Phd records
https://feeds.library.caltech.edu/people/Williams-R-G/Phd.rss
A Caltech Library Repository Feedhttp://www.rssboard.org/rss-specificationpython-feedgenenWed, 31 Jan 2024 20:01:52 +0000The stochastic exit problem for dynamical systems
https://resolver.caltech.edu/CaltechTHESIS:03212013-095136861
Authors: {'items': [{'id': 'Williams-R-G', 'name': {'family': 'Williams', 'given': 'Randall Gary'}, 'show_email': 'NO'}]}
Year: 1978
DOI: 10.7907/rwka-vz48
<p>The problem of "exit against a flow" for dynamical systems
subject to small Gaussian white noise excitation is studied.
Here the word "flow" refers to the behavior in phase space of
the unperturbed system's state variables. "Exit against a flow"
occurs if a perturbation causes the phase point to leave a phase
space region within which it would normally be confined. In
particular, there are two components of the problem of exit
against a flow:</p>
<p>i) the mean exit time</p>
<p>ii) the phase-space distribution of exit locations.</p>
<p>When the noise perturbing the dynamical systems is small, the
solution of each component of the problem of exit against a flow
is, in general, the solution of a singularly perturbed, degenerate
elliptic-parabolic boundary value problem.</p>
<p>Singular perturbation techniques are used to express the
asymptotic solution in terms of an unknown parameter. The unknown
parameter is determined using the solution of the adjoint
boundary value problem.</p>
<p>The problem of exit against a flow for several dynamical
systems of physical interest is considered, and the mean exit
times and distributions of exit positions are calculated. The systems
are then simulated numerically, using Monte Carlo techniques,
in order to determine the validity of the asymptotic solutions.</p>
https://thesis.library.caltech.edu/id/eprint/7540