135,727 research outputs found
Optimal boundary control of a simplified Ericksen--Leslie system for nematic liquid crystal flows in
In this paper, we investigate an optimal boundary control problem for a two
dimensional simplified Ericksen--Leslie system modelling the incompressible
nematic liquid crystal flows. The hydrodynamic system consists of the
Navier--Stokes equations for the fluid velocity coupled with a convective
Ginzburg--Landau type equation for the averaged molecular orientation. The
fluid velocity is assumed to satisfy a no-slip boundary condition, while the
molecular orientation is subject to a time-dependent Dirichlet boundary
condition that corresponds to the strong anchoring condition for liquid
crystals. We first establish the existence of optimal boundary controls. Then
we show that the control-to-state operator is Fr\'echet differentiable between
appropriate Banach spaces and derive first-order necessary optimality
conditions in terms of a variational inequality involving the adjoint state
variables
Discovery of {\gamma}-ray pulsation and X-ray emission from the black widow pulsar PSR J2051-0827
We report the discovery of pulsed {\gamma}-ray emission and X-ray emission
from the black widow millisecond pulsar PSR J2051-0827 by using the data from
the Large Area Telescope (LAT) on board the Fermi Gamma-ray Space Telescope and
the Advanced CCD Imaging Spectrometer array (ACIS-S) on the Chandra X-ray
Observatory. Using 3 years of LAT data, PSR J2051-0827 is clearly detected in
{\gamma}-ray with a signicance of \sim 8{\sigma} in the 0.2 - 20 GeV band. The
200 MeV - 20 GeV {\gamma}-ray spectrum of PSR J2051-0827 can be modeled by a
simple power- law with a photon index of 2.46 \pm 0.15. Significant (\sim
5{\sigma}) {\gamma}-ray pulsations at the radio period were detected. PSR
J2051-0827 was also detected in soft (0.3-7 keV) X-ray with Chandra. By
comparing the observed {\gamma}-rays and X-rays with theoretical models, we
suggest that the {\gamma}-ray emission is from the outer gap while the X-rays
can be from intra-binary shock and pulsar magnetospheric synchrotron emissions.Comment: 10 pages, 4 figures, accepted by ApJ on Jan 28, 201
Discovery of gamma-ray emission from the supernova remnant Kes 17 with Fermi Large Area Telescope
We report the discovery of GeV emission at the position of supernova remnant
Kes 17 by using the data from the Large Area Telescope on board the Fermi
Gamma-ray Space Telescope. Kes 17 can be clearly detected with a significance
of ~12 sigma in the 1 - 20 GeV range. Moreover, a number of gamma-ray sources
were detected in its vicinity. The gamma-ray spectrum of Kes 17 can be well
described by a simple power-law with a photon index of ~ 2.4. Together with the
multi-wavelength evidence for its interactions with the nearby molecular cloud,
the gamma-ray detection suggests that Kes 17 is a candidate acceleration site
for cosmic-rays.Comment: 13 pages, 3 figures, 1 table, accepted for publication in ApJ Lette
Non-Relativistic Limit of Dirac Equations in Gravitational Field and Quantum Effects of Gravity
Based on unified theory of electromagnetic interactions and gravitational
interactions, the non-relativistic limit of the equation of motion of a charged
Dirac particle in gravitational field is studied. From the Schrodinger equation
obtained from this non-relativistic limit, we could see that the classical
Newtonian gravitational potential appears as a part of the potential in the
Schrodinger equation, which can explain the gravitational phase effects found
in COW experiments. And because of this Newtonian gravitational potential, a
quantum particle in earth's gravitational field may form a gravitationally
bound quantized state, which had already been detected in experiments. Three
different kinds of phase effects related to gravitational interactions are
discussed in this paper, and these phase effects should be observable in some
astrophysical processes. Besides, there exists direct coupling between
gravitomagnetic field and quantum spin, radiation caused by this coupling can
be used to directly determine the gravitomagnetic field on the surface of a
star.Comment: 12 pages, no figur
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