Two Effective Theories of Turbulence in Two Dimensions
Mentor Information
Razvan Teodorescu (Department of Mathematics & Statistics) & David A. Rabson (Department of Physics)
Description
Two effective theories are explored with respect to the long search for a theory of turbulence. We start by considering dynamical systems of fractal type, as it applies to both theories. The higher-dimensional effective theory, based on systems of integrable type and non-commutative gauge theories, will be explained along with recent results. Then, a standard lower- dimensional effective theory, coherent structures, is shown to bring with it a common time-frequency localization question of the best way to represent a signal. We show that work on this question also has implications for electronic wave-function basis sets. This material is based in part on work done by DAR while serving at the National Science Foundation. Any opinion, findings, conclusions, or recommendations expressed are those of the authors and do not necessarily reflect the views of the National Science Foundation.
Two Effective Theories of Turbulence in Two Dimensions
Two effective theories are explored with respect to the long search for a theory of turbulence. We start by considering dynamical systems of fractal type, as it applies to both theories. The higher-dimensional effective theory, based on systems of integrable type and non-commutative gauge theories, will be explained along with recent results. Then, a standard lower- dimensional effective theory, coherent structures, is shown to bring with it a common time-frequency localization question of the best way to represent a signal. We show that work on this question also has implications for electronic wave-function basis sets. This material is based in part on work done by DAR while serving at the National Science Foundation. Any opinion, findings, conclusions, or recommendations expressed are those of the authors and do not necessarily reflect the views of the National Science Foundation.
