By using of the discrete variational identity, we obtain Hamiltonian structure of the discrete soliton equation hierarchy. Finally, an integrable coupling system of the soliton equation hierarchy and its Hamiltonian structure are obtained through the discrete variational identity. 相似文献