248 research outputs found

    Coupled Three-Mode Squeezed Vacuum

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    Multipartite entanglement is a key resource for various quantum information tasks. Here, we present a scheme for generating genuine tripartite entanglement via nonlinear optical processes. We derive, in the Fock basis, the corresponding output state which we termed the coupled three-mode squeezed vacuum. We find unintuitive behaviors arise in intensity squeezing between two of the three output modes due to the coupling present. We also show that this state can be genuinely tripartite entangled

    The Research of Product Graphical Information Sharing Technology of Virtual Manufacturing Enterprise in E-Commerce Environment

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    This paper has built a product model by UML and corresponding Product Schema. Then we have illuminated transmit mechanism of the product information by a dumbbell XML document. At last, we have pointed out the direction of the research. This research will provide a significative explore to the product data interchange between the members of virtual manufacturing enterprise in e-commerce environmen

    Standard random walks and trapping on the Koch network with scale-free behavior and small-world effect

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    A vast variety of real-life networks display the ubiquitous presence of scale-free phenomenon and small-world effect, both of which play a significant role in the dynamical processes running on networks. Although various dynamical processes have been investigated in scale-free small-world networks, analytical research about random walks on such networks is much less. In this paper, we will study analytically the scaling of the mean first-passage time (MFPT) for random walks on scale-free small-world networks. To this end, we first map the classical Koch fractal to a network, called Koch network. According to this proposed mapping, we present an iterative algorithm for generating the Koch network, based on which we derive closed-form expressions for the relevant topological features, such as degree distribution, clustering coefficient, average path length, and degree correlations. The obtained solutions show that the Koch network exhibits scale-free behavior and small-world effect. Then, we investigate the standard random walks and trapping issue on the Koch network. Through the recurrence relations derived from the structure of the Koch network, we obtain the exact scaling for the MFPT. We show that in the infinite network order limit, the MFPT grows linearly with the number of all nodes in the network. The obtained analytical results are corroborated by direct extensive numerical calculations. In addition, we also determine the scaling efficiency exponents characterizing random walks on the Koch network.Comment: 12 pages, 8 figures. Definitive version published in Physical Review

    Anomalous behavior of trapping on a fractal scale-free network

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    It is known that the heterogeneity of scale-free networks helps enhancing the efficiency of trapping processes performed on them. In this paper, we show that transport efficiency is much lower in a fractal scale-free network than in non-fractal networks. To this end, we examine a simple random walk with a fixed trap at a given position on a fractal scale-free network. We calculate analytically the mean first-passage time (MFPT) as a measure of the efficiency for the trapping process, and obtain a closed-form expression for MFPT, which agrees with direct numerical calculations. We find that, in the limit of a large network order VV, the MFPT behaves superlinearly as ∼V3/2 \sim V^{{3/2}} with an exponent 3/2 much larger than 1, which is in sharp contrast to the scaling ∼Vθ \sim V^{\theta} with θ≤1\theta \leq 1, previously obtained for non-fractal scale-free networks. Our results indicate that the degree distribution of scale-free networks is not sufficient to characterize trapping processes taking place on them. Since various real-world networks are simultaneously scale-free and fractal, our results may shed light on the understanding of trapping processes running on real-life systems.Comment: 6 pages, 5 figures; Definitive version accepted for publication in EPL (Europhysics Letters

    NeuralStagger: Accelerating Physics-constrained Neural PDE Solver with Spatial-temporal Decomposition

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    Neural networks have shown great potential in accelerating the solution of partial differential equations (PDEs). Recently, there has been a growing interest in introducing physics constraints into training neural PDE solvers to reduce the use of costly data and improve the generalization ability. However, these physics constraints, based on certain finite dimensional approximations over the function space, must resolve the smallest scaled physics to ensure the accuracy and stability of the simulation, resulting in high computational costs from large input, output, and neural networks. This paper proposes a general acceleration methodology called NeuralStagger by spatially and temporally decomposing the original learning tasks into several coarser-resolution subtasks. We define a coarse-resolution neural solver for each subtask, which requires fewer computational resources, and jointly train them with the vanilla physics-constrained loss by simply arranging their outputs to reconstruct the original solution. Due to the perfect parallelism between them, the solution is achieved as fast as a coarse-resolution neural solver. In addition, the trained solvers bring the flexibility of simulating with multiple levels of resolution. We demonstrate the successful application of NeuralStagger on 2D and 3D fluid dynamics simulations, which leads to an additional 10∼100×10\sim100\times speed-up. Moreover, the experiment also shows that the learned model could be well used for optimal control.Comment: ICML 2023 accepte

    Random walks on the Apollonian network with a single trap

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    Explicit determination of the mean first-passage time (MFPT) for trapping problem on complex media is a theoretical challenge. In this paper, we study random walks on the Apollonian network with a trap fixed at a given hub node (i.e. node with the highest degree), which are simultaneously scale-free and small-world. We obtain the precise analytic expression for the MFPT that is confirmed by direct numerical calculations. In the large system size limit, the MFPT approximately grows as a power-law function of the number of nodes, with the exponent much less than 1, which is significantly different from the scaling for some regular networks or fractals, such as regular lattices, Sierpinski fractals, T-graph, and complete graphs. The Apollonian network is the most efficient configuration for transport by diffusion among all previously studied structure.Comment: Definitive version accepted for publication in EPL (Europhysics Letters

    Robust Free-Space Optical Communication Utilizing Polarization

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    Free-space optical (FSO) communication can be subject to various types of distortion and loss as the signal propagates through non-uniform media. In experiment and simulation, we demonstrate that the state of polarization and degree of polarization of light passed though underwater bubbles, causing turbulence, is preserved. Our experimental setup serves as an efficient, low cost alternative approach to long distance atmospheric or underwater testing. We compare our experimental results with those of simulations, in which we model underwater bubbles, and separately, atmospheric turbulence. Our findings suggest potential improvements in polarization based FSO communication schemes.Comment: 13 pages, 5 figure
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