10,900 research outputs found
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
Vortex solutions in axial or chiral coupled non-relativistic spinor- Chern-Simons theory
The interaction of a spin 1/2 particle (described by the non-relativistic
"Dirac" equation of L\'evy-Leblond) with Chern-Simons gauge fields is studied.
It is shown, that similarly to the four dimensional spinor models, there is a
consistent possibility of coupling them also by axial or chiral type currents.
Static self dual vortex solutions together with a vortex-lattice are found with
the new couplings.Comment: Plain TEX, 10 page
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 ,
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
Radiation-induced magnetoresistance oscillations in two-dimensional electron systems under bichromatic irradiation
We analyze the magnetoresistance oscillations in high-mobility
two-dimensional electron systems induced by the combined driving of two
radiation fields of frequency and , based on the
balance-equation approach to magnetotransport for high-carrier-density systems
in Faraday geometry. It is shown that under bichromatic irradiation of
, most of the characterstic peak-valley pairs in the
curve of versus magnetic field in the case of monochromatic
irradiation of either or disappear, except the one around
or . oscillations
show up mainly as new peak-valley structures around other positions related to
multiple photon processes of mixing frequencies ,
, etc. Many minima of these resistance peak-valley pairs can
descend down to negative with enhancing radiation strength, indicating the
possible bichromaticzero-resistance states.Comment: 5 pages, 3 figures. Accepted for publication in Phys. Rev.
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
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