Texas A&M University, College Station, TX
Differential (rather than difference) and pseudo-differential equations on graphs have arisen during the past decade as models of many important physical systems ranging from molecules with conjugated double bonds in chemistry to quantum wires, to photonic crystals, etc. In these cases one deals with propagation of electronic, electromagnetic, or acoustic waves in thin domains forming a graph-like structure. In the asymptotics of a very thin domain, one expects that the wave propagation might be governed by a model on the resulting graph (which is not always the case). The talk will contain a non-technical survey of this area of research with particular emphasis on spectra of waves. The topics that will be addressed include description of the situations when graph models arise naturally, known and conjectured results on convergence to these models, and some conclusions one can derive from them.
Please join us for refreshments before the lecture at 2:30p.m. in room 353 Jabara Hall.
[ Fall 2001]