Particle-hole symmetry and interaction effects in the Kane-Mele-Hubbard model

We prove that the Kane-Mele-Hubbard model with purely imaginary next-nearest-neighbor hoppings has a particle-hole symmetry at half-filling. Such a symmetry has interesting consequences including the absence of charge and spin currents along open edges, and the absence of the sign problem in the determinant quantum Monte-Carlo simulations. Consequentially, the interplay between band topology and strong correlations can be studied at high numeric precisions. The process that the topological band insulator evolves into the antiferromagnetic Mott insulator as increasing interaction strength is studied by calculating both the bulk and edge electronic properties. In agreement with previous theory analyses, the numeric simulations show that the Kane-Mele-Hubbard model exhibits three phases as increasing correlation effects: the topological band insulating phase with stable helical edges, the bulk paramagnetic phase with unstable edges, and the bulk antiferromagnetic phase

Numerical investigation on impacts of leakage sizes and pressures of fluid conveying pipes on aerodynamic behaviors

Small hole leakage of pipes caused by erosion and perforation is the major form leading to the leakage. The leakage rate is an important premise and foundation for consequence computation and risk evaluation. Those published papers fail to systematically study impacts of initial pressures and leakage sizes of a pipe on the leakage rate. More numerical simulation results are not verified by experimental test. This paper applies numerical simulation technology to establish the model of small hole leakage in pipes, designs and processes different leakage modules to simulate different leakage scenes, and then experimentally validates the model correctness. On this basis, this paper studies impacts of initial pressures and leakage sizes on leakage rates and obtains fluid dynamic characteristics around the leakage hole, including velocity distribution and pressure distribution. However, in actual engineering, the position of leakage hole could not be predicted and changed in general. Therefore, this paper further studies impacts of leakage hole positions on the pipe leakage rate. In this way, this research is refined and could provide a theoretical basis for emergency rescue and accident survey of pipe leakage accidents