Kinetic theory based force treatment in lattice Boltzmann equation

In the gas kinetic theory, it showed that the zeroth order of the density distribution function $f^{(0)}$ and local equilibrium density distribution function were the Maxwellian distribution f^{(eq)}(\rho,\emph{\textbf{u}}, T) with an external force term, where $\rho$ the fluid density, \emph{\textbf{u}} the physical velocity and $T$ the temperature, while in the lattice Boltzmann equation (LBE) method numerous force treatments were proposed with a discrete density distribution function $f_i$ apparently relaxed to a given state f^{(eq)}_i(\rho,\emph{\textbf{u}}^*), where the given velocity \emph{\textbf{u}}^* could be different with \emph{\textbf{u}}, and the Chapman-Enskog analysis showed that $f^{(0)}_i$ and local equilibrium density distribution function should be f^{(eq)}_i(\rho,\emph{\textbf{u}}^*) in the literature. In this paper, we start from the kinetic theory and show that the $f^{(0)}_i$ and local equilibrium density distribution function in LBE should obey the Maxwellian distribution f^{(eq)}_i(\rho,\emph{\textbf{u}}) with $f_i$ relaxed to f^{(eq)}_i(\rho,\emph{\textbf{u}}^*), which are consistent with kinetic theory, then the general requirements for the force term are derived, by which the correct hydrodynamic equations could be recovered at Navier-Stokes level, and numerical results confirm our theoretical analysis

Floquet Topological States in Shaking Optical Lattices

In this letter we propose realistic schemes to realize topologically nontrivial Floquet states by shaking optical lattices, using both one-dimension lattice and two-dimensional honeycomb lattice as examples. The topological phase in the two-dimensional model exhibits quantum anomalous Hall effect. The transition between topological trivial and nontrivial states can be easily controlled by shaking frequency and amplitude. Our schemes have two major advantages. First, both the static Hamiltonian and the shaking scheme are sufficiently simple to implement. Secondly, it requires relatively small shaking amplitude and therefore heating can be minimized. These two advantages make our scheme much more practical.Comment: 6 pages including supplementary materials, 3 figure

Quasi-particle Lifetime in a Mixture of Bose and Fermi Superfluids

In this letter, to reveal the effect of quasi-particle interactions in a Bose-Fermi superfluid mixture, we consider the lifetime of quasi-particle of Bose superfluid due to its interaction with quasi-particles in Fermi superfluid. We find that this damping rate, i.e. inverse of the lifetime, has quite different threshold behavior at the BCS and the BEC side of the Fermi superfluid. The damping rate is a constant nearby the threshold momentum in the BCS side, while it increases rapidly in the BEC side. This is because in the BCS side the decay processe is restricted by constant density-of-state of fermion quasi-particle nearby Fermi surface, while such a restriction does not exist in the BEC side where the damping process is dominated by bosonic quasi-particles of Fermi superfluid. Our results are related to collective mode experiment in recently realized Bose-Fermi superfluid mixture.Comment: 8 pages and 3 figures including supplemental materia

Generalized Dynamics in Social Networks With Antagonistic Interactions

In this paper, we investigate a general nonlinear model of opinion dynamics in which both state-dependent susceptibility to persuasion and antagonistic interactions are considered. According to the existing literature and socio-psychological theories, we examine three specializations of state-dependent susceptibility, that is, stubborn positives scenario, stubborn neutrals scenario, and stubborn extremists scenario. Interactions among agents form a signed graph, in which positive and negative edges represent friendly and antagonistic interactions, respectively. Based on Perron-Frobenius property of eventually positive matrices and LaSalle invariance principle, we conduct a comprehensive theoretical analysis of the generalized nonlinear opinion dynamics. We obtain some sufficient conditions such that the states of all agents converge into the subspace spanned by the right positive eigenvector of an eventually positive matrix. When there exists at least one entry of the right positive eigenvector which is not equal to one, the derived results can be used to describe different levels of an opinion. Finally, we present two examples to demonstrate the effectiveness of the theoretical findings.Comment: 14 pages, 9 figure

A Deep Learning Approach for Expert Identification in Question Answering Communities

In this paper, we describe an effective convolutional neural network framework for identifying the expert in question answering community. This approach uses the convolutional neural network and combines user feature representations with question feature representations to compute scores that the user who gets the highest score is the expert on this question. Unlike prior work, this method does not measure expert based on measure answer content quality to identify the expert but only require question sentence and user embedding feature to identify the expert. Remarkably, Our model can be applied to different languages and different domains. The proposed framework is trained on two datasets, The first dataset is Stack Overflow and the second one is Zhihu. The Top-1 accuracy results of our experiments show that our framework outperforms the best baseline framework for expert identification.Comment: 7 pages. arXiv admin note: text overlap with arXiv:1403.6652 by other author

Large deviations for stochastic models of two-dimensional second grade fluids driven by L\'evy noise

In this paper, we establish a large deviation principle for stochastic models of two-dimensional second grade fluids driven by L\'evy noise. The weak convergence method introduced by Budhiraja, Dupuis and Maroulas in [5] plays a key role

HOMs Simulation and Measurement Results of IHEP02 Cavity

In cavities, there exists not only the fundamental mode which is used to accelerate the beam but also higher order modes (HOMs). The higher order modes excited by beam can seriously affect beam quality, especially for the higher R/Q modes. This paper reports on measured results of higher order modes in the IHEP02 1.3GHz low-loss 9-cell superconducting cavity. Using different methods, Qe of the dangerous modes passbands have been got. The results are compared with TESLA cavity results. R/Q of the first three passbands have also been got by simulation and compared with the results of TESLA cavity

Magnetic Order Driven Topological Transition in the Haldane-Hubbard Model

In this letter we study the Haldane model with on-site repulsive interactions at half-filling. We show that the mean-field Hamiltonian with magnetic order effectively modifies parameters in the Haldane Hamiltonian, such as sublattice energy difference and phase in next nearest hopping. As interaction increases, increasing of magnetic order corresponds to varying these parameters and consequently, drives topological transitions. At the mean-field level, one scenario is that the magnetic order continuously increases, and inevitably, the fermion gap closes at the topological transition point with nonzero magnetic order. Beyond the mean-field, interaction between fermions mediated by spin-wave fluctuations can further open up the gap, rendering a first-order transition. Another scenario is a first-order transition at mean-field level across which a canted magnetic order develops discontinuously, avoiding the fermion gap closing. We find that both scenarios exist in the phase diagram of the Haldane-Hubbard model. Our predication is relevant to recent experimental realization of the Haldane model in cold atom system.Comment: 9 pages, 4 figures, with supplementary materia

Generalization Bounds of SGLD for Non-convex Learning: Two Theoretical Viewpoints

Algorithm-dependent generalization error bounds are central to statistical learning theory. A learning algorithm may use a large hypothesis space, but the limited number of iterations controls its model capacity and generalization error. The impacts of stochastic gradient methods on generalization error for non-convex learning problems not only have important theoretical consequences, but are also critical to generalization errors of deep learning. In this paper, we study the generalization errors of Stochastic Gradient Langevin Dynamics (SGLD) with non-convex objectives. Two theories are proposed with non-asymptotic discrete-time analysis, using Stability and PAC-Bayesian results respectively. The stability-based theory obtains a bound of $O\left(\frac{1}{n}L\sqrt{\beta T_k}\right)$, where $L$ is uniform Lipschitz parameter, $\beta$ is inverse temperature, and $T_k$ is aggregated step sizes. For PAC-Bayesian theory, though the bound has a slower $O(1/\sqrt{n})$ rate, the contribution of each step is shown with an exponentially decaying factor by imposing $\ell^2$ regularization, and the uniform Lipschitz constant is also replaced by actual norms of gradients along trajectory. Our bounds have no implicit dependence on dimensions, norms or other capacity measures of parameter, which elegantly characterizes the phenomenon of "Fast Training Guarantees Generalization" in non-convex settings. This is the first algorithm-dependent result with reasonable dependence on aggregated step sizes for non-convex learning, and has important implications to statistical learning aspects of stochastic gradient methods in complicated models such as deep learning

One-Shot Texture Retrieval with Global Context Metric

In this paper, we tackle one-shot texture retrieval: given an example of a new reference texture, detect and segment all the pixels of the same texture category within an arbitrary image. To address this problem, we present an OS-TR network to encode both reference and query image, leading to achieve texture segmentation towards the reference category. Unlike the existing texture encoding methods that integrate CNN with orderless pooling, we propose a directionality-aware module to capture the texture variations at each direction, resulting in spatially invariant representation. To segment new categories given only few examples, we incorporate a self-gating mechanism into relation network to exploit global context information for adjusting per-channel modulation weights of local relation features. Extensive experiments on benchmark texture datasets and real scenarios demonstrate the above-par segmentation performance and robust generalization across domains of our proposed method.Comment: ijcai2019-lastes