31,041 research outputs found

### Fractal space frames and metamaterials for high mechanical efficiency

A solid slender beam of length $L$, made from a material of Young's modulus
$Y$ and subject to a gentle compressive force $F$, requires a volume of
material proportional to $L^{3}f^{1/2}$ [where $f\equiv F/(YL^{2})\ll 1$] in
order to be stable against Euler buckling. By constructing a hierarchical space
frame, we are able to systematically change the scaling of required material
with $f$ so that it is proportional to $L^{3}f^{(G+1)/(G+2)}$, through changing
the number of hierarchical levels $G$ present in the structure. Based on simple
choices for the geometry of the space frames, we provide expressions specifying
in detail the optimal structures (in this class) for different values of the
loading parameter $f$. These structures may then be used to create effective
materials which are elastically isotropic and have the combination of low
density and high crush strength. Such a material could be used to make
light-weight components of arbitrary shape.Comment: 6 pages, 4 figure

### Photometric properties and luminosity function of nearby massive early-type galaxies

We perform photometric analyses for a bright early-type galaxy (ETG) sample
with 2949 galaxies ($M_{\rm r}<-22.5$ mag) in the redshift range of 0.05 to
0.15, drawn from the SDSS DR7 with morphological classification from Galaxy Zoo
1. We measure the Petrosian and isophotal magnitudes, as well as the
corresponding half-light radius for each galaxy. We find that for brightest
galaxies ($M_{\rm r}<-23$ mag), our Petrosian magnitudes, and isophotal
magnitudes to 25 ${\rm mag/arcsec^2}$ and 1\% of the sky brightness are on
average 0.16 mag, 0.20 mag, and 0.26 mag brighter than the SDSS Petrosian
values, respectively. In the first case the underestimations are caused by
overestimations in the sky background by the SDSS PHOTO algorithm, while the
latter two are also due to deeper photometry. Similarly, the typical half-light
radii ($r_{50}$) measured by the SDSS algorithm are smaller than our
measurements. As a result, the bright-end of the $r$-band luminosity function
is found to decline more slowly than previous works. Our measured luminosity
densities at the bright end are more than one order of magnitude higher than
those of Blanton et al. (2003), and the stellar mass densities at $M_{\ast}\sim
5\times10^{11} M_{\odot}$ and $M_{\ast}\sim 10^{12} M_{\odot}$ are a few tenths
and a factor of few higher than those of Bernardi et al. (2010). These results
may significantly alleviate the tension in the assembly of massive galaxies
between observations and predictions of the hierarchical structure formation
model.Comment: 43 pages, 14 figures, version accepted for publication in the
Astrophysical Journa

### Almost sure exponential stability of numerical solutions for stochastic delay differential equations

Using techniques based on the continuous and discrete semimartingale convergence theorems, this paper investigates if numerical methods may reproduce the almost sure exponential stability of the exact solutions to stochastic delay differential equations (SDDEs). The important feature of this technique is that it enables us to study the almost sure exponential stability of numerical solutions of SDDEs directly. This is significantly different from most traditional methods by which the almost sure exponential stability is derived from the moment stability by the Chebyshev inequality and the BorelâCantelli lemma

### Two particle correlations: a probe of the LHC QCD medium

The properties of $\gamma$--jet pairs emitted in heavy-ion collisions provide
an accurate mean to perform a tomographic measurement of the medium created in
the collision through the study of the medium modified jet properties. The idea
is to measure the distribution of hadrons emitted on the opposite side of the
%oppositely by tagging the direct photon. The feasibility of such measurements
is studied by applying the approach on the simulation data, we have
demonstrated that this method allows us to measure, with a good approximation,
both the jet fragmentation and the back-to-back azimuthal alignment of the
direct photon and the jet. Comparing these two observables measured in pp
collisions with the ones measured in AA collisions reveals the modifications
induced by the medium on the jet structure and consequently allows us to infer
the medium properties. In this contribution, we discuss a first attempt of such
measurements applied to real proton-proton data from the ALICE experiment.Comment: 4 pages, 4 figures, Proceedings for Hot Quark 2010 Conferenc

### Microlensing of Sub-parsec Massive Binary Black Holes in Lensed QSOs: Light Curves and Size-Wavelength Relation

Sub-parsec binary massive black holes (BBHs) are long anticipated to exist in
many QSOs but remain observationally elusive. In this paper, we propose a novel
method to probe sub-parsec BBHs through microlensing of lensed QSOs. If a QSO
hosts a sub-parsec BBH in its center, it is expected that the BBH is surrounded
by a circum-binary disk, each component of the BBH is surrounded by a small
accretion disk, and a gap is opened by the secondary component in between the
circum-binary disk and the two small disks. Assuming such a BBH structure, we
generate mock microlensing light curves for some QSO systems that host BBHs
with typical physical parameters. We show that microlensing light curves of a
BBH QSO system at the infrared-optical-UV bands can be significantly different
from those of corresponding QSO system with a single massive black hole (MBH),
mainly because of the existence of the gap and the rotation of the BBH (and its
associated small disks) around the center of mass. We estimate the half-light
radii of the emission region at different wavelengths from mock light curves
and find that the obtained half-light radius vs. wavelength relations of BBH
QSO systems can be much flatter than those of single MBH QSO systems at a
wavelength range determined by the BBH parameters, such as the total mass, mass
ratio, separation, accretion rates, etc. The difference is primarily due to the
existence of the gap. Such unique features on the light curves and half-light
radius-wavelength relations of BBH QSO systems can be used to select and probe
sub-parsec BBHs in a large number of lensed QSOs to be discovered by current
and future surveys, including the Panoramic Survey Telescope and Rapid Response
System (Pan-STARRS), the Large Synoptic Survey telescope (LSST) and Euclid.Comment: 18 pages, 17 figures, accepted for publication in the Astrophysical
Journa

### Delay-dependent robust stability of stochastic delay systems with Markovian switching

In recent years, stability of hybrid stochastic delay systems, one of the important issues in the study of stochastic systems, has received considerable attention. However, the existing results do not deal with the structure of the diffusion but estimate its upper bound, which induces conservatism. This paper studies delay-dependent robust stability of hybrid stochastic delay systems. A delay-dependent criterion for robust exponential stability of hybrid stochastic delay systems is presented in terms of linear matrix inequalities (LMIs), which exploits the structure of the diffusion. Numerical examples are given to verify the effectiveness and less conservativeness of the proposed method

### A Rate-Splitting Based Bound-Approaching Transmission Scheme for the Two-User Symmetric Gaussian Interference Channel with Common Messages

This paper is concerned with a rate-splitting based transmission strategy for the two-user symmetric Gaussian interference channel that contains common messages only. Each transmitter encodes its common message into multiple layers by multiple codebooks that drawn from one separate code book, and transmits the superposition of the messages corresponding to these layers; each receiver decodes the messages from all layers of the two users successively. Two schemes are proposed for decoding order and optimal power allocation among layers respectively. With the proposed decoding order scheme, the sum-rate can be increased by rate-splitting, especially at the optimal number of rate-splitting, using average power allocation in moderate and weak interference regime. With the two proposed schemes at the receiver and the transmitter respectively, the sum-rate achieves the inner bound of HK without time-sharing. Numerical results show that the proposed optimal power allocation scheme with the proposed decoding order can achieve significant improvement of the performance over equal power allocation, and achieve the sum-rate within two bits per channel use (bits/channel use) of the sum capacity

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