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Penn State University
1.
Bakshi, Alok.
Equivariant Asymptotic Morphisms for the Symplectic Plane.
Degree: 2019, Penn State University
URL: https://submit-etda.libraries.psu.edu/catalog/16554aub238
► In this thesis we study equivariant asymptotic morphisms from the C_0 functions on the symplectic plane into the C*-algebra of compact operators. We shall construct…
(more)
▼ In this thesis we study equivariant asymptotic morphisms from the
C_0 functions on the symplectic plane into the C*-algebra of compact
operators. We shall construct two asymptotic morphisms that are
asymptotically equivariant for two different groups of symplectomorphisms, and prove (with additional hypotheses) that there does not
exist any asymptotic morphism that is asymptotically equivariant for
all symplectomorphisms. Furthermore, we shall prove that there exists a unique asymptotic morphism (with additional hypothesis on
equivariance) that is equivariant for the group of affine symplectomorphisms of the plane.
Advisors/Committee Members: Nigel David Higson, Dissertation Advisor/Co-Advisor, Chair%22%29&pagesize-30">
Mark Levi,
Committee Chair/
Co-
Chair,
Paul Frank Baum, Committee Member,
Nathanial Patrick Brown, Committee Member,
Martin Bojowald, Outside Member.
Subjects/Keywords: Quantization; Asymptotic Morphism
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APA ·
Chicago ·
MLA ·
Vancouver ·
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APA (6th Edition):
Bakshi, A. (2019). Equivariant Asymptotic Morphisms for the Symplectic Plane. (Thesis). Penn State University. Retrieved from https://submit-etda.libraries.psu.edu/catalog/16554aub238
Note: this citation may be lacking information needed for this citation format:
Not specified: Masters Thesis or Doctoral Dissertation
Chicago Manual of Style (16th Edition):
Bakshi, Alok. “Equivariant Asymptotic Morphisms for the Symplectic Plane.” 2019. Thesis, Penn State University. Accessed April 19, 2021.
https://submit-etda.libraries.psu.edu/catalog/16554aub238.
Note: this citation may be lacking information needed for this citation format:
Not specified: Masters Thesis or Doctoral Dissertation
MLA Handbook (7th Edition):
Bakshi, Alok. “Equivariant Asymptotic Morphisms for the Symplectic Plane.” 2019. Web. 19 Apr 2021.
Vancouver:
Bakshi A. Equivariant Asymptotic Morphisms for the Symplectic Plane. [Internet] [Thesis]. Penn State University; 2019. [cited 2021 Apr 19].
Available from: https://submit-etda.libraries.psu.edu/catalog/16554aub238.
Note: this citation may be lacking information needed for this citation format:
Not specified: Masters Thesis or Doctoral Dissertation
Council of Science Editors:
Bakshi A. Equivariant Asymptotic Morphisms for the Symplectic Plane. [Thesis]. Penn State University; 2019. Available from: https://submit-etda.libraries.psu.edu/catalog/16554aub238
Note: this citation may be lacking information needed for this citation format:
Not specified: Masters Thesis or Doctoral Dissertation

Penn State University
2.
Hughes, David Rhodri.
Entropy of the Lorentz Gas and Other Results.
Degree: 2019, Penn State University
URL: https://submit-etda.libraries.psu.edu/catalog/16864drh272
► In Chapter 1 we provide relevant definitions and background material on Dynamical Systems and Chaotic Billiards. In Chapter 2 we prove that the topological entropy…
(more)
▼ In Chapter 1 we provide relevant definitions and background material on Dynamical Systems and Chaotic Billiards.
In Chapter 2 we prove that the topological entropy of the Lorentz gas billiard can take any real positive value if the side lengths of the tables are changed (while the area is held fixed). On the other hand, the metric entropy can take any value between 0 and some constant bound M as the side lengths change. We also show that he ratio of the two entropies can take any value in the interval (0,\frac{1}{2}). It is also shown that both continuously depend on the radius of the circular scatterer.
In Chapter 3 we give a new proof of the Gauss-Bonnet Theorem using the inclusion-exclusion formula.
In Chapter 4 we show that the ratio of the metric entropy to the topological entropy of the geodesic flow of a surface of negative curvature can be made to take any value in (0,1) by taking a time change of the flow.
Finally, in Chapter 5 we have a collection of results on the asymptotic vanishing of the topological entropy of the Bunimovich stadium billiard as the table gets longer and thinner (again, volume is held constant), and that any plane curve homeomorphic to the circle can be recovered from its incidence data with a family of lattices.
Advisors/Committee Members: Dmitri Yu Burago, Dissertation Advisor/Co-Advisor, Chair%22%29&pagesize-30">
Mark Levi,
Committee Chair/
Co-
Chair,
Federico Juan Rodriguez Hertz, Committee Member,
Mark Levi, Committee Member,
Martin Bojowald, Outside Member.
Subjects/Keywords: Dynamical Systems; Blliards; Entropy
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❌
APA ·
Chicago ·
MLA ·
Vancouver ·
CSE |
Export
to Zotero / EndNote / Reference
Manager
APA (6th Edition):
Hughes, D. R. (2019). Entropy of the Lorentz Gas and Other Results. (Thesis). Penn State University. Retrieved from https://submit-etda.libraries.psu.edu/catalog/16864drh272
Note: this citation may be lacking information needed for this citation format:
Not specified: Masters Thesis or Doctoral Dissertation
Chicago Manual of Style (16th Edition):
Hughes, David Rhodri. “Entropy of the Lorentz Gas and Other Results.” 2019. Thesis, Penn State University. Accessed April 19, 2021.
https://submit-etda.libraries.psu.edu/catalog/16864drh272.
Note: this citation may be lacking information needed for this citation format:
Not specified: Masters Thesis or Doctoral Dissertation
MLA Handbook (7th Edition):
Hughes, David Rhodri. “Entropy of the Lorentz Gas and Other Results.” 2019. Web. 19 Apr 2021.
Vancouver:
Hughes DR. Entropy of the Lorentz Gas and Other Results. [Internet] [Thesis]. Penn State University; 2019. [cited 2021 Apr 19].
Available from: https://submit-etda.libraries.psu.edu/catalog/16864drh272.
Note: this citation may be lacking information needed for this citation format:
Not specified: Masters Thesis or Doctoral Dissertation
Council of Science Editors:
Hughes DR. Entropy of the Lorentz Gas and Other Results. [Thesis]. Penn State University; 2019. Available from: https://submit-etda.libraries.psu.edu/catalog/16864drh272
Note: this citation may be lacking information needed for this citation format:
Not specified: Masters Thesis or Doctoral Dissertation

Penn State University
3.
He, Andong.
Conformal mapping and variational methods for interfacial dynamics in fluids
.
Degree: 2011, Penn State University
URL: https://submit-etda.libraries.psu.edu/catalog/12053
► In this thesis we will be considering three problems in fluid dynamics whose common features involve free surface dynamics. In a two-dimensional space, these problems…
(more)
▼ In this thesis we will be considering three problems in fluid dynamics whose common features involve free surface dynamics. In a two-dimensional space, these problems can be conveniently formulated by conformal mapping methods. The history and status quo of application of conformal mapping methods to fluid dynamics are briefly discussed in Chapter 1.
In Chapter 2 we study theoretically and experimentally the deformation of a free surface between two fluids in a gravitational field, due to a jet in the lighter fluid impinging at right angles to the surface. A mathematical model is built using the method of conformal mapping. The strength of our method lies in its general applicability to analytically study the interface between two fluids in a gravitational field, one of which has an arbitrary potential velocity field, while the other is assumed to be motionless. An asymptotic solution is derived for the cavity shape with the density ratio of fluids as the small expansion parameter.
We present in Chapter 3 an unsteady nonlinear Darcy's equation which includes inertial effects for flows in a Hele-Shaw cell, and discuss the conditions under which it reduces to the classical Darcy’s law. In the absence of surface tension we derive a generalized Polubarinova-Galin equation in a circular geometry, using the method of conformal mapping. The linear stability of the base-flow
state is examined by perturbing the corresponding conformal map. We show that inertia always tends to stabilize the interface, regardless of whether a less viscous fluid is displacing a more viscous fluid or vice versa.
In Chapter 4 a mathematical model of reactive Hele-Shaw flows when two immiscible fluids meet, chemically react and form an elastic interface is considered. This reaction brings about significant changes in the interfacial tension, which is crucial in determining the stability of such a system. We model this by treating the interface as an elastic membrane whose bending stiffness depends on the local curvature. We derive from energy variation a dynamic boundary condition at the interface. An analysis of the roles that several parameters play in affecting the stability is performed. We are able to qualitatively account for the anomalous fingering instabilities that have been seen experimentally.
Advisors/Committee Members: Mark Levi, Dissertation Advisor/Co-Advisor, Chair%22%29&pagesize-30">Andrew Leonard Belmonte,
Committee Chair/
Co-
Chair,
Chair%22%29&pagesize-30">Mark Levi, Committee Chair/Co-Chair,
Qiang Du, Committee Member,
Diane Marie Henderson, Committee Member,
Tong Qiu, Committee Member.
Subjects/Keywords: interfacial dynamics; fluid dynamics; conformal mapping
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❌
APA ·
Chicago ·
MLA ·
Vancouver ·
CSE |
Export
to Zotero / EndNote / Reference
Manager
APA (6th Edition):
He, A. (2011). Conformal mapping and variational methods for interfacial dynamics in fluids
. (Thesis). Penn State University. Retrieved from https://submit-etda.libraries.psu.edu/catalog/12053
Note: this citation may be lacking information needed for this citation format:
Not specified: Masters Thesis or Doctoral Dissertation
Chicago Manual of Style (16th Edition):
He, Andong. “Conformal mapping and variational methods for interfacial dynamics in fluids
.” 2011. Thesis, Penn State University. Accessed April 19, 2021.
https://submit-etda.libraries.psu.edu/catalog/12053.
Note: this citation may be lacking information needed for this citation format:
Not specified: Masters Thesis or Doctoral Dissertation
MLA Handbook (7th Edition):
He, Andong. “Conformal mapping and variational methods for interfacial dynamics in fluids
.” 2011. Web. 19 Apr 2021.
Vancouver:
He A. Conformal mapping and variational methods for interfacial dynamics in fluids
. [Internet] [Thesis]. Penn State University; 2011. [cited 2021 Apr 19].
Available from: https://submit-etda.libraries.psu.edu/catalog/12053.
Note: this citation may be lacking information needed for this citation format:
Not specified: Masters Thesis or Doctoral Dissertation
Council of Science Editors:
He A. Conformal mapping and variational methods for interfacial dynamics in fluids
. [Thesis]. Penn State University; 2011. Available from: https://submit-etda.libraries.psu.edu/catalog/12053
Note: this citation may be lacking information needed for this citation format:
Not specified: Masters Thesis or Doctoral Dissertation

Penn State University
4.
Ai , Chong.
effect of tidal dissipation on the motion of celestial bodies.
Degree: 2012, Penn State University
URL: https://submit-etda.libraries.psu.edu/catalog/16233
► Tidal effects in celestial bodies manifest themselves in many ways. Tides cause periodic changes in sea and ground levels, they affect the length of day,…
(more)
▼ Tidal effects in celestial bodies manifest themselves in many ways. Tides cause periodic changes in sea and ground levels, they affect the length of day, and even volcanic activity. Tides cause effects on the scale larger than that of an individual body, affecting entire orbits of planets and moons.
In this thesis we focus on the effect of tides on the dynamics of orbits, leaving aside internal effects of tides on planets. This thesis addresses a gap in the literature. On the one hand, the mathematical theory of celestial mechanics is a classical subject going back to Newton, and it reached a high level of development by people like Legendre, Lagrange, Laplace, Jacobi, Poincare, Moser, Arnold and others. Without exception (to our knowledge) this theory treats planets as point masses subject to Newtonian gravitational attraction, and without account for tidal effects. On the other hand, astronomers take more realistic models of the planets, but get few if any rigorous results. In this thesis we study problems which fall in the gap between these two approaches: they do include tidal dissipation on the one hand, making them more realistic than the classical system which completely ignores them, but we make this dissipation simple enough to be tractable mathematically.
To build dissipation into the equations of motion, we use the Routh method of introducing dissipation into Lagrangian equations of motion. According to this method, to write the equations of motion one only needs, in addition to the Lagrangian of the system, also the so – called Routh dissipation function: the power dissipated as a function of generalized coordinates and generalized velocities of the system. We choose a simple class of dissipation functions, leaving more general questions for future work.
In this thesis we study tidal dissipation in two problems: the Kepler problem, and the restricted three – body problem, and ask the question of the long – term behavior of these problems with dissipation. There are two main results. First, we show that all the negative energy solutions of Kepler's problem approach circular motion, and do so with an additional interesting feature.
The second main result of this thesis deals with the restricted three body problem with dissipation. We show that the Lagrangian equilateral configurations become unstable due to tidal dissipation. This is a rather surprising result of dissipation causing instability. In addition, we show that almost all (in the Lebesgue sense) motions end either in a collision or an escape to infinity.
The restricted three body problem, which is infinitely delicate in the classical conservative case, thus admits an essentially complete analysis if one introduces an arbitrarily small dissipation.
Advisors/Committee Members: Mark Levi, Dissertation Advisor/Co-Advisor, Chair%22%29&pagesize-30">
Mark Levi,
Committee Chair/
Co-
Chair,
Sergei Tabachnikov, Committee Member,
Diane Marie Henderson, Committee Member,
Milton Walter Cole, Committee Member.
Subjects/Keywords: tidal effect; tidal dissipation; 3-body problem; dynamical systems; celestial bodies; stability
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❌
APA ·
Chicago ·
MLA ·
Vancouver ·
CSE |
Export
to Zotero / EndNote / Reference
Manager
APA (6th Edition):
Ai , C. (2012). effect of tidal dissipation on the motion of celestial bodies. (Thesis). Penn State University. Retrieved from https://submit-etda.libraries.psu.edu/catalog/16233
Note: this citation may be lacking information needed for this citation format:
Not specified: Masters Thesis or Doctoral Dissertation
Chicago Manual of Style (16th Edition):
Ai , Chong. “effect of tidal dissipation on the motion of celestial bodies.” 2012. Thesis, Penn State University. Accessed April 19, 2021.
https://submit-etda.libraries.psu.edu/catalog/16233.
Note: this citation may be lacking information needed for this citation format:
Not specified: Masters Thesis or Doctoral Dissertation
MLA Handbook (7th Edition):
Ai , Chong. “effect of tidal dissipation on the motion of celestial bodies.” 2012. Web. 19 Apr 2021.
Vancouver:
Ai C. effect of tidal dissipation on the motion of celestial bodies. [Internet] [Thesis]. Penn State University; 2012. [cited 2021 Apr 19].
Available from: https://submit-etda.libraries.psu.edu/catalog/16233.
Note: this citation may be lacking information needed for this citation format:
Not specified: Masters Thesis or Doctoral Dissertation
Council of Science Editors:
Ai C. effect of tidal dissipation on the motion of celestial bodies. [Thesis]. Penn State University; 2012. Available from: https://submit-etda.libraries.psu.edu/catalog/16233
Note: this citation may be lacking information needed for this citation format:
Not specified: Masters Thesis or Doctoral Dissertation

Penn State University
5.
Saadatpour Moghaddam, Assieh.
Dynamic Modeling of Biological and Physical Systems.
Degree: 2012, Penn State University
URL: https://submit-etda.libraries.psu.edu/catalog/15348
► Given the complexity and interactive nature of many biological and physical systems, constructing informative and coherent network models of these systems and subsequently developing efficient…
(more)
▼ Given the complexity and interactive nature of many biological and physical systems, constructing informative and coherent network models of these systems and subsequently developing efficient approaches to analyze the models is of utmost importance. The combination of network modeling and dynamic analysis enables one to investigate the behavior of the underlying system as a whole and to make experimentally testable predictions about less-understood aspects of the processes involved. This dissertation reports on a combination of theoretical and computational approaches for network-based dynamic analysis of several highly interactive biological and physical systems. Various dynamic modeling approaches, ranging from Boolean to continuous models, are employed to carry out a systematic analysis of the long-term behavior (attractors) of the respective systems. First, we employ a Boolean dynamic framework to model two biological systems: the abscisic acid (ABA) signal transduction network in plants and the T-LGL leukemia signaling network in humans. Given the relatively large number of components in these networks, we develop a network reduction technique leading to a significant decrease in the computational burden associated with the
state space analysis of Boolean models while preserving essential dynamical features. For the ABA system, we utilize a synchronous and three different asynchronous Boolean dynamic methods and compare the attractors of the system and their basins of attraction for both unperturbed and perturbed systems. For the T-LGL signaling network, the best-performing asynchronous Boolean dynamic method identified in our first study is used to determine the disease states of the components of the system and to propose several novel candidate therapeutic targets. Next, we apply a Boolean-continuous hybrid (piecewise linear) dynamic formalism to model a pathogen-immune system interaction network, and present the results of a comparative study of the dynamic characteristics of Boolean and hybrid models. Finally, we rely on continuous dynamic modeling to prove the existence of traveling wave solutions in a better-characterized physical system, namely, a chain of coupled pendula in the presence of damping and forcing. Overall, the theoretical and computational approaches developed in this dissertation provide a bird’s-eye-view of the avenues available for model-driven analysis of complex biological and physical systems.
Advisors/Committee Members: Reka Z Albert, Dissertation Advisor/Co-Advisor, Mark Levi, Dissertation Advisor/Co-Advisor, Chair%22%29&pagesize-30">Reka Z Albert,
Committee Chair/
Co-
Chair,
Chair%22%29&pagesize-30">Mark Levi, Committee Chair/Co-Chair,
Andrew Leonard Belmonte, Committee Member,
Timothy Reluga, Committee Member,
John Fricks, Committee Member.
Subjects/Keywords: Dynamic modeling; Biological networks; Boolean models; Piecewise linear models
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❌
APA ·
Chicago ·
MLA ·
Vancouver ·
CSE |
Export
to Zotero / EndNote / Reference
Manager
APA (6th Edition):
Saadatpour Moghaddam, A. (2012). Dynamic Modeling of Biological and Physical Systems. (Thesis). Penn State University. Retrieved from https://submit-etda.libraries.psu.edu/catalog/15348
Note: this citation may be lacking information needed for this citation format:
Not specified: Masters Thesis or Doctoral Dissertation
Chicago Manual of Style (16th Edition):
Saadatpour Moghaddam, Assieh. “Dynamic Modeling of Biological and Physical Systems.” 2012. Thesis, Penn State University. Accessed April 19, 2021.
https://submit-etda.libraries.psu.edu/catalog/15348.
Note: this citation may be lacking information needed for this citation format:
Not specified: Masters Thesis or Doctoral Dissertation
MLA Handbook (7th Edition):
Saadatpour Moghaddam, Assieh. “Dynamic Modeling of Biological and Physical Systems.” 2012. Web. 19 Apr 2021.
Vancouver:
Saadatpour Moghaddam A. Dynamic Modeling of Biological and Physical Systems. [Internet] [Thesis]. Penn State University; 2012. [cited 2021 Apr 19].
Available from: https://submit-etda.libraries.psu.edu/catalog/15348.
Note: this citation may be lacking information needed for this citation format:
Not specified: Masters Thesis or Doctoral Dissertation
Council of Science Editors:
Saadatpour Moghaddam A. Dynamic Modeling of Biological and Physical Systems. [Thesis]. Penn State University; 2012. Available from: https://submit-etda.libraries.psu.edu/catalog/15348
Note: this citation may be lacking information needed for this citation format:
Not specified: Masters Thesis or Doctoral Dissertation
.