We survey some results on travel time tomography. The question is whether we can determine the anisotropic index of refraction of a medium by measuring the travel times of waves going through the medium. This can be r...We survey some results on travel time tomography. The question is whether we can determine the anisotropic index of refraction of a medium by measuring the travel times of waves going through the medium. This can be recast as geometry problems, the boundary rigidity problem and the lens rigidity problem. The boundary rigidity problem is whether we can determine a Riemannian metric of a compact Riemannian manifold with boundary by measuring the distance function between boundary points. The lens rigidity problem problem is to determine a Riemannian metric of a Riemannian manifold with boundary by measuring for every point and direction of entrance of a geodesic the point of exit and direction of exit and its length. The linearization of these two problems is tensor tomography. The question is whether one can determine a symmetric two-tensor from its integrals along geodesics. We emphasize recent results on boundary and lens rigidity and in tensor tomography in the partial data case, with further applications.展开更多
Two-dimensional silicon carbide（2d-SiC） is a viable material for next generation electronics due to its moderate,direct bandgap with huge potential.In particular,its potential for p–n junctions is yet to be explore...Two-dimensional silicon carbide（2d-SiC） is a viable material for next generation electronics due to its moderate,direct bandgap with huge potential.In particular,its potential for p–n junctions is yet to be explored.In this paper,three types of 2d-SiC-based p–n junctions with different doping configuration are modeled.The doping configurations refer to partially replacing carbon with boron or nitrogen atoms along the zigzag or armchair direction,respectively.By employing density functional theory,we calculate the transport properties of the SiC based p–n junctions and obtain negative differential resistance and high rectification ratio.We also find that the junction along the zigzag direction with lower doping density exhibits optimized rectification performance.Our study suggests that 2d-SiC is a promising candidate as a material platform for future nano-devices.展开更多
基金partly supported by NSF(Grant No.DMS-1600327)partly supported by NSF+1 种基金a SiYuan Professorship at HKUSTpartial support from the NSF under(Grant Nos.DMS-1361432 and DMS-1664683 and from a Simons Fellowship)
文摘We survey some results on travel time tomography. The question is whether we can determine the anisotropic index of refraction of a medium by measuring the travel times of waves going through the medium. This can be recast as geometry problems, the boundary rigidity problem and the lens rigidity problem. The boundary rigidity problem is whether we can determine a Riemannian metric of a compact Riemannian manifold with boundary by measuring the distance function between boundary points. The lens rigidity problem problem is to determine a Riemannian metric of a Riemannian manifold with boundary by measuring for every point and direction of entrance of a geodesic the point of exit and direction of exit and its length. The linearization of these two problems is tensor tomography. The question is whether one can determine a symmetric two-tensor from its integrals along geodesics. We emphasize recent results on boundary and lens rigidity and in tensor tomography in the partial data case, with further applications.
基金Project supported by the National Science Foundation of China(Nos.61474099,61674127)the ZJ-NSF(No.Z17F04003)
文摘Two-dimensional silicon carbide（2d-SiC） is a viable material for next generation electronics due to its moderate,direct bandgap with huge potential.In particular,its potential for p–n junctions is yet to be explored.In this paper,three types of 2d-SiC-based p–n junctions with different doping configuration are modeled.The doping configurations refer to partially replacing carbon with boron or nitrogen atoms along the zigzag or armchair direction,respectively.By employing density functional theory,we calculate the transport properties of the SiC based p–n junctions and obtain negative differential resistance and high rectification ratio.We also find that the junction along the zigzag direction with lower doping density exhibits optimized rectification performance.Our study suggests that 2d-SiC is a promising candidate as a material platform for future nano-devices.
