**Instructors:** Prof. F. Nori,
Physics Dept. Prof. R. Ziff, Chemical
Engineering Dept.

- nonlinear dynamics, chaos, fractals
- critical phenomena, phase transitions,
- percolation (and other types of transport phenomena in disordered systems),
- and dynamical instabilities (e.g., avalanches, bursts, chain-reactions, domino-effects, and cascades in jammed systems).

This seminar-style course should be useful to senior/junior and graduate students in engineering, mathematics or one of the sciences (who are interested in research, since the seminar will require students to be exposed and explore current research problems).

The first month 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 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),
atmospheric sciences (lightning strikes),
aerospace/naval/mechanics/fluid dynamics
(chaotic dynamics of falling objects;
intermittency--turbulence and analogs in other systems),
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 intellectually stimulating, of great current interest, and important both at the fundamental level and for applications.

**
Division 799, Course 570, Section 002. **
The seminar meets at *Rackham*,
on thursdays 10am-1pm.
The likely format might be:
a short pedagogical tutorial presentation
from 10:10am to 11am, followed by a break.
Afterwards, discussions; including a brown
bag lunch informal discussion of ideas
related to the initial presentation.