Thesis
A reduced dimensional Monte Carlo method: Preliminary integrations
Washington State University
Master of Science (MS), Washington State University
05/2024
DOI:
https://doi.org/10.7273/000006973
Abstract
A technique for reducing the number of integrals in a Monte Carlo simulation is presented. For multidimensional integrals relying on classical equations of motions with localized weight functions, it is possible to integrate at least half of the variables prior to running a Monte Carlo simulation. An analysis of classical phase space structures shows the dynamics of nonlinear systems is reducible into composite subspaces that are either stable or unstable respectively. The subspaces that are stable leads to a local action-angle-like coordinate system corresponding to each constant of the motion. The techniques necessary for identifying the proper canonical coordinate transformations that decouple the local degrees of freedom are developed and shown to block diagonalize the stability matrix. The simple structure of these degrees of freedom allow them to be
pre-integrated prior to the Monte Carlo simulation. With regards to the unstable subspaces, the technique takes advantage of universal properties of chaotic degrees of freedom to integrate over directions that exponentially contract in phase space. The method is demonstrated by calculating expectation values and return probabilities for a chaotic two dimensional coupled quartic oscillator within a classical Wigner method framework.
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Details
- Title
- A reduced dimensional Monte Carlo method
- Creators
- Jarod Tall
- Contributors
- Steven Tomsovic (Chair)Peter Engels (Committee Member)Michael Forbes (Committee Member)
- Awarding Institution
- Washington State University
- Academic Unit
- Department of Physics and Astronomy
- Theses and Dissertations
- Master of Science (MS), Washington State University
- Publisher
- Washington State University
- Number of pages
- 47
- Identifiers
- 99901125940501842
- Language
- English
- Resource Type
- Thesis