Instructors: Prof. F. Nori, Physics Dept. Prof. R. Ziff, Chemical Engineering Dept.This interdisciplinary course will analyze, discuss, and try to extend our current understanding of a variety of spatio-temporal complex phenomena, including:
The first two months or so of the course will provide an overview of nonlinear dynamics, chaos, fractals, critical phenomena, phase transitions, and transport phenomena in disordered systems (e.g., percolation). Afterwards, we will analyze specific examples of systems, with nonlinearities and disorder, exhibiting complex behavior. Concepts, ideas, some applications, and many analogies among disciplines will be emphasized. Later on, we will critically analyze ways to extend the current thinking in the area of complex spatio-temporal dynamics and nonlinear collective transport in disordered systems.
Examples of current hot research topics that will be discussed during several seminars include very nonlinear transport phenomena, with bursts and avalanches, and dynamic non-equilibrium phase transitions. We plan to discuss examples from a variety of disciplines, including: materials science and mechanical/civil engineering (e.g., granular media, materials under stress, discontinuous yield), astrophysics (e.g., star-quakes, X-ray bursts, pulsars), electrical engineering (electric breakdown in semiconductor devices, quantum logic gates for computation), aerospace/naval/mechanics/fluid dynamics (chaotic dynamics of falling objects; intermittency--turbulence and analogs in other systems), atmospheric sciences (lightning strikes), applied physics, geophysics (chaotic stick-slip motion of coupled faults, sand dunes), and other areas. Transport phenomena in nonlinear disordered systems often produce very complex behavior, and this will be a central theme underlying many seminar discussions. This subject is of great current interest, and important both at the fundamental level and for applications.
Division 799, Course 570, Section 002.