高阶微商系统中正则Ward恒等式和Abel规范理论中动力学质量的产生

基于含复合场的正则Ward恒等式，研究了含高阶微商的Abel理论中动力学规范对称破缺.得到了包括费米子和束缚态的质量谱.讨论了高阶微商项的影响. 关键词： 正则Ward恒等式 约束 动力学对称破缺 Abel规范理论     

Lagrangian submanifolds and the Euler-Lagrange equations in higher-order mechanics

A direct construction of the Euler-Lagrange equations in higher-order mechanics as a submanifold of a higher-order tangent bundle is given, starting from the Lagrangian submanifold defined by the Lagrangian function. This construction uses higher-order tangent bundle geometry, derives the Euler-Lagrange equations as the constraint equations of a submanifold, and makes no assumptions about the regularity of the Lagrangian.     

On the uniqueness of Einstein-Cartan theory: Lagrangian,covariant derivative and equation of motion

In the standard Einstein-Cartan theory, matter fields couple to gravity through the Minimal Coupling Procedure(MCP), and yet leave the theory an ambiguity. Applying MCP to the action or to the equation of motion would lead to different gravitational couplings. We propose a new covariant derivative to remove the ambiguity and discuss the relation between our proposal and previous treatments on this subject.     

高阶微商系统Dirac猜想的一个反例

由扩展正则作用量导出了高阶微商奇异Lagrange量系统的扩展正则Noether恒等式.从广义约束Hamilton系统相空间中对称性分析，给出高阶微商系统Dirac猜想的一个反例. 用正则Noether定理、 正则Noether恒等式和扩展正则Noether恒等式说明在此反例中Dirac猜想失效, 讨论中没有将约束线性化. 关键词： 高阶微商系统 约束Hamilton系统 正则对称性 Dirac猜想     

On the problem of homogenizing one-dimensional systems

The possibility of introducing effective one-dimensional medium parameters in the long-wave approximation is considered. A layered system was used as a model of one-dimensional medium. The effective parameters were shown to be functions of sample thickness. Both periodic and random media were studied; the thicknesses of random samples were assumed to be much smaller than the localization length, which allowed us to ignore the localization effect. The results are compared with the Rytov solution. The wave vector was found to tend to the Rytov value as the thickness of the sample increased, whereas the characteristic impedance had no limit in the long-wave approximation. What is more, the characteristic impedance could differ from the Rytov value by 100%. The results were obtained by computer simulation of the propagation of electromagnetic waves in a layered system.     

Lagrangian relative equilibria for a gyrostat in the three-body problem

In this paper we consider the noncanonical Hamiltonian dynamics of a gyrostat in the three-body problem. By means of geometric mechanics methods, we study the approximate Poisson dynamics that arise when we develop the potential of the system in Legendre series and truncate this to an arbitrary order k. After reduction of the dynamics by means of the two symmetries of the system, we consider the existence and number of equilibria which we denominate of Lagrangian type, in analogy with classic results on the topic. Necessary and sufficient conditions are established for their existence in an approximate dynamics of order k, and explicit expressions for these equilibria are given, this being useful for the subsequent study of their stability. The number of Lagrangian equilibria is thoroughly studied in approximate dynamics of orders zero and one. The main result of this work indicates that the number of Lagrangian equilibria in an approximate dynamics of order k for k ≥1 is independent of the order of truncation of the potential, if the gyrostat S ₀ is almost spherical. In relation to the stability of these equilibria, necessary and sufficient conditions are given for linear stability of Lagrangian equilibria when the gyrostat is almost spherical. In this way, we generalize the classical results on equilibria of the three-body problem and many results provided by other authors using more classical techniques for the case of rigid bodies.      

On quantum stability for systems under quasiperiodic perturbations

We prove that the spectrum defined in terms of the autocorrelation function of a harmonic subject to a quasiperiodic perturbation, is, at resonance, transient absolutely continuous, covering the whole line. In the nonresonant case, and under some supplementary Diophantine condition, it is pure point, coinciding with the spectrum of a special almost-periodic function.     

On mode shapes of a stability problem

This paper presents data of mode shapes of some stable and unstable modes of a free-free beam under direction controlled thrusts. These mode shapes are pertinent in understanding this basic problem and hitherto were not available in the literature. It has been found that the node number of the mode shape corresponding to the first divergence mode increases with the magnitude of the thrust. The main feature of the solution method is given. The instability of a free-free beam under a thrust fixed in direction is pointed out.     

On the stability of delayed feedback controllers for discrete time systems

We consider the stability of delayed feedback control (DFC) scheme for multi-dimensional discrete time systems. We first construct a map whose fixed points correspond to the periodic orbits of the uncontrolled system. Then the stability of the DFC is analyzed as the stability of the corresponding equilibrium point of the constructed map. For each periodic orbit, we construct a characteristic polynomial whose Schur stability corresponds to the stability of DFC scheme.     

Symmetries and constants of the motion for singular Lagrangian systems

A classification of infinitesimal symmetries of singular autonomous and nonautonomous Lagrangian systems is obtained. The relationship between infinitesimal symmetries and constants of the motion is given.     

The stability of impulsive incommensurate fractional order chaotic systems with Caputo derivative

The stability of impulsive incommensurate fractional-order systems is investigated in this paper. Some novel stability criteria for impulsive incommensurate fractional-order systems are proposed. The presented sufficient condition, which is more general than those of the known ones, is suitable for the case of the fractional orders 0 < α₁ ≤ α₂ ≤ ⋅⋅⋅ ≤ α_n ≤ 1. The simulation results by taking the incommensurate fractional-order T–D system and fractional order Chen economical system as two examples are delivered to illustrate the effectiveness of the proposed method.     

A dynamic Lagrangian frequency-time method for the vibration of dry-friction-damped systems

A new frequency-time domain procedure, the dynamic Lagrangian mixed frequency-time method (DLFT), is proposed to calculate the non-linear steady state response to periodic excitation of structural systems subject to dry friction damping. In this formulation, the dynamic Lagrangians are defined as the non-linear contact forces obtained from the equations of motion in the frequency domain, with the adjunction of a penalization on the difference between the interface displacements calculate by the non-linear solver in the frequency domain and those calculated in the time domain from the non-linear contact forces, thus accounting for Coulomb friction and non-penetration conditions. The dynamic Lagrangians allow one to solve for the non-linear forces between two points in contact without using artifacts such as springs. The new DLFT method is thus particularly well suited to handling finite element models of structures in frictional contact, as it does not require a special model for the contact interface. Dynamic Lagrangians are also better suited to frequency-domain friction problems than the traditional time-domain method of augmented Lagrangians. Furthermore, a reduction of the non-linear system to relative interface displacements is introduced to decrease the computation time. The DLFT method is validated for a beam in contact with a flexible dry friction element connected to ground, for frictional constraints that feature two-dimensional relative motion. Results are also obtained for a large-scale structural system with a large number of one-dimensional dry-friction dampers. The DLFT method is shown to be accurate and fast, and it does not suffer from convergence problems, at least in the examples studied.