U.S.-Polish Collaborative Research: Multidimensional Nonlinear Fractal Dynamics in Continuous Media

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This is a U.S.-Polish cooperative research project that will investigate analytical and computational tools for multidimensional nonlinear fractal dynamics in continuous media. Nonlinear and nonlocal advection-dispersion equations involving generators of continuous-time random walks will also be studied. The tools from both probability theory and the theory of nonlinear partial differential equations will be utilized, including theoretical results on critical nonlinearities for Levy conservations laws obtained under prior NSF support. The principal investigators are Dr. Wojbor Woyczynski from Case Western Reserve University and Professor Grzegorz Karch from the University of Wroclaw. The broader impact resulting from the proposed activity is assured by the fact that the dynamics to be studied reflect behavior of a variety of complex systems of a large number of nonlinearly interacting components which operate in uncertain environments and with imperfect information about their initial states. Examples of such systems are networks of servers on the internet, power grids distributing electric power, environmental systems in the presence of turbulent atmosphere and complex oceanic flows, and chemical vapor deposition systems for manufacturing thin semiconductor films.This project in mathematics research fulfills the program objectives of bringing together leading experts in the U.S. and Central/Eastern Europe to combine complementary efforts and capabilities in areas of strong mutual interest and competence on the basis of equality, reciprocity, and mutuality of benefit.