Yuan Qing-Xin

Comment on ‘Approximation for a large-angle simple pendulum period’

In a recent letter, Belendez et al (2009 Eur. J. Phys. 30 L25–8) proposed an alternative of approximation for the period of a simple pendulum suggested earlier by Hite (2005 Phys. Teach. 43 290–2) who set out to improve on the Kidd and Fogg formula (2002 Phys. Teach. 40 81–3). As a response to the approximation scheme, we obtain another analytical approximation for the large-angle pendulum period, which owns the simplicity and accuracy in evaluating the exact period, and moreover, for amplitudes less than 144° the analytical approximate expression is more accurate than others in the literature.

Note on the dog-and-rabbit chase problem in introductory kinematics

A new simple derivation of the critical region for the dog-and-rabbit chase problem is presented, which uses the concept of relative motion in introductory mechanics courses.

Note on the ‘log formulae’ for pendulum motion valid for any amplitude

In this note, we present an improved approximation to the solution of Lima (2008 Eur. J. Phys. 29 1091), which decreases the maximum relative error from 0.6% to 0.084% in evaluating the exact pendulum period.

Computing Ground State Solution of Bose?Einstein Condensates Trapped in One-Dimensional Harmonic Potential

For Bose–Einstein condensates trapped in a harmonic potential well, we present numerical results from solving the time-dependent nonlinear Schrodinger equation based on the Crank–Nicolson method. With this method we are able to find the ground state wave function and energy by evolving the trial initial wave function in real and imaginary time spaces, respectively. In real time space, the results are in agreement with [Phys. Rev. A 51 (1995) 4704], but the trial wave function is restricted in a very small range. On the contrary, in imaginary time space, the trial wave function can be chosen widely, moreover, the results are stable.

The theoretical study of dispersion managementin a photonic crystal fiber

Photonic crystal fiber is widely used in optical communication and ultrafast optics. In this paper, the nonlinear Schrodinger equation in the photonic crystal fiber is studied analytically. With the Horita method, the bilinear form are derived, and the analytic one-soliton solution for the nonlinear Schrodinger equation are obtained. Through the analytic one-soliton solution obtained, the transmission characteristics of solitons in the photonic crystal fiber are analyzed with the different group velocity dispersion. With the help of the dispersion management technology, we discuss the soliton transmission in the case of different group velocity dispersion functions by changing the group velocity dispersion of the photonic crystal fiber. If the group velocity dispersion function of the photonic crystal fiber is constant, the solitons can keep their velocities and shapes during the transmission. If the group velocity dispersion function of the photonic crystal fiber is the trigonometric one, the solitons show the periodic transmission. While the group velocity dispersion function of the photonic crystal fiber is the Gauss one, the properties of local solitons are demonstrated. Moreover, when the group velocity dispersion function of the photonic crystal fiber is the linear one, the soliton compression and amplification in the photonic crystal fiber can be realized simultaneously. The conclusion of this paper provides a theoretical reference for the corresponding dispersion management technology in the photonic crystal fiber.

Numerical Study of ϕ4 Model by Potential Importance Sampling Method

We investigate the phenomena of spontaneous symmetry breaking for 4 model on a square lattice in the parameter space by using the potential importance sampling method, which was proposed by Milchev, Heermann, and Binder [J. Stat. Phys. 44 (1986) 749]. The critical values of the parameters allow us to determine the phase diagram of the model. At the same time, some relevant quantities such as susceptibility and specific heat are also obtained.

Numerical Determination of the Critical Value for the (1+1)-Dimensional Sine-Gordon Model

A new procedure of potential importance sampling method is applied to investigate the phase transition of the (1+1)-dimensional sine-Gordon model. With this method, we obtain the Kosterlitz–Thouless-type phase transition critical value of β28π with a relative error as small as 0.4%.

Electron Transport Through Double-Dot Aharonov-Bohm Interferometer in the Kondo Regime*

By applying the slave boson technique, we have studied the electron transport through double-dot Aharonov–Bohm interferometer in the Kondo regime. For the system with symmetric quantum dots, the linear conductance is shown to be enhanced by Kondo effect, but it is suppressed in the deep dot level regime in the presence of nonzero magnetic flux. The Aharonov–Bohm oscillations of the conductance are also investigated.