Peter J. Mucha
Bowman and Gordon Gray Distinguished Term Professor
Chair, Department of Applied Physical Sciences
Co-Director, Social Network Analysis at Carolina
The University of North Carolina at Chapel Hill
Campus Box #3250, UNC
Chapel Hill, NC 27599-3250
|also affiliated with the
Institute for Advanced Materials, Nanoscience and Technology
and Carolina Center for Interdisciplinary Applied Mathematics
Postdoctoral search ongoing (2012-13): Apply at mathjobs.org.
Office Hours: By appointment (email).
Research: My current research focuses on the mathematical and computational study of networks, developing and understanding tools for the study of real-world data. Networks appear across many academic disciplines and our group activities have included collaborations with Archeology, Biostatistics, Epidemiology, Finance, Infectious Diseases, Neuroscience, Physics, Political Science, Psychology, Public Policy, Sociology, and Statistics. With "nodes" representing actors of interest and "edges" connecting the nodes representing the relationships under study, the concept of a network can be flexibly used in many applications. Most people are familiar with the concept of a network in terms of hyperlinked web pages or online social networks (e.g. Facebook). Such online networks are an area of broad interest (including some of our own work), but networks are also useful for studying a wide variety of connected systems. More information about our work in this area is available below and in our group publications.
Our research group currently includes postdoctoral scholar Nishant Malik, graduate students Feng "Bill" Shi and Simi Wang, and undergraduates Eli Bingham, Drew Cabaniss, Leah Downey, Phillip Maraveyias, Sean Myers, Patrick Short, Kevin Valakushy, Sarah White and Joe Zappa. Each is working on some aspect of the study of networks, including developments in community detection, modeling network dynamics, and collaborating with Greg Forest on model interactions in networked materials. The group continues ongoing collaborations within the NetWiki team (including activities supported by an NSF CAREER award), with numerous faculty and students in the Carolina Population Center (supported by awards from the NIH and NSF), the Duke Network Analysis Center, and with a variety of graduate students from other departments and universities. We were also actively involved in the 2010-11 Program on Complex Networks at the Statistical and Applied Mathematical Sciences Institute (SAMSI), and continue to follow up on collaborations developed then.
Networks: The broad study and application of network analysis has been a hot topic in recent years, with interesting advances and discoveries in the statistical mechanics of networks and in comparison with the traditional areas of social network analysis and graph theory. My primary interests in this area are in developing and applying methodologies to real-world data. Examples of our ongoing investigations include political community structures (the image here depicts committees in the United States House of Representatives) and dynamics on graphs for modeling the spread of influence, disease propagation, and as ranking systems for college football and other sports (see Random Walker Rankings). More information about our ongoing research and the study of networks is available via NetWiki (netwiki.amath.unc.edu), the Duke Network Analysis Center, and our networks publications.
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 included simulations of melting, efficient coupling of rigid bodies and fluids (image on left), granular flows, various fluid-boundary interactions, controlled cloth animations, and virtual rheoscopic visualization of flows. Associated videos are available for download, linked from the publications pages. An NSF Mathematical Sciences Priority Area grant supported Profs. Mucha and Turk to further expand the techniques and applications of such simulations for scientific investigation and visualization of flows at and near interfaces.
Suspensions, Sedimentation, & Fluid-Solid Interactions: My graduate, postdoctoral, and early faculty research included study of 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 this work was 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. These investigations led me to a broader interest in simulation of microscopic and macroscopic models of various interacting particle systems, especially where they have direct applications to the physical, biological, or social sciences. The main goal throughout is to find simplified or reduced models and simulations to determine the properties or make meaningful visualizations of various systems and phenomena. More information is available in our group publications.
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, Nanoscience and Technology at UNC.
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