2,029 research outputs found

    Bulk-deformed potentials for toric Fano surfaces, wall-crossing and period

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    We provide an inductive algorithm to compute the bulk-deformed potentials for toric Fano surfaces via wall-crossing techniques and a tropical-holomorphic correspondence theorem for holomorphic discs. As an application of the correspondence theorem, we also prove a big quantum period theorem for toric Fano surfaces which relates the log descendant Gromov-Witten invariants with the oscillatory integrals of the bulk-deformed potentials.Comment: 44 pages, 9 figures, comments are welcom

    A Finite Element Method for the Multiterm Time-Space Riesz Fractional Advection-Diffusion Equations in Finite Domain

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    We present an effective finite element method (FEM) for the multiterm time-space Riesz fractional advection-diffusion equations (MT-TS-RFADEs). We obtain the weak formulation of MT-TS-RFADEs and prove the existence and uniqueness of weak solution by the Lax-Milgram theorem. For multiterm time discretization, we use the Diethelm fractional backward finite difference method based on quadrature. For spatial discretization, we show the details of an FEM for such MT-TS-RFADEs. Then, stability and convergence of such numerical method are proved, and some numerical examples are given to match well with the main conclusions

    CRKD: Enhanced Camera-Radar Object Detection with Cross-modality Knowledge Distillation

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    In the field of 3D object detection for autonomous driving, LiDAR-Camera (LC) fusion is the top-performing sensor configuration. Still, LiDAR is relatively high cost, which hinders adoption of this technology for consumer automobiles. Alternatively, camera and radar are commonly deployed on vehicles already on the road today, but performance of Camera-Radar (CR) fusion falls behind LC fusion. In this work, we propose Camera-Radar Knowledge Distillation (CRKD) to bridge the performance gap between LC and CR detectors with a novel cross-modality KD framework. We use the Bird's-Eye-View (BEV) representation as the shared feature space to enable effective knowledge distillation. To accommodate the unique cross-modality KD path, we propose four distillation losses to help the student learn crucial features from the teacher model. We present extensive evaluations on the nuScenes dataset to demonstrate the effectiveness of the proposed CRKD framework. The project page for CRKD is https://song-jingyu.github.io/CRKD.Comment: Accepted to CVPR 202

    Piezoelectric Wind Energy Harvesting from Self-Excited Vibration of Square Cylinder

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    Self-excited vibration of a square cylinder has been considered as an effective way in harvesting piezoelectric wind energy. In present work, both of the vortex-induced vibration and unstable galloping phenomenon process are investigated in a reduced velocity (Ur=U/ωn·D) range of 4≤Ur≤20 with load resistance ranging in 100 Ω≤R≤1 MΩ. The vortex-induced vibration covers presynchronization, synchronization, and postsynchronization branches. An aeroelectromechanical model is given to describe the coupling of the dynamic equation of the fluid-structure interaction and the equation of Gauss law. The effects of load resistance are investigated in both the open-circuit and close-circuit system by a linear analysis, which covers the parameters of the transverse displacement, aerodynamic force, output voltage, and harvested power utilized to measure the efficiency of the system. The highest level of the transverse displacement and the maximum value of harvested power of synchronization branch during the vortex-induced vibration and galloping are obtained. The results show that the large-amplitude galloping at high wind speeds can generate energy. Additionally, energy can be harvested by utilization of the lock-in phenomenon of vortex-induced vibration under low wind speed
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