报告人：包维柱

单位：新加坡国立大学

报告时间：2017年07月23日（星期日）10:00

报告地点：7号教学楼7111教室

报告摘要：In this talk, I will present our recent work on mathematical models, asymptotic analysis and numerical simulation for degenerate dipolar quantum gas. As preparatory steps, I begin with the  three-dimensional Gross-Pitaevskii equation  with a long-range dipolar interaction potential which is used to model the degenerate dipolar quantum gas and reformulate it as a Gross-Pitaevskii-Poisson type system by decoupling the two-body dipolar interaction potential which is highly singular into short-range (or local) and long-range interactions (or repulsive and attractive interactions). Based on this new mathematical formulation, we prove rigorously existence and uniqueness as well as nonexistence of the ground states, and discuss the existence of global weak solution and finite time blowup of the dynamics in different parameter regimes of dipolar quantum gas. In addition, a backward Euler sine pseudospectral method is presented for computing the ground states and a time-splitting sine pseudospectral method is proposed for computing the dynamics of dipolar BECs. Due to the adoption of new mathematical formulation, our new numerical methods avoid evaluating integrals with high singularity and thus they are more efficient and accurate than those numerical methods currently used in the literatures for solving the problem. In addition, new mathematical formulations in two-dimensions and one dimension  for dipolar quantum gas are obtained when the external trapping potential is highly confined in one or two directions. Numerical results are presented to confirm our analytical results and demonstrate the efficiency and accuracy of our numerical methods. Some interesting physical phenomena are discussed too.

报告人简介：包维柱，教授。学士,硕士,博士均毕业于清华大学。曾任美国Georgia Institute of Technology助理教授和新加坡国立大学副教授，36岁时被聘为新加坡国立大学教授。1995年获清华大学林家翘应用数学一等奖；2003年获北京市科技二等奖，2008年获新加坡国立大学理学青年科学家奖；2008获新加坡国立大学理学杰出科学家奖；2013年包教授因其在数值分析玻色-爱因斯坦凝聚和计算Schroedinger方程解的杰出成就获“冯康科学计算奖”；2014年8月应邀在韩国汉城举办的第27届国际数学家大会上做了题为“数学在科学和技术中的应用”的45分钟报告。现为Advances in Numerical Analysis, East Asia Journal on Applied Mathematics, Journal of Mathematical Study,Applied Mathematics and Mechanics, Computational Astrophysics and Cosmology, Asian Journal of Mathematics等多个国际期刊的编委（Members of Editorial Boards ）。     

欢迎各位师生的参加！