Kamaran Mohseni Seminar
April 25 @ 11:00 AM - 12:00 PM - BRK 1001
Observable Divergence and Curl Theorems and Their Aplicationsin Physics
Bio:Professor Kamran Mohsenireceived his B.S. degree from the University of Science and Technology, Tehran, his M.S. degree in Aeronautics and Applied Mathematics from the Imperial College, London, and his Ph.D. degree from the California Institute of Technology (Caltech), Pasadena, CA, in 2000. He was a Postdoctoral Fellow in Control and Dynamical Systems at Caltech for almost a year. In 2001, he joined the Department of Aerospace Engineering Sciences, University of Colorado at Boulder. In 2011, he joined the University of Florida, Gainesville, FL, as the W.P. Bushnell Endowed Professor in the Department of Electrical and Computer Engineering and the Department of Mechanical and Aerospace Engineering. He is the Director of the Institute for Networked Autonomous Systems.
Abstract:Turbulence, shock formation, and sharp interfaces in inviscid flows are prone to high wavenumber mode generations. This continuous generation of high wavemodesresults in a cascade of energy to an ever smaller scales in turbulence, creation of shocks in compressible flows, and generation of sharp interfaces in two-phase flows. I dub this feature as wavenumber-infinity irregularity. Traditionally, this high wavenumber irregularity is remedied by the addition of a Laplacian term (viscous term) in both compressible and incompressible flows. In this talk, I introduce the concept of observability of field quantities and the consequence of that on the Gauss divergence theorem and Stokes curl theorem. An observable Gauss and Stokes theorem are then derived. These theorems allow the derivation of `regularized’ field quantities from basic conservation laws. To this end, `observable’ Euler and Navier-Stokes equations are formally derived. It is expected that these equations simultaneously regularize shocks, turbulence, and sharp interfaces. Several theoretical results (including existence, uniqueness, convergence to entropy solutions, and observable Lie bracket) and numerical simulations (including 3D turbulence, shock-turbulence interaction, and two-phase flows) will be presented and compared with existing numerical methods. Finally, I will discuss how the observable field theory could be applied in other disciplines involving problems with wavenumber-infinity irregularities such at fracture, crack propagation, heat transfer, sharp interfaces in electromagnetism, etc.
- Jaime Turner