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Rank-1 Saddle Transport in Three or More Degrees of Freedom Scattering Reactions


Brunton, Steven Lee (2006) Rank-1 Saddle Transport in Three or More Degrees of Freedom Scattering Reactions. Senior thesis (Minor), California Institute of Technology. doi:10.7907/2RY2-FT38.


A computationally effective method is developed to study rank-1 saddle transport. In particular, the lifetime distribution is calculated for the planar, nonzero angular momentum scattering reaction of H2 with H2O. The scattering model uses the approximate potential of Wiesenfeld et al.[14], which has 3 essential degrees of freedom (DOF) and a rotating transition state (TS) at physically relevant energies. A Monte Carlo sampling of the energy surface on a transverse cut near the TS provides a representative set of trajectories which are integrated forward and backward to test for reactivity. Reactive trajectories are then integrated forward into the bound state until they escape the reaction, resulting in orbit/collision data for each trajectory. This data is collected and binned until the standard deviation of the data in each bin is within a user defined tolerance, yielding a lifetime distribution with bounded error terms. To test this method, it is applied to the well studied phenomena of electron scattering in the Rydberg atom with crossed fields[1,4] and compared with the literature.

Item Type:Thesis (Senior thesis (Minor))
Subject Keywords:Rank-1 saddle, invariant manifold transport, geometric mechanics, transition state theory, Monte Carlo methods
Degree Grantor:California Institute of Technology
Division:Physics, Mathematics and Astronomy
Major Option:Mathematics
Minor Option:Control and Dynamical Systems
Thesis Availability:Public (worldwide access)
Research Advisor(s):
  • Marsden, Jerrold E. (co-advisor)
  • Koon, Wang Sang (co-advisor)
Thesis Committee:
  • None, None
Defense Date:10 June 2006
Non-Caltech Author Email:sbrunton (AT)
Record Number:CaltechTHESIS:07212010-224814072
Persistent URL:
Brunton, Steven Lee0000-0002-6565-5118
Default Usage Policy:No commercial reproduction, distribution, display or performance rights in this work are provided.
ID Code:5977
Deposited By: Steven L. Brunton
Deposited On:30 Jul 2010 20:14
Last Modified:26 Mar 2020 23:15

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