Perturbed Three Vortex Dynamics

It is well known that the dynamics of three point vortices moving in an ideal fluid in the plane can be expressed in Hamiltonian form, where the resulting equations of motion are completely integrable in the sense of Liouville and Arnold. The focus of this investigation is on the persistence of regular behavior (especially periodic motion) associated to completely integrable systems for certain (admissible) kinds of Hamiltonian perturbations of the three vortex system in a plane. After a brief survey of the dynamics of the integrable planar three vortex system, it is shown that the admissible class of perturbed systems is broad enough to include three vortices in a half-plane, three coaxial slender vortex rings in three-space, and `restricted' four vortex dynamics in a plane. Included are two basic categories of results for admissible perturbations: (i) general theorems for the persistence of invariant tori and periodic orbits using Kolmogorov-Arnold-Moser and Poincare-Birkhoff type arguments; and (ii) more specific and quantitative conclusions of a classical perturbation theory nature guaranteeing the existence of periodic orbits of the perturbed system close to cycles of the unperturbed system, which occur in abundance near centers. In addition, several numerical simulations are provided to illustrate the validity of the theorems as well as indicating their limitations as manifested by transitions to chaotic dynamics.Comment: 26 pages, 9 figures, submitted to the Journal of Mathematical Physic

Evolution and Realms of Service Leadership and Leadership Models

This paper presents a lesson plan in a course entitled “Service Leadership” at The Hong Kong Polytechnic University. In that lecture, three basic aspects of the service leadership model are presented. First, the origin of service leadership from an evolutionary anthropology perspective is outlined. Second, three realms of service leadership with reference to self, others and systems are presented. Third, two leadership models (i.e. top-down and bottom-up models) are introduced, and their strengths and weaknesses are examined. Students are also invited to reflect on their assumptions of men with reference to leadership. Several class activities including role-play, self-reflection exercises and questionnaire survey are designed to help students achieve the learning outcomes. The paper ends by highlighting topics which can help students to have critical thinking and reflections

Exact Master Equation and Quantum Decoherence of Two Coupled Harmonic Oscillators in a General Environment

In this paper we derive an exact master equation for two coupled quantum harmonic oscillators interacting via bilinear coupling with a common environment at arbitrary temperature made up of many harmonic oscillators with a general spectral density function. We first show a simple derivation based on the observation that the two-harmonic oscillator model can be effectively mapped into that of a single harmonic oscillator in a general environment plus a free harmonic oscillator. Since the exact one harmonic oscillator master equation is available [Hu, Paz and Zhang, Phys. Rev. D \textbf{45}, 2843 (1992)], the exact master equation with all its coefficients for this two harmonic oscillator model can be easily deduced from the known results of the single harmonic oscillator case. In the second part we give an influence functional treatment of this model and provide explicit expressions for the evolutionary operator of the reduced density matrix which are useful for the study of decoherence and disentanglement issues. We show three applications of this master equation: on the decoherence and disentanglement of two harmonic oscillators due to their interaction with a common environment under Markovian approximation, and a derivation of the uncertainty principle at finite temperature for a composite object, modeled by two interacting harmonic oscillators. The exact master equation for two, and its generalization to $N$, harmonic oscillators interacting with a general environment are expected to be useful for the analysis of quantum coherence, entanglement, fluctuations and dissipation of mesoscopic objects towards the construction of a theoretical framework for macroscopic quantum phenomena.Comment: 35 pages, revtex, no figures, 2nd version, references added, to appear in PR

Character Strengths in Chinese Philosophies: Relevance to Service Leadership

According to the Hong Kong Institute of Service Leadership and Management, moral character or character strength is an important attribute of an effective service leader. In connection to this, “Character Strengths in Chinese Philosophies” is one of the lecture topics taught in a course titled “Service Leadership” in a university in Hong Kong. Several topics are covered in that lecture. First, the relevance of Chinese philosophies to service leadership is discussed. Second, the core virtues in Confucian thoughts are presented. Third, the relevance of Confucian virtues to service leadership is examined. Finally, conclusions and reflections on the relevance of Confucian virtues to service leadership are outlined. In addition to one warm-up activity at the beginning of the lecture, three major activities are designed for related parts of the content. During the lecture, students are encouraged to reflect on their qualities in terms of Confucian virtues and explore effective ways to promote the development of such virtues

Electric Transport Theory of Dirac Fermions in Graphene

Using the self-consistent Born approximation to the Dirac fermions under finite-range impurity scatterings, we show that the current-current correlation function is determined by four-coupled integral equations. This is very different from the case for impurities with short-range potentials. As a test of the present approach, we calculate the electric conductivity in graphene for charged impurities with screened Coulomb potentials. The obtained conductivity at zero temperature varies linearly with the carrier concentration, and the minimum conductivity at zero doping is larger than the existing theoretical predictions, but still smaller than that of the experimental measurement. The overall behavior of the conductivity obtained by the present calculation at room temperature is similar to that at zero temperature except the minimum conductivity is slightly larger.Comment: 6 pages, 3 figure

The complex morphology of the young disk MWC 758: Spirals and dust clumps around a large cavity

We present Atacama Large Millimeter Array (ALMA) observations at an angular resolution of 0.1-0.2" of the disk surrounding the young Herbig Ae star MWC 758. The data consist of images of the dust continuum emission recorded at 0.88 millimeter, as well as images of the 13CO and C18O J = 3-2 emission lines. The dust continuum emission is characterized by a large cavity of roughly 40 au in radius which might contain a mildly inner warped disk. The outer disk features two bright emission clumps at radii of about 47 and 82 au that present azimuthal extensions and form a double-ring structure. The comparison with radiative transfer models indicates that these two maxima of emission correspond to local increases in the dust surface density of about a factor 2.5 and 6.5 for the south and north clumps, respectively. The optically thick 13CO peak emission, which traces the temperature, and the dust continuum emission, which probes the disk midplane, additionally reveal two spirals previously detected in near-IR at the disk surface. The spirals seen in the dust continuum emission present, however, a slight shift of a few au towards larger radii and one of the spirals crosses the south dust clump. Finally, we present different scenarios in order to explain the complex structure of the disk.Comment: 15 pages, 11 figures. The paper has been published in ApJ. References added and typos correcte

Radiation-induced magnetoresistance oscillation in a two-dimensional electron gas in Faraday geometry

Microwave-radiation induced giant magnetoresistance oscillations recently discovered in high-mobility two-dimensional electron systems in a magnetic field, are analyzed theoretically. Multiphoton-assisted impurity scatterings are shown to be the primary origin of the oscillation. Based on a model which considers the interaction of electrons with the electromagnetic fields in Faraday geometry, we are able not only to reproduce the correct period, phase and the negative resistivity of the main oscillation, but also to obtain secondary peaks and additional maxima and minima in the resistivity curve, some of which were already observed in the experiments.Comment: 4 pages, 1 figure, revised version to be published in Phys. Rev. Let