The composite trapezoidal rule for the computation of Hadamard finite-part integrals in boundary element methods with the hypersingular kernel I/sin2（x- s） is discussed, and the main part of the asymptotic expansion...The composite trapezoidal rule for the computation of Hadamard finite-part integrals in boundary element methods with the hypersingular kernel I/sin2（x- s） is discussed, and the main part of the asymptotic expansion of error function is obtained. Based on the main part of the asymptotic expansion, a series is constructed to approach the singular point. An extrapolation algorithm is presented and the convergence rate is proved. Some numerical results are also presented to confirm the theoretical results and show the efficiency of the algorithms.展开更多
MnSi in the B20 structure is a prototypical helimagnet that forms a skyrmion lattice, a vortex-like spin texture under applied magnetic field. We have systematically explored the synthesis of single crystal MnSi nanow...MnSi in the B20 structure is a prototypical helimagnet that forms a skyrmion lattice, a vortex-like spin texture under applied magnetic field. We have systematically explored the synthesis of single crystal MnSi nanowires via controlled oxide-assisted chemical vapor deposition and observed a characteristic signature of skyrmion magnetic ordering in the MnSi nanowires. The thickness of the SiO2 layer on the Si substrate plays the key role in obtaining a high yield of B20 MnSi skyrmion nanowires. A growth mechanism was proposed that is consistent with the existence of an optimum SiO2 thickness. A growth phase diagram was constructed based on the extensive studies of various growth conditions for various MnSi nanostructures. The persistence of both the helicoidal and skyrmion magnetic ordering in the one-dimensional wires was directly revealed by ac and dc magnetic measurements.展开更多
基金supported by National Natural Science Foundation of China(Grant Nos. 11101247 and 11201209)Shandong Provincial Natural Science Foundation of China (Grant No.ZR2011AQ020)+3 种基金a project of Shandong Province Higher Educational Science and Technology Program (GrantNo. J11LE08)supported by National Natural Science Foundation of China (GrantNo. 11101317)supported by National Basic Research Program of China (Grant No.2005CB321701)the Reward Fund of CAS for National Prize
文摘The composite trapezoidal rule for the computation of Hadamard finite-part integrals in boundary element methods with the hypersingular kernel I/sin2（x- s） is discussed, and the main part of the asymptotic expansion of error function is obtained. Based on the main part of the asymptotic expansion, a series is constructed to approach the singular point. An extrapolation algorithm is presented and the convergence rate is proved. Some numerical results are also presented to confirm the theoretical results and show the efficiency of the algorithms.
文摘MnSi in the B20 structure is a prototypical helimagnet that forms a skyrmion lattice, a vortex-like spin texture under applied magnetic field. We have systematically explored the synthesis of single crystal MnSi nanowires via controlled oxide-assisted chemical vapor deposition and observed a characteristic signature of skyrmion magnetic ordering in the MnSi nanowires. The thickness of the SiO2 layer on the Si substrate plays the key role in obtaining a high yield of B20 MnSi skyrmion nanowires. A growth mechanism was proposed that is consistent with the existence of an optimum SiO2 thickness. A growth phase diagram was constructed based on the extensive studies of various growth conditions for various MnSi nanostructures. The persistence of both the helicoidal and skyrmion magnetic ordering in the one-dimensional wires was directly revealed by ac and dc magnetic measurements.
