【10月20日】数学学术讲座

信息来源： 作者：　 发布时间：2021-07-03
报告题目: Recent Developments in Numerical Methods of Finding Saddle Points and its Applications in Materials

报告人: 张磊研究员 北京大学北京国际数学研究中心、北京大学定量生物学中心

报告地点：北院卓远楼305（统计与数学学院会议室）
报告时间：2017年10月20日（星期五）15：00-16:00

报告主持人：王汉权教授 统计与数学学院副院长

报告摘要：
Nucleation is one of the most common physical phenomena in physical, chemical, biological and materials sciences. Due to the difficulties and challenges in making direct experimental observation, many computational methods have been developed to model and simulate various nucleation events. In my talk, I will provide a sampler of some newly developed numerical algorithms that are widely applicable to many nucleation and phase transformation problems. I first describe some recent progress on the design of efficient numerical methods for computing saddle points and minimum energy paths, and then illustrate their applications to the study of nucleation events associated with several different physical systems. Nucleation is a complex multiscale problem. Development of efficient numerical algorithms and modeling approaches is bringing new light to this challenging subject.

报告人简介：张磊博士现任北京大学北京国际数学研究中心、北京大学定量生物学中心研究员、博士生导师，为国家“青年千人计划”入选者。曾获北京大学学士学位、中国科学院数学与系统科学研究院硕士学位、美国宾州州立大学数学系博士学位。主要研究兴趣为复杂生物系统的可计算建模，稀有事件及过渡态在生物中的应用，噪声对细胞命运和基因不确定性的影响，肠道隐窝的干细胞发育和细胞系模型。在大规模科学计算与数学建模，计算材料，计算生物等研究领域取得了许多创造性成果，并在Molecular Systems Biology、BMC Systems Biology、Commun. Comput. Phys.、Physical Review Letters等顶尖学术期刊发表论文。


报告题目: Non-relativistic limit of the nonlinear Dirac equation and its numerical methods

报告人: 蔡勇勇研究员 北京计算科学研究中心

报告地点：北院卓远楼305（统计与数学学院会议室）
报告时间：2017年10月20日（星期五）16：00-17:00

报告主持人：王汉权教授 统计与数学学院副院长

报告摘要：
We consider the (nonlinear) Dirac equation in the non-relativistic limit regime, involving a small parameter inversely proportional to the speed of light. The (nonlinear) Dirac equation converges to the (nonlinear) Schrodinger equation in the non-relativistic limit. By a careful analysis, we obtain a semi-relativistic limit of the nonlinear Dirac equation, which enables a design of uniformly accurate multi-scale numerical method. The major difficulty of the problem is that the solution has a rapid oscillation in time depending on the small parameter.

报告人简介：蔡勇勇博士现任中国工程物理研究院--北京计算科学研究中心研究员，为国家“青年海外高层次人才引进计划”入选者。曾获北京大学学士学位、硕士学位、新加坡国立大学博士学位。在数值分析与科学计算、多相流数值计算方法等研究领域取得了许多创造性成果，并在SIAM Journal on Applied Math.，SIAM Journal of Numerical Analysis， Journal of Computational. Physics，Physical Review A，Mathematics of Computation等顶尖学术期刊发表论文20余篇。

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