Blow-up criteria for Boussinesq system and MHD system and Landau-Lifshitz equations in a bounded domain

In this paper, we prove some blow-up criteria for the 3D Boussinesq system with zero heat conductivity and MHD system and Landau-Lifshitz equations in a bounded domain.Comment: 20 page

Quality-Gated Convolutional LSTM for Enhancing Compressed Video

The past decade has witnessed great success in applying deep learning to enhance the quality of compressed video. However, the existing approaches aim at quality enhancement on a single frame, or only using fixed neighboring frames. Thus they fail to take full advantage of the inter-frame correlation in the video. This paper proposes the Quality-Gated Convolutional Long Short-Term Memory (QG-ConvLSTM) network with bi-directional recurrent structure to fully exploit the advantageous information in a large range of frames. More importantly, due to the obvious quality fluctuation among compressed frames, higher quality frames can provide more useful information for other frames to enhance quality. Therefore, we propose learning the "forget" and "input" gates in the ConvLSTM cell from quality-related features. As such, the frames with various quality contribute to the memory in ConvLSTM with different importance, making the information of each frame reasonably and adequately used. Finally, the experiments validate the effectiveness of our QG-ConvLSTM approach in advancing the state-of-the-art quality enhancement of compressed video, and the ablation study shows that our QG-ConvLSTM approach is learnt to make a trade-off between quality and correlation when leveraging multi-frame information. The project page: https://github.com/ryangchn/QG-ConvLSTM.git.Comment: Accepted to IEEE International Conference on Multimedia and Expo (ICME) 201

Human Pose Estimation using Global and Local Normalization

In this paper, we address the problem of estimating the positions of human joints, i.e., articulated pose estimation. Recent state-of-the-art solutions model two key issues, joint detection and spatial configuration refinement, together using convolutional neural networks. Our work mainly focuses on spatial configuration refinement by reducing variations of human poses statistically, which is motivated by the observation that the scattered distribution of the relative locations of joints e.g., the left wrist is distributed nearly uniformly in a circular area around the left shoulder) makes the learning of convolutional spatial models hard. We present a two-stage normalization scheme, human body normalization and limb normalization, to make the distribution of the relative joint locations compact, resulting in easier learning of convolutional spatial models and more accurate pose estimation. In addition, our empirical results show that incorporating multi-scale supervision and multi-scale fusion into the joint detection network is beneficial. Experiment results demonstrate that our method consistently outperforms state-of-the-art methods on the benchmarks.Comment: ICCV201

Spatial second-order positive and asymptotic preserving filtered PNP_N schemes for nonlinear radiative transfer equations

A spatial second-order scheme for the nonlinear radiative transfer equations is introduced in this paper. The discretization scheme is based on the filtered spherical harmonics ($FP_N$) method for the angular variable and the unified gas kinetic scheme (UGKS) framework for the spatial and temporal variables respectively. In order to keep the scheme positive and second-order accuracy, firstly, we use the implicit Monte Carlo linearization method [6] in the construction of the UGKS numerical boundary fluxes. Then, by carefully analyzing the constructed second-order fluxes involved in the macro-micro decomposition, which is induced by the $FP_N$ angular discretization, we establish the sufficient conditions that guarantee the positivity of the radiative energy density and material temperature. Finally, we employ linear scaling limiters for the angular variable in the $P_N$ reconstruction and for the spatial variable in the piecewise linear slopes reconstruction respectively, which are shown to be realizable and reasonable to enforce the sufficient conditions holding. Thus, the desired scheme, called the $PPFP_N$-based UGKS, is obtained. Furthermore, in the regime $\epsilon\ll 1$ and the regime $\epsilon=O(1)$, a simplified spatial second-order scheme, called the $PPFP_N$-based SUGKS, is presented, which possesses all the properties of the non-simplified one. Inheriting the merit of UGKS, the proposed schemes are asymptotic preserving. By employing the $FP_N$ method for the angular variable, the proposed schemes are almost free of ray effects. To our best knowledge, this is the first time that spatial second-order, positive, asymptotic preserving and almost free of ray effects schemes are constructed for the nonlinear radiative transfer equations without operator splitting. Various numerical experiments are included to validate the properties of the proposed schemes

Fabrication and Characterization of Electrospun Alumina Nanofibre Reinforced Polycarbonate Composites

PhDFibres with ultra-high tensile strength have attracted unprecedented attention due to the rapidly increasing demand for strong fibre reinforced composites in various fields. However, despite a theoretical strength as high as around 46 GPa, current commercial alumina fibres only reach strength value of around 3.3 GPa because of the defects between the grains. Electrospinning provides a method to produce ceramic nanofibres with diameters reduced to nano-scale with effectively enhanced strength. Different calcination procedures were applied to study the morphology and crystal structure growth of alumina. Tested with a custom-built AFM-SEM system, the tensile strength of single crystal α-alumina nanofibres were found to have little dependence on diameter variations, with an average value of 11.4±1.1 GPa. While the strength of polycrystalline γ-alumina nanofibres were controlled by defects, showing a diameter dependent mechanism. Apart from the intrinsic properties of the fibre and matrix, the interface between them also plays an important role in determining composite mechanical properties. Collected by a rotating drum during electrospinning, aligned fibres were used to reinforce polycarbonate matrix for fabricating composite. The composite mechanical properties were successfully improved after surface modification with silane coupling agent. With a fibre volume fraction of around 7.5%, the composite strength doubled and the Young’s modulus increased by a factor of 4 when compared with the pure polycarbonate. Apart from surface modification, the fibre/matrix interface can also be affected by transcrystallinity. Transcrystalline layers were formed in the alumina reinforced polycarbonate composites after annealing. Significant enhancement of the Young’s modulus of the crystallized polycarbonate by a factor of 3 compared to the amorphous phase was measured directly using AFM based nanoindentation. Optimization of the Young’s modulus is suggested as a balance between extending the annealing time to grow the transcrystalline layer and reducing the processing time to suppress void development in the PC matrix.Queen Mary, University of London and Chinese Scholarship Counci

Robust and Efficient Hamiltonian Learning

With the fast development of quantum technology, the sizes of both digital and analog quantum systems increase drastically. In order to have better control and understanding of the quantum hardware, an important task is to characterize the interaction, i.e., to learn the Hamiltonian, which determines both static and dynamic properties of the system. Conventional Hamiltonian learning methods either require costly process tomography or adopt impractical assumptions, such as prior information on the Hamiltonian structure and the ground or thermal states of the system. In this work, we present a robust and efficient Hamiltonian learning method that circumvents these limitations based only on mild assumptions. The proposed method can efficiently learn any Hamiltonian that is sparse on the Pauli basis using only short-time dynamics and local operations without any information on the Hamiltonian or preparing any eigenstates or thermal states. The method has a scalable complexity and a vanishing failure probability regarding the qubit number. Meanwhile, it performs robustly given the presence of state preparation and measurement errors and resiliently against a certain amount of circuit and shot noise. We numerically test the scaling and the estimation accuracy of the method for transverse field Ising Hamiltonian with random interaction strengths and molecular Hamiltonians, both with varying sizes and manually added noise. All these results verify the robustness and efficacy of the method, paving the way for a systematic understanding of the dynamics of large quantum systems.Comment: 41 pages, 6 figures, Open source implementation available at https://github.com/zyHan2077/HamiltonianLearnin