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arXiv 2018年

作者： Zhen, Maoding He, Jinchun Xu, Haoyuan Yang, Meihua School of Mathematics and Statistics Huazhong University of Science and Technology Wuhan430074 China Hubei Key Laboratory of Engineering Modeling and Scientific Computing Huazhong University of Science and Technology Wuhan430074 China

In this paper, we consider the following fractional Laplacian system with one critical exponent and one subcritical exponent (formula presented), where (−∆)s is the fractional Laplacian, 0 2s, λ ∗−1 and 2∗ = N2−N2s is the Sobolev critical exponent. By using the Nehari manifold, we show that there exists a µ0 ∈ (0, 1), such that when 0 µ0, there exists a λµ,ν (formula presented) such that if λ > λµ,ν, the system has a positive ground state solution, if λ µ,ν, the system has no ground state solution. Copyright © 2018, The Authors. All rights reserved.

关键词： Laplace transforms

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Compensated projected Euler method for stochastic differential equations with jumps under global monotonicity condition

arXiv

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arXiv 2018年

作者： Li, Min Huang, Chengming School of Mathematics and Statistics Huazhong University of Science and Technology Wuhan430074 China Hubei Key Laboratory of Engineering Modeling and Scientific Computing Huazhong University of Science and Technology Wuhan430074 China

This paper presents and analyzes the compensated projected Euler-Maruyama method for stochastic differential equations with jumps under a global monotonicity condition. Compared with existing conditions, this condition allows the jump-diffusion coefficient to be growth superlinearly. Moreover, the method is proved to be convergent with strongly order 1/2 on the discrete time level. Finally, some numerical experiments are carried out to confirm the theoretical results. Copyright © 2018, The Authors. All rights reserved.

关键词： Differential equations

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Potential numerical techniques and challenges for atmospheric modeling

Potential numerical techniques and challenges for atmospheri...

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作者： Li, J. Steppeler, J. Fang, F. Pain, C.C. Zhu, J. Peng, X. Dong, L. Li, Y. Tao, L. Leng, W. Wang, Y. Zheng, J. International Center for Climate and Environment Sciences Institute of Atmospheric Physics Chinese Academy of Sciences Beijing China Hamburg Germany Applied Modelling and Computation Group Department of Earth Science and Engineering Imperial College London London United Kingdom International Center for Climate and Environment Sciences Institute of Atmospheric Physics Chinese Academy of Sciences Department of Atmospheric Sciences University of Chinese Academy of Sciences Beijing China State Key Laboratory of Severe Weather Chinese Academy of Meteorological Sciences Beijing China State Key Laboratory of Numerical Modeling for Atmospheric Sciences and Geophysical Fluid Dynamics Institute of Atmospheric Physics Chinese Academy of Sciences Beijing China State Key Laboratory of Scientific and Engineering Computing Chinese Academy of Sciences Beijing China School of Mathematics and Statistics Henan University Kaifeng China Center for Excellence in Regional Atmospheric Environment Institute of Urban Environment Chinese Academy of Sciences Xiamen China

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Lattice Boltzmann model for high-order nonlinear partial differential equations

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Physical Review E 2018年第1期97卷 013304-013304页

作者： Zhenhua Chai Nanzhong He Zhaoli Guo Baochang Shi School of Mathematics and Statistics Huazhong University of Science and Technology Wuhan 430074 China Hubei Key Laboratory of Engineering Modeling and Scientific Computing Huazhong University of Science and Technology Wuhan 430074 China State Key Laboratory of Coal Combustion Huazhong University of Science and Technology Wuhan 430074 China School of Mathematics and Computer Wuhan Textile University Wuhan 430200 China

In this paper, a general lattice Boltzmann (LB) model is proposed for the high-order nonlinear partial differential equation with the form ∂tϕ+∑k=1mαk∂xkΠk(ϕ)=0 (1≤k≤m≤6), αk are constant coefficients, Πk(ϕ) are some known differential functions of ϕ. As some special cases of the high-order nonlinear partial differential equation, the classical (m)KdV equation, KdV-Burgers equation, K(n,n)-Burgers equation, Kuramoto-Sivashinsky equation, and Kawahara equation can be solved by the present LB model. Compared to the available LB models, the most distinct characteristic of the present model is to introduce some suitable auxiliary moments such that the correct moments of equilibrium distribution function can be achieved. In addition, we also conducted a detailed Chapman-Enskog analysis, and found that the high-order nonlinear partial differential equation can be correctly recovered from the proposed LB model. Finally, a large number of simulations are performed, and it is found that the numerical results agree with the analytical solutions, and usually the present model is also more accurate than the existing LB models [H. Lai and C. Ma, Sci. China Ser. G 52, 1053 (2009); H. Lai and C. Ma, Phys. A (Amsterdam) 388, 1405 (2009)] for high-order nonlinear partial differential equations.

关键词： Lattice-Boltzmann methods

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Third-order discrete unified gas kinetic scheme for continuum and rarefied flows: Low-speed isothermal case

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Physical Review E 2018年第2期97卷 023306-023306页

作者： Chen Wu Baochang Shi Chang Shu Zhen Chen State Key Laboratory of Coal Combustion Huazhong University of Science and Technology Wuhan 430074 China School of Mathematics and Statistics Huazhong University of Science and Technology Wuhan 430074 China Hubei Key Laboratory of Engineering Modeling and Scientific Computing Huazhong University of Science and Technology Wuhan 430074 China Department of Mechanical Engineering National University of Singapore 10 Kent Ridge Crescent Singapore 119260 Singapore

An efficient third-order discrete unified gas kinetic scheme (DUGKS) is presented in this paper for simulating continuum and rarefied flows. By employing a two-stage time-stepping scheme and the high-order DUGKS flux reconstruction strategy, third order of accuracy in both time and space can be achieved in the present method. It is also analytically proven that the second-order DUGKS is a special case of the present method. Compared with the high-order lattice Boltzmann equation-based methods, the present method is capable to deal with the rarefied flows by adopting the Newton-Cotes quadrature to approximate the integrals of moments. Instead of being constrained by the second order (or lower order) of accuracy in the time-splitting scheme as in the conventional high-order Runge-Kutta-based kinetic methods, the present method solves the original Boltzmann equation, which overcomes the limitation in time accuracy. Typical benchmark tests are carried out for comprehensive evaluation of the present method. It is observed in the tests that the present method is advantageous over the original DUGKS in accuracy and capturing delicate flow structures. Moreover, the efficiency of the present third-order method is also shown in simulating rarefied flows.

关键词： Boltzmann theory

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Extended Very-High-Energy Gamma-Ray Emission Surrounding PSR J0622+3749 Observed by LHAASO-KM2A

引用

Physical Review Letters 2021年第24期126卷 241103-241103页

作者： F. Aharonian Q. An Axikegu L. X. Bai Y. X. Bai Y. W. Bao D. Bastieri X. J. Bi Y. J. Bi H. Cai J. T. Cai Z. Cao J. Chang J. F. Chang X. C. Chang B. M. Chen J. Chen L. Chen M. J. Chen M. L. Chen Q. H. Chen S. H. Chen S. Z. Chen T. L. Chen X. L. Chen Y. Chen N. Cheng Y. D. Cheng S. W. Cui X. H. Cui Y. D. Cui B. Z. Dai H. L. Dai Z. G. Dai Danzengluobu D. della Volpe B. D’Ettorre Piazzoli X. J. Dong J. H. Fan Y. Z. Fan Z. X. Fan J. Fang K. Fang C. F. Feng L. Feng S. H. Feng Y. L. Feng B. Gao C. D. Gao Q. Gao W. Gao M. M. Ge L. S. Geng G. H. Gong Q. B. Gou M. H. Gu J. G. Guo X. L. Guo Y. Q. Guo Y. Y. Guo Y. A. Han H. H. He H. N. He J. C. He S. L. He X. B. He Y. He M. Heller Y. K. Hor C. Hou X. Hou H. B. Hu S. Hu S. C. Hu X. J. Hu D. H. Huang Q. L. Huang W. H. Huang X. T. Huang Z. C. Huang F. Ji X. L. Ji H. Y. Jia K. Jiang Z. J. Jiang C. Jin D. Kuleshov K. Levochkin B. B. Li C. Li F. Li H. B. Li H. C. Li H. Y. Li J. Li K. Li W. L. Li X. Li X. R. Li Y. Li Y. Z. Li Z. Li E. W. Liang Y. F. Liang S. J. Lin B. Liu C. Liu D. Liu H. Liu H. D. Liu J. Liu J. L. Liu J. S. Liu J. Y. Liu M. Y. Liu R. Y. Liu S. M. Liu W. Liu Y. N. Liu Z. X. Liu W. J. Long R. Lu H. K. Lv B. Q. Ma L. L. Ma X. H. Ma J. R. Mao A. Masood W. Mitthumsiri T. Montaruli Y. C. Nan B. Y. Pang P. Pattarakijwanich Z. Y. Pei M. Y. Qi D. Ruffolo V. Rulev A. Sáiz L. Shao O. Shchegolev X. D. Sheng J. R. Shi H. C. Song Yu. V. Stenkin V. Stepanov Q. N. Sun X. N. Sun Z. B. Sun P. H. T. Tam Z. B. Tang W. W. Tian B. D. Wang C. Wang H. Wang H. G. Wang J. C. Wang J. S. Wang L. P. Wang L. Y. Wang R. N. Wang W. Wang X. G. Wang X. J. Wang X. Y. Wang Y. D. Wang Y. J. Wang Y. P. Wang Z. Wang Z. H. Wang Z. X. Wang D. M. Wei J. J. Wei Y. J. Wei T. Wen C. Y. Wu H. R. Wu S. Wu W. X. Wu X. F. Wu S. Q. Xi J. Xia J. J. Xia G. M. Xiang G. Xiao H. B. Xiao G. G. Xin Y. L. Xin Y. Xing D. L. Xu R. X. Xu L. Xue D. H. Yan C. W. Yang F. F. Yang J. Y. Yang L. L. Yang M. J. Yang R. Z. Yang S. B. Yang Y. H. Yao Z. G. Yao Y. M. Ye L. Q. Yin N. Yin X. H. You Z. Y. You Y. H. Yu Q. Yuan H. D. Zeng T. Dublin Institute for Advanced Studies 31 Fitzwilliam Place 2 Dublin Ireland Max-Planck-Institut for Nuclear Physics P.O. Box 103980 69029 Heidelberg Germany State Key Laboratory of Particle Detection and Electronics 100049 Beijing China University of Science and Technology of China 230026 Hefei Anhui China School of Physical Science and Technology & School of Information Science and Technology Southwest Jiaotong University 610031 Chengdu Sichuan China College of Physics Sichuan University 610065 Chengdu Sichuan China Key Laboratory of Particle Astrophyics & Experimental Physics Division & Computing Center Institute of High Energy Physics Chinese Academy of Sciences 100049 Beijing China TIANFU Cosmic Ray Research Center Chengdu 610000 Sichuan China School of Astronomy and Space Science Nanjing University 210023 Nanjing Jiangsu China Center for Astrophysics Guangzhou University 510006 Guangzhou Guangdong China University of Chinese Academy of Sciences 100049 Beijing China School of Physics and Technology Wuhan University 430072 Wuhan Hubei China Key Laboratory of Dark Matter and Space Astronomy Purple Mountain Observatory Chinese Academy of Sciences 210023 Nanjing Jiangsu China Hebei Normal University 050024 Shijiazhuang Hebei China Key Laboratory of Cosmic Rays (Tibet University) Ministry of Education 850000 Lhasa Tibet China National Astronomical Observatories Chinese Academy of Sciences 100101 Beijing China School of Physics and Astronomy & School of Physics (Guangzhou) Sun Yat-sen University 519082 Zhuhai Guangdong China School of Physics and Astronomy Yunnan University 650091 Kunming Yunnan China Département de Physique Nucléaire et Corpusculaire Faculté de Sciences Université de Genève 24 Quai Ernest Ansermet 1211 Geneva Switzerland Dipartimento di Fisica dell’Università di Napoli “Federico II ” Complesso Universitario di Monte Sant’Angelo via Cinthia 80126 Napoli Italy Institute of Frontier and Interdisciplinary Science Shandong Universi

We report the discovery of an extended very-high-energy (VHE) gamma-ray source around the location of the middle-aged (207.8 kyr) pulsar PSR J0622+3749 with the Large High-Altitude Air Shower Observatory (LHAASO). The source is detected with a significance of 8.2σ for E>25 TeV assuming a Gaussian template. The best-fit location is (right ascension, declination) =(95.47°±0.11°,37.92°±0.09°), and the extension is 0.40°±0.07°. The energy spectrum can be described by a power-law spectrum with an index of −2.92±0.17stat±0.02sys. No clear extended multiwavelength counterpart of the LHAASO source has been found from the radio to sub-TeV bands. The LHAASO observations are consistent with the scenario that VHE electrons escaped from the pulsar, diffused in the interstellar medium, and scattered the interstellar radiation field. If interpreted as the pulsar halo scenario, the diffusion coefficient, inferred for electrons with median energies of ∼160 TeV, is consistent with those obtained from the extended halos around Geminga and Monogem and much smaller than that derived from cosmic ray secondaries. The LHAASO discovery of this source thus likely enriches the class of so-called pulsar halos and confirms that high-energy particles generally diffuse very slowly in the disturbed medium around pulsars.

关键词： Cosmic ray acceleration Cosmic ray propagation Cosmic ray sources Gamma ray astronomy

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Energy efficiency optimization of generalized spatial modulation with sub-connected hybrid precoding 4

Energy efficiency optimization of generalized spatial modula...

引用

4th IEEE International Conference on Computer and Communications, ICCC 2018

作者： Chen, Kai Yang, Jing Ge, Xiaohu Li, Yonghui Tian, Lin Shi, Jinglin Huazhong University of Science and Technology School of Electronic Information and Communications Wuhan Hubei China School of Electrical and Information Engineering University of Sydney Sydney Australia Beijing Key Laboratory of Mobile Computing and Pervasive Devices Institute of Computing Technology Chinese Academy of Sciences China University of Chinese Academy of Sciences China

ISBN: (纸本)9781538683392

Energy efficiency (EE) optimization of millimeter wave (mm-Wave) massive multiple-input multiple-output (MI-MO) systems is emerging as an important challenge for the fifth generation (5G) mobile communication systems. However, the power of radio frequency (RF) chains increases sharply due to the high carrier frequency in mm-Wave massive MIMO systems. To overcome this issue, a new energy efficiency optimization solution is proposed based on the structure of the generalized spatial modulation (GSM) and sub-connected hybrid precoding (HP). Moreover, the computation power of mm-Wave massive MIMO systems is considered for optimizing the EE. Simulation results indicate that the EE of the GSM-HP scheme outperforms the full digital precoding (FDP) scheme in the mm-Wave massive MIMO scene, and 88% computation power can be saved by the proposed GSM-HP scheme. © 2018 IEEE.

关键词： Energy efficiency

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Fast IMEX time integration of nonlinear stiff fractional differential equations

arXiv

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arXiv 2019年

作者： Zhou, Yongtao Suzuki, Jorge L. Zhang, Chengjian Zayernouri, Mohsen School of Mathematics and Statistics Huazhong University of Science and Technology Wuhan430074 China Department of Mechanical Engineering Michigan State University East LansingMI48824 United States Department of Mechanical Engineering Michigan State University East LansingMI48824 United States School of Mathematics and Statistics Huazhong University of Science and Technology Wuhan430074 China Hubei Key Laboratory of Engineering Modeling and Scientific Computing Huazhong University of Science and Technology Wuhan430074 China Department of Mechanical Engineering Department of Statistics and Probability Michigan State University East LansingMI48824 United States

Efficient long-time integration of nonlinear fractional differential equations is significantly challenging due to the integro-differential nature of the fractional operators. In addition, the inherent non-smoothness introduced by the inverse power-law kernels deteriorates the accuracy and efficiency of many existing numerical methods. We develop two efficient first- and second-order implicit-explicit (IMEX) methods for accurate time-integration of stiff/nonlinear fractional differential equations with fractional order α ∈ (0, 1] and prove their convergence and linear stability properties. The developed methods are based on a linear multi-step fractional Adams-Moulton method (FAMM), followed by the extrapolation of the nonlinear force terms. In order to handle the singularities nearby the initial time, we employ Lubich-like corrections to the resulting fractional operators. The obtained linear stability regions of the developed IMEX methods are larger than existing IMEX methods in the literature. Furthermore, the size of the stability regions increase with the decrease of fractional order values, which is suitable for stiff problems. We also rewrite the resulting IMEX methods in the language of nonlinear Toeplitz systems, where we employ a fast inversion scheme to achieve a computational complexity of O(N log N), where N denotes the number of time-steps. Our computational results demonstrate that the developed schemes can achieve global first- and second-order accuracy for highly-oscillatory stiff/nonlinear problems with singularities. Copyright © 2019, The Authors. All rights reserved.

关键词： Matrix algebra

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Invariant foliations for stochastic dynamical systems with multiplicative stable Lévy noise

arXiv

引用

arXiv 2018年

作者： Chao, Ying Wei, Pingyuan Yuan, Shenglan School of Mathematics and Statistics Center for Mathematical Sciences Hubei Key Laboratory of Engineering Modeling and Scientific Computing Huazhong University of Sciences and Technology Wuhan430074 China

This work deals with the dynamics of a class of stochastic dynamical systems with a multiplicative non-Gaussian Lévy noise. We first establish the existence of stable and unstable foliations for this kind of system via the Lyapunov-Perron method. Then we examine the geometric structure of the invariant foliations, and their relation with invariant manifolds. Finally, we illustrate our results in an example. Copyright © 2018, The Authors. All rights reserved.

关键词： Differential equations

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A generic transformation to enable optimal repair in MDS codes for distributed storage systems

A generic transformation to enable optimal repair in MDS cod...

引用

作者： Li, Jie Tang, Xiaohu Tian, Chao Information Security and National Computing Grid Laboratory Southwest Jiaotong University Chengdu610031 China Hubei Key Laboratory of Applied Mathematics Faculty of Mathematics and Statistics Hubei University Wuhan430062 China Department of Electrical Engineering and Computer Science University of Tennessee KnoxvilleTN37996 United States Department of Electrical and Computer Engineering Texas A and M University College StationTX77843 United States

We propose a generic transformation that can convert any nonbinary (n=k{+}r,k)maximum distance separable (MDS) code into another (n,k) MDS code over the same field such that: 1) some arbitrarily chosen r nodes have the optimal repair bandwidth and the optimal rebuilding access;2) for the remaining k nodes, the normalized repair bandwidth and the normalized rebuilding access (over the file size) are preserved;and 3) the sub-packetization level is increased only by a factor of r. Two immediate applications of this generic transformation are then presented. The first application is that we can transform any nonbinary MDS code with the optimal repair bandwidth or the optimal rebuilding access for the systematic nodes only, into a new MDS code which possesses the corresponding repair optimality for all nodes. The second application is that by applying the transformation multiple times, any nonbinary (n,k) scalar MDS code can be converted into an (n,k) MDS code with the optimal repair bandwidth and the optimal rebuilding access for all nodes, or only a subset of nodes, whose sub-packetization level is also optimal. © 1963-2012 IEEE.

关键词： Repair

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