Abstract: In this talk, a projection gradient method is presented for computing the ground state of spin-2 Bose-Einstein condensates (BEC). We first propose the general projection gradient method for solving the energy functional minimization problem under multiple constraints, in which the energy functional takes real functions as independent variables. We next extend the method to solve the same problem, where the energy functional now takes complex functions as independent variables. We finally employ the method into finding the ground state of spin-2 BEC. The key of our method is: by constructing continuous gradient flows, the ground state of spin-2 BEC can be computed as the steady state solution of such CGFs. We discretized the CGFs by a conservative finite difference method along with a proper way to deal with the nonlinear terms. We show that the numerical discretization is normalization and magnetization conservative and energy diminishing. Numerical results of the ground state and their energy of spin-2 BEC are reported to demonstrate the effectiveness of the numerical method. 

报告人简介：王汉权，男，汉族，新加坡国立大学数学系博士，香港科技大学数学系博士后。现任云南财经大学统计与数学学院教授、统计与数学学院数学系副主任、中国工业与应用数学学会会员。2006年至2011年期间，曾多次前往新加坡国立大学数学系、香港科技大学数学系做访问学者。目前从事科学研究的领域包括计算数学与科学工程计算、偏微分方程的数值解法设计、计算机模拟玻色-爱因斯坦凝聚态中的涡旋现象和材料科学中的晶体位错现象、超强激光与基本物质相互作用等。曾担任多个国际计算数学期刊论文的通信评审人。2012年7月，被聘为教育部留学回国人员科研启动基金评审专家。2013年入选教育部新世纪优秀人才支持计划。目前正主持国家自然科学基金一项，已经完成国家自然科学基金青年基金、教育部“留学回国人员科研启动基金”、云南省教育厅科学研究重点项目、云南财经大学科研启动基金等各一项。在计算数学与科学工程计算领域至今已经发表SCI收录的高水平科研论文二十余篇，并在科学出版社出版专著一部。

Date&Time: December 23, 2013 (Monday), 9:30-10:30 a.m.
Location: 606 Conference Room, No.3 Heqing Road, Haidian District