25,013 research outputs found
Structural Parameters for 10 Halo Globular Clusters in M33
In this paper, we present the properties of 10 halo globular clusters with
luminosities in the Local Group galaxy M33
using the images of {\it Hubble Space Telescope} Wide Field Planetary Camera 2
in the F555W and F814W bands. We obtained ellipticities, position angles and
surface brightness profiles for them. In general, the ellipticities of M33
sample clusters are similar to those of M31 clusters. The structural and
dynamical parameters are derived by fitting the profiles to three different
models combined with mass-to-light ratios ( values) from
population-synthesis models. The structural parameters include core radii,
concentration, half-light radii {\bf and} central surface brightness. The
dynamical parameters include the integrated cluster mass, integrated binding
energy, central surface mass density {\bf and} predicted line-of-sight velocity
dispersion at the cluster center. The velocity dispersions of four clusters
predicted here agree well with the observed dispersions by Larsen et al. The
results here showed that the majority of the sample halo globular clusters are
well fitted by King model as well as by Wilson model, and better than by
S\'ersic model. In general, the properties of clusters in M33, M31 and the
Milky Way fall in the same regions of parameter spaces. The tight correlations
of cluster properties indicate a "fundamental plane" for clusters, which
reflects some universal physical conditions and processes operating at the
epoch of cluster formation.Comment: Accepted for Publication in AJ, 27 pages, 23 figures and 6 table
New photometry of 234 M33 star clusters
This is the second paper of our series. In this paper, we present
photometry for 234 star clusters in the field of M33. For most of these star
clusters, there is photometry in only two bands in previous studies. The
photometry of these star clusters is performed using archival images from the
Local Group Galaxies Survey, which covers 0.8 deg along the major axis of
M33. Detailed comparisons show that, in general, our photometry is consistent
with previous measurements, especially, our photometry is in good agreement
with Zloczewski & Kaluzny. Combined with the star clusters' photometry in
previous studies, we present some results: none of the M33 youngest clusters
( yr) have masses approaching ; comparisons with
models of simple stellar populations suggest a large range of ages of M33 star
clusters, and some as old as the Galactic globular clusters.Comment: Accepted for Publication in AJ, 23 pages, 9 figures and 3 tables.
arXiv admin note: text overlap with arXiv:1205.482
Asymptotically exact a posteriori error estimates of eigenvalues by the Crouzeix-Raviart element and enriched Crouzeix-Raviart element
Two asymptotically exact a posteriori error estimates are proposed for
eigenvalues by the nonconforming Crouzeix--Raviart and enriched Crouzeix--
Raviart elements. The main challenge in the design of such error estimators
comes from the nonconformity of the finite element spaces used. Such
nonconformity causes two difficulties, the first one is the construction of
high accuracy gradient recovery algorithms, the second one is a computable high
accuracy approximation of a consistency error term. The first difficulty was
solved for both nonconforming elements in a previous paper. Two methods are
proposed to solve the second difficulty in the present paper. In particular,
this allows the use of high accuracy gradient recovery techniques. Further, a
post-processing algorithm is designed by utilizing asymptotically exact a
posteriori error estimators to construct the weights of a combination of two
approximate eigenvalues. This algorithm requires to solve only one eigenvalue
problem and admits high accuracy eigenvalue approximations both theoretically
and numerically.Comment: arXiv admin note: text overlap with arXiv:1802.0189
Negative Magneto-Resistance Beyond Weak Localization in Three-Dimensional Billiards: Effect of Arnold Diffusion
We investigate a semiclassical conductance for ballistic open
three-dimensional (3-d) billiards. For partially or completely broken-ergodic
3-d billiards such as SO(2) symmetric billiards, the dependence of the
conductance on the Fermi wavenumber is dramatically changed by the lead
orientation. Application of a symmetry-breaking weak magnetic field brings
about mixed phase-space structures of 3-d billiards which ensures a novel
Arnold diffusion that cannot be seen in 2-d billiards. In contrast to the 2-d
case, the anomalous increment of the conductance should inevitably include a
contribution arising from Arnold diffusion as well as a weak localization
correction. Discussions are devoted to the physical condition for observing
this phenomenon.Comment: 14 pages, 3 figure
Structural parameters for globular clusters in M31
In this paper, we present surface brightness profiles for 79 globular
clusters in M31, using images observed with {\it Hubble Space Telescope}, some
of which are from new observations. The structural and dynamical parameters are
derived from fitting the profiles to several different models for the first
time. The results show that in the majority of cases, King models fit the M31
clusters as well as Wilson models, and better than S\'{e}rsic models. However,
there are 11 clusters best fitted by S\'{e}rsic models with the S\'{e}rsic
index , meaning that they have cuspy central density profiles. These
clusters may be the well-known core-collapsed candidates. There is a bimodality
in the size distribution of M31 clusters at large radii, which is different
from their Galactic counterparts. In general, the properties of clusters in M31
and the Milky Way fall in the same regions of parameter spaces. The tight
correlations of cluster properties indicate a "fundamental plane" for clusters,
which reflects some universal physical conditions and processes operating at
the epoch of cluster formation.Comment: Accepted for Publication in AJ, 17 pages, 15 figures and 7 table
Superconvergence of both the Crouzeix-Raviart and Morley elements
In this paper, a new method is proposed to prove the superconvergence of both
the Crouzeix-Raviart and Morley elements. The main idea is to fully employ
equivalences with the first order Raviart-Thomas element and the first order
Hellan-Herrmann-Johnson element, respectively. In this way, some special
conformity of discrete stresses is explored and superconvergence of mixed
elements can be used to analyze superconvergence of nonconforming elements.
Finally, a half order superconvergence by postprocessing is proved for both
nonconforming elements.Comment: 16 pages, 6 figure
Coupling motion of colloidal particles in quasi-two-dimensional confinement
Brownian motion of colloidal particles in the quasi-two-dimensional (qTD)
confinement displays distinct kinetic characters from that in bulk. Here we
experimentally report a dynamic evolution of Brownian particles in the qTD
system. The dynamic system displays a quasi-equilibrium state of colloidal
particles performing Brownian motion. In the quasi-equilibrium process, the qTD
confinement results in the coupling of particle motions, which slowly dampens
the motion and interaction of particles until the final equilibrium state
reaches. The theory is developed to explain coupling motions of Brownian
particles in the qTD confinement.Comment: 7 pages, 4 figure
High accuracy methods for eigenvalues of elliptic operators by nonconforming elements
In this paper, three high-accuracy methods for eigenvalues of second order
elliptic operators are proposed by using the nonconforming Crouzeix-Raviart(CR
for short) element and the nonconforming enriched Crouzeix-Raviart(ECR for
short) element. They are based on a crucial full one order superconvergence of
the first order mixed Raviart-Thomas(RT for short) element. The main ingredient
of such a superconvergence analysis is to employ a discrete Helmholtz
decomposition of the difference between the canonical interpolation and the
finite element solution of the RT element. In particular, it allows for some
vital cancellation between terms in one key sum of boundary terms.
Consequently, a full one order superconvergence follows from a special relation
between the CR element and the RT element, and the equivalence between the ECR
element and the RT element for these two nonconforming elements. These
superconvergence results improve those in literature from a half order to a
full one order for the RT element, the CR element and the ECR element. Based on
the aforementioned superconvergence of the RT element, asymptotic expansions of
eigenvalues are established and employed to achieve high accuracy extrapolation
methods for these two nonconforming elements. In contrast to a classic analysis
in literature, the novelty herein is to use not only the canonical
interpolations of these nonconforming elements but also that of the RT element
to analyze such asymptotic expansions. Based on the superconvergence of these
nonconforming elements, asymptotically exact a posteriori error estimators of
eigenvalues are constructed and analyzed for them. Finally, two post-processing
methods are proposed to improve accuracy of approximate eigenvalues by
employing these a posteriori error estimators.Numerical tests are provided to
justify and compare the performance of the aforementioned methods
Conforming mixed triangular prism and nonconforming mixed tetrahedral elements for the linear elasticity problem
We propose two families of mixed finite elements for solving the classical
Hellinger-Reissner mixed problem of the linear elasticity equations in three
dimensions. First, a family of conforming mixed triangular prism elements is
constructed by product of elements on triangular meshes and elements in one
dimension. The well-posedness is established for all elements with ,
which are of order convergence for both the stress and displacement.
Besides, a family of reduced stress spaces is proposed by dropping the degrees
of polynomial functions associated with faces. As a result, the lowest order
conforming mixed triangular prism element has 93 plus 33 degrees of freedom on
each element. Second, we construct a new family of nonconforming mixed
tetrahedral elements. The shape function spaces of our stress spaces are
different from those of the elements in literature
An Equivalence of Fully Connected Layer and Convolutional Layer
This article demonstrates that convolutional operation can be converted to
matrix multiplication, which has the same calculation way with fully connected
layer. The article is helpful for the beginners of the neural network to
understand how fully connected layer and the convolutional layer work in the
backend. To be concise and to make the article more readable, we only consider
the linear case. It can be extended to the non-linear case easily through
plugging in a non-linear encapsulation to the values like this
denoted as .Comment: 9 page
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