248 research outputs found
Coupled Three-Mode Squeezed Vacuum
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
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
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
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 , the MFPT behaves superlinearly as with an exponent 3/2 much larger than 1, which is in sharp contrast
to the scaling with , 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
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 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
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
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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