64,425 research outputs found

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

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    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

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    STAR has recently reported charge-dependent azimuthal correlations that are sensitive to the charge separation effect in Au+Au collisions at sNN\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 sNN\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

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    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 sNN\sqrt{s_{\rm NN}} = 200 GeV and compare with results from recent three particle correlation measurements. We also report balance functions for relative pseudorapidity (Δη\Delta \eta), relative rapidity (Ξ”y\Delta y), and relative azimuthal angle (Δϕ\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

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    If (G1,G2)(G_1, G_2) is a dual reductive pair of type I in Sp(W)Sp(W), it is known that the degree 88 metaplectic cover of Sp(W)Sp(W) splits over G1G2G_1G_2, with one obvious exception. In this paper we replace G1G2G_1G_2 by a larger subgroup obtained via similitude groups, and show that the degree 88 metaplectic cover splits, with the same obvious exception.Comment: 17 pages, a revised versio

    On the local theta representation

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    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 H1H_1, H2H_2. In particular, we examine when and how such a correspondence can be extended to bigger groups G1G_1, G2G_2 containing H1H_1, H2H_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 BsJβˆ—B^{*}_{sJ} Mesons by Improved Bethe-Salpeter Method

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    We calculate the masses and the strong decays of orbitally excited states Bs0B_{s0}, Bs1β€²B'_{s1}, Bs1B_{s1} and Bs2B_{s2} by the improved Bethe-Salpeter method. The predicted masses of Bs0B_{s0} and Bs1β€²B'_{s1} are MBs0=5.723Β±0.280GeVM_{B_{s0}}=5.723\pm0.280 {\rm GeV}, MBs1β€²=5.774Β±0.330GeVM_{B'_{s1}}=5.774\pm0.330 {\rm GeV}. We calculate the isospin symmetry violating decay processes Bs0β†’BsΟ€B_{s0}\to B_s \pi and Bs1β€²β†’Bsβˆ—Ο€B'_{s1}\to B_s^* \pi through Ο€0βˆ’Ξ·\pi^0-\eta mixing and get small widths. Considering the uncertainties of the masses, for Bs0B_{s0} and Bs1β€²B'_{s1}, we also calculate the OZI allowed decay channels: Bs0β†’BKΛ‰B_{s0}\to B\bar K and Bs1β€²β†’Bβˆ—KΛ‰B'_{s1}\to B^*\bar K. For Bs1B_{s1} and Bs2B_{s2}, the OZI allowed decay channels Bs1β†’Bβˆ—KΛ‰B_{s1}\to B^{*}\bar K, Bs2β†’BKΛ‰B_{s2}\to B\bar K and Bs2β†’Bβˆ—KΛ‰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 GBs0BsΟ€G_{B_{s0}B_s\pi}, GBs0BKΛ‰G_{B_{s0}B\bar K}, GBs1β€²Bsβˆ—Ο€G_{B'_{s1}B_s^*\pi}, FBs1β€²Bsβˆ—Ο€F_{B'_{s1}B_s^*\pi}, GBs1β€²Bβˆ—KΛ‰G_{B'_{s1}B^*\bar K}, FBs1β€²Bβˆ—KΛ‰F_{B'_{s1}B^*\bar K}, GBs1Bβˆ—KΛ‰G_{B_{s1}B^{*}\bar K}, FBs1Bβˆ—KΛ‰F_{B_{s1}B^{*}\bar K}, GBs2BKΛ‰G_{B_{s2}B\bar K} and GBs2Bβˆ—KΛ‰G_{B_{s2}B^{*}\bar K}.Comment: 21 pages, 1 figure, 4 table

    Physical Layer Security in Millimeter Wave Cellular Networks

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    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

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    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

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    In 1996, A. Norton and D. Sullivan asked the following question: If f:T2β†’T2f:\mathbb{T}^2\rightarrow\mathbb{T}^2 is a diffeomorphism, h:T2β†’T2h:\mathbb{T}^2\rightarrow\mathbb{T}^2 is a continuous map homotopic to the identity, and hf=Tρhh f=T_{\rho} h where ρ∈R2\rho\in\mathbb{R}^2 is a totally irrational vector and Tρ:T2β†’T2, z↦z+ρT_{\rho}:\mathbb{T}^2\rightarrow\mathbb{T}^2,\, z\mapsto z+\rho is a translation, are there natural geometric conditions (e.g. smoothness) on ff that force hh 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∞C^{\infty} category: In general, not even the infinite smoothness condition can force hh to be a homeomorphism. In this article, we give a negative answer in the CΟ‰C^{\omega} category: We construct a real-analytic conservative and minimal totally irrational pseudo-rotation of T2\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∞C^\infty conjugacies in the proof of [J. Wang and Z. Zhang, GAFA 2018] by the CΟ‰C^\omega conjugacies in this articl

    The Lower The Simpler: Simplifying Hierarchical Recurrent Models

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    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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