Lecture
This lecture delves into the core concepts behind physically-important equations, such as the connection between polymers and random walks. It explores the history of Brownian motion, from Robert Brown's observations to Perrin's experiments, highlighting the molecular nature of matter. The lecture discusses the hypothesis versus description of Brownian motion, emphasizing the fundamental physical property of fluids. It covers Langevin's solution of Brownian motion, explaining the mean-square displacement and the diffusion constant. The implementation of Langevin equations and various methods for measuring Brownian motion, like single particle tracking and fluorescence correlation spectroscopy, are also explored. The lecture concludes by discussing the significance of noise in cells and how random walks play a crucial role in various cellular processes.