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Peszynska's research interests are in mathematical and computational modeling of of flow and transport in porous media and other phenomena of similar character. At continuum scale these are described by nonlinear coupled differential equations with highly heterogeneous and multiscale data, and at discrete scale by various statistical mechanics and network models. She is interested in the analysis of solutions as well as in the development and analysis of numerical algorithms working across continuum and discrete scales, and in various issues concerning uncertainty quantification. Currently, she is involved in modeling methane hydrates, coalbed methane, carbon sequestration, and solar cells within the interdisciplinary projects: NSF-DMS 1115827 "Hybrid modeling in porous media" , DMS 1035513 " SOLAR: Enhanced Photovoltaic Efficiency through Heterojunction Assisted Impact Ionization", and three DOE-NETL projects on modeling and uncertainty of carbon sequestration.
Peszynska was Chair of SIAM Activity Group on Geosciences in 2011-12, Program Officer in 2009-2011, and chaired the Organizing Committee for SIAM Conference on Mathematical and Computational Issues in the Geosciences 2011. Currently she is serving on the Organizing Committee for SIAM Annual 2014, and for Interpore 2014