Mar. 17, 2008
James A. Sethian
Department of Mathematics, UC Berkeley
Mathematics Department, Lawrence Berkeley National Laboratory
Advances in Advancing Interfaces: Building Semiconductors, Inkjet Plotters, Medical Scanners, and Robotic Devices
Propagating interfaces occur in a wide variety of settings, and include ocean
waves, burning flames, and material boundaries. Less obvious
boundaries are equally important, and include iso-intensity
contours in images, handwritten characters, and shapes against boundaries.
In addition, problems not thought of as moving interface problems
often can be recast as advancing fronts, including robotic
navigation and finding shortest paths on contorted surfaces.
One way to frame moving interface problems is by casting them as solutions
to partial differential equations, and this has led to Fast Marching Methods
and Level Set Methods. There are some advantages to this view; in particular,
they easily accommodate merging boundaries, problems in three dimensions,
and very subtle motions of boundaries. In many settings, they been proven
valuable. The speaker will try to provide an overview of these approaches,
with an eye towards fundamental mathematical ideas and their geometric and
algorithmic interpretation.
Along the way, we will discuss a large collection of applications, with a
particular emphasis on industrial engineering collaborations which have
led to robust codes for semiconductor manufacturing, the manufacturing of
inkjet plotters for building plasma displays, image segmentation and tracking
in cardiac scanners, robotic navigation around obstacles, and seismic imaging
in oil recovery.
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