12,539 research outputs found
An advanced meshless method for time fractional diffusion equation
Recently, because of the new developments in sustainable engineering and renewable energy, which are usually governed by a series of fractional partial differential equations (FPDEs), the numerical modelling and simulation for fractional calculus are attracting more and more attention from researchers. The current dominant numerical method for modeling FPDE is Finite Difference Method (FDM), which is based on a pre-defined grid leading to inherited issues or shortcomings including difficulty in simulation of problems with the complex problem domain and in using irregularly distributed nodes. Because of its distinguished advantages, the meshless method has good potential in simulation of FPDEs. This paper aims to develop an implicit meshless collocation technique for FPDE. The discrete system of FPDEs is obtained by using the meshless shape functions and the meshless collocation formulation. The stability and convergence of this meshless approach are investigated theoretically and numerically. The numerical examples with regular and irregular nodal distributions are used to validate and investigate accuracy and efficiency of the newly developed meshless formulation. It is concluded that the present meshless formulation is very effective for the modeling and simulation of fractional partial differential equations
Top-N Recommendation on Graphs
Recommender systems play an increasingly important role in online
applications to help users find what they need or prefer. Collaborative
filtering algorithms that generate predictions by analyzing the user-item
rating matrix perform poorly when the matrix is sparse. To alleviate this
problem, this paper proposes a simple recommendation algorithm that fully
exploits the similarity information among users and items and intrinsic
structural information of the user-item matrix. The proposed method constructs
a new representation which preserves affinity and structure information in the
user-item rating matrix and then performs recommendation task. To capture
proximity information about users and items, two graphs are constructed.
Manifold learning idea is used to constrain the new representation to be smooth
on these graphs, so as to enforce users and item proximities. Our model is
formulated as a convex optimization problem, for which we need to solve the
well-known Sylvester equation only. We carry out extensive empirical
evaluations on six benchmark datasets to show the effectiveness of this
approach.Comment: CIKM 201
Direct Evidence from Spitzer for a low-luminosity AGN at the center of the Elliptical Galaxy NGC 315
We present the {\it Spitzer} Space Telescope InfraRed Array Camera (IRAC) and
Multiband Imaging Photometer (MIPS) observations of the elliptical galaxy NGC
315. After removal of the host galaxy's stellar emission, we detected for the
first time an infrared-red nucleus in NGC 315. We measured the spectral energy
distribution (SED) for this active nucleus with wavelength range covering from
radio to X-ray, and obtained the bolometric luminosity of , corresponding to an extremely low Eddington
ratio (L/L) of 4.97 10. Our results confirm that
the physical nature of the nucleus of NGC 315 is a low-luminosity AGN,
consistent with the recent optical and {\it Chandra} X-ray observations.Comment: 4 pages, accepted for publication in ApJ Letter
A Cosmological Model with Dark Spinor Source
In this paper, we discuss the system of Friedman-Robertson-Walker metric
coupling with massive nonlinear dark spinors in detail, where the thermodynamic
movement of spinors is also taken into account. The results show that, the
nonlinear potential of the spinor field can provide a tiny negative pressure,
which resists the Universe to become singular. The solution is oscillating in
time and closed in space, which approximately takes the following form
g_{\mu\nu}=\bar R^2(1-\delta\cos t)^2\diag(1,-1,-\sin^2r ,-\sin^2r
\sin^2\theta), with light year, and
. The present time is about .Comment: 13 pages, no figure, to appear in IJMP
Effective generation of Ising interaction and cluster states in coupled microcavities
We propose a scheme for realizing the Ising spin-spin interaction and atomic
cluster states utilizing trapped atoms in coupled microcavities. It is shown
that the atoms can interact with each other via the exchange of virtual photons
of the cavities. Through suitably tuning the parameters, an effective Ising
spin-spin interaction can be generated in this optical system, which is used to
produce the cluster states. This scheme does not need the preparation of
initial states of atoms and cavity modes, and is insensitive to cavity decay.Comment: 11pages, 2 figures, Revtex
Multipole polarizability of a graded spherical particle
We have studied the multipole polarizability of a graded spherical particle
in a nonuniform electric field, in which the conductivity can vary radially
inside the particle. The main objective of this work is to access the effects
of multipole interactions at small interparticle separations, which can be
important in non-dilute suspensions of functionally graded materials. The
nonuniform electric field arises either from that applied on the particle or
from the local field of all other particles. We developed a differential
effective multipole moment approximation (DEMMA) to compute the multipole
moment of a graded spherical particle in a nonuniform external field. Moreover,
we compare the DEMMA results with the exact results of the power-law graded
profile and the agreement is excellent. The extension to anisotropic DEMMA will
be studied in an Appendix.Comment: LaTeX format, 2 eps figures, submitted for publication
Nonlinear alternating current responses of graded materials
When a composite of nonlinear particles suspended in a host medium is
subjected to a sinusoidal electric field, the electrical response in the
composite will generally consist of alternating current (AC) fields at
frequencies of higher-order harmonics. The situation becomes more interesting
when the suspended particles are graded, with a spatial variation in the
dielectric properties. The local electric field inside the graded particles can
be calculated by the differential effective dipole approximation, which agrees
very well with a first-principles approach. In this work, a nonlinear
differential effective dipole approximation and a perturbation expansion method
have been employed to investigate the effect of gradation on the nonlinear AC
responses of these composites. The results showed that the fundamental and
third-harmonic AC responses are sensitive to the dielectric-constant and/or
nonlinear-susceptibility gradation profiles within the particles. Thus, by
measuring the AC responses of the graded composites, it is possible to perform
a real-time monitoring of the fabrication process of the gradation profiles
within the graded particles.Comment: 18 pages, 4 figure
Hidden Broad Line Seyfert 2 Galaxies in the CfA and 12micron Samples
We report the results of a spectropolarimetric survey of the CfA and 12micron
samples of Seyfert 2 galaxies (S2s). Polarized (hidden) broad line regions
(HBLRs) are confirmed in a number of galaxies, and several new cases
(F02581-1136, MCG -3-58-7, NGC 5995, NGC 6552, NGC 7682) are reported. The
12micron S2 sample shows a significantly higher incidence of HBLR (50%) than
its CfA counterpart (30%), suggesting that the latter may be incomplete in
hidden AGNs. Compared to the non-HBLR S2s, the HBLR S2s display distinctly
higher radio power relative to their far-infrared output and hotter dust
temperature as indicated by the f25/f60 color. However, the level of
obscuration is indistinguishable between the two types of S2. These results
strongly support the existence of two intrinsically different populations of
S2: one harboring an energetic, hidden S1 nucleus with BLR, and the other, a
``pure S2'', with weak or absent S1 nucleus and a strong, perhaps dominating
starburst component. Thus, the simple purely orientation-based unification
model is not applicable to all Seyfert galaxies.Comment: 5 pages with embedded figs, ApJ Letters, in pres
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