2,029 research outputs found
Bulk-deformed potentials for toric Fano surfaces, wall-crossing and period
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
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
Recommended from our members
Periodic symplectic cohomologies and obstructions to exact Lagrangian immersions
Given a Liouville manifold, symplectic cohomology is defined as the Hamiltonian Floer homology for the symplectic action functional on the free loop space. In this thesis, we propose two versions of periodic S^1-equivariant homology or S^1-equivariant Tate homology for the natural S^1-action on the free loop space. The first version is called periodic symplectic cohomology. We prove that there is a localization theorem or a fix point property for periodic symplectic cohomology. The second version is called the completed periodic symplectic cohomology which satisfies Goodwillie's excision isomorphism.
Inspired by the work of Seidel and Solomon on the existence of dilations on symplectic cohomology, we formulate the notion of Liouville manifolds admitting higher dilations using Goodwillie's excision isomorphism on the completed periodic symplectic cohomology. As an application, we derive obstructions to existence of certain exact Lagrangian immersions in Liouville manifolds admitting higher dilations
CRKD: Enhanced Camera-Radar Object Detection with Cross-modality Knowledge Distillation
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
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
- …