Academy of Mathematics and Systems Science, CAS
Colloquia & Seminars

Speaker:	Dr. Yitzhak Fouxon，Technion – Israel Institute of Technology
Inviter:	于海军副研究员
Title:	Introduction to stochastic process, random walks and turbulence
Time & Venue:	2019.5.7,8,10,11 8:30-11:30 Z311
Abstract:	Statistical physics is a branch of physics that uses methods of probability theory and statistics, and particularly the mathematical tools for dealing with large populations and approximations, in solving physical problems. It can describe a wide variety of fields with an inherently stochastic nature. Its applications include many problems in the fields of physics, biology, chemistry, neuroscience, and even some social sciences, such as sociology and linguistics. In this intensive course of lectures we will provide the introduction to some areas of modern statistical physics, with particular emphasis on anomalous diffusion and turbulence. The tentative hourly plan is found below. 具体安排： 5月7日: 8:30-12:30 Z311 第1讲: White noise and Brownian motion. 第2讲: The Langevin equation and the Onsager principle. 第3讲: Fluctuation-dissipation theorem 第4讲: We will derive the Fokker-Planck equation. 5月8日: 8:30-12:30 Z311 第5讲: The entropy functional 第6讲: The Feynman-Kac formula 第7讲: Large number of independent random variables 第8讲: Large deviations 5月10日: 8:30-12:30 Z311 第9讲: Infinite and finite-time Lyapunov exponents. 第10讲: When traditional central limit theorem breaks down. 第11讲: Anomalous diffusions and Levy walks. 第12讲: Continuous time random walks 5月11日: 8:30-12:30 Z311 第13讲: Fractional Laplace equation 第14讲: Kolmogorov relation of turbulence 第15讲: Anomalous scaling. 第16讲: Kraichnan model flow Some references [1] Shang-Keng Ma, Statistical Mechanics [2] Reichl, L.E., 1999. A modern course in statistical physics. [3] Frisch, U. and Kolmogorov, A.N., 1995. Turbulence: the legacy of AN Kolmogorov. Cambridge university press. [4] Falkovich, G., Gaw?dzki, K. and Vergassola, M., 2001. Particles and fieldsin fluid turbulence. Reviews of modern Physics, 73(4), p.913.