Twist Property of Periodic Motion of an Atom Near a Charged Wire

We study the Lyapunov stability of periodic motion of an atom in the vicinity of an infinite straight wire with an oscillating uniform charge, which serves as a mechanism for trapping cold neutral atoms. It is proved by King and Leséniewski that the system has classical periodic motion for a certain range of parameters. In this Letter, we will prove, using the Birkhoff Normal Forms and Morse Twist Theorem, that such a periodic state is of twist type. As a result, besides the stability of the periodic state in the sense of Lyapunov, the system has infinitely many interesting bound states such as subharmonics and quasi-periodic states.     

周期运动实验仪的研制

周期运动是自然界常见的基本运动形式,但在超出视觉停留范围时,直接观测周期运动(例如像转动、振动)就非常困难。周期运动实验仪的研制,实现了对高速运动的"慢速"观察。     

带电粒子束的等时周期场聚焦

在质子直线加速器中经常利用等时周期场对粒子束进行聚焦. 这种周期场的特点是周期长度不等而粒子经过每一周期的时间为常数,本文讨论等时周期场聚焦的基本理论,并将它推广到周期长度缓慢变化的周期场.     

Velocity Multistability vs. Ergodicity Breaking in a Biased Periodic Potential

Multistability, i.e., the coexistence of several attractors for a given set of system parameters, is one of the most important phenomena occurring in dynamical systems. We consider it in the velocity dynamics of a Brownian particle, driven by thermal fluctuations and moving in a biased periodic potential. In doing so, we focus on the impact of ergodicity—A concept which lies at the core of statistical mechanics. The latter implies that a single trajectory of the system is representative for the whole ensemble and, as a consequence, the initial conditions of the dynamics are fully forgotten. The ergodicity of the deterministic counterpart is strongly broken, and we discuss how the velocity multistability depends on the starting position and velocity of the particle. While for non-zero temperatures the ergodicity is, in principle, restored, in the low temperature regime the velocity dynamics is still affected by initial conditions due to weak ergodicity breaking. For moderate and high temperatures, the multistability is robust with respect to the choice of the starting position and velocity of the particle.     

Time Periodic Electroosmotic Flow of The Generalized Maxwell Fluids in a Semicircular Microchannel

Analytical solutions are presented using method of separation of variables for the time periodic electroosmotic flow (EOF) of linear viscoelastic fluids in semicircular microchannel. The linear viscoelastic fluids used here are described by the general Maxwell model. The solution involves analytically solving the linearized Poisson-Boltzmann (P -B) equation, together with the Cauchy momentum equation and the general Maxwell constitutive equation. By numerical computations, the influences of electric oscillating Reynolds number Re and Deborah number De on velocity amplitude are presented. For small Re, results show that the larger velocity amplitude is confined to the region near the charged wall when De is small. With the increase of the Deborah number De, the velocity far away the charged wall becomes larger for large Deborah number De. However, for larger Re, the oscillating characteristic of the velocity amplitude occurs and becomes significant with the increase of De, especially for larger Deborah number.     

Electrostatic Surface Trap for Cold Polar Molecules with a Charged Circular Wire

We propose a novel scheme to trap cold polar molecules on the surface of an insulating substrate （i.e. a chip） by using an inhomogeneous electrostatic field, which is generated by the combination of a circular charged wire （a ring electrode） and a grounded metal plate. The spatial distributions of the electrostatic field from the above charged wire layout and its Stark potentials for CO molecules are calculated. Our study shows that when the voltage applied to the wire is U = 15 kV, a ring radius is R = 5 mm, the thickness of the insulating substrate is b = 5 mm, and a wire radius is r = 1mm, the maximum efficient trapping potential （i.e., as equivalent temperature） for CO molecules is greater than 141.7mK, which is high enough to trap cold polar molecules with a temperature of 50 mK in the low-field-seeking states.     

激光空泡在近自由液面运动特性的实验研究

采用激光技术聚焦击穿液体产生空泡,利用高速摄像系统开展激光空泡与自由液面的相互作用的实验研究。实验研究发现,空泡与自由液面之间的无量纲距离对水下空泡的脉动特性和自由液面的水冢现象存在影响。通过大量实验总结了无量纲距离与空泡半径、空泡脉动周期、自由液面水柱的最大高度和产生水冢时间的相互关系。实验表明无量纲距离越小,空泡脉动周期越短,自由面的水冢现象越明显。同时统计出了在不同无量纲距离范围内所出现的5种不同水冢现象的规律。研究内容为空泡与自由液面相互作用的理论提供了实验依据。     

Vacuum Fluctuations and Motion of a Charged Test Particle in a Cylindrical Spacetime

The effects of quantum electromagnetic fluctuations upon the motion of a test charged particle are examined in a cylindrical spacetime in which one spatial is compactified. The mean squared fluctuations in the velocity and position of the test particle are calculated. It is found that the random motion of the test particle will be anisotropic. The possible consequences for theories with extra compactified spatial dimensions are discussed.     

Chaotic Behavior of a Brownian Particle in a Periodic Potential

The classical deterministic dynamics of a Brownian particle with a time-dependent periodic perturbation in a spatially periodic potential is investigated. We have constructed a perturbed chaotic solution near the heteroclinic orbit of the nonlinear dynamics system by using the Constant-Variation method. Theoretical analysis and numerical result show that the motion of the Brownian particle is a kind of chaotic motion. The corresponding chaotic region in parameter space is obtained analytically and numerically.     

The Shell of Incoherent Charged Matter Falling onto a Charged Rotating Black Hole

The motion of the shell of charged testparticles falling radially from rest at infinity withzero total angular momentum onto a Kerr–Newmanblack hole is studied. The shell, initially spherical,becomes prolate along the axis of symmetry of the holeduring the fall. The shape of the shell from theviewpoint of distant observers is characterized by meansof the photons moving along geodesics of the outgoing principal null congruence. The motion of theshell is examined analytically for large distances andnear the horizon. In the special case, when at largedistances of the hole the attractive Newtongravitational force is compensated by the repulsive Coulombforce, the complete motion is given explicitly in termsof elementary functions.     

Chaotic Behavior of a Brownian Particle in a Periodic Potential

The classical deterministic dynamics of a Brownian particle with a time-dependent periodic perturbation in a spatially periodic potential is investigated. We have constructed a perturbed chaotic solution near the heteroclinic orbit of the nonlinear dynamics system by using the Constant-Variation method. Theoretical analysis and numerical result show that the motion of the Brownian particle is a kind of chaotic motion. The corresponding chaotic region in parameter space is obtained analytically and numerically.     

The Motion of a Pair of Charged Particles

We revisit the problem of two (oppositely) charged particles interacting electromagnetically in one dimension with retarded potentials and no radiation reaction. The specific quantitative result of interest is the time it takes for the particles to fall in towards one another. Starting with the nonrelativistic form, we answer this question while adding layers of complexity until we arrive at the full relativistic delay differential equation that governs this problem. That case can be solved using the Synge method, which we describe and discuss.     

Alternative Simulating Technique for Periodic Motion in the Presence of Multiplicative White Noise

An effective approach for simulating the periodic motion of an overdamped particle subjected to a multiplicative white-noise source is described. The accurate calculations for the velocity of the particle and its correlation function can be realized by introducing an inertial term. The results show that fluctuation around a time-averaged quantity increases with decreasing time step in the overdamped white-noise algorithm, however, a massive white-noise technique greatly reduces this spurious drift. In particular, the present algorithm converges on the correct values of the calculated quantities, while the mass of the particle approaches to zero.     

基础水平运动的弹簧摆的周期解与稳定性

针对基础水平运动的弹簧摆的非线性动力学响应进行研究,利用拉格朗日方程建立了系统的动力学方程.将离散傅里叶变换、谐波平衡法以及同伦延拓方法相结合,对系统的周期响应进行求解,避免了传统方法计算中使用泰勒展开引起的小振幅的限制,与数值计算结果的对比表明该求解方法具有较高的精确度.利用Floquet理论分析了周期响应的稳定性,给出了基础运动振幅和频率对系统周期响应的影响.研究发现:对应某些基础频率和振幅,系统的周期响应可能发生Hopf分岔;利用数值计算研究了Hopf分岔后系统响应随基础频率和振幅的变化,发现系统出现了倍周期运动、拟周期运动和混沌等复杂的动力学行为.研究表明系统进入混沌的主要路径是拟周期环面破裂和阵发性.     

基于周期性截断灰色系统的电力负荷预测

电力负荷预测是电力系统调度和电力生产计划制定的重要依据。电力负荷时间序列有着明显的周期性特征。传统的电力负荷预测主要侧重于预测方法的研究,而忽略了电力负荷数据周期性特性的分析,影响了预测的准确性。针对电力负荷时间序列的周期性特征,提出了一种基于周期性截断的灰色系统模型来进行电力负荷预测。该模型利用周期性截断来反映负荷数据的周期性特征,提高了预测的精度。仿真采用EUNITE Network的公开负荷数据进行算法性能的测试,并与一些主流的电力负荷预测算法：BP神经网络、极限学习机、自回归模型以及传统的灰色系统模型做比较。仿真结果表明,周期性截断的灰色系统负荷预测的归一化均方误差和绝对平均误差是最小的。周期性截断的灰色系统为电力系统负荷预测提供了一种新的有效方法。     

Dissipative Cyclotron Motion of a Charged Quantum-Oscillator and Third Law

In this work, low temperature thermodynamic behavior in the context of cyclotron motion of a charged-oscillator with different coupling schemes is analyzed. We find that finite dissipation substitutes the zero-coupling result of exponential decay of entropy by a power law behavior at low temperature. The power of the power law explicitly depends on the nature of the power spectrum of the heat bath. It is seen that velocity–velocity coupling is the most advantageous coupling scheme to ensure the third law of thermodynamics. The cases of confinement (ω ₀≠0) and without confinement (ω ₀=0) are discussed separately. It is also revealed that different thermodynamic functions are independent of magnetic field at very low temperature for ω ₀≠0, but they depend on cyclotron frequency (ω _c =eB/mc) for ω ₀=0.     

“带电粒子在电场和磁场中的运动”课程思政设计

大学物理课程应注重科学伦理和科学思维方法的教育,培养学生的不畏艰险、勇攀科学高峰、追求真理的精神.课程思政建设要有机融入课堂教学,需要把思政元素融入教材编审、教案课件、教学大纲、课程目标设计各个方面,贯穿于课程授课、学生课堂讨论、作业和考试等各环节.以"带电粒子在电场和磁场中的运动"课思政设计为例,把课程思政融入知识传授,使物理课程成为立德树人的重要阵地.     

Coagulation of Charged Aerosols

We consider the coagulation of an aerosol embedded in a stationary atmosphere of bipolar ions. Particles respond to the ionic environment by developing an instantaneous charge the fluctuations of which may produce attraction or repulsion between the particles. The governing parameter is the charge asymmetry factor which quantifies the relative charging efficiency of positive and negative ions. We use a Monte Carlo method to solve the coagulation equation in the free-molecule regime. We perform simulations for conditions ranging from symmetric and nearly symmetric environments (e.g. flames, ionizers), which result in particles that are on the average neutral to highly asymmetric conditions (low-pressure plasmas), which produce a substantial non-zero net charge. In symmetric ionic atmospheres we find that electrostatic interactions are unimportant and particles grow as if in the absence of charging ions. In asymmetric bipolar atmospheres, electrostatic interactions between particles are repulsive, the mean particle size grows logarithmically in time and the resulting size distributions are significantly narrower than the classical self preserving distributions.     

Tunneling Radiation of the Charged Particles for Charged Spherical Black Hole in VGM

Applying Parikh’s semi-classical tunneling method, Hawking radiation of charged massive particles via tunneling from charged spherical black hole in vacuum for Vector Graviton Metric theory (VGM) of gravitation is investigated. Because the derivation respects conservation of energy and charge, the tunneling rate of particles is relevant to the change of Bekenstein-Hawking entropy and the exact spectrum is not precisely thermal. The result employs an underlying unitary theory. PACS numbers: 04.70.-s, 97.60. Lf