Fall 2009 Teaching: I am teaching Math 233 Multivariable Calculus this semester. I also remain active helping coordinate the Biocalculus @ UNC initiative. Information about these and other courses I've taught is available through my courses pages.

Fall 2009 Office Hours: Mondays 8-10, Tuesdays 2-4, and by appointment (email).

CV: (pdf).

My primary research areas  include the study and simulation of microscopic and macroscopic models of various interacting particle systems and agent-based models. I am particularly interested in systems with direct applications, whether physical, biological, or social, including networks, neutrally-buoyant and sedimenting suspensions, granular materials, colloidal systems, and swarming. 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 below and in our group publications.

Mucha's research group  currently includes graduate students Lauren Cooper (model fluid-solid simulations), Mandi Traud (social and epidemiological networks), and Feng "Bill" Shi (model interactions in small scale rods); and undergraduates Noel Cody, Nick Cook, Jennifer Dixon, Nitin Krishnan, Saang Lee, Kevin Macon, Sean Myers, Scott Powers, Cindy Rush (working on various projects in network science, agent-based models, and quantitative analysis of sports). The group also continues ongoing collaborations with Greg Turk's group at Georgia Tech (supported by an NSF MSPA award), with the NetWiki collaboration 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), along with a number of other ongoing collaborations with graduate students from other departments.

Group publications  are listed chronologically (with abstracts) and by research area (with pictures), along with links to videos where appropriate.

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 flows at and near interfaces.

Networks: The broad study and application of network analysis 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 areas of social network analysis and graph theory. My primary interests in this area are in 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 random walkers on graphs as ranking systems for college football (see rankings.amath.unc.edu). More information about our ongoing research and the study of networks is available via NetWiki (netwiki.amath.unc.edu).

Suspensions and Sedimentation: I maintain a long-standing interest in 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 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 former M.S. student Swathi Guda.

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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