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University of Southern California
1.
Ostrovskyi, Vitalii.
Point singularities on 2D surfaces.
Degree: PhD, Applied Mathematics, 2013, University of Southern California
URL: http://digitallibrary.usc.edu/cdm/compoundobject/collection/p15799coll3/id/281618/rec/5086 
► This work studies point vortices on a sphere and complex point singularities on a plane. The motivation for the study is to get deeper understanding…
(more)
▼ This work studies point vortices on a sphere and
complex point singularities on a plane. The motivation for the
study is to get deeper understanding of the dynamics of symmetric
configurations of point vortices and point singularities. Equations
of point vortex motion are derived from the Euler equations.
Geometric description of the phase space is given along with
symplectic structure and Lie-Poisson brackets. Symplectic reduction
is performed and reduced Hamiltonian is found. Configuration matrix
approach is used to find fixed equilibrium configurations of point
singularities and relative equilibrium configurations of point
vortices. Based on this method, relative equilibria in the form of
tetrahedron, octahedron, cube, icosahedron, dodecahedron are
described. Using energy-momentum method conducted study of
stability of general tetrahedral and octahedral configurations. For
the cubic, icosahedral and dodecahedral cases studied stability of
superpositions of axis-symmetric configurations. For the
tetrahedral, cubic and icosahedral configuration regions of
stability are plotted. Instability results for special cases of
cubic and icosahedral configurations are proved. ❧ Fixed
equilibrium configurations of point singularities on a plane are
found. Theorems about existence and uniqueness of the equilibria
are proved. For each of the configuration, singular value
decomposition is performed. The singular values are used to obtain
probability distribution and Shannon entropy for the configurations
is computed. Relative equilibria for even and odd number of point
singularities are described. Relative equilibria for 2, 3, 4 point
singularities are studied. For higher number of singularities
method of finding relative equilibria is provided.
Advisors/Committee Members: Newton, Paul K. (Committee Chair), Kukavica, Igor (Committee Member), Kanso, Eva (Committee Member).
Subjects/Keywords: point singularity; point vortex; relative equilibria; stability; vortex dynamics
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APA (6th Edition):
Ostrovskyi, V. (2013). Point singularities on 2D surfaces. (Doctoral Dissertation). University of Southern California. Retrieved from http://digitallibrary.usc.edu/cdm/compoundobject/collection/p15799coll3/id/281618/rec/5086
Chicago Manual of Style (16th Edition):
Ostrovskyi, Vitalii. “Point singularities on 2D surfaces.” 2013. Doctoral Dissertation, University of Southern California. Accessed February 26, 2021.
http://digitallibrary.usc.edu/cdm/compoundobject/collection/p15799coll3/id/281618/rec/5086.
MLA Handbook (7th Edition):
Ostrovskyi, Vitalii. “Point singularities on 2D surfaces.” 2013. Web. 26 Feb 2021.
Vancouver:
Ostrovskyi V. Point singularities on 2D surfaces. [Internet] [Doctoral dissertation]. University of Southern California; 2013. [cited 2021 Feb 26].
Available from: http://digitallibrary.usc.edu/cdm/compoundobject/collection/p15799coll3/id/281618/rec/5086.
Council of Science Editors:
Ostrovskyi V. Point singularities on 2D surfaces. [Doctoral Dissertation]. University of Southern California; 2013. Available from: http://digitallibrary.usc.edu/cdm/compoundobject/collection/p15799coll3/id/281618/rec/5086
University of Southern California
2.
Reis, Ednei F.
Asymptotic expansion for solutions of the Navier-Stokes
equations with potential forces.
Degree: PhD, Mathematics, 2011, University of Southern California
URL: http://digitallibrary.usc.edu/cdm/compoundobject/collection/p15799coll127/id/615244/rec/976
► We derive an asymptotic expansion for smooth solutions of the Navier-Stokes equations in weighted spaces. This result removes previous restrictions on the number of terms…
(more)
▼ We derive an asymptotic expansion for smooth solutions
of the Navier-Stokes equations in weighted spaces. This result
removes previous restrictions on the number of terms of the
asymptotics, as well as on the range of the polynomial weights. We
also write the expansion in terms of expressions involving
non-linear quantities.
Advisors/Committee Members: Kukavica, Igor (Committee Chair), Ziane, Mohammed (Committee Member), Newton, Paul K. (Committee Member).
Subjects/Keywords: Navier-Stokes equation; asymptotic expansion
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APA (6th Edition):
Reis, E. F. (2011). Asymptotic expansion for solutions of the Navier-Stokes
equations with potential forces. (Doctoral Dissertation). University of Southern California. Retrieved from http://digitallibrary.usc.edu/cdm/compoundobject/collection/p15799coll127/id/615244/rec/976
Chicago Manual of Style (16th Edition):
Reis, Ednei F. “Asymptotic expansion for solutions of the Navier-Stokes
equations with potential forces.” 2011. Doctoral Dissertation, University of Southern California. Accessed February 26, 2021.
http://digitallibrary.usc.edu/cdm/compoundobject/collection/p15799coll127/id/615244/rec/976.
MLA Handbook (7th Edition):
Reis, Ednei F. “Asymptotic expansion for solutions of the Navier-Stokes
equations with potential forces.” 2011. Web. 26 Feb 2021.
Vancouver:
Reis EF. Asymptotic expansion for solutions of the Navier-Stokes
equations with potential forces. [Internet] [Doctoral dissertation]. University of Southern California; 2011. [cited 2021 Feb 26].
Available from: http://digitallibrary.usc.edu/cdm/compoundobject/collection/p15799coll127/id/615244/rec/976.
Council of Science Editors:
Reis EF. Asymptotic expansion for solutions of the Navier-Stokes
equations with potential forces. [Doctoral Dissertation]. University of Southern California; 2011. Available from: http://digitallibrary.usc.edu/cdm/compoundobject/collection/p15799coll127/id/615244/rec/976
University of Southern California
3.
Aslam, Kamran.
A stochastic Markov chain approach for tennis: Monte Carlo
simulation and modeling.
Degree: PhD, Aerospace Engineering, 2012, University of Southern California
URL: http://digitallibrary.usc.edu/cdm/compoundobject/collection/p15799coll3/id/12697/rec/371
► This dissertation describes the computational formulation of probability density functions (pdfs) that facilitate head-to-head match simulations in tennis along with ranking systems developed from their…
(more)
▼ This dissertation describes the computational
formulation of probability density functions (pdfs) that facilitate
head-to-head match simulations in tennis along with ranking systems
developed from their use. A background on the statistical method
used to develop the pdfs, the Monte Carlo method, and the resulting
rankings are included along with a discussion on ranking methods
currently being used both in professional sports and in other
applications. Using an analytical theory developed by
Newton and
Keller that defines a tennis player’s probability of winning a
game, set, match and single elimination tournament, a computational
simulation has been developed in Matlab that allows further
modeling not previously possible with the analytical theory alone.
Such experimentation consists of the exploration of non-iid
effects, considers the concept the varying importance of points in
a match and allows an unlimited number of matches to be simulated
between unlikely opponents. The results of these studies have
provided pdfs that accurately model an individual tennis player’s
ability along with a realistic, fair and mathematically sound
platform for ranking them.
Advisors/Committee Members: Newton, Paul K. (Committee Chair), Kanso, Eva (Committee Member), Fulman, Jason (Committee Member).
Subjects/Keywords: monte carlo; markov chain; tennis
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APA (6th Edition):
Aslam, K. (2012). A stochastic Markov chain approach for tennis: Monte Carlo
simulation and modeling. (Doctoral Dissertation). University of Southern California. Retrieved from http://digitallibrary.usc.edu/cdm/compoundobject/collection/p15799coll3/id/12697/rec/371
Chicago Manual of Style (16th Edition):
Aslam, Kamran. “A stochastic Markov chain approach for tennis: Monte Carlo
simulation and modeling.” 2012. Doctoral Dissertation, University of Southern California. Accessed February 26, 2021.
http://digitallibrary.usc.edu/cdm/compoundobject/collection/p15799coll3/id/12697/rec/371.
MLA Handbook (7th Edition):
Aslam, Kamran. “A stochastic Markov chain approach for tennis: Monte Carlo
simulation and modeling.” 2012. Web. 26 Feb 2021.
Vancouver:
Aslam K. A stochastic Markov chain approach for tennis: Monte Carlo
simulation and modeling. [Internet] [Doctoral dissertation]. University of Southern California; 2012. [cited 2021 Feb 26].
Available from: http://digitallibrary.usc.edu/cdm/compoundobject/collection/p15799coll3/id/12697/rec/371.
Council of Science Editors:
Aslam K. A stochastic Markov chain approach for tennis: Monte Carlo
simulation and modeling. [Doctoral Dissertation]. University of Southern California; 2012. Available from: http://digitallibrary.usc.edu/cdm/compoundobject/collection/p15799coll3/id/12697/rec/371
University of Southern California
4.
Marinov, Radoslav T.
Applications of Stein's method on statistics of random
graphs.
Degree: PhD, Applied Mathematics, 2013, University of Southern California
URL: http://digitallibrary.usc.edu/cdm/compoundobject/collection/p15799coll3/id/307970/rec/871
► We look at the background of Stein's Method, its ties with the field of Markov Chains, and the connections of both those subjects and the…
(more)
▼ We look at the background of Stein's Method, its ties
with the field of Markov Chains, and the connections of both those
subjects and the Neighbourhood Attack Voter-type model. ❧ On the
basis of that background, we provide two examples of applications
of Stein's Method, one in the context of a pair of Voter Models,
and one in the context of the uniform recursive tree.
Advisors/Committee Members: Fulman, Jason (Committee Chair), Bartroff, Jay (Committee Member), Newton, Paul K. (Committee Member).
Subjects/Keywords: mathematics; probability; Stein'; s method; random graphs; uniform recursive tree; voter models; Markov chains; bounds on rates of convergence
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APA (6th Edition):
Marinov, R. T. (2013). Applications of Stein's method on statistics of random
graphs. (Doctoral Dissertation). University of Southern California. Retrieved from http://digitallibrary.usc.edu/cdm/compoundobject/collection/p15799coll3/id/307970/rec/871
Chicago Manual of Style (16th Edition):
Marinov, Radoslav T. “Applications of Stein's method on statistics of random
graphs.” 2013. Doctoral Dissertation, University of Southern California. Accessed February 26, 2021.
http://digitallibrary.usc.edu/cdm/compoundobject/collection/p15799coll3/id/307970/rec/871.
MLA Handbook (7th Edition):
Marinov, Radoslav T. “Applications of Stein's method on statistics of random
graphs.” 2013. Web. 26 Feb 2021.
Vancouver:
Marinov RT. Applications of Stein's method on statistics of random
graphs. [Internet] [Doctoral dissertation]. University of Southern California; 2013. [cited 2021 Feb 26].
Available from: http://digitallibrary.usc.edu/cdm/compoundobject/collection/p15799coll3/id/307970/rec/871.
Council of Science Editors:
Marinov RT. Applications of Stein's method on statistics of random
graphs. [Doctoral Dissertation]. University of Southern California; 2013. Available from: http://digitallibrary.usc.edu/cdm/compoundobject/collection/p15799coll3/id/307970/rec/871
University of Southern California
5.
Keshavarzzadeh, Vahid.
Design optimization under uncertainty for rotor blades of
horizontal axis wind turbines.
Degree: PhD, Civil Engineering (Structural Engineering), 2016, University of Southern California
URL: http://digitallibrary.usc.edu/cdm/compoundobject/collection/p15799coll3/id/422612/rec/1872
► This dissertation is motivated by challenges involved in the design optimization under uncertainty for the structures undergoing fluid structure interaction phenomena. In particular, this study…
(more)
▼ This dissertation is motivated by challenges involved
in the design optimization under uncertainty for the structures
undergoing fluid structure interaction phenomena. In particular,
this study focuses on the aerodynamic simulation and optimization
under uncertainty for rotor blades of Horizontal Axis Wind Turbines
(HAWT). To that end, a reliability‐based design framework
integrating the aeroelastic computation based on the blade element
method with a stochastic optimization, is developed. The wind model
is a stochastic process which accounts for the variation in time
and space. The aeroelastic calculation determines the aerodynamic
forces on the blade. The uncertainty propagated in the aerodynamic
forces stems from the uncertain characteristics of the wind.
Another source of uncertainty is introduced in the material
property of the blade which results in random structural parameters
such as stiffness and capacity. These sources of uncertainty lead
to a random objective function and constraints. The objective
function is the generated power subjected to the constraints on
stresses in the blade. The reliability is defined based on the
probability of the safety in the system. The design variables are
considered to be shape parameters, namely twist angles along the
blade. In order to show the effect of uncertainty in the design,
the result of the deterministic optimization is obtained and
compared with the optimization results under uncertainty.
Polynomial chaos expansion is used in various parts of this work as
a mathematical tool for the uncertainty propagation. In particular,
polynomial chaos expansion can be used to characterize the solution
of stochastic differential equations such as the governing equation
of the motion of the blade. Significant computational challenges
are associated with the polynomial chaos expansion approach for
problems with high dimensional parameter space. This challenge is
addressed in the present dissertation by developing a methodology
for convergence acceleration of polynomial chaos‐based stochastic
Galerkin solutions. Specifically, Nonlinear sequence
transformations are adapted to these expansions, viewed as a
one‐parameter family of functions with the parameter being the
polynomial degree of the expansion. Stochastic Galerkin approach
yields polynomial chaos representations that have the requisite
analytical properties to ensure suitable convergence of these
nonlinear sequence transformations. In particular, the properties
of Shanks and Levin transformations are explored in the context of
a stochastic initial value problem and a stochastic elliptic
problem.
Advisors/Committee Members: Ghanem, Roger G. (Committee Chair), Masri, Sami F. (Committee Member), Newton, Paul K. (Committee Member).
Subjects/Keywords: aerodynamic optimization; blade element method; reliability based design optimization; polynomial chaos expansion; convergence acceleration; stochastic differential equation; nonlinear sequence transformation
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APA ·
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MLA ·
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to Zotero / EndNote / Reference
Manager
APA (6th Edition):
Keshavarzzadeh, V. (2016). Design optimization under uncertainty for rotor blades of
horizontal axis wind turbines. (Doctoral Dissertation). University of Southern California. Retrieved from http://digitallibrary.usc.edu/cdm/compoundobject/collection/p15799coll3/id/422612/rec/1872
Chicago Manual of Style (16th Edition):
Keshavarzzadeh, Vahid. “Design optimization under uncertainty for rotor blades of
horizontal axis wind turbines.” 2016. Doctoral Dissertation, University of Southern California. Accessed February 26, 2021.
http://digitallibrary.usc.edu/cdm/compoundobject/collection/p15799coll3/id/422612/rec/1872.
MLA Handbook (7th Edition):
Keshavarzzadeh, Vahid. “Design optimization under uncertainty for rotor blades of
horizontal axis wind turbines.” 2016. Web. 26 Feb 2021.
Vancouver:
Keshavarzzadeh V. Design optimization under uncertainty for rotor blades of
horizontal axis wind turbines. [Internet] [Doctoral dissertation]. University of Southern California; 2016. [cited 2021 Feb 26].
Available from: http://digitallibrary.usc.edu/cdm/compoundobject/collection/p15799coll3/id/422612/rec/1872.
Council of Science Editors:
Keshavarzzadeh V. Design optimization under uncertainty for rotor blades of
horizontal axis wind turbines. [Doctoral Dissertation]. University of Southern California; 2016. Available from: http://digitallibrary.usc.edu/cdm/compoundobject/collection/p15799coll3/id/422612/rec/1872
University of Southern California
6.
Pei, Yuan.
Certain regularity problems in fluid dynamics.
Degree: PhD, Applied Mathematics, 2014, University of Southern California
URL: http://digitallibrary.usc.edu/cdm/compoundobject/collection/p15799coll3/id/432069/rec/1275
► In the first chapter of this dissertation, we address the partial regularity for a suitable weak solutions of the Navier-Stokes system in a bounded space‐time…
(more)
▼ In the first chapter of this dissertation, we address
the partial regularity for a suitable weak solutions of the
Navier-Stokes system in a bounded space‐time domain D. We show that
the parabolic fractal dimension of the singular set is less than or
equal to 45/29, which is an improvement of the earlier result from
[K4]. Also, we introduce the new λ-fractal dimension and prove that
the dimension of the singular set is bounded by 3/2 for a certain
range of λ. The second chapter addresses the existence and
uniqueness of the solutions for the primitive equations of the
ocean with continuous initial datum. We split the initial data into
a regular finite energy part and a small bounded part and show that
the equations are preserved by the splitting, which enables us to
prove the well‐posedness of solutions. We provide a priori
estimates and the construction of the solutions.
Advisors/Committee Members: Kukavica, Igor (Committee Chair), Ziane, Mohammed (Committee Member), Newton, Paul K. (Committee Member).
Subjects/Keywords: Navier-Stokes equations; weak solutions; fractal dimension; regularity; primitive equations
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APA (6th Edition):
Pei, Y. (2014). Certain regularity problems in fluid dynamics. (Doctoral Dissertation). University of Southern California. Retrieved from http://digitallibrary.usc.edu/cdm/compoundobject/collection/p15799coll3/id/432069/rec/1275
Chicago Manual of Style (16th Edition):
Pei, Yuan. “Certain regularity problems in fluid dynamics.” 2014. Doctoral Dissertation, University of Southern California. Accessed February 26, 2021.
http://digitallibrary.usc.edu/cdm/compoundobject/collection/p15799coll3/id/432069/rec/1275.
MLA Handbook (7th Edition):
Pei, Yuan. “Certain regularity problems in fluid dynamics.” 2014. Web. 26 Feb 2021.
Vancouver:
Pei Y. Certain regularity problems in fluid dynamics. [Internet] [Doctoral dissertation]. University of Southern California; 2014. [cited 2021 Feb 26].
Available from: http://digitallibrary.usc.edu/cdm/compoundobject/collection/p15799coll3/id/432069/rec/1275.
Council of Science Editors:
Pei Y. Certain regularity problems in fluid dynamics. [Doctoral Dissertation]. University of Southern California; 2014. Available from: http://digitallibrary.usc.edu/cdm/compoundobject/collection/p15799coll3/id/432069/rec/1275
University of Southern California
7.
Ignatova, Mihaela I.
Quantitative unique continuation and complexity of solutions
to partial differential equations.
Degree: PhD, Mathematics, 2011, University of Southern California
URL: http://digitallibrary.usc.edu/cdm/compoundobject/collection/p15799coll127/id/617952/rec/5358
► In the first part of the thesis, we address the strong unique continuation properties for 1D higher order parabolic partial differential equations with coefficients in…
(more)
▼ In the first part of the thesis, we address the strong
unique continuation properties for 1D higher order parabolic
partial differential equations with coefficients in the Gevrey
class G^σ for σ>1. We establish a quantitative estimate of
unique continuation (observability estimate) under a mild
assumption on the Gevrey exponent σ. Also, we improve the existing
upper bounds on the size of the level sets of solutions and remove
the analyticity requirement on the coefficients. Next, we consider
the strong unique continuation problem for elliptic and parabolic
equations in higher space dimensions. As an application, we provide
a polynomial upper bound on the Hausdorff measure of the nodal
(zero) sets of solutions in terms of the coefficients. In
particular, we cover the case of the Navier-Stokes equations with
non-analytic forcing. For this purpose, we provide Carleman-type
inequalities with the same singular weight for the Laplacian and
for the heat operator.
Advisors/Committee Members: Kukavica, Igor (Committee Chair), Friedlander, Susan (Committee Member), Ziane, Mohammed (Committee Member), Newton, Paul K. (Committee Member).
Subjects/Keywords: Carleman estimates; Navier-Stokes equation; strong unique continuation; complexity of solutions; Gevrey class
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APA ·
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MLA ·
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Manager
APA (6th Edition):
Ignatova, M. I. (2011). Quantitative unique continuation and complexity of solutions
to partial differential equations. (Doctoral Dissertation). University of Southern California. Retrieved from http://digitallibrary.usc.edu/cdm/compoundobject/collection/p15799coll127/id/617952/rec/5358
Chicago Manual of Style (16th Edition):
Ignatova, Mihaela I. “Quantitative unique continuation and complexity of solutions
to partial differential equations.” 2011. Doctoral Dissertation, University of Southern California. Accessed February 26, 2021.
http://digitallibrary.usc.edu/cdm/compoundobject/collection/p15799coll127/id/617952/rec/5358.
MLA Handbook (7th Edition):
Ignatova, Mihaela I. “Quantitative unique continuation and complexity of solutions
to partial differential equations.” 2011. Web. 26 Feb 2021.
Vancouver:
Ignatova MI. Quantitative unique continuation and complexity of solutions
to partial differential equations. [Internet] [Doctoral dissertation]. University of Southern California; 2011. [cited 2021 Feb 26].
Available from: http://digitallibrary.usc.edu/cdm/compoundobject/collection/p15799coll127/id/617952/rec/5358.
Council of Science Editors:
Ignatova MI. Quantitative unique continuation and complexity of solutions
to partial differential equations. [Doctoral Dissertation]. University of Southern California; 2011. Available from: http://digitallibrary.usc.edu/cdm/compoundobject/collection/p15799coll127/id/617952/rec/5358
University of Southern California
8.
Kelly, Jonathan Scott.
On temporal and spatial calibration for high accuracy
visual-inertial motion estimation.
Degree: PhD, Computer Science, 2011, University of Southern California
URL: http://digitallibrary.usc.edu/cdm/compoundobject/collection/p15799coll3/id/198919/rec/4534
► The majority of future autonomous robots will be mobile, and will need to navigate reliably in unknown and dynamic environments. Visual and inertial sensors, together,…
(more)
▼ The majority of future autonomous robots will be
mobile, and will need to navigate reliably in unknown and dynamic
environments. Visual and inertial sensors, together, are able to
supply accurate motion estimates and are well-suited for use in
many robot navigation tasks. Beyond egomotion estimation, fusing
high-rate inertial sensing with monocular vision enables other
capabilities, such as independent motion segmentation and tracking,
moving obstacle detection and ranging, and dense metric 3D mapping,
all from a mobile platform. ❧ A fundamental requirement in any
multisensor system is precision calibration. To ensure optimal
performance, the sensors must be properly calibrated, both
intrinsically and relative to one another. In a visual-inertial
system, the camera and the inertial measurement unit (IMU) require
both temporal and spatial calibration – estimates of the relative
timing of measurements from each sensor and of the six
degrees-of-freedom transform between the sensors are needed.
Obtaining this calibration information is typically difficult and
time-consuming, however. Ideally, we would like to build
power-on-and-go robots that are able to operate for long periods
without the usual requisite manual sensor (re-) calibration. ❧ This
dissertation describes work on combining visual and inertial
sensing for navigation applications, with an emphasis on the
ability to temporally and spatially (self-) calibrate a camera and
an IMU. Self-calibration refers to the use of data exclusively from
the sensors themselves to improve estimates of related system
parameters. ❧ The primary difficultly in temporal calibration is
that the correspondences between measurements from the different
sensors are initially unknown, and hence the relative time delay
between the data streams cannot be computed directly. We instead
formulate temporal calibration as a registration problem, and
introduce an algorithm called Time Delay Iterative Closest Point
(TD-ICP) as a novel solution. The algorithm operates by aligning
curves in a three-dimensional orientation space, and incorporates
in a principled way the uncertainty in the camera and IMU
measurements. ❧ We then develop a sequential filtering approach for
calibration of the spatial transform between the sensors. We
estimate the transform parameters using a sigma point Kalman filter
(SPKF). Our formulation rests on a differential geometric analysis
of the observability of the camera-IMU system; this analysis shows
for the first time that the IMU pose and velocity, the gyroscope
and accelerometer biases, the gravity vector, the metric scene
structure, and the sensor-to-sensor transform, can be recovered
from camera and IMU measurements alone. While calibrating the
transform we simultaneously localize the IMU and build a map of the
surroundings. No additional hardware or prior knowledge about the
environment in which a robot is operating is necessary. ❧ Results
from extensive simulation studies and from laboratory experiments
are presented, which demonstrate accurate camera-IMU temporal…
Advisors/Committee Members: Sukhatme, Gaurav S. (Committee Chair), Schaal, Stefan (Committee Member), Matthies, Larry H. (Committee Member), Newton, Paul K. (Committee Member).
Subjects/Keywords: calibration; inertial navigation; simultaneous localization and mapping; SLAM; sensor fusion; monocular vision; observability
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APA ·
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MLA ·
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CSE |
Export
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Manager
APA (6th Edition):
Kelly, J. S. (2011). On temporal and spatial calibration for high accuracy
visual-inertial motion estimation. (Doctoral Dissertation). University of Southern California. Retrieved from http://digitallibrary.usc.edu/cdm/compoundobject/collection/p15799coll3/id/198919/rec/4534
Chicago Manual of Style (16th Edition):
Kelly, Jonathan Scott. “On temporal and spatial calibration for high accuracy
visual-inertial motion estimation.” 2011. Doctoral Dissertation, University of Southern California. Accessed February 26, 2021.
http://digitallibrary.usc.edu/cdm/compoundobject/collection/p15799coll3/id/198919/rec/4534.
MLA Handbook (7th Edition):
Kelly, Jonathan Scott. “On temporal and spatial calibration for high accuracy
visual-inertial motion estimation.” 2011. Web. 26 Feb 2021.
Vancouver:
Kelly JS. On temporal and spatial calibration for high accuracy
visual-inertial motion estimation. [Internet] [Doctoral dissertation]. University of Southern California; 2011. [cited 2021 Feb 26].
Available from: http://digitallibrary.usc.edu/cdm/compoundobject/collection/p15799coll3/id/198919/rec/4534.
Council of Science Editors:
Kelly JS. On temporal and spatial calibration for high accuracy
visual-inertial motion estimation. [Doctoral Dissertation]. University of Southern California; 2011. Available from: http://digitallibrary.usc.edu/cdm/compoundobject/collection/p15799coll3/id/198919/rec/4534
University of Southern California
9.
Ghaemi Oskouei, Babak.
Stability of body-vortex systems: Application to aquatic
locomotion.
Degree: PhD, Aerospace & Mechanical Engineering (Dynamics &
Control), 2013, University of Southern California
URL: http://digitallibrary.usc.edu/cdm/compoundobject/collection/p15799coll127/id/451808/rec/6029
► Mathematical modeling and analysis of biological systems such as swimming and flying is an interdisciplinary research field with an extensive range of applications including the…
(more)
▼ Mathematical modeling and analysis of biological
systems such as swimming and flying is an interdisciplinary
research field with an extensive range of applications including
the design of unmanned underwater robots and swarm of robots that
swim together in a coordinated way similar to schooling fish. One
of the main objectives of our work is to develop mathematical
models for certain aspect of schooling. In particular, we examine
(1) the interaction of a single fish with ambient vorticity
possibly generated by other neighboring fish; and (2) the
interaction of multiple fish wakes in large fish schools.; For the
first part, we propose a reduced model of a rigid body interacting
with point vortices in potential fluid and demonstrate that the
rigid body can swim upstream in the direction opposite to the
motion of point vortices at no energy cost. Indeed, the rigid body
itself does not generate any force and its motion is due entirely
to the energy exploited from the presence of the point vortices. We
comment on the stability of these motions and propose
under-actuated active control methods to achieve locomotion in
unsteady wakes.; In the second part, we consider the interaction of
multiple reverse von K´arm´an vortex streets as a model of the
mid-wake region of large fish schools. We focus on the wake
dynamics to gain insight into the role of the fluid in transporting
oxygen and nutrients to inner fish as well as its role in
facilitating or acting as flow barriers to passive locomotion.; We
examine the topology of the streamline patterns in a frame moving
with the same translational velocity as the streets which lends
insight into fluid transport through the mid-wake
region.
Advisors/Committee Members: Kanso, Eva (Committee Chair), Newton, Paul K. (Committee Member), Redekopp, Larry G. (Committee Member), Mitra, Urbashi (Committee Member).
Subjects/Keywords: point vortex; dynamical systems; stability analysis; vortex wake; fish; fish schooling; solid body; fluid; interaction; floquet theory; inviscid; incompressible; irrotational flow; 2D flow; ellipse; circle; Kirchhoff Routh; classical; Milne Thomson; circle theorem; complex potential; velocity; kinematics; submerged; Grobli; periodic; thrust; drag; von Karman; street; mid wake; streamline; pattern; topology; time scale; bifurcation; Doubly-Infinite Array; zeta function; vortex lattice; orientation control; elongated body; staggered street; symmetric street; convergence; integral test; dynamics; control; ideal fluid; aquatic locomotion; propulsion
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APA (6th Edition):
Ghaemi Oskouei, B. (2013). Stability of body-vortex systems: Application to aquatic
locomotion. (Doctoral Dissertation). University of Southern California. Retrieved from http://digitallibrary.usc.edu/cdm/compoundobject/collection/p15799coll127/id/451808/rec/6029
Chicago Manual of Style (16th Edition):
Ghaemi Oskouei, Babak. “Stability of body-vortex systems: Application to aquatic
locomotion.” 2013. Doctoral Dissertation, University of Southern California. Accessed February 26, 2021.
http://digitallibrary.usc.edu/cdm/compoundobject/collection/p15799coll127/id/451808/rec/6029.
MLA Handbook (7th Edition):
Ghaemi Oskouei, Babak. “Stability of body-vortex systems: Application to aquatic
locomotion.” 2013. Web. 26 Feb 2021.
Vancouver:
Ghaemi Oskouei B. Stability of body-vortex systems: Application to aquatic
locomotion. [Internet] [Doctoral dissertation]. University of Southern California; 2013. [cited 2021 Feb 26].
Available from: http://digitallibrary.usc.edu/cdm/compoundobject/collection/p15799coll127/id/451808/rec/6029.
Council of Science Editors:
Ghaemi Oskouei B. Stability of body-vortex systems: Application to aquatic
locomotion. [Doctoral Dissertation]. University of Southern California; 2013. Available from: http://digitallibrary.usc.edu/cdm/compoundobject/collection/p15799coll127/id/451808/rec/6029
University of Southern California
10.
Jing, Fangxu.
Part I: Viscous evolution of point vortex equilibria; Part
II: Effects of body elasticity on stability of fish motion.
Degree: PhD, Aerospace Engineering, 2011, University of Southern California
URL: http://digitallibrary.usc.edu/cdm/compoundobject/collection/p15799coll127/id/652897/rec/4933
► Vortex dynamics and solid-fluid interactions are two of the most important and most studied topics in fluid dynamics for their relevance to a wide range…
(more)
▼ Vortex dynamics and solid-fluid interactions are two
of the most important and most studied topics in fluid dynamics for
their relevance to a wide range of applications from geophysical
flows to locomotion in moving fluids. In this work, we investigate
two problems in two parts: Part I studies the viscous evolution of
point vortex equilibria; Part II studies the effects of body
elasticity on the passive stability of submerged bodies. ❧ In Part
I, we describe the viscous evolution of point vortex configurations
that, in the absence of viscosity, are in a state of fixed or
relative equilibrium. In particular, we examine four cases, three
of them correspond to relative equilibria in the inviscid point
vortex model and one corresponds to a fixed equilibrium. Our goal
is to elucidate the dominant transient dynamical features of the
flow. A multi- Gaussian “core growing” type of model is typically
used in high fidelity numerical simulations, but we propose to
implement it as a low-order model for the flow field. We show that
all four configurations immediately begin to rotate unsteadily. We
then examine in detail the qualitative and quantitative evolution
of the structures as they evolve, and for each case show the
sequence of topological bifurcations that occur both in a fixed
reference frame, and in an appropriately chosen rotating reference
frame. Comparisons between the cases help to reveal different
features of the viscous evolution for short and intermediate time
scales of vortex structures. We examine the dynamical evolution of
passive particles in the viscously evolving flows and interpret it
in relation to the evolving streamline patterns. Although the
low-order multi-Gaussian model does not exactly coincide with the
Navier-Stokes solution, the two results show remarkable
resemblances in many aspects. ❧ In Part II, we examine the effects
of body geometry and elasticity on the passive stability of motion
in a perfect fluid. Our main motivation is to understand the role
of body elasticity on the stability of fish swimming. The fish is
modeled as an articulated body made of N links (assumed to be
identical ellipses in 2D or identical ellipsoids in 3D)
interconnected by hinge joints. It can undergo shape changes by
varying the relative angles between the links. Body elasticity is
accounted for via the torsional springs at the joints. The
unsteadiness of the flow is modeled using the added mass effect.
Equations of motion for the body-fluid system are derived using
Newtonian and Lagrangian approaches for both hydrodynamically
decoupled and coupled models in 2D and 3D. We specifically examine
the stability associated with a relative equilibrium of the
equations, traditionally referred to as the “coast motion” (proved
to be unstable for a rigid elongated body model), and found that
body elasticity does stabilize the system. Stable regions are
identified based on linear stability analysis in the parameter
space spanned by aspect ratio (body geometry) and spring constants
(muscle stiffness), and the findings based on the…
Advisors/Committee Members: Kanso, Eva (Committee Chair), Newton, Paul K. (Committee Member), Flashner, Henryk (Committee Member), Friedlander, Susan (Committee Member), Redekopp, Larry G. (Committee Member).
Subjects/Keywords: vortex dynamics; fish stability
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APA ·
Chicago ·
MLA ·
Vancouver ·
CSE |
Export
to Zotero / EndNote / Reference
Manager
APA (6th Edition):
Jing, F. (2011). Part I: Viscous evolution of point vortex equilibria; Part
II: Effects of body elasticity on stability of fish motion. (Doctoral Dissertation). University of Southern California. Retrieved from http://digitallibrary.usc.edu/cdm/compoundobject/collection/p15799coll127/id/652897/rec/4933
Chicago Manual of Style (16th Edition):
Jing, Fangxu. “Part I: Viscous evolution of point vortex equilibria; Part
II: Effects of body elasticity on stability of fish motion.” 2011. Doctoral Dissertation, University of Southern California. Accessed February 26, 2021.
http://digitallibrary.usc.edu/cdm/compoundobject/collection/p15799coll127/id/652897/rec/4933.
MLA Handbook (7th Edition):
Jing, Fangxu. “Part I: Viscous evolution of point vortex equilibria; Part
II: Effects of body elasticity on stability of fish motion.” 2011. Web. 26 Feb 2021.
Vancouver:
Jing F. Part I: Viscous evolution of point vortex equilibria; Part
II: Effects of body elasticity on stability of fish motion. [Internet] [Doctoral dissertation]. University of Southern California; 2011. [cited 2021 Feb 26].
Available from: http://digitallibrary.usc.edu/cdm/compoundobject/collection/p15799coll127/id/652897/rec/4933.
Council of Science Editors:
Jing F. Part I: Viscous evolution of point vortex equilibria; Part
II: Effects of body elasticity on stability of fish motion. [Doctoral Dissertation]. University of Southern California; 2011. Available from: http://digitallibrary.usc.edu/cdm/compoundobject/collection/p15799coll127/id/652897/rec/4933
University of Southern California
11.
Mason, Jeremy.
A stochastic Markov chain model to describe cancer
metastasis.
Degree: PhD, Mechanical Engineering, 2013, University of Southern California
URL: http://digitallibrary.usc.edu/cdm/compoundobject/collection/p15799coll3/id/331809/rec/372
► A stochastic Markov chain model for metastatic progression is developed for primary 8 major cancer types based on a network construction of metastatic sites with…
(more)
▼ A stochastic Markov chain model for metastatic
progression is developed for primary 8 major cancer types based on
a network construction of metastatic sites with dynamics modeled as
an ensemble of random walkers on the network. We calculate a
transition matrix for each primary cancer and use it to construct a
circular bi-directional network of primary and metastatic locations
based on postmortem tissue analysis of 3827 autopsies on untreated
patients documenting all primary tumor locations and metastatic
sites from this population. The resulting 50 potential metastatic
sites are connected by directed edges with distributed weightings,
where the site connections and weightings are obtained by
calculating the entries of an ensemble of transition matrices so
that the steady-state distribution obtained from the long-time
limit of the Markov chain dynamical system corresponds to the
ensemble metastatic distribution obtained from the autopsy dataset.
We condition our search for a transition matrix on an initial
distribution of metastatic tumors obtained from the dataset.
Through an iterative numerical search procedure, we adjust the
entries of a sequence of approximations until a transition matrix
with the correct steady-state is found (up to a numerical
threshold). Once the transition matrix for a given cancer type is
computed, our metastatic progression model is based Monte Carlo
simulations of collections of random walkers all leaving the
primary tumor location and executing a random walk across the
directed graph from site to site. The model allows us to simulate
and quantify disease progression pathways and timescales of
progression from the primary tumor location to other sites. Pathway
diagrams are created that classify metastatic tumors as 'spreaders'
or 'sponges' and quantif es three types of multidirectional
mechanisms of progression: (i)self-seeding of the primary tumor,
(ii) reseeding of the primary tumor from a metastatic site (primary
reseeding), and (iii) reseeding of metastatic tumors (metastasis
reseeding). The entire process is replicated for additional primary
tumors in the dataset of for individual analysis and comparative
purposes. ❧ A second contribution of this work is to introduce a
quantitative notion of 'metastatic entropy' for cancer and use it
to compare the complexity and predictability associated with the 12
most common cancer types worldwide. We apply these notions of
entropy and predictability directly to the autopsy dataset used to
create our Markov model. The raw data, which contains the number of
metastases found at all of the anatomical sites for each cadaver
(whose primary tumor location is also recorded), is normalized
(yielding their empirical distribution) so that we can interpret
the histograms as probability mass functions (PMFs) representing
the large scale (whole body) metastatic 'signature' of each primary
cancer. We characterize the power-law distributions associated with
metastatic tumor distributions for each primary cancer type. Then
we calculate the entropy associated with…
Advisors/Committee Members: Newton, Paul K. (Committee Chair), Kanso, Eva (Committee Member), Macklin, Paul (Committee Member), Ghanem, Roger G. (Committee Member), Pinkston, Timothy M. (Committee Member).
Subjects/Keywords: cancer; metastasis; Markov chain
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APA ·
Chicago ·
MLA ·
Vancouver ·
CSE |
Export
to Zotero / EndNote / Reference
Manager
APA (6th Edition):
Mason, J. (2013). A stochastic Markov chain model to describe cancer
metastasis. (Doctoral Dissertation). University of Southern California. Retrieved from http://digitallibrary.usc.edu/cdm/compoundobject/collection/p15799coll3/id/331809/rec/372
Chicago Manual of Style (16th Edition):
Mason, Jeremy. “A stochastic Markov chain model to describe cancer
metastasis.” 2013. Doctoral Dissertation, University of Southern California. Accessed February 26, 2021.
http://digitallibrary.usc.edu/cdm/compoundobject/collection/p15799coll3/id/331809/rec/372.
MLA Handbook (7th Edition):
Mason, Jeremy. “A stochastic Markov chain model to describe cancer
metastasis.” 2013. Web. 26 Feb 2021.
Vancouver:
Mason J. A stochastic Markov chain model to describe cancer
metastasis. [Internet] [Doctoral dissertation]. University of Southern California; 2013. [cited 2021 Feb 26].
Available from: http://digitallibrary.usc.edu/cdm/compoundobject/collection/p15799coll3/id/331809/rec/372.
Council of Science Editors:
Mason J. A stochastic Markov chain model to describe cancer
metastasis. [Doctoral Dissertation]. University of Southern California; 2013. Available from: http://digitallibrary.usc.edu/cdm/compoundobject/collection/p15799coll3/id/331809/rec/372
University of Southern California
12.
Lee, Angela Meeyoun.
Modeling and simulation of circulating tumor cells in flow.
Part I: Low-dimensional deformation models for circulating tumor
cells in flow; Part II: Procoagulant circulating tumor cells in
flow.
Degree: PhD, Aerospace Engineering, 2014, University of Southern California
URL: http://digitallibrary.usc.edu/cdm/compoundobject/collection/p15799coll3/id/412034/rec/4126
► In this thesis, we mathematically model and computationally simulate several aspects associated with the dynamics of circulating tumor cells in the bloodstream. We focus on…
(more)
▼ In this thesis, we mathematically model and
computationally simulate several aspects associated with the
dynamics of circulating tumor cells in the bloodstream. We focus on
physical processes that initiate cancer metastasis, such as
intravasation and the subsequent diffusion of thrombin by the
expression of tissue factor (TF) on the surface of the circulating
tumor cells that are of epithelial origin. ❧ In Part I, we develop
a low‐dimensional parametric deformation model of a cancer cell
under shear flow. The surface deformation of MDA‐MB‐213 cells is
imaged using DIC microscopy imaging techniques until the cell
releases into the flow. We post‐process the time sequence of images
using an Active Shape Model (ASM) to obtain the principal
components of deformation, which are then used as parameters in an
empirical constitutive equation to model the cell deformations as a
function of the fluid normal and shear forces imparted. The cell
surface is modeled as a 2D Gaussian interface with three active
parameters: H (height), σₓ (x-width), and σy (y-width). Fluid
forces are calculated on the cell surface by discretizing the
surface with regularized Stokeslets, and the flow is driven by a
stochastically fluctuating pressure gradient. The Stokeslet
strengths are obtained so that viscous boundary conditions are
enforced on the surface of the cell and the surrounding plate. We
show that the low‐dimensional model is able to capture the
principal deformations of the cell reasonably well and argue that
Active Shape Models can be exploited further as a useful tool to
bridge the gap between experiments, models, and numerical
simulations in this biological setting. ❧ In Part II, we describe a
mathematical and computational model for diffusion‐limited
procoagulant circulating tumor cells (CTCs) in flow. We first build
a model based on an exact formulation of Green's function solutions
for domains with a blood vessel wall and for closed domains.
Time‐dependent gradient trackers are used to highlight the result
that concentration fields build up near boundaries (vessel walls),
in regions surrounding the diffusing particles, and in complex
time‐dependent regions of the flow where fields associated with
different particles overlap. Then, as a next step to deal with more
complex blood vessel geometries and actual CTC shapes obtained from
DIC images of fluid biopsy samples, we use COMSOL Multiphysics and
Cell Profiler software to simulate initial configurations and
various geometries relevant to venule sizes in the body. We develop
CFD models based on finite element meshes of the imaged single
cells and circulating tumor cell clusters. Our results indicate
that the thrombin chemical fields diffuse to and collect at the
blood vessel walls, and that the domain geometry combined with the
spatial distribution of CTCs in flow determine local thrombin
concentrations. The final chapter outlines what would be the next
steps in the model developments of both Part I and Part II of the
thesis.
Advisors/Committee Members: Newton, Paul K. (Committee Chair), Kanso, Eva (Committee Member), Macklin, Paul (Committee Member), McCarty, Owen J. T. (Committee Member).
Subjects/Keywords: intravastion models; low-dimensional deformation; procoagulant circulating tumor cells; chemical gradient tracking; tissue factor and coagulation; prothombin and thrombin fields; circulating tumor cell induced hypercoagulation
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❌
APA ·
Chicago ·
MLA ·
Vancouver ·
CSE |
Export
to Zotero / EndNote / Reference
Manager
APA (6th Edition):
Lee, A. M. (2014). Modeling and simulation of circulating tumor cells in flow.
Part I: Low-dimensional deformation models for circulating tumor
cells in flow; Part II: Procoagulant circulating tumor cells in
flow. (Doctoral Dissertation). University of Southern California. Retrieved from http://digitallibrary.usc.edu/cdm/compoundobject/collection/p15799coll3/id/412034/rec/4126
Chicago Manual of Style (16th Edition):
Lee, Angela Meeyoun. “Modeling and simulation of circulating tumor cells in flow.
Part I: Low-dimensional deformation models for circulating tumor
cells in flow; Part II: Procoagulant circulating tumor cells in
flow.” 2014. Doctoral Dissertation, University of Southern California. Accessed February 26, 2021.
http://digitallibrary.usc.edu/cdm/compoundobject/collection/p15799coll3/id/412034/rec/4126.
MLA Handbook (7th Edition):
Lee, Angela Meeyoun. “Modeling and simulation of circulating tumor cells in flow.
Part I: Low-dimensional deformation models for circulating tumor
cells in flow; Part II: Procoagulant circulating tumor cells in
flow.” 2014. Web. 26 Feb 2021.
Vancouver:
Lee AM. Modeling and simulation of circulating tumor cells in flow.
Part I: Low-dimensional deformation models for circulating tumor
cells in flow; Part II: Procoagulant circulating tumor cells in
flow. [Internet] [Doctoral dissertation]. University of Southern California; 2014. [cited 2021 Feb 26].
Available from: http://digitallibrary.usc.edu/cdm/compoundobject/collection/p15799coll3/id/412034/rec/4126.
Council of Science Editors:
Lee AM. Modeling and simulation of circulating tumor cells in flow.
Part I: Low-dimensional deformation models for circulating tumor
cells in flow; Part II: Procoagulant circulating tumor cells in
flow. [Doctoral Dissertation]. University of Southern California; 2014. Available from: http://digitallibrary.usc.edu/cdm/compoundobject/collection/p15799coll3/id/412034/rec/4126
University of Southern California
13.
Kianercy, Ardeshir.
Adaptive agents on evolving network: an evolutionary game
theory approach.
Degree: PhD, Mechanical Engineering, 2013, University of Southern California
URL: http://digitallibrary.usc.edu/cdm/compoundobject/collection/p15799coll3/id/243712/rec/511
► We consider the dynamics of Q-learning in two – player two – action games with a Boltzmann exploration mechanism. For any non-zero exploration rate the dynamics is…
(more)
▼ We consider the dynamics of Q-learning in two – player
two – action games with a Boltzmann exploration mechanism. For any
non-zero exploration rate the dynamics is dissipative, which
guarantees that agent strategies converge to rest points that are
generally different from the game's Nash Equlibria (NE). We provide
a comprehensive characterization of the rest point structure for
different games, and examine the sensitivity of this structure with
respect to the noise due to exploration. Our results indicate that
for a class of games with multiple NE the asymptotic behavior of
learning dynamics can undergo drastic changes at critical
exploration rates. Furthermore, we demonstrate that for certain
games with a single NE, it is possible to have additional rest
points (not corresponding to any NE) that persist for a finite
range of the exploration rates and disappear when the exploration
rates of both players tend to zero. ❧ In addition to Boltzmann
Q-learning, we study adaptive dynamics in games where players
abandon the population at a given rate, and are replaced by naive
players characterized by a prior distribution over the admitted
strategies. We show how the Nash equilibria are modified by the
turnover, and study the changes in dynamical features of the system
for prototypical examples such as different classes of two-action
games played between two distinct populations. ❧ Finally, we
presents a model of network formation in repeated games where the
players adapt their strategies and network ties simultaneously
using a simple reinforcement learning scheme. It is demonstrated
that the co-evolutionary dynamics of such systems can be described
via coupled replicator equations. We provide a comprehensive
analysis for three-player two-action games, which is the minimum
system size with non-trivial structural dynamics. In particular, we
characterize the Nash Equilibria (NE) in such game, and examine the
local stability of the rest points corresponding to those
equilibria. We also study general N-player networks via both
simulations and analytical methods, and find that in the absence of
exploration, the stable equilibria consist of star motifs as the
main building blocks of the network. Furthermore, in all stable
equilibria the agents play pure strategies, even when the game
allows mixed NE. Finally, we study the impact of exploration on
learning outcomes, and observe that there is a critical exploration
rate above which the symmetric and uniformly connected network
topology becomes stable.
Advisors/Committee Members: Newton, Paul K. (Committee Chair), Galstyan, Aram (Committee Member), Ghanem, Roger G. (Committee Member), Carrillo, Juan D. (Committee Member).
Subjects/Keywords: learning in games; evolutionary dynamics; network formation; evolutionary game theory; replicator dynamics; replicator equation; Q-learning; Boltzmann distribution; soft-max learning; phase transition; bifurcation; reinforcement learning; economic network; social network; co-evolutionary dynamics; games on network; free energy minimization; coordination game; homophily; contagion
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APA ·
Chicago ·
MLA ·
Vancouver ·
CSE |
Export
to Zotero / EndNote / Reference
Manager
APA (6th Edition):
Kianercy, A. (2013). Adaptive agents on evolving network: an evolutionary game
theory approach. (Doctoral Dissertation). University of Southern California. Retrieved from http://digitallibrary.usc.edu/cdm/compoundobject/collection/p15799coll3/id/243712/rec/511
Chicago Manual of Style (16th Edition):
Kianercy, Ardeshir. “Adaptive agents on evolving network: an evolutionary game
theory approach.” 2013. Doctoral Dissertation, University of Southern California. Accessed February 26, 2021.
http://digitallibrary.usc.edu/cdm/compoundobject/collection/p15799coll3/id/243712/rec/511.
MLA Handbook (7th Edition):
Kianercy, Ardeshir. “Adaptive agents on evolving network: an evolutionary game
theory approach.” 2013. Web. 26 Feb 2021.
Vancouver:
Kianercy A. Adaptive agents on evolving network: an evolutionary game
theory approach. [Internet] [Doctoral dissertation]. University of Southern California; 2013. [cited 2021 Feb 26].
Available from: http://digitallibrary.usc.edu/cdm/compoundobject/collection/p15799coll3/id/243712/rec/511.
Council of Science Editors:
Kianercy A. Adaptive agents on evolving network: an evolutionary game
theory approach. [Doctoral Dissertation]. University of Southern California; 2013. Available from: http://digitallibrary.usc.edu/cdm/compoundobject/collection/p15799coll3/id/243712/rec/511
University of Southern California
14.
Comboul, Maud.
Stochastic and multiscale models for urban and natural
ecology.
Degree: PhD, Civil Engineering (Environmental
Engineering), 2012, University of Southern California
URL: http://digitallibrary.usc.edu/cdm/compoundobject/collection/p15799coll3/id/72481/rec/6071
► This research reflects on both particular cases of ecologies: sensor networks in urban water distribution systems and forest dynamics under changing disturbance regime, and the…
(more)
▼ This research reflects on both particular cases of
ecologies: sensor networks in urban water distribution systems and
forest dynamics under changing disturbance regime, and the
elaboration of exploration tools to investigate and assess those
complex ecologies. The predictive models that emerged from this
work rely on sophisticated computer simulations designed based on
stochastic and multiscale principles, and contribute to
characterizing and evaluating the knowledge and information that is
available about the systems under investigation. This thesis is
organized into three distinct projects, each of which confronts
specific challenges encountered when modeling complex systems. The
first project considers the monitoring of water distribution
networks where we describe a stochastic parameterization and
analysis of uncertainty for the design of single-stage as well as
two-stage sensor networks aimed at maximizing the probability of
detection of accidents and intrusions in water distribution
systems. Next, this study explores the ecological and evolutionary
impacts of different disturbance regimes (generated following a
stochastic Poisson process) on forests using the framework of a
spatially explicit and individual-based forest model designed
around four functional traits of trees. The final project
investigates a multiscale characterization of forest dynamics using
Monte-Carlo simulations of the fine scale dynamics to synthesize a
coarse-grain stochastic model describing the dynamics of the system
on larger spatial scales. In addition to modeling aspects, all
three projects yield adequate computational performance, thereby
assessing a recurrent challenge associated with the computational
feasibility and performance of relevant numerical
algorithms.
Advisors/Committee Members: Ghanem, Roger G. (Committee Chair), Newton, Paul K. (Committee Member), Nakano, Aiichiro (Committee Member), Masri, Sami F. (Committee Member), Johnson, Erik A. (Committee Member).
Subjects/Keywords: stochastic optimization; greedy algorithm; sensor network; Monte Carlo simulations agent-based model; Markov dynamics; multiscale dynamics; forest dynamics
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APA ·
Chicago ·
MLA ·
Vancouver ·
CSE |
Export
to Zotero / EndNote / Reference
Manager
APA (6th Edition):
Comboul, M. (2012). Stochastic and multiscale models for urban and natural
ecology. (Doctoral Dissertation). University of Southern California. Retrieved from http://digitallibrary.usc.edu/cdm/compoundobject/collection/p15799coll3/id/72481/rec/6071
Chicago Manual of Style (16th Edition):
Comboul, Maud. “Stochastic and multiscale models for urban and natural
ecology.” 2012. Doctoral Dissertation, University of Southern California. Accessed February 26, 2021.
http://digitallibrary.usc.edu/cdm/compoundobject/collection/p15799coll3/id/72481/rec/6071.
MLA Handbook (7th Edition):
Comboul, Maud. “Stochastic and multiscale models for urban and natural
ecology.” 2012. Web. 26 Feb 2021.
Vancouver:
Comboul M. Stochastic and multiscale models for urban and natural
ecology. [Internet] [Doctoral dissertation]. University of Southern California; 2012. [cited 2021 Feb 26].
Available from: http://digitallibrary.usc.edu/cdm/compoundobject/collection/p15799coll3/id/72481/rec/6071.
Council of Science Editors:
Comboul M. Stochastic and multiscale models for urban and natural
ecology. [Doctoral Dissertation]. University of Southern California; 2012. Available from: http://digitallibrary.usc.edu/cdm/compoundobject/collection/p15799coll3/id/72481/rec/6071
University of Southern California
15.
Karthikeyan, Anantha.
LQ feedback formulation for H∞ output feedback
control.
Degree: PhD, Electrical Engineering, 2013, University of Southern California
URL: http://digitallibrary.usc.edu/cdm/compoundobject/collection/p15799coll3/id/290208/rec/3893
► In this thesis we present a simple, unified formula for discrete and continuous-time H∞ "all-solutions" controllers. By observing a "cost" equivalence between the standard H∞…
(more)
▼ In this thesis we present a simple, unified formula
for discrete and continuous-time H∞ "all-solutions" controllers. By
observing a "cost" equivalence between the standard H∞ control
problem and a certain LQ optimal regulator problem, an elegant
controller structure reminiscent of an LQG optimal controller is
developed. Our choice of notation also simplifies the derivation
and existence conditions considerably, whereby all unnecessary
assumptions on plant state-space matrices and "loop-shifting"
transformations are eliminated. Additionally, with our focus
entirely on input-output weighting "cost functions" this derivation
offers a "behavioral" theory interpretation for all solutions of a
standard H∞ control problem. ❧ In this thesis we also present a
simplified matrix pencil formula for solving the H∞ control problem
for the case where the maximum singular value of (D₁₁) is less than
γ. This formula is useful in developing a more numerically robust
algorithm in H∞ control. A significant feature of this formula is
that each element of the pencils is expressed directly in terms of
the original descriptor-form state space matrices of the plant and
even pencil eigenspaces computed using a numerically robust even
pencil algorithm. There are no data-corrupting numerical operations
required to form any of the matrices that appear in our
"all-solutions" controller formula.
Advisors/Committee Members: Safonov, Michael G. (Committee Chair), Jonckheere, Edmond A. (Committee Member), Qin, Si-Zhao (Committee Member), Newton, Paul K. (Committee Member), Udwadia, Firdaus E. (Committee Member).
Subjects/Keywords: H∞ optimal control; LQ feedback control; output feedback; robust control
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APA (6th Edition):
Karthikeyan, A. (2013). LQ feedback formulation for H∞ output feedback
control. (Doctoral Dissertation). University of Southern California. Retrieved from http://digitallibrary.usc.edu/cdm/compoundobject/collection/p15799coll3/id/290208/rec/3893
Chicago Manual of Style (16th Edition):
Karthikeyan, Anantha. “LQ feedback formulation for H∞ output feedback
control.” 2013. Doctoral Dissertation, University of Southern California. Accessed February 26, 2021.
http://digitallibrary.usc.edu/cdm/compoundobject/collection/p15799coll3/id/290208/rec/3893.
MLA Handbook (7th Edition):
Karthikeyan, Anantha. “LQ feedback formulation for H∞ output feedback
control.” 2013. Web. 26 Feb 2021.
Vancouver:
Karthikeyan A. LQ feedback formulation for H∞ output feedback
control. [Internet] [Doctoral dissertation]. University of Southern California; 2013. [cited 2021 Feb 26].
Available from: http://digitallibrary.usc.edu/cdm/compoundobject/collection/p15799coll3/id/290208/rec/3893.
Council of Science Editors:
Karthikeyan A. LQ feedback formulation for H∞ output feedback
control. [Doctoral Dissertation]. University of Southern California; 2013. Available from: http://digitallibrary.usc.edu/cdm/compoundobject/collection/p15799coll3/id/290208/rec/3893
University of Southern California
16.
Lakeland, Daniel L.
Continuum modeling techniques and their application to the
physics of soil liquefaction and dissipative vibrations.
Degree: PhD, Civil Engineering, 2014, University of Southern California
URL: http://digitallibrary.usc.edu/cdm/compoundobject/collection/p15799coll3/id/346615/rec/1630
► The research in this dissertation encompasses four main thrusts: mathematical modeling techniques for building continuum models of systems that are explicitly acknowledged to be non-continuous…
(more)
▼ The research in this dissertation encompasses four
main thrusts: mathematical modeling techniques for building
continuum models of systems that are explicitly acknowledged to be
non-continuous at the finest scale of observation, application of a
continuum model of water flow in porous media to the problem of
“drained vs undrained” processes in soil liquefaction, an example
model for the dissipation of waves in a system of molecules
decoupled from any radiative process, where the total energy stays
constant, and the application of Bayesian Statistics to identifying
the parameters of these physical models.
Advisors/Committee Members: Ghanem, Roger G. (Committee Chair), Rechenmacher, Amy Lynn (Committee Member), Newton, Paul K. (Committee Member), Lynett, Patrick J. (Committee Member), Ben-Zion, Yehuda (Committee Member).
Subjects/Keywords: soil liquefaction; energy dissipation; vibrations; continuum models; nonstandard analysis; statistical mechanics; Bayesian statistics
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APA ·
Chicago ·
MLA ·
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CSE |
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Manager
APA (6th Edition):
Lakeland, D. L. (2014). Continuum modeling techniques and their application to the
physics of soil liquefaction and dissipative vibrations. (Doctoral Dissertation). University of Southern California. Retrieved from http://digitallibrary.usc.edu/cdm/compoundobject/collection/p15799coll3/id/346615/rec/1630
Chicago Manual of Style (16th Edition):
Lakeland, Daniel L. “Continuum modeling techniques and their application to the
physics of soil liquefaction and dissipative vibrations.” 2014. Doctoral Dissertation, University of Southern California. Accessed February 26, 2021.
http://digitallibrary.usc.edu/cdm/compoundobject/collection/p15799coll3/id/346615/rec/1630.
MLA Handbook (7th Edition):
Lakeland, Daniel L. “Continuum modeling techniques and their application to the
physics of soil liquefaction and dissipative vibrations.” 2014. Web. 26 Feb 2021.
Vancouver:
Lakeland DL. Continuum modeling techniques and their application to the
physics of soil liquefaction and dissipative vibrations. [Internet] [Doctoral dissertation]. University of Southern California; 2014. [cited 2021 Feb 26].
Available from: http://digitallibrary.usc.edu/cdm/compoundobject/collection/p15799coll3/id/346615/rec/1630.
Council of Science Editors:
Lakeland DL. Continuum modeling techniques and their application to the
physics of soil liquefaction and dissipative vibrations. [Doctoral Dissertation]. University of Southern California; 2014. Available from: http://digitallibrary.usc.edu/cdm/compoundobject/collection/p15799coll3/id/346615/rec/1630
University of Southern California
17.
Akopian, Vardan.
Modeling of Earth's ionosphere and variational approach for
data assimilation.
Degree: PhD, Applied Mathematics, 2008, University of Southern California
URL: http://digitallibrary.usc.edu/cdm/compoundobject/collection/p15799coll127/id/71573/rec/4143
► The Earth's ionosphere plays an important role in wireless communication. One of the primary goals of this research is to improve the techniques for monitoring…
(more)
▼ The Earth's ionosphere plays an important role in
wireless communication. One of the primary goals of this research
is to improve the techniques for monitoring and forecasting of the
conditions of the Earth's ionosphere. The work in this thesis
focuses on modeling of the ion and electron density changes in the
Earth's ionosphere and the assimilation of remote sensing
measurements into the numerical model. The governing equations of
the ionosphere consist of equations of fluid for chemically active
plasma in the ionosphere. These equations form a system of coupled
nonlinear convection-diffusion equations. In this thesis, we
establish the well-posedness of the equations in some special
cases. We also establish the numerical stability and consistency of
the approximation. The resulting numerical model of the ionosphere
produces stable and physically meaningful predictions of densities
for all major ion species in the ionosphere. The numerical method
is used in this research as a basis for the development of
a4-dimensional variational (4DVAR) data assimilation approach to
help in the estimation of the driving forces in the ionosphere. The
4DVAR technique uses the adjoint approach in the computation of the
gradient of performance functional.; In addition to theoretical
discussions on the mathematical properties of the basic ionospheric
model and its numerical implementation, extensive work has been
devoted to the validation of both the basic ionospheric model and
4DVAR implementation. In this work we demonstrate that the new
model can accurately reproduce all major characteristics of the
ionosphere and the 4DVAR approach can be effective in determining
the crucial drivers of the Earth's ionosphere.
Advisors/Committee Members: Wang, Chunming (Committee Chair), Rosen, Gary (Committee Member), Newton, Paul K. (Committee Member).
Subjects/Keywords: ionosphere; 4DVAR; variational approach for data assimilation; modeling; GAIM
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APA ·
Chicago ·
MLA ·
Vancouver ·
CSE |
Export
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Manager
APA (6th Edition):
Akopian, V. (2008). Modeling of Earth's ionosphere and variational approach for
data assimilation. (Doctoral Dissertation). University of Southern California. Retrieved from http://digitallibrary.usc.edu/cdm/compoundobject/collection/p15799coll127/id/71573/rec/4143
Chicago Manual of Style (16th Edition):
Akopian, Vardan. “Modeling of Earth's ionosphere and variational approach for
data assimilation.” 2008. Doctoral Dissertation, University of Southern California. Accessed February 26, 2021.
http://digitallibrary.usc.edu/cdm/compoundobject/collection/p15799coll127/id/71573/rec/4143.
MLA Handbook (7th Edition):
Akopian, Vardan. “Modeling of Earth's ionosphere and variational approach for
data assimilation.” 2008. Web. 26 Feb 2021.
Vancouver:
Akopian V. Modeling of Earth's ionosphere and variational approach for
data assimilation. [Internet] [Doctoral dissertation]. University of Southern California; 2008. [cited 2021 Feb 26].
Available from: http://digitallibrary.usc.edu/cdm/compoundobject/collection/p15799coll127/id/71573/rec/4143.
Council of Science Editors:
Akopian V. Modeling of Earth's ionosphere and variational approach for
data assimilation. [Doctoral Dissertation]. University of Southern California; 2008. Available from: http://digitallibrary.usc.edu/cdm/compoundobject/collection/p15799coll127/id/71573/rec/4143
University of Southern California
18.
Glatt-Holtz, Nathan Edward.
Well posedness and asymptotic analysis for the stochastic
equations of geophysical fluid dynamics.
Degree: PhD, Applied Mathematics, 2008, University of Southern California
URL: http://digitallibrary.usc.edu/cdm/compoundobject/collection/p15799coll127/id/82250/rec/7888
► This work collects three interrelated projects that develop rigorous mathematical tools for the study of the stochastically forced equations of geophysical fluid dynamics and turbulence.…
(more)
▼ This work collects three interrelated projects that
develop rigorous mathematical tools for the study of the
stochastically forced equations of geophysical fluid dynamics and
turbulence. Since the presence of persistent random fluctuations
are ubiquitous in fluid flow problems, the development of new
analytical techniques in this setting are ultimately of paramount
practical interest in the pursuit of more accurate models.; The
first two projects address the question of well posedness. One work
considers the Primitive equations of the ocean. These systems are
widely used in numerical studies of geophysical scale fluid flow.
We consider a two dimensional model forced by multiplicative noise
terms. For the case when the initial data and its vertical gradient
take values in L2, we prove the global existence and uniqueness of
solutions in a fixed probability space. The proof is based on
finite dimensional approximations, anisotropic Sobolev estimates,
and weak convergence techniques. The work concludes with a sketch
of the physical derivation of the governing equations.; The second
project introduces new results for the stochastic Navier-Stokes
system on bounded domains in space dimensions two and three. We
establish the local existence and uniqueness of pathwise solutions
evolving in H1. For the two dimensional case global existence is
established without employing moment estimates at fixed times. The
proof relies on a pairwise comparison technique facilitated by
decompositions into high and low modes to surmount the critical
issue of compactness.; In the final chapter we introduce a class of
singular perturbation systems in the presence of a small white
noise. Modifying the renormalization group procedure developed by
Chen, Goldenfeld and Oono, we derive an associated reduced system
which we use to construct an approximate solution that separates
scales. Rigorous results demonstrating that these approximate
solutions remain valid with high probability on large time
intervals are established. As a special case we infer new small
noise asymptotic results for a class of processes exhibiting a
physically motivated cancellation property in the nonlinear term.
We next consider some concrete perturbation systems arising in
geophysical fluid dynamics and in the study of turbulence. For each
system we exhibit the associated renormalization group which is
seen to decouple the interactions between the different scales
inherent in the original system. The article concludes with a
general result concerning slowly varying processes that forms the
backbone of the proof of the main theorem. Appendixes collect
mostly classical results on the stochastic convolution and further
novel small noise asymptotic results.
Advisors/Committee Members: Ziane, Mohammed (Committee Chair), Newton, Paul K. (Committee Member), Kukavica, Igor (Committee Member).
Subjects/Keywords: stochastic partial differential equations; Navier-Stokes equations; primitive equations; geophysical fluid dynamics; asymptotic analysis
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APA ·
Chicago ·
MLA ·
Vancouver ·
CSE |
Export
to Zotero / EndNote / Reference
Manager
APA (6th Edition):
Glatt-Holtz, N. E. (2008). Well posedness and asymptotic analysis for the stochastic
equations of geophysical fluid dynamics. (Doctoral Dissertation). University of Southern California. Retrieved from http://digitallibrary.usc.edu/cdm/compoundobject/collection/p15799coll127/id/82250/rec/7888
Chicago Manual of Style (16th Edition):
Glatt-Holtz, Nathan Edward. “Well posedness and asymptotic analysis for the stochastic
equations of geophysical fluid dynamics.” 2008. Doctoral Dissertation, University of Southern California. Accessed February 26, 2021.
http://digitallibrary.usc.edu/cdm/compoundobject/collection/p15799coll127/id/82250/rec/7888.
MLA Handbook (7th Edition):
Glatt-Holtz, Nathan Edward. “Well posedness and asymptotic analysis for the stochastic
equations of geophysical fluid dynamics.” 2008. Web. 26 Feb 2021.
Vancouver:
Glatt-Holtz NE. Well posedness and asymptotic analysis for the stochastic
equations of geophysical fluid dynamics. [Internet] [Doctoral dissertation]. University of Southern California; 2008. [cited 2021 Feb 26].
Available from: http://digitallibrary.usc.edu/cdm/compoundobject/collection/p15799coll127/id/82250/rec/7888.
Council of Science Editors:
Glatt-Holtz NE. Well posedness and asymptotic analysis for the stochastic
equations of geophysical fluid dynamics. [Doctoral Dissertation]. University of Southern California; 2008. Available from: http://digitallibrary.usc.edu/cdm/compoundobject/collection/p15799coll127/id/82250/rec/7888
University of Southern California
19.
Gates, Wess.
A simulation of particle dynamics in a two dimensional fluid
body under the influence of standing gravity waves.
Degree: MS, Aerospace & Mechanical Engineering (Computational
Fluid & Solid Mechanics), 2007, University of Southern California
URL: http://digitallibrary.usc.edu/cdm/compoundobject/collection/p15799coll127/id/593725/rec/359
► An overview of the equations governing surface gravity waves in linear water wave theory is presented. These equations are used to derive an expression for…
(more)
▼ An overview of the equations governing surface gravity
waves in linear water wave theory is presented. These equations are
used to derive an expression for the stream function for standing
gravity waves in a two dimensional water body of uniform depth H.
Derivatives of the stream function yield a system of coupled
ordinary differential equations describing the particle velocities
tangent to the stream function everywhere inside the water body
boundaries.; Matlab and Simulink are used to numerically integrate
the velocity equations for particle position within the boundary.
The solutions presented describe the motion of a single particle
for varying initial conditions within the boundary. The simulation
is extended to test a two mode superposition for the system of
equations, for the same set of boundary conditions, in an effort to
understand the system behavior for various modes of standing
gravity waves.
Advisors/Committee Members: Newton, Paul K. (Committee Chair), Redekopp, Larry G. (Committee Member), Pottebaum, Tait Sherman (Committee Member).
Subjects/Keywords: standing gravity waves; two dimensional fluid body
Record Details
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APA ·
Chicago ·
MLA ·
Vancouver ·
CSE |
Export
to Zotero / EndNote / Reference
Manager
APA (6th Edition):
Gates, W. (2007). A simulation of particle dynamics in a two dimensional fluid
body under the influence of standing gravity waves. (Masters Thesis). University of Southern California. Retrieved from http://digitallibrary.usc.edu/cdm/compoundobject/collection/p15799coll127/id/593725/rec/359
Chicago Manual of Style (16th Edition):
Gates, Wess. “A simulation of particle dynamics in a two dimensional fluid
body under the influence of standing gravity waves.” 2007. Masters Thesis, University of Southern California. Accessed February 26, 2021.
http://digitallibrary.usc.edu/cdm/compoundobject/collection/p15799coll127/id/593725/rec/359.
MLA Handbook (7th Edition):
Gates, Wess. “A simulation of particle dynamics in a two dimensional fluid
body under the influence of standing gravity waves.” 2007. Web. 26 Feb 2021.
Vancouver:
Gates W. A simulation of particle dynamics in a two dimensional fluid
body under the influence of standing gravity waves. [Internet] [Masters thesis]. University of Southern California; 2007. [cited 2021 Feb 26].
Available from: http://digitallibrary.usc.edu/cdm/compoundobject/collection/p15799coll127/id/593725/rec/359.
Council of Science Editors:
Gates W. A simulation of particle dynamics in a two dimensional fluid
body under the influence of standing gravity waves. [Masters Thesis]. University of Southern California; 2007. Available from: http://digitallibrary.usc.edu/cdm/compoundobject/collection/p15799coll127/id/593725/rec/359
University of Southern California
20.
Basilio, Ralph Ramos.
Controlled and uncontrolled motion in the circular,
restricted three-body problem: dynamically-natural spacecraft
formations.
Degree: PhD, Aerospace Engineering, 2007, University of Southern California
URL: http://digitallibrary.usc.edu/cdm/compoundobject/collection/p15799coll127/id/500238/rec/1644
► Spacecraft formation flying involves operating multiple spacecraft in a pre-determined geometrical shape such that the configuration yields both individual and system benefits. One example is…
(more)
▼ Spacecraft formation flying involves operating
multiple spacecraft in a pre-determined geometrical shape such that
the configuration yields both individual and system benefits. One
example is an over-flight of the same spatial position by
spacecraft in geocentric orbit with the intent to create a
complementary data set of remotely sensed observables. Another
example is controlling to a high degree of accuracy the distance
between spacecraft in heliocentric orbit to create a virtual,
large-diameter interferometer telescope. Although Keplerian orbits
provide the basic framework for general and precision spacecraft
formation flying they also present limitations. Spacecraft are
generally constrained to operate only in circular and elliptical
orbits, parabolic paths, or hyperbolic trajectories around
celestial bodies. Applying continuation methods and bifurcation
theory techniques to the circular, restricted three-body problem –
where stable and unstable periodic orbits exist around equilibrium
points – creates an environment that is more orbit rich. After
surmounting a similar challenge with test particles in the
circular, restricted three-vortex problem in fluid mechanics as a
proof-of-concept, it was shown that spacecraft traveling in
uncontrolled motion along separate and distinct planar or
three-dimensional periodic orbits could be placed in controlled
motion, i.e. a controller is enabled and later disabled at
precisely the proper positions, to have them phase-locked on a
single periodic orbit. Although it was possible to use this
controller in a resonant frequency/orbit approach to establish a
formation, it was clearly shown that a separate controller could be
used in conjunction with the first to expedite the formation
establishment process.; Creation of these dynamically natural
spacecraft formations or multi-spacecraft platforms will enable the
'loiter, synchronize/coordinate, and observe' approach for future
engineering and scientific missions where flexibility is a
top-level requirement and key to mission success.
Advisors/Committee Members: Newton, Paul K. (Committee Chair), Baxendale, Peter H. (Committee Member), Redekopp, Larry G. (Committee Member).
Subjects/Keywords: dynamics; spacecraft; formations
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Record Details
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APA ·
Chicago ·
MLA ·
Vancouver ·
CSE |
Export
to Zotero / EndNote / Reference
Manager
APA (6th Edition):
Basilio, R. R. (2007). Controlled and uncontrolled motion in the circular,
restricted three-body problem: dynamically-natural spacecraft
formations. (Doctoral Dissertation). University of Southern California. Retrieved from http://digitallibrary.usc.edu/cdm/compoundobject/collection/p15799coll127/id/500238/rec/1644
Chicago Manual of Style (16th Edition):
Basilio, Ralph Ramos. “Controlled and uncontrolled motion in the circular,
restricted three-body problem: dynamically-natural spacecraft
formations.” 2007. Doctoral Dissertation, University of Southern California. Accessed February 26, 2021.
http://digitallibrary.usc.edu/cdm/compoundobject/collection/p15799coll127/id/500238/rec/1644.
MLA Handbook (7th Edition):
Basilio, Ralph Ramos. “Controlled and uncontrolled motion in the circular,
restricted three-body problem: dynamically-natural spacecraft
formations.” 2007. Web. 26 Feb 2021.
Vancouver:
Basilio RR. Controlled and uncontrolled motion in the circular,
restricted three-body problem: dynamically-natural spacecraft
formations. [Internet] [Doctoral dissertation]. University of Southern California; 2007. [cited 2021 Feb 26].
Available from: http://digitallibrary.usc.edu/cdm/compoundobject/collection/p15799coll127/id/500238/rec/1644.
Council of Science Editors:
Basilio RR. Controlled and uncontrolled motion in the circular,
restricted three-body problem: dynamically-natural spacecraft
formations. [Doctoral Dissertation]. University of Southern California; 2007. Available from: http://digitallibrary.usc.edu/cdm/compoundobject/collection/p15799coll127/id/500238/rec/1644
University of Southern California
21.
Mayberry, John.
The effects of noise on bifurcations in circle maps with
applications to integrate-and-fire models in neural biology.
Degree: PhD, Applied Mathematics, 2008, University of Southern California
URL: http://digitallibrary.usc.edu/cdm/compoundobject/collection/p15799coll127/id/50285/rec/6665
► A stochastic bifurcation is generally defined as either a change in the number of stable invariant measures (dynamical or D-bifurcations) or a change in the…
(more)
▼ A stochastic bifurcation is generally defined as
either a change in the number of stable invariant measures
(dynamical or D-bifurcations) or a change in the qualitative shape
of invariant measures (phenomenological or P-bifurcations) for a
stochastic dynamical system. Some authors have observed that these
definitions can fail to capture important information regarding the
evolution of certain Markov Chains arising from first-passage-time
distributions of stochastic differential equations since the
definitions deal only with static information about the chain (i.e.
information regarding invariant or stationary distributions). In
this work we perform a more rigorous investigation of these
observations by studying changes to the spectra of transition
operators for two different classes of examples of Markov Chains
obtained by taking small perturbations of deterministic dynamical
systems. The first class deals with small Gaussian perturbations of
discrete time dynamical systems on the circle while the second
class arises naturally from the study of sequences of firing times
in noisy integrate-and-fire models for chemical potential in
neurons. We show that bifurcations in the deterministic system can
often lead to changes in the number of eigenvalues of the
transition operator for the corresponding perturbed process which
approach the unit circle as the noise intensity goes to 0, a
phenomenon we call a lambda-bifurcation. Although in both classes
of examples, the perturbed process always has a unique stationary
distribution, these changes in the number of eigenvalues with
modulus close to 1 can have significant effects on both the shape
of and the rate of convergence to the stationary distribution of
the process.
Advisors/Committee Members: Baxendale, Peter (Committee Chair), Ziane, Mohammed (Committee Member), Newton, Paul K. (Committee Member).
Subjects/Keywords: stochastic bifurcations; integrate-and-fire models; Markov chains; transition operators; first passage times; Gaussian perturbations; Ornstein-Uhlenbeck process
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Record Details
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APA ·
Chicago ·
MLA ·
Vancouver ·
CSE |
Export
to Zotero / EndNote / Reference
Manager
APA (6th Edition):
Mayberry, J. (2008). The effects of noise on bifurcations in circle maps with
applications to integrate-and-fire models in neural biology. (Doctoral Dissertation). University of Southern California. Retrieved from http://digitallibrary.usc.edu/cdm/compoundobject/collection/p15799coll127/id/50285/rec/6665
Chicago Manual of Style (16th Edition):
Mayberry, John. “The effects of noise on bifurcations in circle maps with
applications to integrate-and-fire models in neural biology.” 2008. Doctoral Dissertation, University of Southern California. Accessed February 26, 2021.
http://digitallibrary.usc.edu/cdm/compoundobject/collection/p15799coll127/id/50285/rec/6665.
MLA Handbook (7th Edition):
Mayberry, John. “The effects of noise on bifurcations in circle maps with
applications to integrate-and-fire models in neural biology.” 2008. Web. 26 Feb 2021.
Vancouver:
Mayberry J. The effects of noise on bifurcations in circle maps with
applications to integrate-and-fire models in neural biology. [Internet] [Doctoral dissertation]. University of Southern California; 2008. [cited 2021 Feb 26].
Available from: http://digitallibrary.usc.edu/cdm/compoundobject/collection/p15799coll127/id/50285/rec/6665.
Council of Science Editors:
Mayberry J. The effects of noise on bifurcations in circle maps with
applications to integrate-and-fire models in neural biology. [Doctoral Dissertation]. University of Southern California; 2008. Available from: http://digitallibrary.usc.edu/cdm/compoundobject/collection/p15799coll127/id/50285/rec/6665
University of Southern California
22.
Shokraneh, Houman.
N-vortex problem on a rotating sphere.
Degree: PhD, Mechanical Engineering, 2007, University of Southern California
URL: http://digitallibrary.usc.edu/cdm/compoundobject/collection/p15799coll127/id/598303/rec/4315
► The evolution, interaction, and scattering of 2N-point vortices grouped into equal and opposite pairs (N-dipoles) on a rotating unit sphere is studied. A new coordinate…
(more)
▼ The evolution, interaction, and scattering of 2N-point
vortices grouped into equal and opposite pairs (N-dipoles) on a
rotating unit sphere is studied. A new coordinate system made up of
the centers-of-vorticity and centroids associated with each dipole
is introduced. With these coordinates, the nonlinear equations for
an isolated dipole diagonalize and one directly obtains the
equation for geodesic motion on the sphere for the dipole centroid.
When two or more dipoles interact, the equations are viewed as an
interacting billiard system on the sphere – charged billiards –
with long range interactions causing the centroid trajectories to
deviate from their geodesic paths. Canonical interactions are
studied both with and without rotation. For two dipoles, the four
basic interactions are described as exchange scattering,
non-exchange scattering, loop scattering (head-on) and loop
scattering (chasing) interactions. For three or more dipoles, one
obtains a richer variety of interactions, although the interactions
identified in the two-dipole case remain fundamental.
Advisors/Committee Members: Newton, Paul K. (Committee Chair), Redekopp, Larry G. (Committee Member), Ziane, Mohammed (Committee Member).
Subjects/Keywords: N-vortex problem; dipole scattering; charged billiard equations
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APA ·
Chicago ·
MLA ·
Vancouver ·
CSE |
Export
to Zotero / EndNote / Reference
Manager
APA (6th Edition):
Shokraneh, H. (2007). N-vortex problem on a rotating sphere. (Doctoral Dissertation). University of Southern California. Retrieved from http://digitallibrary.usc.edu/cdm/compoundobject/collection/p15799coll127/id/598303/rec/4315
Chicago Manual of Style (16th Edition):
Shokraneh, Houman. “N-vortex problem on a rotating sphere.” 2007. Doctoral Dissertation, University of Southern California. Accessed February 26, 2021.
http://digitallibrary.usc.edu/cdm/compoundobject/collection/p15799coll127/id/598303/rec/4315.
MLA Handbook (7th Edition):
Shokraneh, Houman. “N-vortex problem on a rotating sphere.” 2007. Web. 26 Feb 2021.
Vancouver:
Shokraneh H. N-vortex problem on a rotating sphere. [Internet] [Doctoral dissertation]. University of Southern California; 2007. [cited 2021 Feb 26].
Available from: http://digitallibrary.usc.edu/cdm/compoundobject/collection/p15799coll127/id/598303/rec/4315.
Council of Science Editors:
Shokraneh H. N-vortex problem on a rotating sphere. [Doctoral Dissertation]. University of Southern California; 2007. Available from: http://digitallibrary.usc.edu/cdm/compoundobject/collection/p15799coll127/id/598303/rec/4315
University of Southern California
23.
Chen, Cheng-Yuan Jerry.
Multiple degree of freedom inverted pendulum dynamics:
modeling, computation, and experimentation.
Degree: PhD, Aerospace & Mechanical Engineering (Dynamics &
Control), 2009, University of Southern California
URL: http://digitallibrary.usc.edu/cdm/compoundobject/collection/p15799coll127/id/238695/rec/4275
► A pendulum is statically unstable in its upright inverted state due to the Earth's gravitional attraction which points downward. However, with proper forcing, the pendulum…
(more)
▼ A pendulum is statically unstable in its upright
inverted state due to the Earth's gravitional attraction which
points downward. However, with proper forcing, the pendulum can be
stabilized in its upright inverted state. Special interest is on
periodic vertical forcing applied to the pendulum's base to
stabilize it around the upright inverted equilibrium. Many
researchers have studied how to stabilize the system by varying
various parameters, in particular its amplitude and frequency. Most
have focused on the single degree of freedom inverted pendulum
case, which with linear assumption can be described via Mathieu's
equation. The system stability can then be characterized by Floquet
theory. Our focus is on searching for the periodic solutions inside
the linearly stable region of the pendulum's inverted state when
the pendulum is under proper periodic forcing. Our research shows
that under appropriate excitation by controlling the forcing
amplitude and frequency, the pendulum can maintain certain periodic
orbits around its inverted state which we characterize in a
systematic way.; In this thesis, we applied four different kinds of
geometric realizations of the system response: system time traces,
system phase portraits, three dimensional views of the system phase
portrait as a function of input forcing, and the system's power
spectral density diagram. By analyzing these four diagrams
simultaneously, we characterize different kinds of multi-frequency
periodic behavior around the pendulum's inverted state. To further
discuss the effect of the nonlinearity, we applied perturbation
techniques using the normalized forcing amplitude as a perturbation
parameter to carry out the approximate periodic solutions on a
single degree of freedom inverted pendulum nonlinear model.; We
also discuss the multiple degree of freedom inverted pendulum
system. Both numerical simulation and experiments were performed
and detailed comparisons are discussed. Our numerical simulations
show close qualitative agreement with experiments.
Advisors/Committee Members: Newton, Paul K. (Committee Chair), Redekopp, Larry G. (Committee Member), Flashner, Henryk (Committee Member), Jonckheere, Edmond A. (Committee Member).
Subjects/Keywords: inverted pendulum; nonlinear dynamics; parametric excitation; Mathieu'; s equation; Floquet theory
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APA (6th Edition):
Chen, C. J. (2009). Multiple degree of freedom inverted pendulum dynamics:
modeling, computation, and experimentation. (Doctoral Dissertation). University of Southern California. Retrieved from http://digitallibrary.usc.edu/cdm/compoundobject/collection/p15799coll127/id/238695/rec/4275
Chicago Manual of Style (16th Edition):
Chen, Cheng-Yuan Jerry. “Multiple degree of freedom inverted pendulum dynamics:
modeling, computation, and experimentation.” 2009. Doctoral Dissertation, University of Southern California. Accessed February 26, 2021.
http://digitallibrary.usc.edu/cdm/compoundobject/collection/p15799coll127/id/238695/rec/4275.
MLA Handbook (7th Edition):
Chen, Cheng-Yuan Jerry. “Multiple degree of freedom inverted pendulum dynamics:
modeling, computation, and experimentation.” 2009. Web. 26 Feb 2021.
Vancouver:
Chen CJ. Multiple degree of freedom inverted pendulum dynamics:
modeling, computation, and experimentation. [Internet] [Doctoral dissertation]. University of Southern California; 2009. [cited 2021 Feb 26].
Available from: http://digitallibrary.usc.edu/cdm/compoundobject/collection/p15799coll127/id/238695/rec/4275.
Council of Science Editors:
Chen CJ. Multiple degree of freedom inverted pendulum dynamics:
modeling, computation, and experimentation. [Doctoral Dissertation]. University of Southern California; 2009. Available from: http://digitallibrary.usc.edu/cdm/compoundobject/collection/p15799coll127/id/238695/rec/4275
University of Southern California
24.
Campagnola, Stefano.
New techniques in astrodynamics for moon systems
exploration.
Degree: PhD, Aerospace Engineering, 2010, University of Southern California
URL: http://digitallibrary.usc.edu/cdm/compoundobject/collection/p15799coll127/id/295664/rec/4411
► ESA and NASA scientific missions to the Jupiter and Saturn systems will answer fundamental questions on the habitability of icy worlds. The missions include unprecedented…
(more)
▼ ESA and NASA scientific missions to the Jupiter and
Saturn systems will answer fundamental questions on the
habitability of icy worlds. The missions include unprecedented
challenges, as the spacecraft will be placed in closed, stable
orbits near the surface of the moons. This thesis presents methods
to design trajectories that tour the moons and ultimately insert
the spacecraft into orbits around them, while mitigating the
mission costs and/or risks.; A first technique is the endgame, a
sequence of moon flyby preceding the orbit insertion. Historically,
the endgame is designed with two approaches with different results:
the v∞-leveraging transfer (VILT) approach leads to high-Δv
(hundreds of m/s), short time-of-flight (months) endgames, while
the multi-body approach leads to low-Δv (tens of m/s), long
time-of-flight (years) endgames. This work analyzes and develops
both approaches.; We introduce a fast design method to
automatically compute VILT endgames, which were previously designed
in an ad-hoc manner. We also derive an important simple quadrature
formula for the minimum Δv attainable with this approach. This
formula is the first important result of this work, as it provides
a lower bound for assessment studies.; We explain and develop the
complex multi-body approach introducing the Tisserand-Poincaré
(T-P) graph, which is the second important result of this work. It
provides a link between the two approaches, and shows the
intersections between low-energy trajectories around different
moons. With the T-P graph we design a five-month transfer between
low-altitude orbits at Europa and Ganymede, using almost half the
Δv of the Hohmann transfer.; We then focus on missions to low-mass
moons, like Enceladus. We show that nontangent VILT (an extension
of the traditional VILT) significantly reduce the Δv while
maintaining a satisfactory transfer time (< 4 years in the
Saturn system). With a new design method we compute a 52
gravity-assist trajectory from Titan to Enceladus. The time of
flight is 2.7 years, and the Δv is almost 10 times better then the
Titan-Enceladus Hohmann-like transfer. This trajectory and the
design method are the third important contribution of this work;
they enable a new class of missions which were previously
considered unfeasible.; Finally we study the capture problem, which
seeks chaotic trajectories with multiple orbit insertion
opportunities. We explore the solution space extending the design
techniques used by ESA for the BepiColombo mission capture to
Mercury. Such problems are better modeled in the spatial, elliptic,
restricted three-body problem, which we analyze in detail. We
define new regions of motions and to compute new families of
periodic orbits and their stability properties. This analysis is
the fourth important contribution of this work. Finally we show
that capture trajectories shadow the manifolds of special periodic
and quasi periodic orbits. This is the last important contribution
of this report, as if both explains the complex dynamics of capture
trajectories, and…
Advisors/Committee Members: Newton, Paul K. (Committee Chair), Kanso, Eva (Committee Member), Flashner, Henryk (Committee Member), Ghanem, Roger Georges (Committee Member), Baxendale, Peter H. (Committee Member).
Subjects/Keywords: elliptic, restricted, three-body problem; endgame; Jupiter moons; Saturn moons; resonant orbits; space trajectories; v-infinity leveraging; optimization
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MLA ·
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to Zotero / EndNote / Reference
Manager
APA (6th Edition):
Campagnola, S. (2010). New techniques in astrodynamics for moon systems
exploration. (Doctoral Dissertation). University of Southern California. Retrieved from http://digitallibrary.usc.edu/cdm/compoundobject/collection/p15799coll127/id/295664/rec/4411
Chicago Manual of Style (16th Edition):
Campagnola, Stefano. “New techniques in astrodynamics for moon systems
exploration.” 2010. Doctoral Dissertation, University of Southern California. Accessed February 26, 2021.
http://digitallibrary.usc.edu/cdm/compoundobject/collection/p15799coll127/id/295664/rec/4411.
MLA Handbook (7th Edition):
Campagnola, Stefano. “New techniques in astrodynamics for moon systems
exploration.” 2010. Web. 26 Feb 2021.
Vancouver:
Campagnola S. New techniques in astrodynamics for moon systems
exploration. [Internet] [Doctoral dissertation]. University of Southern California; 2010. [cited 2021 Feb 26].
Available from: http://digitallibrary.usc.edu/cdm/compoundobject/collection/p15799coll127/id/295664/rec/4411.
Council of Science Editors:
Campagnola S. New techniques in astrodynamics for moon systems
exploration. [Doctoral Dissertation]. University of Southern California; 2010. Available from: http://digitallibrary.usc.edu/cdm/compoundobject/collection/p15799coll127/id/295664/rec/4411
University of Southern California
25.
Kobilarov, Marin.
Discrete geometric motion control of autonomous
vehicles.
Degree: PhD, Computer Science (Robotics &
Automation), 2008, University of Southern California
URL: http://digitallibrary.usc.edu/cdm/compoundobject/collection/p15799coll127/id/109355/rec/2035
► The goal of this work is to develop methods to optimally control autonomous robotic vehicles in natural environments. The main contribution is the derivation of…
(more)
▼ The goal of this work is to develop methods to
optimally control autonomous robotic vehicles in natural
environments. The main contribution is the derivation of
state-space structure respecting integration and optimization
schemes for mechanical systems with symmetries, controllable shape
dynamics, and nonholonomic constraints based on the theory of
discrete mechanics. At the core of this approach lies the
discretization of variational principles of mechanics that results
in various numerical benefits previously unexplored in the area.
The resulting framework is then used as a basis for developing
optimal control methods applicable to various systems. Developed
examples include simplified models of a car, a helicopter, a
snakeboard, and a boat. The resulting algorithms are numerically
stable, preserve the mechanical geometric structure, and are
numerically competitive to existing methods. In addition, two
important extensions with view towards practical applications are
proposed. First, complex constraints are handled morerobustly using
homotopy continuation – the process of relaxing nontrivial motion
constraints arising either from complicated dynamics or from
obstacles in the environment and then smoothly transforming the
solution of such easier problem into the original one by deforming
the constraints back to their original shape. Second, the
optimality and computational efficiency of solution trajectories is
addressed by combining discrete mechanics and optimal control
(DMOC) with sampling-based roadmaps – a motion planning method
focused on global exploration of the state-space. This allows the
composition of simple locally optimal DMOC solution trajectories
into near globally optimal motions that can handle complex,
cluttered environments.
Advisors/Committee Members: Sukhatme, Gaurav S. (Committee Chair), Newton, Paul K. (Committee Member), Schaal, Stefan (Committee Member), Marsden, Jerrold (Committee Member), Desbrun, Mathieu (Committee Member).
Subjects/Keywords: robotics; motion planning; discrete mechanics; optimal control; probabilistic roadmap; homotopy; continuation
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APA ·
Chicago ·
MLA ·
Vancouver ·
CSE |
Export
to Zotero / EndNote / Reference
Manager
APA (6th Edition):
Kobilarov, M. (2008). Discrete geometric motion control of autonomous
vehicles. (Doctoral Dissertation). University of Southern California. Retrieved from http://digitallibrary.usc.edu/cdm/compoundobject/collection/p15799coll127/id/109355/rec/2035
Chicago Manual of Style (16th Edition):
Kobilarov, Marin. “Discrete geometric motion control of autonomous
vehicles.” 2008. Doctoral Dissertation, University of Southern California. Accessed February 26, 2021.
http://digitallibrary.usc.edu/cdm/compoundobject/collection/p15799coll127/id/109355/rec/2035.
MLA Handbook (7th Edition):
Kobilarov, Marin. “Discrete geometric motion control of autonomous
vehicles.” 2008. Web. 26 Feb 2021.
Vancouver:
Kobilarov M. Discrete geometric motion control of autonomous
vehicles. [Internet] [Doctoral dissertation]. University of Southern California; 2008. [cited 2021 Feb 26].
Available from: http://digitallibrary.usc.edu/cdm/compoundobject/collection/p15799coll127/id/109355/rec/2035.
Council of Science Editors:
Kobilarov M. Discrete geometric motion control of autonomous
vehicles. [Doctoral Dissertation]. University of Southern California; 2008. Available from: http://digitallibrary.usc.edu/cdm/compoundobject/collection/p15799coll127/id/109355/rec/2035
University of Southern California
26.
Vicol, Vlad Cristian.
Analyticity and Gevrey-class regularity for the Euler
equations.
Degree: PhD, Mathematics, 2010, University of Southern California
URL: http://digitallibrary.usc.edu/cdm/compoundobject/collection/p15799coll127/id/351483/rec/821
► The Euler equations are the classical model for the motion of an incompressible inviscid homogeneous fluid. This thesis addresses geometric qualitative properties of smooth solutions…
(more)
▼ The Euler equations are the classical model for the
motion of an incompressible inviscid homogeneous fluid. This thesis
addresses geometric qualitative properties of smooth solutions to
the Euler equations, namely the persistence of analyticity and
Gevrey-class regularity on domains with smooth boundary.; The
structure of the spectrum of solutions to the three-dimensional
Euler equations is a problem of fundamental interest in turbulence
theory. The size of the uniform real-analyticity radius of the
solution provides an estimate for the scale below which the Fourier
coefficients decay exponentially; it moreover gives the rate of
this exponential decay. This thesis also addresses the problem of
finding sharp lower bounds for the uniform real-analyticity and
Gevrey-class regularity radius of the solutions. We prove that the
rate of decay of the radius depends at most exponentially on the
supremum of the velocity gradient, and algebraically on the higher
Sobolev norms of the solution.
Advisors/Committee Members: Kukavica, Igor (Committee Chair), Friedlander, Susan (Committee Member), Lototsky, Sergey Vladimir (Committee Member), Newton, Paul K. (Committee Member), Ziane, Mohammed (Committee Member).
Subjects/Keywords: analyticity radius; Euler equations; Gevrey-class
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APA ·
Chicago ·
MLA ·
Vancouver ·
CSE |
Export
to Zotero / EndNote / Reference
Manager
APA (6th Edition):
Vicol, V. C. (2010). Analyticity and Gevrey-class regularity for the Euler
equations. (Doctoral Dissertation). University of Southern California. Retrieved from http://digitallibrary.usc.edu/cdm/compoundobject/collection/p15799coll127/id/351483/rec/821
Chicago Manual of Style (16th Edition):
Vicol, Vlad Cristian. “Analyticity and Gevrey-class regularity for the Euler
equations.” 2010. Doctoral Dissertation, University of Southern California. Accessed February 26, 2021.
http://digitallibrary.usc.edu/cdm/compoundobject/collection/p15799coll127/id/351483/rec/821.
MLA Handbook (7th Edition):
Vicol, Vlad Cristian. “Analyticity and Gevrey-class regularity for the Euler
equations.” 2010. Web. 26 Feb 2021.
Vancouver:
Vicol VC. Analyticity and Gevrey-class regularity for the Euler
equations. [Internet] [Doctoral dissertation]. University of Southern California; 2010. [cited 2021 Feb 26].
Available from: http://digitallibrary.usc.edu/cdm/compoundobject/collection/p15799coll127/id/351483/rec/821.
Council of Science Editors:
Vicol VC. Analyticity and Gevrey-class regularity for the Euler
equations. [Doctoral Dissertation]. University of Southern California; 2010. Available from: http://digitallibrary.usc.edu/cdm/compoundobject/collection/p15799coll127/id/351483/rec/821
University of Southern California
27.
Chamoun, George C.
Vortex lattice theory: a linear algebra approach.
Degree: PhD, Aerospace & Mechanical Engineering (Dynamics &
Control), 2008, University of Southern California
URL: http://digitallibrary.usc.edu/cdm/compoundobject/collection/p15799coll127/id/199701/rec/7863
► Vortex lattices are prevalent in a large class of physical settings that are characterized by different mathematical models. We present a coherent and generalized Hamiltonian…
(more)
▼ Vortex lattices are prevalent in a large class of
physical settings that are characterized by different mathematical
models. We present a coherent and generalized Hamiltonian fluid
mechanics-based formulation that reduces all vortex lattices into a
classic problem in linear algebra for a non-normal matrix A. Via
Singular Value Decomposition (SVD), the solution lies in the null
space of the matrix (i.e., we require nullity(A) > 0) as well as
the distribution of its singular values. We demonstrate that this
approach provides a good model for various types of vortex
lattices, and makes it possible to extract a rich amount of
information on them. The contributions of this thesis can be
classified into four main points. The first is asymmetric
equilibria. A "Brownian ratchet" construct was used which converged
to asymmetric equilibria via a random walk scheme that utilized the
smallest singular value of A. Distances between configurations and
equilibria were measured using the Frobenius norm . F and 2-norm .
2, and conclusions were made on the density of equilibria within
the general configuration space. The second contribution used
Shannon Entropy, which we interpret as a scalar measure of the
robustness, or likelihood of lattices to occur in a physical
setting. Third, an analytic model was produced for vortex street
patterns on the sphere by using SVD in conjunction with expressions
for the center of vorticity vector and angular velocity.
Equilibrium curves within the configuration space were presented as
a function of the geometry, and pole vortices were shown to have a
critical role in the formation and destruction of vortex streets.
The fourth contribution entailed a more complete perspective of the
streamline topology of vortex streets, linking the bifurcations to
critical points on the equilibrium curves.
Advisors/Committee Members: Newton, Paul K. (Committee Chair), Kukavica, Igor (Committee Member), Browand, Frederick (Committee Member), Friedlander, Susan (Committee Member), Ghanem, Roger (Committee Member).
Subjects/Keywords: vortex; Hamiltonian; lattice; SVD; fluid mechanics
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❌
APA ·
Chicago ·
MLA ·
Vancouver ·
CSE |
Export
to Zotero / EndNote / Reference
Manager
APA (6th Edition):
Chamoun, G. C. (2008). Vortex lattice theory: a linear algebra approach. (Doctoral Dissertation). University of Southern California. Retrieved from http://digitallibrary.usc.edu/cdm/compoundobject/collection/p15799coll127/id/199701/rec/7863
Chicago Manual of Style (16th Edition):
Chamoun, George C. “Vortex lattice theory: a linear algebra approach.” 2008. Doctoral Dissertation, University of Southern California. Accessed February 26, 2021.
http://digitallibrary.usc.edu/cdm/compoundobject/collection/p15799coll127/id/199701/rec/7863.
MLA Handbook (7th Edition):
Chamoun, George C. “Vortex lattice theory: a linear algebra approach.” 2008. Web. 26 Feb 2021.
Vancouver:
Chamoun GC. Vortex lattice theory: a linear algebra approach. [Internet] [Doctoral dissertation]. University of Southern California; 2008. [cited 2021 Feb 26].
Available from: http://digitallibrary.usc.edu/cdm/compoundobject/collection/p15799coll127/id/199701/rec/7863.
Council of Science Editors:
Chamoun GC. Vortex lattice theory: a linear algebra approach. [Doctoral Dissertation]. University of Southern California; 2008. Available from: http://digitallibrary.usc.edu/cdm/compoundobject/collection/p15799coll127/id/199701/rec/7863
University of Southern California
28.
Das, Sonjoy.
Model, identification & analysis of complex stochastic
systems: applications in stochastic partial differential equations
and multiscale mechanics.
Degree: PhD, Civil Engineering, 2008, University of Southern California
URL: http://digitallibrary.usc.edu/cdm/compoundobject/collection/p15799coll127/id/79306/rec/4117
► This dissertation focusses on characterization, identification and analysis of stochastic systems. A stochastic system refers to a physical phenomenon with inherent uncertainty in it, and…
(more)
▼ This dissertation focusses on characterization,
identification and analysis of stochastic systems. A stochastic
system refers to a physical phenomenon with inherent uncertainty in
it, and is typically characterized by a governing conservation law
or partial differential equation (PDE) with some of its parameters
interpreted as random processes, or/and a model-free random matrix
operator. In this work, three data-driven approaches are first
introduced to characterize and construct consistent probability
models of non-stationary and non-Gaussian random processes or
fields within the polynomial chaos (PC) formalism. The resulting PC
representations would be useful to probabilistically characterize
the system input-output relationship for a variety of applications.
Second, a novel hybrid physics- and data-based approach is proposed
to characterize a complex stochastic systems by using random matrix
theory. An application of this approach to multiscale mechanics
problems is also presented. In this context, a new homogenization
scheme, referred here as "nonparametric" homogenization, is
introduced. Also discussed in this work is a simple,
computationally efficient and experiment-friendly coupling scheme
based on frequency response function. This coupling scheme would be
useful for analysis of a complex stochastic system consisting of
several subsystems characterized by, e.g., stochastic PDEs or/and
model-free random matrix operators. While chapter 1 sets up the
stage for the work presented in this dissertation, further
highlight of each chapter is included at the outset of the
respective chapter.
Advisors/Committee Members: Ghanem, Roger (Committee Chair), Masri, Sami F. (Committee Member), Johnson, Erik A. (Committee Member), Bardet, Jean-Pierre (Committee Member), Newton, Paul K. (Committee Member).
Subjects/Keywords: random matrix theory; polynomial chaos representation; homogenization; multiscale mechanics; data uncertainty; modeling uncertainty; non-Gaussian and nonstationary random processes and
fields
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Record Details
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❌
APA ·
Chicago ·
MLA ·
Vancouver ·
CSE |
Export
to Zotero / EndNote / Reference
Manager
APA (6th Edition):
Das, S. (2008). Model, identification & analysis of complex stochastic
systems: applications in stochastic partial differential equations
and multiscale mechanics. (Doctoral Dissertation). University of Southern California. Retrieved from http://digitallibrary.usc.edu/cdm/compoundobject/collection/p15799coll127/id/79306/rec/4117
Chicago Manual of Style (16th Edition):
Das, Sonjoy. “Model, identification & analysis of complex stochastic
systems: applications in stochastic partial differential equations
and multiscale mechanics.” 2008. Doctoral Dissertation, University of Southern California. Accessed February 26, 2021.
http://digitallibrary.usc.edu/cdm/compoundobject/collection/p15799coll127/id/79306/rec/4117.
MLA Handbook (7th Edition):
Das, Sonjoy. “Model, identification & analysis of complex stochastic
systems: applications in stochastic partial differential equations
and multiscale mechanics.” 2008. Web. 26 Feb 2021.
Vancouver:
Das S. Model, identification & analysis of complex stochastic
systems: applications in stochastic partial differential equations
and multiscale mechanics. [Internet] [Doctoral dissertation]. University of Southern California; 2008. [cited 2021 Feb 26].
Available from: http://digitallibrary.usc.edu/cdm/compoundobject/collection/p15799coll127/id/79306/rec/4117.
Council of Science Editors:
Das S. Model, identification & analysis of complex stochastic
systems: applications in stochastic partial differential equations
and multiscale mechanics. [Doctoral Dissertation]. University of Southern California; 2008. Available from: http://digitallibrary.usc.edu/cdm/compoundobject/collection/p15799coll127/id/79306/rec/4117
. 
Open Access Theses and Dissertations