Clock frequency estimation under spontaneous emission

We investigate the quantum dynamics of a driven two-level system under spontaneous emission and its application in clock frequency estimation. By using the Lindblad equation to describe the system, we analytically obtain its exact solutions, which show three different regimes: Rabi oscillation, damped oscillation, and overdamped decay. From the analytical solutions, we explore how the spontaneous emission affects the clock frequency estimation. We find that under a moderate spontaneous emission rate, the transition frequency can still be inferred from the Rabi oscillation. Our results enable potential practical applications in frequency measurement and quantum control under decoherence.     

Analytical solution of transverse oscillation in cyclotron using LP method

We have carried out an approximate analytical solution to precisely consider the influence of magnetic field on the transverse oscillation of particles in a cyclotron.The differential equations of transverse oscillation are solved from the Lindstedt-Poincare method.After careful deduction,accurate first-order analytic solutions are obtained.The analytical solutions are applied to the magnetic field from an isochronous cyclotron with four spiral sectors.The accuracy of these analytical solutions is verified and confirmed from comparison with a numerical method.Finally,we discussed the transverse oscillation at v_0=N/2,using the same analytical solution.     

Harmonic balancing approach to nonlinear oscillations of a punctual charge in the electric field of charged ring

The harmonic balance method is used to construct approximate frequency-amplitude relations and periodic solutions to an oscillating charge in the electric field of a ring. By combining linearization of the governing equation with the harmonic balance method, we construct analytical approximations to the oscillation frequencies and periodic solutions for the oscillator. To solve the nonlinear differential equation, firstly we make a change of variable and secondly the differential equation is rewritten in a form that does not contain the square-root expression. The approximate frequencies obtained are valid for the complete range of oscillation amplitudes and excellent agreement of the approximate frequencies and periodic solutions with the exact ones are demonstrated and discussed.     

有界非局域非线性介质中空间光孤子传输的研究

对有界非局域非线性介质边界对孤子传输的影响进行了研究.基于非局域非线性薛定谔方程以及热传导的泊松方程,采用格林函数法求出了强非局域介质铅玻璃的响应函数和临界功率;从光线方程出发得到了偏离材料中心入射的光束中心振荡轨迹以及周期的解析解.通过数值模拟证明了该结果在不靠近样品边界的范围内都是准确的. 关键词： 空间光孤子 铅玻璃 非局域非线性     

Nonlinear Neutral Delay Differential Equations of Fourth-Order: Oscillation of Solutions

The objective of this paper is to study oscillation of fourth-order neutral differential equation. By using Riccati substitution and comparison technique, new oscillation conditions are obtained which insure that all solutions of the studied equation are oscillatory. Our results complement some known results for neutral differential equations. An illustrative example is included.     

环形腔中激光振荡输出的横向斑图及向光学湍流的转变

在研究环形腔中激光振荡输出的分岔与混沌的基础上,采用耦合映象格子模型研究了其空间扩展系统的横向效应.数值模拟表明,随着参数的改变,空间扩展系统由均匀稳态、行波解向时空混沌演化.在一定的参数条件下,空间扩展系统从光场取入射平面波(均匀分布)开始,经对称破缺向光学湍流转变. 关键词： 横向斑图 时空混沌 湍流 数值模拟     

Bifurcation, amplitude death and oscillation patterns in a system of three coupled van der Pol oscillators with diffusively delayed velocity coupling

In this paper, we study a system of three coupled van der Pol oscillators that are coupled through the damping terms. Hopf bifurcations and amplitude death induced by the coupling time delay are first investigated by analyzing the related characteristic equation. Then the oscillation patterns of these bifurcating periodic oscillations are determined and we find that there are two kinds of critical values of the coupling time delay: one is related to the synchronous periodic oscillations, the other is related to eight branches of asynchronous periodic solutions bifurcating simultaneously from the zero solution. The stability of these bifurcating periodic solutions are also explicitly determined by calculating the normal forms on center manifolds, and the stable synchronous and stable phase-locked periodic solutions are found. Finally, some numerical simulations are employed to illustrate and extend our obtained theoretical results and numerical studies also describe the switches of stable synchronous and phase-locked periodic oscillations.     

The effect of viscosity changes in the vocal folds on the range of oscillation

Changes in vocal fold oscillation threshold pressure were induced in excised canine larynges by experimentally causing fluid movement into and out of the vocal folds. The transport was facilitated by exposing the vocal folds to various osmotic solutions, and it was assumed that changes in hydration caused changes in the internal tissue viscosity. A range of oscillation threshold pressures was measured for each condition of hydration by varying length and glottal width. The oscillation threshold pressure shifted as predicted. Decreased hydration (increased viscosity) raised the threshold of oscillation, and increased hydration (decreased viscosity) lowered the threshold of oscillation. This apparently represents the first in vitro model for the study of the effect of viscosity changes of the internal environment of the vocal folds on phonation.     

光学双稳性的强迫振动模型

本文提出一个新的光学双稳性模型.基于平均场近似,慢变振幅近似和绝热近似的思想,把光学双稳系统看成一个“黑箱”,类比非线性振动理论,指出不同的光学双稳过程(包括不同的工作物质和不同的腔(F-P腔或环腔)),能用一个恰当的强迫振动方程统一地描述.方程中所包含的都是可测量的宏观参量,使得可能直接用实验拟合,与理论结果进行定量对照.用振动理论的方法,把方程演变成自治方程组,从而方便地得到光学双稳性稳态和动态解的一般形式.并用若干已报道的具体例子验证了这个模型的普适性.     

Uniqueness and Stability of Riemann Solutions¶with Large Oscillation in Gas Dynamics

We prove the uniqueness of Riemann solutions in the class of entropy solutions in with arbitrarily large oscillation for the 3 × 3 system of Euler equations in gas dynamics. The proof for solutions with large oscillation is based on a detailed analysis of the global behavior of shock curves in the phase space and the singularity of centered rarefaction waves near the center in the physical plane. The uniqueness of Riemann solutions yields their inviscid large-time stability under arbitrarily large perturbation of the Riemann initial data, as long as the corresponding solutions are in L ^∞ and have local bounded total variation satisfying a natural condition on its growth with time. No specific reference to any particular method for constructing the entropy solutions is needed. The uniqueness result for Riemann solutions can easily be extended to entropy solutions U(x,t), piecewise Lipschitz in x, for any t > 0, with arbitrarily large oscillation. Received: 23 April 2001 / Accepted: 20 September 2001     

讨论简谐振动不容忽视的问题

指出了分析判断简谐振动时易被忽视的一个问题,给出了简洁明了的分析方法和实例,进而明确了一定振动系统的运动性质与坐标原点选择无关,以及振动系统的能量守恒与势能零参考点的选择无关等基本结论．     

On a classical analog of the isospectral Schrödinger problem

It is shown that the problem of potential deformations that preserve the energy dependence of the oscillation frequency corresponds in the classical limit to the isospectral problem for the Schrödinger equation. The solutions of the corresponding evolutionary equations for the potential (with respect to the deformation parameter) are simple Riemann waves. The relation between such solutions and the solutions of the inverse problem of mechanics — the problem of reconstructing the potential given the energy dependence of the oscillation frequency — is determined.     

Asymptotic analysis of Bloch-Floquet waves in a thin bi-material strip with a periodic array of finite-length cracks

We present an asymptotic algorithm to solve a problem of wave propagation in a thin bi-material strip with an array of cracks situated at the interface between two materials. For small frequencies we construct an asymptotic solution which takes into account the singular behavior near the crack tips and the smooth nature of the oscillation far away from them. We construct the boundary layer solutions near the crack tips. The boundary layers are harmonic solutions in scaled domains. Dispersion equations are derived and solved within the frame of the asymptotic model.     

Asymptotic analysis of Bloch–Floquet waves in a thin bi-material strip with a periodic array of finite-length cracks

We present an asymptotic algorithm to solve a problem of wave propagation in a thin bi-material strip with an array of cracks situated at the interface between two materials. For small frequencies we construct an asymptotic solution which takes into account the singular behavior near the crack tips and the smooth nature of the oscillation far away from them. We construct the boundary layer solutions near the crack tips. The boundary layers are harmonic solutions in scaled domains. Dispersion equations are derived and solved within the frame of the asymptotic model.     

Application of energy balance method and variational iteration method to an oscillation of a mass attached to a stretched elastic wire

This letter applies energy balance method and variational iteration method to a nonlinear oscillation of a mass attached to a stretched wire. Comparison of the period of oscillation and obtained solutions with the exact one shows that both methods are very effective and convenient and quite accurate to nonlinear engineering problems.     

The cubic period-distance relation for the Kate reversible pendulum

We describe the correct cubic relation between the mass configuration of a Kater reversible pendulum and its period of oscillation. From an analysis of its solutions we conclude that there could be as many as three distinct mass configurations for which the periods of small oscillations about the two pivots of the pendulum have the same value. We also discuss a real compound Kater pendulum that realizes this property.     

Hysteresis and bistability in a realistic cell model for calcium oscillations and action potential firing

Many cells reveal oscillatory behavior. Some cells reveal action-potential firing resulting from Hodgkin-Huxley (HH) type dynamics of ion channels in the cell membrane. Another type of oscillation relates to periodic inositol triphospate (IP3)-mediated calcium transients in the cytosol. In this study we present a bifurcation analysis of a cell with an excitable membrane and an IP3-mediated intracellular calcium oscillator. With IP3 concentration as a control parameter the model reveals a complex, rich spectrum of both stable and unstable solutions with hysteresis corresponding to experimental data. Our results reveal the emergence of complex behavior due to interactions between subcomponents with a relatively simple dynamical behavior.     

S波段四腔强流相对论速调管的设计和实验研究

本文根据四腔强流相对论速调管设计过程中出现的高次模振荡现象,采用电磁场软件模拟,分析了这种振荡的产生原因,给出抑制这种高次模振荡的方法.利用二维和三维模拟软件,研究了谐振腔谐振频率、谐振腔Q值、漂移管长度、特性阻抗等参数的变化对高次模振荡的影响,模拟上验证了高次模振荡抑制方法的有效性,并在输出端模拟获得了功率2.13 GW、效率26%、增益60 dB的输出微波,实现了2D,3D中高次模振荡的有效抑制.最终在实验中获得了功率1.9 GW、效率24%、增益61 dB的输出微波.     

Coherent spin-current oscillations in transverse magnetic fields

We address the coherence of the dynamics of spin-currents with components transverse to an external magnetic field for the spin-1/2 Heisenberg chain. We study current autocorrelations at finite temperatures and the real-time dynamics of currents at zero temperature. Besides a coherent Larmor oscillation, we find an additional collective oscillation at higher frequencies, emerging as a coherent many-magnon effect at low temperatures. Using numerical and analytical methods, we analyze the oscillation frequency and decay time of this coherent current-mode versus temperature and magnetic field.     

一类具时滞的厄尔尼诺-南方涛动充电-放电振子模型的Hopf分岔与周期解问题

研究了一类具时滞的厄尔尼诺-南方涛动充电-放电振子模型. 给出了产生Hopf分岔的临界时滞条件, 利用Mawhin重合度理论,探讨了该模型的周期解问题. 关键词： 时滞 厄尔尼诺-南方涛动模型 Hopf分岔 周期解