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Exponential
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Exponential

June 23, 2010
Exponential "Exponential," from the Gallery of Eric J. Heller. Explanation of image, as taken from Heller Gallery: The Transport series (of which Exponential is a part) renders electron flow paths in a "two dimensional electron gas" (2DEG), Inspired by the experiments of Mark Topinka, Brian Leroy, and professor Robert Westervelt at Harvard. Our group was responsible for the theoretical treatment of the problem, primarily Scot Shaw, and myself. Exponential is based on the electron flow patterns for electrons riding over a bumpy landscape, which is what they encounter in the 2DEG. The electrons have more than enough energy to ride over any bump in the landscape, and the concentrations of electron flow seen here are unexpected indirect effects of that bumpy ride. The channeling or branching was a surprise, and has real implications for small electronic devices of the future. "Exponential" gets its name from the exponential divergence of trajectories which start out very close to each other. This is a hallmark of the unstable dynamics which leads to chaos. Over 100,000 individual electron paths were traced out, starting at the top right, where they were launched on their journey, each with a slightly different direction. In this image, the white regions show the paths preferred by the electrons. Some paths taken by individual electrons can be seen. Code written in Fortran computed the trajectories, and wrote information about them to a very large raster image. The algorithm used to write to pixels which had already been accessed by previous electron paths gives the peculiar shading and form to this image. The electron tracks in Exponential are an excellent example of the wonderful way nature emulates herself in different contexts. The branching pattern is reminiscent of familiar natural forms. Heller's work was included in the exhibit "Approaching Chaos," shown at the National Science Foundation (NSF) headquarters in Arlington, Va., July thru October 2002, as part of "The Art of Science Project." The Art of Science Project was conceived and implemented by a cross-directorate committee of NSF staff. Its purpose is to bring to NSF, original works of art that visually explore the connections between artistic and scientific expression. This image is copyright and was included in the NSF Multimedia Gallery with permission from the owner. See "Restrictions" below regarding use of this image. [Research supported by Harvard's NSEC (NSF) grant.] (Date of Image: 2001)