Lecture 1
Title: Approximation of long time statistical properties of large dissipative chaotic dynamical systems
Speaker: Prof. Xiaoming Wang, Southern University of Science and Technology
Time: 16:00-17:00 pm, September 30, 2022, GMT+8
Venue: Zoom Meeting ID: 816 2032 5162 Password: 987654
Abstract:
It is well-known that physical laws for large chaotic systems are revealed statistically. We consider temporal and spatial approximations of stationary statistical properties of dissipative chaotic dynamical systems. We demonstrate that appropriate temporal/spatial discretization viewed as discrete dynamical system is able to capture asymptotically the stationary statistical properties of the underlying continuous dynamical system provided that appropriate Lax type criteria are satisfied. We also show a general framework on when the long-time statistics of the system can be well-approximated by BDF2 based schemes. Application to the infinite Prandtl number model for convection as well as the two-dimensional barotropic quasi-geostrophic equations will be discussed.
Biography:
Prof. Wang received his Ph.D. in Applied Mathematics from Indiana University - Bloomington in 1996. He was a postdoctoral fellow / Courant Instructor at the Courant Institute from 1996 to 1998. Dr. Wang joined Iowa State University in 1998 where he was promoted to Associate Professor with Tenure in 2001. He moved to Florida State University in 2003 where he was promoted to Tenured Professor and served as the Chair of the Math Department at Florida State University before he returned to his motherland in 2017. He is currently a Chair Professor of Mathematics and the Chair of the Department of Mathematics at Southern University of Science and Technology.
Prof. Wang's current research focuses on modern applied mathematics, especially problems related to fluid dynamics, groundwater research, geophysical fluid dynamics and turbulence, and big data and machine learning. He develops and utilizes tools from Partial Differential Equations, Dynamical Systems, Stochastic Analysis, Numerical Analysis and Scientific Computing in his research. A distinctive feature of his work is the combination of rigorous mathematics with genuine physical applications.
Lecture 2
Title: Implicit finite difference schemes for viscous gas dynamics problems
Speaker: Prof. Georgy Kobelkov, Lomonosov Moscow State University
Time: 17:00-18:00 pm, September 30, 2022, GMT+8
Venue: Zoom Meeting ID: 816 2032 5162 Password: 987654
Abstract:
In one-dimensional case implicit monotone finite difference schemes are proposed to approximate gas dynamics problems. It is proved that a solution to FDEs exists and is unique. The schemes proposed can be extended to many-dimensional case. Numerical solution of some gas dynamics problems is demonstrated.
Biography:
Georgy Kobelkov graduated from high school with a gold medal. In 1970 he graduated from the Faculty of Mechanics and Mathematics of Lomonosov Moscow State University in the Department of Computational Mathematics. He completed his thesis work under the guidance of Academician A.N.Tikhonov. He defended his Ph.D. thesis in 1975 (supervisor - Academician N.S.Bakhvalov). Doctor of Physical and Mathematical Sciences since 1985. Professor since 1987. Since 1991 he has been the head of the laboratory of computer modeling at the Faculty of Mechanics and Mathematics of Moscow State University. Since 2007 he has been the head of the Department of Computational Mathematics, a leading researcher at the Marchuk Institute of Computational Mathematics of RAS.
Awards: Laureate of the Prize of the Department of Mathematics of the USSR Academy of Sciences (1989), Laureate of the Prize. M. V. Lomonosov (1998), Laureate of the Prize. M. V. Lomonosov for pedagogical activity (2010)
Source: SRMC
