学　术

　　人力资源部教师发展中心“学者论坛”第62期活动安排如下，欢迎广大师生参加。

　　一、时　间：2017年6月1日（周四）14:00

　　二、地　点：清水河校区主楼A1-512

　　三、主题一：Stretching of Viscous Threads

　　主讲人：香港城市大学数学系 Jonathan J. Wylie教授

　　内容简介：

　　Despite extensive research on extensional flows, there is no complete explanation for why highly viscous fluids extending under gravity can form such persistent and stable filaments with no sign of destabilization from surface tension. We therefore investigate the motion of a slender axisymmetric viscous thread that is supported at its top by a fixed horizontal surface and extends downward under gravity. In the case in which inertia and surface tension are initially negligible, we consider the long- wavelength equations for the full initial–boundary-value problem for a thread of arbitrary initial shape. We show that, eventually, the accelerations in the thread become sufficiently large that the inertial terms become important. Thus, we keep the inertial terms and, using matched asymptotic expansions, obtain solutions for the full initial–boundary-value problem. We show that the dynamics can be divided into two generic cases that exhibit very different behaviour. In the first case, the thread develops a long thin region that joins together two fluid masses. In this case, we use order-of-magnitude estimates to show that surface-tension-driven pinching will not occur if the square root of the Reynolds number is much greater than the initial aspect ratio divided by the Bond number. In the second case, the thread becomes thin near the horizontal surface. In this case, we show that the long-wavelength equations will ultimately break down and discuss the role of inertia in determining the dynamics. The asymptotic procedures require a number of novel techniques and the resulting solutions exhibit surprisingly rich behaviour. The solution allows us to understand the mechanisms that underlie highly persistent filaments.

　　主讲人简介：

　　Prof. Jonathan J. Wylie's research is focused on fluid mechanics, granular materials and other industrially motivated problems. He obtained his PhD and was subsequently awarded a Junior Research Fellowship from King's College, Cambridge. He is the author of a number of research papers and has publications in "Science" and "Physical Review Letters". He is an associate editor of IMA Journal of Applied Mathematics. "Mathematics-in-Industry: Case Studies" which is a new journal launched by the Fields Institute, Canada. He was a member of the organising committee for the "International Conference on Applied Mathematics: Modeling, Analysis and Computations" in CityU (2008)

　　四、 主题二：Recent developments in mathematical finance

　　主讲人：香港城市大学数学系 Qiang Zhang教授

　　内容简介：

　　Long-term portfolio management is an important issue in modern finance and practice. We have analyzed various known continuous-time strategies in portfolio management, with a focus on bankruptcy probabilities under these strategies. We show that, for each strategy, there is a threshold in the target return rate. When the target return rate is set above this threshold, the application of the strategy for a long investment horizon leads to certain bankruptcy. For a target return rate lower than this threshold, bankruptcy never occurs. Bankruptcy probabilities under a finite investment horizon are also studied. An empirical study based on the Dow Jones Industrial Average Index confirms these results.

　　主讲人简介：

　　Prof. Qiang Zhang receives his BSc from Fudan University, MA and PhD from New York University. Prior to joining City University of Hong Kong, Prof. Zhang had been with New York University and State University at Stony Brook. Prof. Zhang's research interests include financial mathematics, risk management, optional portfolio selection, fluid dynamics, granular materials and mathematical physics.

　　五、主持人：数学科学学院 吴永科

　　六、主办单位：人力资源部教师发展中心

　　　　承办单位：数学科学学院

　　　　　　　　　　　　　　　　　　人力资源部教师发展中心

　　　　　　　　　　　　　　　　　　　　2017年5月27日