For more information about this meeting, contact Sergei Tabachnikov.

Title: | An invariant manifold in molecular dynamics and its macroscopic implications |

Seminar: | Department of Mathematics Colloquium |

Speaker: | Richard James, University of Minnesota |

Abstract: |

Perhaps the most important deformations in solid mechanics are those that represent the bending, twisting and extension of beams. The most important flows in fluid mechanics are viscometric flows. In both cases these are the motions that, when compared with the corresponding experiments, are used to measure the material constants. We give a universal molecular level interpretation of these motions. We argue that these motions are associated at molecular level with a time-dependent invariant manifold of the equations of molecular dynamics. The mathematical description of the manifold is independent of the nature of the atomic forces and independent of the complexity of the molecules. The presence of this manifold can be used to simplify molecular-level computations, and deliver elastic and viscometric properties in the absence of a constitutive relation. Interesting links to theories of turbulence, to the Boltzmann and Langevin equations, to the dynamics of nanostructures, and to the theory of viscometry will be briefly discussed. Joint work with Kaushik Dayal, Traian Dumitrica and Stefan Mueller. |

### Room Reservation Information

Room Number: | MB114 |

Date: | 04 / 28 / 2011 |

Time: | 04:00pm - 05:00pm |