TY - JOUR

T1 - Geometric Approaches in Phase Space Transport and Partial Control of Escaping Dynamics

AU - Naik, Shibabrat

PY - 2016

Y1 - 2016

N2 - This dissertation presents geometric approaches of understanding chaotic
transport in phase space that is fundamental across many disciplines in
physical sciences and engineering. This approach is based on analyzing
phase space transport using boundaries and regions inside these
boundaries in presence of perturbation. We present a geometric view of
defining such boundaries and study the transport that occurs by crossing
such phase space structures. The structure in two dimensional
non-autonomous system is the codimension 1 stable and unstable manifolds
(that is R1 geometry) associated with the hyperbolic fixed points. The
manifolds separate regions with varied dynamical fates and their time
evolution encodes how the initial conditions in a given region of phase
space get transported to other regions. In the context of four
dimensional autonomous systems, the corresponding structure is the
stable and unstable manifolds (that is S1 x R1 geometry) of unstable
periodic orbits which reside in the bottlenecks of energy surface. The
total energy and the cylindrical (or tube) manifolds form the necessary
and sufficient condition for global transport between regions of phase
space. Furthermore, we adopt the geometric view to define escaping zones
for avoiding transition/ escape from a potential well using partial
control. In this approach, the objective is two fold: finding the
minimum control that is required for avoiding escape and obtaining
discrete representation called disturbance of continuous noise that is
present in physical sciences and engineering. In the former scenario,
along with avoiding escape, the control is constrained to be smaller
than the disturbance so that it can not exactly cancel out the
disturbances. The work presented was funded by Virginia Tech and
National Science Foundation under award #1150456 and #1537349.

AB - This dissertation presents geometric approaches of understanding chaotic
transport in phase space that is fundamental across many disciplines in
physical sciences and engineering. This approach is based on analyzing
phase space transport using boundaries and regions inside these
boundaries in presence of perturbation. We present a geometric view of
defining such boundaries and study the transport that occurs by crossing
such phase space structures. The structure in two dimensional
non-autonomous system is the codimension 1 stable and unstable manifolds
(that is R1 geometry) associated with the hyperbolic fixed points. The
manifolds separate regions with varied dynamical fates and their time
evolution encodes how the initial conditions in a given region of phase
space get transported to other regions. In the context of four
dimensional autonomous systems, the corresponding structure is the
stable and unstable manifolds (that is S1 x R1 geometry) of unstable
periodic orbits which reside in the bottlenecks of energy surface. The
total energy and the cylindrical (or tube) manifolds form the necessary
and sufficient condition for global transport between regions of phase
space. Furthermore, we adopt the geometric view to define escaping zones
for avoiding transition/ escape from a potential well using partial
control. In this approach, the objective is two fold: finding the
minimum control that is required for avoiding escape and obtaining
discrete representation called disturbance of continuous noise that is
present in physical sciences and engineering. In the former scenario,
along with avoiding escape, the control is constrained to be smaller
than the disturbance so that it can not exactly cancel out the
disturbances. The work presented was funded by Virginia Tech and
National Science Foundation under award #1150456 and #1537349.

M3 - Article (Academic Journal)

JO - ProQuest Dissertations And Theses; Thesis (Ph.D.)--Virginia Polytechnic Institute and State University, 2016.; Publication Number: AAT 10647593; ISBN: 9780355210651; Source: Dissertation Abstracts International

JF - ProQuest Dissertations And Theses; Thesis (Ph.D.)--Virginia Polytechnic Institute and State University, 2016.; Publication Number: AAT 10647593; ISBN: 9780355210651; Source: Dissertation Abstracts International

ER -