64,425 research outputs found

### Exact solution for growth-induced large bending deformation of a hyperelastic plate

In this paper, the growth-induced bending deformation of a thin hyperelastic
plate is studied. For a plane-strain problem, the governing PDE system is
formulated, which is composed of the mechanical equilibrium equations, the
constraint equation and the boundary conditions. By adopting a gradient growth
field with the growth value changes linearly along the thickness direction, the
exact solution to the governing PDE system can be derived. With the obtained
solution, some important features of the bending deformation in the plate can
be found and the effects of the different growth parameters can be revealed.
This exact solution can serve as a benchmark one for testing the correctness of
numerical schemes and approximate plate models in growth theory

### Study of charge-dependent azimuthal correlations using reaction-plane-dependent balance functions

STAR has recently reported charge-dependent azimuthal correlations that are
sensitive to the charge separation effect in Au+Au collisions at $\sqrt{s_{\rm
NN}}$ = 200 GeV. Qualitatively, these results agree with some of the
theoretical predictions for local parity violation in heavy-ion collisions.
However, a study using reaction-plane-dependent balance functions shows an
alternative origin of this signal. The balance function, which measures the
correlation between oppositely charged pairs, is sensitive to the mechanisms of
charge formation and the subsequent relative diffusion of the balancing
charges. The reaction-plane-dependent balance function measurements can be
related to STAR's charge-dependent azimuthal correlations. We report
reaction-plane-dependent balance functions for Au+Au collisions at
$\sqrt{s_{\rm NN}}$ = 200, 62.4, 39, 11.5, and 7.7 GeV using the STAR detector.
The model of Schlichting and Pratt incorporating local charge conservation and
elliptic flow reproduces most of the three-particle azimuthal correlation
results at 200 GeV. The experimental charge-dependent azimuthal charge
correlations observed at 200 GeV can be explained in terms of local charge
conservation and elliptic flow.Comment: Proceedings of the 22nd International Conference on
Ultra-Relativistic Nucleus-Nucleus Collisions (Annecy, France, 23-28 May
2011

### Reaction Plane and Beam Energy Dependence Of The Balance Function at RHIC

The balance function, which measures the correlation between opposite sign
charge pairs, is sensitive to the mechanisms of charge formation and the
subsequent relative diffusion of the balancing charges. The study of the
balance function can provide information about charge creation time as well as
the subsequent collective behavior of particles. In this paper, we present a
reaction-plane-dependent balance function study for Au+Au collisions at
$\sqrt{s_{\rm NN}}$ = 200 GeV and compare with results from recent three
particle correlation measurements. We also report balance functions for
relative pseudorapidity ($\Delta \eta$), relative rapidity ($\Delta y$), and
relative azimuthal angle ($\Delta \phi$) from the recent RHIC beam energy scan
data.Comment: Proceedings of the 27th Winter Workshop on Nuclear Dynamics, Winter
Park, CO, February 6-13, 201

### Splitting metaplectic cover groups

If $(G_1, G_2)$ is a dual reductive pair of type I in $Sp(W)$, it is known
that the degree $8$ metaplectic cover of $Sp(W)$ splits over $G_1G_2$, with one
obvious exception. In this paper we replace $G_1G_2$ by a larger subgroup
obtained via similitude groups, and show that the degree $8$ metaplectic cover
splits, with the same obvious exception.Comment: 17 pages, a revised versio

### On the local theta representation

We study the algebraic framework in which one can define, in the manner of
the theta correspondence, a correspondence between representations of two
locally profinite groups $H_1$, $H_2$. In particular, we examine when and how
such a correspondence can be extended to bigger groups $G_1$, $G_2$ containing
$H_1$, $H_2$ respectively as normal subgroups. As an application, we discuss
the theta correspondence for a reductive dual pair of the similitude groups in
the non-archimedean case.Comment: A revised version. Comments welcom

### The Strong Decays of Orbitally Excited $B^{*}_{sJ}$ Mesons by Improved Bethe-Salpeter Method

We calculate the masses and the strong decays of orbitally excited states
$B_{s0}$, $B'_{s1}$, $B_{s1}$ and $B_{s2}$ by the improved Bethe-Salpeter
method. The predicted masses of $B_{s0}$ and $B'_{s1}$ are
$M_{B_{s0}}=5.723\pm0.280 {\rm GeV}$, $M_{B'_{s1}}=5.774\pm0.330 {\rm GeV}$. We
calculate the isospin symmetry violating decay processes $B_{s0}\to B_s \pi$
and $B'_{s1}\to B_s^* \pi$ through $\pi^0-\eta$ mixing and get small widths.
Considering the uncertainties of the masses, for $B_{s0}$ and $B'_{s1}$, we
also calculate the OZI allowed decay channels: $B_{s0}\to B\bar K$ and
$B'_{s1}\to B^*\bar K$. For $B_{s1}$ and $B_{s2}$, the OZI allowed decay
channels $B_{s1}\to B^{*}\bar K$, $B_{s2}\to B\bar K$ and $B_{s2}\to B^{*}\bar
K$ are studied. In all the decay channels, the reduction formula, PCAC relation
and low energy theorem are used to estimate the decay widths. We also obtain
the strong coupling constants $G_{B_{s0}B_s\pi}$, $G_{B_{s0}B\bar K}$,
$G_{B'_{s1}B_s^*\pi}$, $F_{B'_{s1}B_s^*\pi}$, $G_{B'_{s1}B^*\bar K}$,
$F_{B'_{s1}B^*\bar K}$, $G_{B_{s1}B^{*}\bar K}$, $F_{B_{s1}B^{*}\bar K}$,
$G_{B_{s2}B\bar K}$ and $G_{B_{s2}B^{*}\bar K}$.Comment: 21 pages, 1 figure, 4 table

### Physical Layer Security in Millimeter Wave Cellular Networks

Recent researches show that millimeter wave (mmWave) communications can offer
orders of magnitude increases in the cellular capacity. However, the secrecy
performance of a mmWave cellular network has not been investigated so far.
Leveraging the new path-loss and blockage models for mmWave channels, which are
significantly different from the conventional microwave channel, this paper
comprehensively studies the network-wide physical layer security performance of
the downlink transmission in a mmWave cellular network under a stochastic
geometry framework. We first study the secure connectivity probability and the
average number of perfect communication links per unit area in a noise-limited
mmWave network for both non-colluding and colluding eavesdroppers scenarios,
respectively. Then, we evaluate the effect of the artificial noise (AN) on the
secrecy performance, and derive the analysis result of average number of
perfect communication links per unit area in an interference-limited mmWave
network. Numerical results are demonstrated to show the network-wide secrecy
performance, and provide interesting insights into how the secrecy performance
is influenced by various network parameters: antenna array pattern, base
station (BS) intensity, and AN power allocation, etc

### A refinement of a theorem by Franks

In this paper, we give a refinement of a theorem by Franks, which answers two
questions raised by Kang.Comment: 6 page

### A question of Norton-Sullivan in the analytic case

In 1996, A. Norton and D. Sullivan asked the following question: If
$f:\mathbb{T}^2\rightarrow\mathbb{T}^2$ is a diffeomorphism,
$h:\mathbb{T}^2\rightarrow\mathbb{T}^2$ is a continuous map homotopic to the
identity, and $h f=T_{\rho} h$ where $\rho\in\mathbb{R}^2$ is a totally
irrational vector and $T_{\rho}:\mathbb{T}^2\rightarrow\mathbb{T}^2,\, z\mapsto
z+\rho$ is a translation, are there natural geometric conditions (e.g.
smoothness) on $f$ that force $h$ to be a homeomorphism? In [ J. Wang and Z.
Zhang, GAFA 2018 ], the first author and Z. Zhang gave a negative answer to the
above question in the $C^{\infty}$ category: In general, not even the infinite
smoothness condition can force $h$ to be a homeomorphism. In this article, we
give a negative answer in the $C^{\omega}$ category: We construct a
real-analytic conservative and minimal totally irrational pseudo-rotation of
$\mathbb{T}^2$ that is semi-conjugate to a translation but not conjugate to a
translation, which simultaneously answers a question raised in [ J. Wang and Z.
Zhang, GAFA 2018 ].Comment: 12 pages. arXiv admin note: text overlap with arXiv:1708.02529. In
the proof of our main theorem, we use the same approximation by conjugation
scheme in our preceding article [J. Wang and Z. Zhang, GAFA 2018,
arXiv:1708.02529]. The different is that we have to replace the $C^\infty$
conjugacies in the proof of [J. Wang and Z. Zhang, GAFA 2018] by the
$C^\omega$ conjugacies in this articl

### The Lower The Simpler: Simplifying Hierarchical Recurrent Models

To improve the training efficiency of hierarchical recurrent models without
compromising their performance, we propose a strategy named as `the lower the
simpler', which is to simplify the baseline models by making the lower layers
simpler than the upper layers. We carry out this strategy to simplify two
typical hierarchical recurrent models, namely Hierarchical Recurrent
Encoder-Decoder (HRED) and R-NET, whose basic building block is GRU.
Specifically, we propose Scalar Gated Unit (SGU), which is a simplified variant
of GRU, and use it to replace the GRUs at the middle layers of HRED and R-NET.
Besides, we also use Fixed-size Ordinally-Forgetting Encoding (FOFE), which is
an efficient encoding method without any trainable parameter, to replace the
GRUs at the bottom layers of HRED and R-NET. The experimental results show that
the simplified HRED and the simplified R-NET contain significantly less
trainable parameters, consume significantly less training time, and achieve
slightly better performance than their baseline models.Comment: NAACL-HLT 201

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