1,448 research outputs found
A WENO Algorithm of the Temperature and Ionization Profiles around a Point Source
We develop a numerical solver for radiative transfer problems based on the
weighted essentially nonoscillatory (WENO) scheme modified with anti-diffusive
flux corrections, in order to solve the temperature and ionization profiles
around a point source of photons in the reionization epoch. Algorithms for such
simulation must be able to handle the following two features: 1. the sharp
profiles of ionization and temperature at the ionizing front (I-front) and the
heating front (T-front), and 2. the fraction of neutral hydrogen within the
ionized sphere is extremely small due to the stiffness of the rate equations of
atom processes. The WENO scheme can properly handle these two features, as it
has been shown to have high order of accuracy and good convergence in capturing
discontinuities and complicated structures in fluid as well as to be
significantly superior over piecewise smooth solutions containing
discontinuities. With this algorithm, we show the time-dependence of the
preheated shell around a UV photon source. In the first stage the I-front and
T-front are coincident, and propagate with almost the speed of light. In later
stage, when the frequency spectrum of UV photons is hardened, the speeds of
propagation of the ionizing and heating fronts are both significantly less than
the speed of light, and the heating front is always beyond the ionizing front.
In the spherical shell between the I- and T-fronts, the IGM is heated, while
atoms keep almost neutral. The time scale of the preheated shell evolution is
dependent on the intensity of the photon source. We also find that the details
of the pre-heated shell and the distribution of neutral hydrogen remained in
the ionized sphere are actually sensitive to the parameters used. The WENO
algorithm can provide stable and robust solutions to study these details.Comment: 24 pages, 7 figures, accepted in New Astronom
A WENO Algorithm for the Radiative Transfer and Ionized Sphere at Reionization
We show that the algorithm based on the weighted essentially nonoscillatory
(WENO) scheme with anti-diffusive flux corrections can be used as a solver of
the radiative transfer equations. This algorithm is highly stable and robust
for solving problems with both discontinuities and smooth solution structures.
We test this code with the ionized sphere around point sources. It shows that
the WENO scheme can reveal the discontinuity of the radiative or ionizing
fronts as well as the evolution of photon frequency spectrum with high accuracy
on coarse meshes and for a very wide parameter space. This method would be
useful to study the details of the ionized patch given by individual source in
the epoch of reionization. We demonstrate this method by calculating the
evolution of the ionized sphere around point sources in physical and frequency
spaces. It shows that the profile of the fraction of neutral hydrogen and the
ionized radius are sensitively dependent on the intensity of the source.Comment: Elsart Latex file, 20 pages, 8 figures included, accepted for
publication in New Astronom
Higher rank numerical ranges of normal matrices
The higher rank numerical range is closely connected to the construction of
quantum error correction code for a noisy quantum channel. It is known that if
a normal matrix has eigenvalues , then its higher
rank numerical range is the intersection of convex polygons with
vertices , where . In this paper, it is shown that the higher rank numerical range of a
normal matrix with distinct eigenvalues can be written as the intersection
of no more than closed half planes. In addition, given a convex
polygon a construction is given for a normal matrix
with minimum such that . In particular, if
has vertices, with , there is a normal matrix with such that .Comment: 12 pages, 9 figures, to appear in SIAM Journal on Matrix Analysis and
Application
21 cm Signals from Early Ionizing Sources
We investigate the 21 cm signals from the UV ionizing sources in the
reionization epoch. The formation and evolution of 21 cm emission and
absorption regions depend essentially on the kinetics of photons in the
physical and frequency spaces. To solve the radiative transfer equation, we use
the WENO algorithm, which is effective to capture the sharp ionization profile
and the cut-off at the front of light and to handle the small fraction
of neutral hydrogen and helium in the ionized sphere. We show that a spherical
shell of 21 cm emission and absorption will develop around a point source once
the speed of the ionization front (I-front) is significantly lower than the
speed of light. The 21 cm shell extends from the I-front to the front of light;
its inner part is the emission region and its outer part is the absorption
region. The 21 cm emission region depends strongly on the intensity,
frequency-spectrum and life-time of the UV ionizing source. For a source of
short life-time, no 21 cm emission region can be formed if the source dies out
before the I-front speed is significantly lower than the speed of light. Yet, a
21 cm absorption region can form and develop even after the emission of the
source ceases.Comment: 25 pages, 9 figures, accepted by Ap
RF-thermal-structural-RF coupled analysis on the travelling wave disk-loaded accelerating structure
Travelling wave (TW) disk-loaded accelerating structure is one of the key
components in normal conducting (NC) linear accelerators, and has been studied
for many years. In the design process, usually after the dimensions of each
cell and the two couplers are finalized, the structure is fabricated and tuned,
and then the whole structure characteristics can be measured by the vector
network analyzer. Before the structure fabrication, the whole structure
characteristics are less simulated limited by the available computer
capability. In this paper, we described the method to do the
RF-thermal-structural-RF coupled analysis on the TW disk-loaded structure with
one single PC. In order to validate our method, we first analyzed and compared
our RF simulation results on the 3m long BEPCII structure with the
corresponding experimental results, which shows very good consistency. Finally,
the RF-thermal-structure-RF coupled analysis results on the 1.35m long NSC KIPT
linac accelerating structure are presented.Comment: 5 pages, 16 figures, Submitted to the Chinese Physics C (Formerly
High Energy Physics and Nuclear Physics
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