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Peter J. Mucha Associate Professor, Department of Mathematics Carolina Center for Interdisciplinary Applied Mathematics Institute for Advanced Materials, Nanoscience and Technology The University of North Carolina at Chapel Hill Campus Box #3250, UNC Chapel Hill, NC 27599-3250 Phone: 919/843-2550 Fax: 919/962-9345 Office: Phillips 304B mucha@unc.edu |
News & Notes:
Teaching: In Fall 2008, I will be teaching BioCalculus I, part of the BioCalculus @ UNC initiative, as a "special section" of Math 231. Information about other courses I've taught is also available, through my courses pages.
Summer 2008 Office Hours: By appointment. Appointments can be arranged by email.
CV: (pdf).
My primary research areas include the study and simulation of microscopic and macroscopic models of various interacting particle systems. I am particularly interested in systems with direct applications, whether physical, biological, or social, including neutrally-buoyant and sedimenting suspensions, granular materials, colloidal systems, swarming, and networks. The main goal throughout is to find simplified or reduced models and simulations to determine the properties or make meaningful visualizations of various physical phenomena. More information is available below and in our publications.
Mucha's research group currently includes graduate students Matt Christian (small-scale locomotion), Lauren Cooper (model fluid-solid simulations), and Mandi Traud (network science); undergraduates (and recent alumni) Jennifer Dixon, Kevin Macon, Trent McCotter, Nitin Krishnan, Scott Powers, Thomas Richardson, Peter Wang and Jiemin Zeng (working on various projects in network science and agent-based models); and ongoing collaborations with Greg Turk's group at Georgia Tech (supported by an NSF MSPA award) and with numerous faculty and students in the Carolina Population Center (supported by awards from the NIH and NSF).
Group publications are listed chronologically (with abstracts) and by research area (with pictures), along with links to videos where appropriate.
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Suspensions and Sedimentation: A significant portion of my research career has been spent in studying the fluid dynamics of solid particles suspended in fluids (liquids or gases), with special interest in sedimentation at small Reynolds numbers, that is, small, slow, or highly viscous flows. Part of work has been aimed at understanding fluctuations in sedimentation, visualized as swirls in the image on the left, the underlying density and velocity fluctuations of which are important to characterize properly for accurate modeling of the macroscopic transport of the sedimenting particles. Current projects include investigation of the details in different sedimentation instabilities, working with Swathi Guda. |
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Computer-Generated Animation: During my time at Georgia Tech, I started collaborating with computer scientists on rapidly efficient physically-based models for animation of various fluid flows. Working with GT CoC faculty Greg Turk and Irfan Essa, graduate students Mark Carlson, Nipun Kwatra, Huamin Wang and Chris Wojtan), and undergraduate student Nathan Bell, our collaborations have included simulations of melting, efficient coupling of rigid bodies and fluids (image on left), granular flows, various fluid-boundary interactions, and controlled cloth animations. Video is available for download, linked from the publications pages. A recent NSF Mathematical Sciences Priority Area grant supports Profs. Mucha and Turk to further expand the techniques and applications of such simulations for scientific investigation and visualization of a number of flows at and near interfaces. |
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Network Science: The broad study and application of ideas in networks has been a hot topic in recent years, with interesting developments and discoveries in the statistical mechanics of networks and in comparison with the traditional mathematical area of graph theory. My primary interests in this area are in applying methodologies to real-world data. Examples of our ongoing investigations include the hierarchical committee structure of the United States House of Representatives (image on left) and random walkers on graphs as ranking systems for college football (below). More information about our ongoing research and the science of networks is available via NetWiki (netwiki.amath.unc.edu). |
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Mathematics in Sports: We have developed an algorithmic system for ranking college football teams, motivated from a simple model interpretation in terms of random walkers on a graph, moving so simply one might refer to them as monkeys (of 1000 typewriters fame; image on left taken shamelessly from the ESPN: The Magazine coverage of our work). Our ongoing investigations include applications of this method and of other networks models to other sports. More information is available at rankings.amath.unc.edu. |
Biographical Sketch: After a childhood spent mostly in Minnesota, I moved east to attend college at Cornell University where I majored in Engineering Physics. I then took a Churchill Scholarship to study in the Cavendish Laboratory at Cambridge with an M.Phil. in Physics. Returning to the States, I continued my studies at Princeton, leading to an M.A. and Ph.D. in Applied and Computational Mathematics. Following a postdoctoral instructorship in applied mathematics at MIT, and a tenure-track assistant professorship in Mathematics at Georgia Tech, I moved to Chapel Hill to join the Department of Mathematics and the Institute for Advanced Materials at UNC.
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