Mar 21, Monday, 12:00, Maury 110
I.M.Segal, University of Notre Dame, Some mathematical questions of
the theory of Bose-Einstein condensation.
See Differential equations page.
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March 23, Wed. 3:30, Kerchof 326
David Ross, Rochester Inst. of Technology
Temperature-Dependent Vibrations of Micro-Beams
(with a brief introduction to MEMS)
By the late 1980's the methods used to fabricate microelectronic
devices had become sufficiently sophisticated that microelectronics
engineers could build tiny machines on computer chips. This brought
about a new engineering discipline: Micro-Electro-Mechanical Systems,
or MEMS. In this talk, Professor Ross will introduce the methods and
applications of MEMS from a mathematical perspective. He will then
focus on a particular problem that arose in the design of a MEMs
micro-actuator. The actuator is a bimetallic beam clamped at both
ends. Experiments show that the natural frequency of such a beam
decreases as a function of the beam's temperature at low
temperatures, then increases at higher temperatures. Professor Ross
will describe a mathematical model of the vibrations of a bimetallic
beam, at the core of which is a non-linear fourth-order PDE.
He will discuss numerical and analytical results for this equation,
and he will show how this model explains the temperature-dependence of
the beam's frequency. He will present some open mathematical problems
regarding this equation. He will conclude by describing two
inventions, which are now patented, that were suggested by the
mathematical analysis.