Research Interaction Team Plan, Fall 2002

Team name: Fluid Behavior in Classical, Kinetic and Quantum Regimes

Team directors: David Levermore, Robert Pego

Research focus: We will study mathematical aspects of various fluid-dynamical regimes. These might include well-posedness, long-time behavior, attractor dynamics, stability of coherent structures, fluid-dynamical limits, moment approximations, numerical methods and transition-regime models. Applications might include dilute gases, Bose-Einstein condensates, semiconductors, radiative transport, charged particles, or neutronics.

Graduate prerequisites: Analysis (Math 630), or PDEs (Math 673) or ODEs (Math 414 or 670), or numerics (AMSC 666 or 660). Some knowledge of fluid mechanics or quantum mechanics would be useful. Permission of an instructor.

Undergraduate prerequisites: Advanced calculus (Math 241) and differential equations (Math 246). Any of the following are useful but not required: complex variables (Math 463), ODE (Math 414), PDE (Math 462), scientific computation (Math 241 or AMSC 460), some knowledge of physics would be useful (mechanics, quantum, electrodynamics). Permission of an instructor.

Graduate program: Team members will make presentations either on readings of fundamental papers or book chapters, or on their own analytical and/or numerical investigations. When appropriate, these may be developed into more formal presentations for seminars, conferences, or publication. Team members will be asked to help mentor more junior team members.

Undergraduate program: Same as above, as appropriate to the background of the student.

Work schedule: Readings and projects will be matched with participants at an initial meeting. Meetings will be held weekly. These sometimes may be held jointly with related RITs.

Updated 2 August 2002