PHYSICAL MATHEMATICS SEMINAR

TOPIC:	MEAN-FIELD AND ANOMALOUS BEHAVIOR
	ON A SMALL-WORLD NETWORK


SPEAKER:  MATTHEW HASTINGS
	  Center for Nonlinear Studies
	  Los Alamos National Laboratory

ABSTRACT:

Recently, the study of systems on networks, general graphs with some
combination of nodes and vertices, has become of great interest.
Practical examples of these systems include the spread of epidemic disease
over the network of human social contacts, the electric power grid, and
the Internet.

These systems often combine both short- and long-range interactions.  For
example, transmission of disease typically occurs between people living
close to each other geographically, but occasional long-range contact can
occur due to air travel.  I will consider a particular network that
captures these long-range interactions: the small world network, which has
become a standard model in the field.  I will show that for a wide range
of systems the behavior on this network can be described by a mean-field
theory, and I will analyze the crossover to this behavior and discuss the
implications of these results.

Finally, I will finish with the example of the Edwards-Wilkinson equation.
Recent work of Toroczkai, Korniss, and others, has shown the relevance of
this equation to synchronization in parallel processing.  I will apply the
results above to this example, and find that in some cases the mean-field
behavior applies and in some cases it does not.

(Some of this is joint work with B. Kozma and G. Korniss.)

DATE:		TUESDAY, FEBRUARY 24, 2004

TIME:		2:30 PM

LOCATION:	Building 2, Room 338

Refreshments at 3:30 PM in Room 2-349.

Massachusetts Institute of Technology, Department of Mathematics
Cambridge, MA  02139