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The global existence and large time behavior of smooth compressible fluid in an infinitely expanding ball, III: The 3-D Boltzmann equation

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arXiv 2017年

作者： Yin, Huicheng Zhao, Wenbin School of Mathematical Sciences Jiangsu Provincial Key Laboratory for Numerical Simulation of Large Scale Complex Systems Nanjing Normal University Nanjing210023 China Department of Mathematics and IMS Nanjing University Nanjing210093 China

This paper is a continuation of the works in [34] and [36], where the authors have established the global existence of smooth compressible flows in infinitely expanding balls for inviscid gases and viscid gases, respectively. In this paper, we are concerned with the global existence and large time behavior of compressible Boltzmann gases in an infinitely expanding ball. Such a problem is one of the interesting models in studying the theory of global smooth solutions to multidimensional compressible gases with time dependent boundaries and vacuum states at infinite time. Due to the conservation of mass, the fluid in the expanding ball becomes rarefied and eventually tends to a vacuum state meanwhile there are no appearances of vacuum domains in any part of the expansive ball, which is easily observed in finite time. In the present paper, we will confirm this physical phenomenon for the Boltzmann equation by obtaining the exact lower and upper bound on the macroscopic density function. Copyright © 2017, The Authors. All rights reserved.

关键词： Boltzmann equation

The global existence and large time behavior of smooth compressible fluid in an infinitely expanding ball, I: 3D Euler equations

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arXiv 2017年

作者： Xu, Gang Yin, Huicheng Faculty of Science Jiangsu University Zhenjiang Jiangsu212013 China School of Mathematical Sciences Jiangsu Provincial Key Laboratory for Numerical Simulation of Large Scale Complex Systems Nanjing Normal University Nanjing210023 China

We concern with the global existence and large time behavior of compressible fluids (including the inviscid gases, viscid gases, and Boltzmann gases) in an infinitely expanding ball. Such a problem is one of the interesting models in studying the theory of global smooth solutions to multidimensional compressible gases with time dependent boundaries and vacuum states at infinite time. Due to the conservation of mass, the fluid in the expanding ball becomes rarefied and eventually tends to a vacuum state meanwhile there are no appearances of vacuum domains in any part of the expansive ball, which is easily observed in finite time. In this paper, as the first part of our three papers, we will confirm this physical phenomenon for the compressible inviscid fluids by obtaining the exact lower and upper bound on the density function. Copyright © 2017, The Authors. All rights reserved.

关键词： Euler equations

On the global existence and stability of 3-D viscous cylindrical circulatory flows

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arXiv 2017年

作者： Yin, Huicheng Zhang, Lin School of Mathematical Sciences Jiangsu Provincial Key Laboratory for Numerical Simulation of Large Scale Complex Systems Nanjing Normal University Nanjing210023 China Department of Mathematics and IMS Nanjing University Nanjing210093 China

In this paper, we are concerned with the global existence and stability of a 3-D perturbed viscous circulatory flow around an infinite long cylinder. This flow is described by 3-D compressible Navier-Stokes equations. By introducing some suitably weighted energy spaces and establishing a priori estimates, we show that the 3-D cylindrical symmetric circulatory flow is globally stable in time when the corresponding initial states are perturbed suitably small. Copyright © 2017, The Authors. All rights reserved.

关键词： Viscous flow

Beyond bilinear: Generalized multimodal factorized high-order pooling for visual question answering

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arXiv 2017年

作者： Yu, Zhou Yu, Jun Xiang, Chenchao Fan, Jianping Tao, Dacheng Key Laboratory of Complex Systems Modeling and Simulation School of Computer Science and Technology Hangzhou Dianzi University China Department of Computer Science University of North Carolina Charlotte United States UBTECH Sydney Artificial Intelligence Centre School of Information Technologies Faculty of Engineering and Information Technologies University of Sydney DarlingtonNSW2008 Australia

Visual question answering (VQA) is challenging because it requires a simultaneous understanding of both visual content of images and textual content of questions. To support the VQA task, we need to find good solutions for the following three issues: 1) fine-grained feature representations for both the image and the question;2) multi-modal feature fusion that is able to capture the complex interactions between multi-modal features;3) automatic answer prediction that is able to consider the complex correlations between multiple diverse answers for the same question. For fine-grained image and question representations, a 'co-attention' mechanism is developed by using a deep neural network architecture to jointly learn the attentions for both the image and the question, which can allow us to reduce the irrelevant features effectively and obtain more discriminative features for image and question representations. For multi-modal feature fusion, a generalized Multi-modal Factorized High-order pooling approach (MFH) is developed to achieve more effective fusion of multi-modal features by exploiting their correlations sufficiently, which can further result in superior VQA performance as compared with the state-of-the-art approaches. For answer prediction, the KL (Kullback-Leibler) divergence is used as the loss function to achieve precise characterization of the complex correlations between multiple diverse answers with same or similar meaning, which can allow us to achieve faster convergence rate and obtain slightly better accuracy on answer prediction. A deep neural network architecture is designed to integrate all these aforementioned modules into a unified model for achieving superior VQA performance. With an ensemble of our MFH models, we achieve the state-of-the-art performance on the large-scale VQA datasets and win the runner-up in VQA Challenge 2017. Copyright © 2017, The Authors. All rights reserved.

关键词： Deep neural networks

Quasi-two-body decays Bc → D(s)[ρ(770), ρ(1450), ρ(1700) →]ππ in the perturbative QCD factorization approach

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arXiv 2017年

作者： Ma, Ai-Jun Li, Ya Xiao, Zhen-Jun Department of Physics and Institute of Theoretical Physics Nanjing Normal University Nanjing Jiangsu210023 China Jiangsu Key Laboratory for Numerical Simulation of Large Scale Complex Systems Nanjing Normal University Nanjing Jiangsu210023 China

In this paper, we studied the quasi-two-body Bc → D(s)[ρ(770), ρ(1450), ρ(1700) →]ππ decays by employing the perturbative QCD (PQCD) factorization approach. The two-pion distribution amplitudes φππ are applied to include the final-state interactions between the pion pair, while the time-like form factors Fπ(w2) associated with the P-wave resonant states ρ(770), ρ(1450) and ρ(1700) are extracted from the experimental data of the e+e-annihilation. We found that: (a) the PQCD predictions for the branching ratios of the quasi-two-body Bc → D(s)[ρ(770), ρ(1450), ρ(1700) →]ππ decays are in the order of 10-9 to 10-5 and the direct CP violations around (10 - 40)% in magnitude;(b) the two sets of the large hierarchy R1a,1b,1c and R2a,2b,2c for the ratios of the branching ratios of the considered decays are defined and can be understood in the PQCD factorization approach, while the self-consistency between the quasi-two-body and two-body framework for Bc → D(s)[ρ(770) →]ππ and Bc → D(s)ρ(770) decays are confirmed by our numerical results;(c) taking currently known B(ρ(1450) → ππ) and B(ρ(1700) → ππ) as input, we extracted the theoretical predictions for B(Bc → Dρ(1450)) and B(Bc → Dρ(1700)) from the PQCD predictions for the decay rates of the quasi-two-body decays Bc → D[ρ(1450), ρ(1700) →]ππ. All the PQCD predictions will be tested in the future experiments. Copyright © 2017, The Authors. All rights reserved.

关键词： Hadrons

Explore K-Anycast Information Dissemination in Mobile Opportunistic Networks

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Explore K-Anycast Information Dissemination in Mobile Opport...

IEEE Wireless Communications and Networking Conference

作者： Peng Liu Jia Xu Biao Xu Key Laboratory of Complex Systems Modeling and Simulation School of Computer Science and Technology Hangzhou Dianzi University

ISBN: (纸本)9781467398152

In Mobile Opportunistic Networks, there are special cases of multicast in which destinations (except the total number) are not predetermined. E.g., a person tries to find another three players to play poker without knowing them. Achieving efficient data routing in this scenario (target any k destinations among m of them) can be very challenge due to (1) no predetermined destinations, (2) extra delay cost by the destinations collision, and (3) difficulty of the receiver quantity control. We define this as a K-Anycast problem, the goal is to route copies of the message to any k destinations with the shortest average delay. In this paper, we first propose a matching method to solve the problem in a centralized way. We then bring forward a layered hierarchical structure where nodes are organized according to their degree of activities. Based on the structure, two routing algorithms are proposed where K-Cast initializes exactly k copies of the message without replication in the middle, K-Epidemic performs epidemic routing only in a controlled range. Both algorithms will first forward copies upwards along the structure and then downwards to the destinations. Experiments on real data trace show that the proposed algorithms achieve much better delay, delivery ratio and lower forwarding numbers.

关键词： Mobile Opportunistic Network Anycast Data routing Destination collision

Touching PBSData — An exploratory study of visual analytics for public bicycle system supporting multi-touch device

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Touching PBSData — An exploratory study of visual analytics...

IEEE International Conference on Progress in Informatics and Computing (PIC)

作者： Xiaoying Shi Zhenhai Yu Xinyu Qu Key Laboratory of Complex Systems Modeling and Simulation Hangzhou Dianzi University Hangzhou China Zhejiang Institute of Communications

ISBN: (纸本)9781509034857

Public bicycle sharing services are becoming popular over the past decade. The behavior of using public bicycle system (PBS) produces numerous hire records involving citizens' movement. This paper presents a visual analytics system-Touching PBSData, to help both traffic administrators and ordinary citizens visually explore and understand PBS data on multi-touch devices. Tasks and design principles are put forward firstly. Four views are designed to show different aspects of the dataset, including the geographical distribution, the spatio-temporal pattern and personal relevant information. In order to enhance the flexibility and usability of system, the organization mode of views and rich user interaction suitable for multi-touch device are further studied. By adopting real PBS dataset, the results of case studies certify that our method is able to help analyzers to find stations' main function and citizens' travel habits. Moreover, the feedback from the participants with various backgrounds is very affirmative through the user study.

关键词： Data visualization Visualization Bicycles Urban areas Organizations Switches Bars

Uniform convergence of multigrid finite element method for time-dependent riesz tempered fractional problem

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arXiv 2017年

作者： Chen, Minghua Bu, Weiping Qi, Wenya Wang, Yantao School of Mathematics and Statistics Gansu Key Laboratory of Applied Mathematics and Complex Systems Lanzhou University Lanzhou730000 China School of Mathematics and Computational Science Hunan Key Laboratory for Computation and Simulation in Science and Engineering Xiangtan University Xiangtan411105 China South University of Science and Technology of China Shenzhen518055 China

In this article a theoretical framework for the Galerkin finite element approximation to the time-dependent Riesz tempered fractional problem is provided without the fractional regularity assumption. Because the time-dependent problems should become easier to solve as the time step τ → 0, which correspond to the mass matrix dominant [R. E. Bank and T. Dupont, Math. Comp., 153 (1981), pp. 35-51]. Based on the introduced and analysis of the fractional τ-norm, the uniform convergence estimates of the V-cycle multigrid method with the time-dependent fractional problem is strictly proved, which means that the convergence rate of the V-cycle MGM is independent of the mesh size h and the time step τ. The numerical experiments are performed to verify the convergence with only O(NlogN) complexity by the fast Fourier transform method, where N is the number of the grid points. To the best of our knowledge, this is the first proof for the convergence rate of the V-cycle multigrid finite element method with τ → 0. Copyright © 2017, The Authors. All rights reserved.

关键词： Fast Fourier transforms

The Schrödinger equation for general non-hermitian quantum system

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arXiv 2017年

作者： Xiong, Ye Tong, Peiqing Department of Physics and Institute of Theoretical Physics Nanjing Normal University Nanjing210023 China National Laboratory of Solid State Microstructures Nanjing University Nanjing210093 China Jiangsu Key Laboratory for Numerical Simulation of Large Scale Complex Systems Nanjing Normal University Nanjing210023 China

We derive a new time-dependent Schrödinger equation(TDSE) for quantum models with nonhermitian Hamiltonian. Within our theory, the TDSE is symmetric in the two Hilbert spaces spanned by the left and the right eigenstates, respectively. The physical quantities are also identical in these two spaces. Based on this TDSE, we show that exchanging two quasi-particles in a non-hermitian model can generate arbitrary geometric phase. The system can also violate the Lieb-Robinson bound in non-relativistic quantum mechanics so that an action in one place will immediately cause a change in the distance. We show that the above two surprising behaviors can also appear in anyonic model, which makes us propose that the non-hermitian single particle model may possess many common features with anyonic model. Copyright © 2017, The Authors. All rights reserved.

关键词： Quantum optics