Momentum-dependent symmetries and non-Noether conserved quantities for nonholonomic nonconservative Hamilton canonical systems

This paper investigates the momentum-dependent symmetries for nonholonomic nonconservative Hamilton canonical systems. The definition and determining equations of the momentum-dependent symmetries are presented, based on the invariance of differential equations under infinitesimal transformations with respect to the generalized coordinates and generalized momentums. The structure equation and the non-Noether conserved quantities of the systems are obtained. The inverse issues associated with the momentum-dependent symmetries are discussed. Finally, an example is discussed to further illustrate the applications.

LARGE TIME BEHAVIORS OF THE ISENTROPIC BIPOLAR COMPRESSIBLE NAVIER-STOKES-POISSON SYSTEM

The isentropic bipolar compressible Navier-Stokes-Poisson （BNSP） system is investigated in R3 in the present paper. The optimal time decay rate of global strong solution is established. When the regular initial data belong to the Sobolev space H l（R3） ∩ B˙ s 1,1 （R3） with l ≥ 4 and s ∈ （0, 1], it is shown that the momenta of the charged particles decay at the optimal rate （1＋t） 1 4 s 2 in L2 -norm, which is slower than the rate （1＋t） 3 4 s 2 for the compressible Navier-Stokes （NS） equations [14]. In particular, a new phenomenon on the charge transport is observed. The time decay rate of total density and momentum was both （1 ＋ t） 3 4 due to the cancellation effect from the interplay interaction of the charged particles.

Partition method for impact dynamics of flexible multibody systems based on contact constraint

The impact dynamics of a flexible multibody system is investigated. By using a partition method, the system is divided into two parts, the local impact region and the region away from the impact. The two parts are connected by specific boundary conditions, and the system after partition is equivalent to the original system. According to the rigid-flexible coupling dynamic theory of multibody system, system＇s rigid-flexible coupling dynamic equations without impact are derived. A local impulse method for establishing the initial impact conditions is proposed. It satisfies the compatibility con- ditions for contact constraints and the actual physical situation of the impact process of flexible bodies. Based on the contact constraint method, system＇s impact dynamic equa- tions are derived in a differential-algebraic form. The contact/separation criterion and the algorithm are given. An impact dynamic simulation is given. The results show that system＇s dynamic behaviors including the energy, the deformations, the displacements, and the impact force during the impact process change dramatically. The impact makes great effects on the global dynamics of the system during and after impact.

Symplectic-energy-first integrators of discrete mechanico-electrical dynamical systems

A discrete total variation calculus with variable time steps is presented for mechanico-electrical systems where there exist non-potential and dissipative forces. By using this discrete variation calculus, the symplectic-energy-first integrators for mechanico-electrical systems are derived. To do this, the time step adaptation is employed. The discrete variational principle and the Euler-Lagrange equation are derived for the systems. By using this discrete algorithm it is shown that mechanico-electrical systems are not symplectic and their energies are not conserved unless they are Lagrange mechanico-electrical systems. A practical example is presented to illustrate these results.

New two-mode intermediate momentum-coordinate representation with quantum entanglement and its application

We construct four linear composite operators for a two-particle system and give common eigenvectors of those operators. The technique of integration within an ordered product （IWOP） of operators is employed to prove that those common eigenvectors are complete and orthonormal. Therefore, a new two-mode intermediate momentum-coordinate representation which involves quantum entanglement for a two-particle system is proposed and applied to some twobody dynamic problems. Moreover, the pure-state density matrix ｜ξ1,ξ2｜ C,D C,D（ξ1, ξ2｜ is a Radon transform of Wigner operator.

Nonlinear dynamical symmetries of Smorodinsky-Winternitz and and Fokas-Lagerstorm systems

General solutions of the Smorodinsky-Winternitz system and the Fokas-Lagerstorm system, which are superintegrable in two-dimensional Euclidean space, are obtained using the algebraic method （structure function）. Their dynamical symmetries, which are governed by deformed angular momentum algebras, are revealed.

Momentum Distribution Functions in Quark-Gluon Plasma

Based on the constituent quasiparticle model of the quark-gluon plasma (QGP), the Wigner function is presented in the form of a color path integral. The Monte Carlo calculations of the quark and gluon densities, pair correlation functions and the momentum distribution functions for strongly coupled QGP plasma in thermal equilibrium at barion chemical potential equal to zero have been carried out. Analysis of the pair correlation functions points out on arising glueballs and related gluon bound states. Comparison results between the momentum distribution functions and Maxwell-Boltzmann distributions show the significant influence of the interparticle interaction on the high energy asymptotics of the momentum distribution functions resulting in the appearance of quantum “tails”.

TIME ASYMPTOTIC BEHAVIOR OF THE BIPOLAR NAVIER-STOKES-POISSON SYSTEM

The bipolar Navier-Stokes-Poisson system （BNSP） has been used to simulate the transport of charged particles （ions and electrons for instance） under the influence of electrostatic force governed by the self-consistent Poisson equation. The optimal L^2 time convergence rate for the global classical solution is obtained for a small initial perturbation of the constant equilibrium state. It is shown that due to the electric field, the difference of the charge densities tend to the equilibrium states at the optimal rate （1 ＋ t）^-3/4 in L^2-norm, while the individual momentum of the charged particles converges at the optimal rate （1 ＋ t）^-1/4 which is slower than the rate （1 ＋ t）^-3/4 for the compressible Navier-Stokes equations （NS）. In addition, a new phenomenon on the charge transport is observed regarding the interplay between the two carriers that almost counteracts the influence of the electric field so that the total density and momentum of the two carriers converges at a faster rate （1 ＋ t）^-3/4＋ε for any small constant ε 〉 0. The above estimates reveal the essential difference between the unipolar and the bipolar Navier-Stokes-Poisson systems.

Diagrammatic Approach for Investigating Two Dimensional Elastic Collisions in Momentum Space II: Special Relativity

The diagrammatic approach to the collision problems in Newtonian mechanics is useful. We show in this article that the same technique can be applied to the case of the special relativity. The two circles play an important role in Newtonian mechanics, while in the special relativity, we need one circle and one ellipse. The circle shows the collision in the center-of-mass system. And the ellipse shows the collision in the laboratory system. These two figures give all information on two dimensional elastic collisions in the special relativity.

Diagrammatic Approach for Investigating Two Dimensional Elastic Collisions in Momentum Space I: Newtonian Mechanics

We present the usefulness of the diagrammatic approach for analyzing two dimensional elastic collision in momentum space. In the mechanics course, we have two major purposes of studying the collision problems. One is that we have to obtain velocities of the two particles after the collision from initial velocities by using conservation laws of momentum and energy. The other is that we have to study two ways of looking collisions, i.e. laboratory system and center-of-mass system. For those two major purposes, we propose the diagrammatic technique. We draw two circles. One is for the center-of-mass system and the other is for the laboratory system. Drawing these two circles accomplish two major purposes. This diagrammatic technique can help us understand the collision problems quantitatively and qualitatively.

Quasi-momentum theorem in Riemann-Cartan space

The geometric formulation of motion of the first-order linear homogenous scleronomous nonholonomic system subjected to active forces is studied with the non- holonomic mapping theory. The quasi-Newton law, the quasi-momentum theorem, and the second kind Lagrange equation of dynamical systems are obtained in the Riemann- Cartan configuration spaces. By the nonholonomic mapping, a Euclidean configuration space or a Riemann configuration space of a dynamical system can be mapped into a Riemann-Cartan configuration space with torsion. The differential equations of motion of the dynamical system can be obtained in its Riemann-Cartan configuration space by the quasi-Newton law or the quasi-momentum theorem. For a constrained system~ the differential equations of motion in its Riemann-Cartan configuration space may be sim- pler than the equations in its Euclidean configuration space or its Riemann configuration space. Therefore, the nonholonomic mapping theory can solve some constrained prob- lems, which are difficult to be solved by the traditional analytical mechanics method. Three examples are given to illustrate the effectiveness of the method.

Global Static Solutions of the Spherically Symmetric Vlasov-Einstein-Maxwell (VEM) System for Low Charge

We consider the VEM system in the context of spherical symmetry and we try to establish a global static solutions with isotropic pressure that approaches Minkowski spacetime at infinity and have a regular center. To be in accordance with numerical investigation we take here low charge particles.

书法擒纵论

擒纵是总结吸收前人用笔经验的基础上所提出的技法。擒是内擫笔法,表现为蓄势紧束与劲健。纵是外拓笔法,表现为郁勃奔放与开阔。用擒纵能高效地控制笔锋,写出的线条节奏变化丰富,点画生动美妙,书风通灵超脱,从而遏制因平拖直过单一运笔所形成的点画僵滞、书风呆板的缺点。擒纵是对书家用笔技巧难度和高度的协调统一。知擒纵才可以明晰收放之度,字法才开张奇险,章法字字侵让连贯不断,表现书写主体雄肆的气势与激昂的情志。擒纵也代表着破法、变法与创新,是书写主体创造力的张扬。

非质心系的角动量定理

选择适当的参考点在解决刚体运动问题中至关重要,能有效简化问题处理.相对于质心转轴,非质心系提供更为灵活的视角.本文通过推导非质心系的角动量定理,以小球碰撞自由杆模型为例,展示了其在实际问题中的应用.本文为读者提供了处理刚体运动问题的新思路,特别是在复杂情境下更为直观.

基于动量梯度下降的回声消除算法

针对极端环境话音系统下声学回波影响工作人员正常施工,且常规声学回声消除算法收敛速度慢的问题,提出一种基于动量梯度下降的基于l0范数的改进系数成比例归一化最小均方误差算法(L0⁃IPNLMS)。该算法将动量因子引入L0⁃IPNLMS算法中,解决在算法运行过程中梯度下降时梯度摆动幅度可能过大的问题,也提高了自适应滤波器的收敛速度,且残余回声下降明显,声学回波抑制效果更好。仿真实验表明,与L0⁃IPNLMS算法相比,新算法在模拟随机多音信号与真实语音信号输入时,均方误差(MSE)可以降低3.47 dB和3.69 dB,回波抑制比(ERLE)提高了3.46 dB和3.68 dB,在低信噪比情况下,使用新算法对真实语音信号进行回声消除,收敛速度高于L0⁃IPNLMS等算法,且收敛效果有明显改进。

基于飞轮储能技术的可再生能源发电系统广义动量补偿控制研究

提出一种利用飞轮储能装置调控可再生能源发电系统的方法,用于解决系统的能量补偿问题;同时,将广义动量概念引入电力系统,通过建立飞轮储能系统和可再生能源发电系统的广义动量模型,提出广义动量补偿控制方法。将飞轮储能装置接入可再生能源发电系统的电压中枢点,实时检测电压中枢点母线电压、飞轮角速度,计算发电系统等效惯性参数和飞轮储能装置瞬时动量;计算可再生能源发电系统相对于标准状态的动量增量;对飞轮角速度进行调节,使飞轮储能装置的动量增量等于可再生能源发电系统的动量增量。该方法不仅能实时计算电网能量的不平衡程度,对该电网系统进行快速、准确补偿,而且该装置运行寿命长,对环境无污染,可广泛应用于太阳能光伏发电系统、风力发电系统和海浪能发电系统等。

中国式现代化背景下铁路网高质量发展指标体系研究

铁路作为国家战略性、先导性、关键性重大基础设施,铁路网能力总体上基本适应经济社会发展需要,为构建现代化综合交通运输体系发挥着重要作用。从推动铁路网运输保障供给、扩大铁路网通达服务范围、增强铁路网绿色低碳发展能力、加强铁路网互联互通建设、提升铁路网智能化水平、注重铁路网发展安全等方面,阐释中国式现代化对铁路网高质量发展要求。在此基础上,以铁路网高质量发展为指标体系核心,以发展基础、发展途径、发展动力、发展目标为指标体系维度定位,以规模密度、布局覆盖、路网结构、效率效益、服务保障、骨干作用、绿色创新、安全韧性为指标体系维度,建立铁路网高质量发展指标体系框架,分析诊断铁路网高质量发展指标体系关键指标,为推动铁路高质量发展提供研究支撑。

高水平铁饼运动员旋转中的系统角动量特征研究

旋转效果是影响铁饼投掷成绩的主要因素,主要从人体-铁饼系统角动量的视角探讨铁饼投掷过程中系统总角动量以及在各坐标轴的分角动量的特征,旨在揭示旋转与成绩的关系。选取了20多年来美国队最高水平的比赛中,在同一场比赛、同一名运动员投掷最远和较差两投相差5 m多的28位女运动员和15位男运动员的86投进行3D数据分析。结果表明:1)两种投掷成绩差距的主要因素是空气动力学距离,占总成绩差值的77.45%(女子)、65.43%(男子),因此,应该重视提高空气动力学距离;2)高水平女子铁饼运动员在投掷较远时比较近时,系统总角动量在左脚离地瞬间、左脚着地瞬间存在显著性差异(P≤0.023),X轴向负方向的角动量在左脚离地瞬间、左脚着地瞬间和出手瞬间存在显著性差异(P≤0.007),Z轴向在左脚着地瞬间和出手瞬间有较大的正旋转,存在显著性差异(P≤0.009);3)高水平男子铁饼运动员在投掷较远时比较近时,左脚着地瞬间,在X轴向负方向的角动量和Y轴正方向的角动量存在显著性差异(P≤0.042),系统总角动量在出手瞬间较小,存在显著性差异(P≤0.043)。结论:高水平铁饼运动员应更重视旋转过程中系统角动量的控制,进而提升真空距离和空气动力学距离;女运动员应该控制X轴的负旋转,增大围绕垂直轴的正旋转,即可以采用继续旋转的随前缓冲动作;男运动员应该控制X轴的旋转,增大Y轴和Z轴的正旋转,进而提升出手效果。

一种改进的降落伞动力学模型

为更准确地模拟降落伞动力学特性,根据质点系动量定理和动量矩定理推导出一种改进的降落伞动力学模型。基于该模型对某十字型伞开展了稳降阶段的编程计算,获得了降落伞和载荷体的速度及姿态角的变化情况,数值计算结果和空投试验结果有很好的一致性。该模型易于编程,相较于传统模型能得到更准确的降落伞速度和姿态角的振荡频率,是传统降落伞动力学模型的有益补充。

风环境中水面实时模拟

动态水面模拟是计算机图形学的研究热点.为进一步丰富水面场景,将质点弹簧模型与粒子系统相结合,实时模拟不同风场环境中的水面场景.首先,引入质点弹簧模型实现水面的建模,采用四边形网格的连接方式,大大减少了渲染的基本图元数,有效提高了实时性;其次,为真实模拟风场,引入粒子系统,将风场离散表示为一群风粒子,赋予风粒子位置、速度、质量等属性,有效且丰富地表达了风场模型的物理特性;再次,根据碰撞检测算法和动量守恒定律,由风粒子完成风力对水面的能量传播,实现风吹水面形成涟漪的效果,同时对边界的处理增强了细节展现;最后,使用Cg语言实现水面的反射和折射,增强了场景的真实感.