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Texas A&M University
1.
Owusu Kwaakwah, Emma.
Implementation of Algorithms Related to Convex Hulls and Tropical Varieties for Visualization.
Degree: MS, Mathematics, 2016, Texas A&M University
URL: http://hdl.handle.net/1969.1/157790 
► The study of the zero sets of polynomials is one of the main themes in Algebraic Geometry. In the study of the zero sets, the…
(more)
▼ The study of the zero sets of polynomials is one of the main themes in Algebraic Geometry. In the study of the zero sets, the Archimedean tropical variety can be a helpful tool in approximating the norms of the zeros of a given polynomial.
The main goal of this thesis is to implement the algorithm for graphically constructing the Archimedean tropical variety of polynomials in two variables (bivariate polynomials) using Sage, a free open-source mathematics software. In the process of graphically constructing the Archimedean tropical variety of bivariate polynomials, the convex hull of points in 3D will be required. This will lead us to write a Sage function based on methods and functions in Sage that will return the convex hull of points in 3D in Sage.
Advisors/Committee Members: Rojas, J. Maurice (advisor), Rowell, Eric (committee member), Stiller, Peter (committee member), Mortari, Daniele (committee member).
Subjects/Keywords: ArchTrop; Archnewt; Amoeba; Newton polygon; Archimedean tropical variety
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APA (6th Edition):
Owusu Kwaakwah, E. (2016). Implementation of Algorithms Related to Convex Hulls and Tropical Varieties for Visualization. (Masters Thesis). Texas A&M University. Retrieved from http://hdl.handle.net/1969.1/157790
Chicago Manual of Style (16th Edition):
Owusu Kwaakwah, Emma. “Implementation of Algorithms Related to Convex Hulls and Tropical Varieties for Visualization.” 2016. Masters Thesis, Texas A&M University. Accessed March 07, 2021.
http://hdl.handle.net/1969.1/157790.
MLA Handbook (7th Edition):
Owusu Kwaakwah, Emma. “Implementation of Algorithms Related to Convex Hulls and Tropical Varieties for Visualization.” 2016. Web. 07 Mar 2021.
Vancouver:
Owusu Kwaakwah E. Implementation of Algorithms Related to Convex Hulls and Tropical Varieties for Visualization. [Internet] [Masters thesis]. Texas A&M University; 2016. [cited 2021 Mar 07].
Available from: http://hdl.handle.net/1969.1/157790.
Council of Science Editors:
Owusu Kwaakwah E. Implementation of Algorithms Related to Convex Hulls and Tropical Varieties for Visualization. [Masters Thesis]. Texas A&M University; 2016. Available from: http://hdl.handle.net/1969.1/157790
Texas A&M University
2.
Phillipson, Kaitlyn Rose.
Quantitative Aspects of Sums of Squares and Sparse Polynomial Systems.
Degree: PhD, Mathematics, 2016, Texas A&M University
URL: http://hdl.handle.net/1969.1/157880
► Computational algebraic geometry is the study of roots of polynomials and polynomial systems. We are familiar with the notion of degree, but there are other…
(more)
▼ Computational algebraic geometry is the study of roots of polynomials and polynomial systems. We are familiar with the notion of degree, but there are other ways to consider a polynomial: How many variables does it have? How many terms does it have? Considering the sparsity of a polynomial means we pay special attention to the number of terms. One can sometimes profit greatly by making use of sparsity when doing computations by utilizing tools from linear programming and integer matrix factorization. This thesis investigates several problems from the point of view of sparsity. Consider a system F of n polynomials over n variables, with a total of n + k distinct exponent vectors over any local field L. We discuss conjecturally tight bounds on the maximal number of non-degenerate roots F can have over L, with all coordinates having fixed phase, as a function of n, k, and L only. In particular, we give new explicit systems with number of roots approaching the best known upper bounds. We also give a complete classification for when an n-variate n + 2-nomial positive polynomial can be written as a sum of squares of polynomials. Finally, we investigate the problem of approximating roots of polynomials from the viewpoint of sparsity by developing a method of approximating roots for binomial systems that runs more efficiently than other current methods. These results serve as building blocks for proving results for less sparse polynomial systems.
Advisors/Committee Members: Rojas, J. Maurice (advisor), Matusevich, Laura (committee member), Stiller, Peter (committee member), Mortari, Daniele (committee member).
Subjects/Keywords: sparsity; sums of squares; approximations
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APA (6th Edition):
Phillipson, K. R. (2016). Quantitative Aspects of Sums of Squares and Sparse Polynomial Systems. (Doctoral Dissertation). Texas A&M University. Retrieved from http://hdl.handle.net/1969.1/157880
Chicago Manual of Style (16th Edition):
Phillipson, Kaitlyn Rose. “Quantitative Aspects of Sums of Squares and Sparse Polynomial Systems.” 2016. Doctoral Dissertation, Texas A&M University. Accessed March 07, 2021.
http://hdl.handle.net/1969.1/157880.
MLA Handbook (7th Edition):
Phillipson, Kaitlyn Rose. “Quantitative Aspects of Sums of Squares and Sparse Polynomial Systems.” 2016. Web. 07 Mar 2021.
Vancouver:
Phillipson KR. Quantitative Aspects of Sums of Squares and Sparse Polynomial Systems. [Internet] [Doctoral dissertation]. Texas A&M University; 2016. [cited 2021 Mar 07].
Available from: http://hdl.handle.net/1969.1/157880.
Council of Science Editors:
Phillipson KR. Quantitative Aspects of Sums of Squares and Sparse Polynomial Systems. [Doctoral Dissertation]. Texas A&M University; 2016. Available from: http://hdl.handle.net/1969.1/157880
Texas A&M University
3.
Ergur, Alperen Ali.
Sparsity, Randomness and Convexity in Applied Algebraic Geometry.
Degree: PhD, Mathematics, 2016, Texas A&M University
URL: http://hdl.handle.net/1969.1/157846
► In this dissertation we study three problems in applied algebraic geometry. The first problem is to construct an algorithmically efficient approximation to the real part…
(more)
▼ In this dissertation we study three problems in applied algebraic geometry. The first problem is to construct an algorithmically efficient approximation to the real part of the zero set of an exponential sum. We construct such a polyhedral approximation using techniques from tropical geometry. We prove precise distance bounds between our polyhedral approximation and the real part of the zero set. Our bounds depend on the number of terms of the exponential sum and the minimal distance between the exponents. Despite the computational hardness of the membership problem for the real part of the zero set, we prove that our polyhedral approximation can be computed by linear programing on the real BSS machine.
The second problem is to study the ratio of sums of squares polynomials inside the set of nonnegative polynomials. Our focus is on the effect of fixed monomial structure to the ratio of these two sets. We study this problem quantitatively by combining convex geometry and algebra. Some of our methods work for arbitrary Newton polytopes; however our main theorem is stated for multi-homogenous polynomials. Our main theorem provides quantitative versions of some known algebraic facts, and also refines earlier quantitative results.
The third problem is to study the condition number of polynomial systems ‘on average’. Condition number is a vital invariant of polynomial systems which controls their computational complexity. We analyze the condition number of random polynomial systems for a broad family of distributions. Our work shows that earlier results derived for the polynomial systems with real Gaussian independent random coefficients can be extended to the broader family of sub-Gaussian random variables allowing dependencies. Our results are near optimal for overdetermined systems but there is room for improvement in the case of square systems of random polynomials.
The main idea binding our three problems is to observe structure and randomness phenomenon in the space of polynomials. We used combinatorial algebraic geometry to observe the ‘structure’ and convex geometric analysis to understand the ‘randomness’. We believe results presented in this dissertation are just the first steps of the interaction between these two fields.
Advisors/Committee Members: Rojas, J. Maurice (advisor), Paouris, Grigoris (advisor), Kerr, David (committee member), Yan, Catherine H (committee member), Mortairi, Daniele (committee member).
Subjects/Keywords: convex geometric analysis; algebraic geometry; tropical geometry; condition number; random polynomials; sums of squares; semidefinite programing
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APA (6th Edition):
Ergur, A. A. (2016). Sparsity, Randomness and Convexity in Applied Algebraic Geometry. (Doctoral Dissertation). Texas A&M University. Retrieved from http://hdl.handle.net/1969.1/157846
Chicago Manual of Style (16th Edition):
Ergur, Alperen Ali. “Sparsity, Randomness and Convexity in Applied Algebraic Geometry.” 2016. Doctoral Dissertation, Texas A&M University. Accessed March 07, 2021.
http://hdl.handle.net/1969.1/157846.
MLA Handbook (7th Edition):
Ergur, Alperen Ali. “Sparsity, Randomness and Convexity in Applied Algebraic Geometry.” 2016. Web. 07 Mar 2021.
Vancouver:
Ergur AA. Sparsity, Randomness and Convexity in Applied Algebraic Geometry. [Internet] [Doctoral dissertation]. Texas A&M University; 2016. [cited 2021 Mar 07].
Available from: http://hdl.handle.net/1969.1/157846.
Council of Science Editors:
Ergur AA. Sparsity, Randomness and Convexity in Applied Algebraic Geometry. [Doctoral Dissertation]. Texas A&M University; 2016. Available from: http://hdl.handle.net/1969.1/157846
Texas A&M University
4.
Martin Del Campo Sanchez, Abraham.
Galois Groups of Schubert Problems.
Degree: PhD, Mathematics, 2012, Texas A&M University
URL: http://hdl.handle.net/1969.1/ETD-TAMU-2012-08-11605
► The Galois group of a Schubert problem is a subtle invariant that encodes intrinsic structure of its set of solutions. These geometric invariants are difficult…
(more)
▼ The Galois group of a Schubert problem is a subtle invariant that encodes intrinsic structure of its set of solutions. These geometric invariants are difficult to determine in general. However, based on a special position argument due to Schubert and a combinatorial criterion due to Vakil, we show that the Galois group of any Schubert problem involving lines in projective space contains the alternating group.
The result follows from a particular inequality of Schubert intersection numbers which are Kostka numbers of two-rowed tableaux. In most cases, the inequality follows from a combinatorial injection. For the remaining cases, we use that these Kostka numbers appear in the tensor product decomposition of sl2C-modules. Interpreting the tensor product as the action of certain Toeplitz matrices and using spectral analysis, the inequality can be rewritten as an integral. We establish the inequality by estimating this integral using only elementary Calculus.
Advisors/Committee Members: Sottile, Frank (advisor), Matusevich, Laura (committee member), Rojas, J. Maurice (committee member), Dos Reis, Gabriel (committee member).
Subjects/Keywords: Schubert calculus; Galois groups; Schubert problems
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APA (6th Edition):
Martin Del Campo Sanchez, A. (2012). Galois Groups of Schubert Problems. (Doctoral Dissertation). Texas A&M University. Retrieved from http://hdl.handle.net/1969.1/ETD-TAMU-2012-08-11605
Chicago Manual of Style (16th Edition):
Martin Del Campo Sanchez, Abraham. “Galois Groups of Schubert Problems.” 2012. Doctoral Dissertation, Texas A&M University. Accessed March 07, 2021.
http://hdl.handle.net/1969.1/ETD-TAMU-2012-08-11605.
MLA Handbook (7th Edition):
Martin Del Campo Sanchez, Abraham. “Galois Groups of Schubert Problems.” 2012. Web. 07 Mar 2021.
Vancouver:
Martin Del Campo Sanchez A. Galois Groups of Schubert Problems. [Internet] [Doctoral dissertation]. Texas A&M University; 2012. [cited 2021 Mar 07].
Available from: http://hdl.handle.net/1969.1/ETD-TAMU-2012-08-11605.
Council of Science Editors:
Martin Del Campo Sanchez A. Galois Groups of Schubert Problems. [Doctoral Dissertation]. Texas A&M University; 2012. Available from: http://hdl.handle.net/1969.1/ETD-TAMU-2012-08-11605
Texas A&M University
5.
Torres, Joseph Lawrence.
Extension Phenomena of Integrable Holomorphic Functions in Reinhardt Domains of Holomorphy.
Degree: PhD, Mathematics, 2020, Texas A&M University
URL: http://hdl.handle.net/1969.1/192391
► Holomorphic functions of several complex variables showcase many interesting extension phenomena which have historically motivated much of the development of the discipline. The purpose of…
(more)
▼ Holomorphic functions of several complex variables showcase many interesting extension phenomena which have historically motivated much of the development of the discipline. The purpose of this thesis is to explore the extension phenomena of integrable holomorphic functions, an important subclass of the holomorphic functions. We give two classification theorems for two-dimensional Reinhardt L⅟ₕ-domains of holomorphy, as well as two partial results towards classifying n-dimensional Reinhardt L⅟ₕ-domains of holomorphy. Both classification theorems for the two-dimensional domains are geometric classifications in terms of elementary Reinhardt domains. The first gives a classification in terms of monomial inequality representations of elementary Reinhardt domains, while the second gives a classification in terms of a parameterization of such domains by points on the unit circle. While we did not achieve a complete classification of n-dimensional domains, we demonstrate that all bounded Reinhardt domains of holomorphy are themselves L⅟ₕ -domains of holomorphy. Furthermore, while fat L⅟ₕ-domains of holomorphy have been characterized via functional analysis in the past, we provide a geometric characterization of such domains in terms of elementary Reinhardt domains.
Advisors/Committee Members: Boas, Harold P. (advisor), Straube, Emil J. (committee member), Rojas, J. Maurice (committee member), Kronenberg, Andreas K. (committee member).
Subjects/Keywords: holomorphic functions of several complex variables; complex analysis; integrable holomorphic functions; Reinhardt domains; analytic continuation
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APA (6th Edition):
Torres, J. L. (2020). Extension Phenomena of Integrable Holomorphic Functions in Reinhardt Domains of Holomorphy. (Doctoral Dissertation). Texas A&M University. Retrieved from http://hdl.handle.net/1969.1/192391
Chicago Manual of Style (16th Edition):
Torres, Joseph Lawrence. “Extension Phenomena of Integrable Holomorphic Functions in Reinhardt Domains of Holomorphy.” 2020. Doctoral Dissertation, Texas A&M University. Accessed March 07, 2021.
http://hdl.handle.net/1969.1/192391.
MLA Handbook (7th Edition):
Torres, Joseph Lawrence. “Extension Phenomena of Integrable Holomorphic Functions in Reinhardt Domains of Holomorphy.” 2020. Web. 07 Mar 2021.
Vancouver:
Torres JL. Extension Phenomena of Integrable Holomorphic Functions in Reinhardt Domains of Holomorphy. [Internet] [Doctoral dissertation]. Texas A&M University; 2020. [cited 2021 Mar 07].
Available from: http://hdl.handle.net/1969.1/192391.
Council of Science Editors:
Torres JL. Extension Phenomena of Integrable Holomorphic Functions in Reinhardt Domains of Holomorphy. [Doctoral Dissertation]. Texas A&M University; 2020. Available from: http://hdl.handle.net/1969.1/192391
6.
Hein, Nickolas Jason.
Reality and Computation in Schubert Calculus.
Degree: PhD, Mathematics, 2013, Texas A&M University
URL: http://hdl.handle.net/1969.1/151084
► The Mukhin-Tarasov-Varchenko Theorem (previously the Shapiro Conjecture) asserts that a Schubert problem has all solutions distinct and real if the Schubert varieties involved osculate a…
(more)
▼ The Mukhin-Tarasov-Varchenko Theorem (previously the Shapiro Conjecture) asserts that a Schubert problem has all solutions distinct and real if the Schubert varieties involved osculate a rational normal curve at real points. When conjectured, it sparked interest in real osculating Schubert calculus, and computations played a large role in developing the surrounding theory. Our purpose is to uncover generalizations of the Mukhin-Tarasov-Varchenko Theorem, proving them when possible. We also improve the state of the art of computationally solving Schubert problems, allowing us to more effectively study ill-understood phenomena in Schubert calculus.
We use supercomputers to methodically solve real osculating instances of Schubert problems. By studying over 300 million instances of over 700 Schubert problems, we amass data significant enough to reveal generalizations of the Mukhin-Tarasov- Varchenko Theorem and compelling enough to support our conjectures. Combining algebraic geometry and combinatorics, we prove some of these conjectures. To improve the efficiency of solving Schubert problems, we reformulate an instance of a Schubert problem as the solution set to a square system of equations in a higher- dimensional space.
During our investigation, we found the number of real solutions to an instance of a symmetrically defined Schubert problem is congruent modulo four to the number of complex solutions. We proved this congruence, giving a generalization of the Mukhin-Tarasov-Varchenko Theorem and a new invariant in enumerative real algebraic geometry. We also discovered a family of Schubert problems whose number of real solutions to a real osculating instance has a lower bound depending only on the number of defining flags with real osculation points.
We conclude that our method of computational investigation is effective for uncovering phenomena in enumerative real algebraic geometry. Furthermore, we point out that our square formulation for instances of Schubert problems may facilitate future experimentation by allowing one to solve instances using certifiable numerical methods in lieu of more computationally complex symbolic methods. Additionally, the methods we use for proving the congruence modulo four and for producing an
Advisors/Committee Members: Sottile, Frank (advisor), Landsberg, Joseph (committee member), Rojas, J. Maurice (committee member), Amato, Nancy (committee member).
Subjects/Keywords: Schubert Calculus; Square Systems; Certification; Real Algebraic Geometry; Computational Algebraic Geometry; Enumerative Algebraic Geometry
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APA (6th Edition):
Hein, N. J. (2013). Reality and Computation in Schubert Calculus. (Doctoral Dissertation). Texas A&M University. Retrieved from http://hdl.handle.net/1969.1/151084
Chicago Manual of Style (16th Edition):
Hein, Nickolas Jason. “Reality and Computation in Schubert Calculus.” 2013. Doctoral Dissertation, Texas A&M University. Accessed March 07, 2021.
http://hdl.handle.net/1969.1/151084.
MLA Handbook (7th Edition):
Hein, Nickolas Jason. “Reality and Computation in Schubert Calculus.” 2013. Web. 07 Mar 2021.
Vancouver:
Hein NJ. Reality and Computation in Schubert Calculus. [Internet] [Doctoral dissertation]. Texas A&M University; 2013. [cited 2021 Mar 07].
Available from: http://hdl.handle.net/1969.1/151084.
Council of Science Editors:
Hein NJ. Reality and Computation in Schubert Calculus. [Doctoral Dissertation]. Texas A&M University; 2013. Available from: http://hdl.handle.net/1969.1/151084
7.
Missel, Jonathan William.
Active Space Debris Removal using Capture and Ejection.
Degree: PhD, Aerospace Engineering, 2013, Texas A&M University
URL: http://hdl.handle.net/1969.1/149391
► Low Earth Orbit is over-cluttered with rogue objects that threaten existing technological assets and interfere with allocating new ones. Traditional satellite missions are not efficient…
(more)
▼ Low Earth Orbit is over-cluttered with rogue objects that threaten existing technological assets and interfere with allocating new ones. Traditional satellite missions are not efficient enough to collect an appreciable amount of debris due to the high cost of orbit transfers. Many alternate proposals are politically controversial, costly, or dependent on undeveloped technology. This dissertation attempts to solve the problem by introducing a new mission architecture, Space Sweeper, and bespoke hardware, Sling-Sat, that sequentially captures and ejects debris plastically. Resulting momentum exchanges are exploited to aid in subsequent orbit transfers, thus saving fuel. Sling-Sat is a spinning satellite that captures debris at the ends of adjustable-length arms. Arm length controls the angular rate to achieve a desired tangential ejection speed. Timing the release exacts the ejection angle. This process redirects debris to burn up in the atmosphere, or reduce its lifetime, by lowering its perigee.
This dissertation establishes feasibility of principles fundamental to the proposed concept. Hardware is conceptualized to accommodate Space Sweeper ’s specialized needs. Mathematical models are built for the purpose of analysis and simulation. A kinematic analysis investigates system demands and long-term behavior resulting from repeated debris interaction. A successful approach to enforce debris capture is established through optimal control techniques. A study of orbital parameters and their response to debris interactions builds an intuition for missions of this nature. Finally, a J2-compliant technique for path optimization is demonstrated. The results strongly support feasibility of the proposed mission.
Advisors/Committee Members: Mortari, Daniele (advisor), Junkins, John (committee member), Valasek, John (committee member), Rojas, J. Maurice (committee member).
Subjects/Keywords: Active; space; debris; removal; Sling-sat; sweeper
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APA (6th Edition):
Missel, J. W. (2013). Active Space Debris Removal using Capture and Ejection. (Doctoral Dissertation). Texas A&M University. Retrieved from http://hdl.handle.net/1969.1/149391
Chicago Manual of Style (16th Edition):
Missel, Jonathan William. “Active Space Debris Removal using Capture and Ejection.” 2013. Doctoral Dissertation, Texas A&M University. Accessed March 07, 2021.
http://hdl.handle.net/1969.1/149391.
MLA Handbook (7th Edition):
Missel, Jonathan William. “Active Space Debris Removal using Capture and Ejection.” 2013. Web. 07 Mar 2021.
Vancouver:
Missel JW. Active Space Debris Removal using Capture and Ejection. [Internet] [Doctoral dissertation]. Texas A&M University; 2013. [cited 2021 Mar 07].
Available from: http://hdl.handle.net/1969.1/149391.
Council of Science Editors:
Missel JW. Active Space Debris Removal using Capture and Ejection. [Doctoral Dissertation]. Texas A&M University; 2013. Available from: http://hdl.handle.net/1969.1/149391
8.
Ruffo, James Vincent.
A straightening law for the Drinfel'd Lagrangian Grassmannian.
Degree: PhD, Mathematics, 2009, Texas A&M University
URL: http://hdl.handle.net/1969.1/ETD-TAMU-1550
► The Drinfel’d Lagrangian Grassmannian compactifies the space of algebraic maps of fixed degree from the projective line into the Lagrangian Grassmannian. It has a natural…
(more)
▼ The Drinfel’d Lagrangian Grassmannian compactifies the space of algebraic maps of fixed degree from the projective line into the Lagrangian Grassmannian. It has a natural projective embedding arising from the highest weight embedding of the ordinary Lagrangian Grassmannian, and one may study its defining ideal in this embedding.The Drinfel’d Lagrangian Grassmannian is singular. However, a concrete description of generators for the defining ideal of the Schubert subvarieties of the Drinfel’d Lagrangian Grassmannian would implythat the singularities are modest. I prove that the defining ideal of any Schubert subvariety is generated by polynomials which give a straightening law on an ordered set. Using this fact, I show that any such subvariety is Cohen-Macaulay and Koszul. These results represent a partial extension of standard monomial theory to the Drinfel’d Lagrangian Grassmannian.
Advisors/Committee Members: Sottile, Frank (advisor), Keyser, John (committee member), Rojas, J. Maurice (committee member), Schenck, Henry (committee member).
Subjects/Keywords: quasimaps; algebras with straightening law
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APA (6th Edition):
Ruffo, J. V. (2009). A straightening law for the Drinfel'd Lagrangian Grassmannian. (Doctoral Dissertation). Texas A&M University. Retrieved from http://hdl.handle.net/1969.1/ETD-TAMU-1550
Chicago Manual of Style (16th Edition):
Ruffo, James Vincent. “A straightening law for the Drinfel'd Lagrangian Grassmannian.” 2009. Doctoral Dissertation, Texas A&M University. Accessed March 07, 2021.
http://hdl.handle.net/1969.1/ETD-TAMU-1550.
MLA Handbook (7th Edition):
Ruffo, James Vincent. “A straightening law for the Drinfel'd Lagrangian Grassmannian.” 2009. Web. 07 Mar 2021.
Vancouver:
Ruffo JV. A straightening law for the Drinfel'd Lagrangian Grassmannian. [Internet] [Doctoral dissertation]. Texas A&M University; 2009. [cited 2021 Mar 07].
Available from: http://hdl.handle.net/1969.1/ETD-TAMU-1550.
Council of Science Editors:
Ruffo JV. A straightening law for the Drinfel'd Lagrangian Grassmannian. [Doctoral Dissertation]. Texas A&M University; 2009. Available from: http://hdl.handle.net/1969.1/ETD-TAMU-1550
9.
Kadhe, Swanand Ravindra.
Coding for the Clouds: Coding Techniques for Enabling Security, Locality, and Availability in Distributed Storage Systems.
Degree: PhD, Electrical Engineering, 2017, Texas A&M University
URL: http://hdl.handle.net/1969.1/173263
► Cloud systems have become the backbone of many applications such as multimedia streaming, e-commerce, and cluster computing. At the foundation of any cloud architecture lies…
(more)
▼ Cloud systems have become the backbone of many applications such as multimedia
streaming, e-commerce, and cluster computing. At the foundation of any cloud architecture
lies a large-scale, distributed, data storage system. To accommodate the massive
amount of data being stored on the cloud, these distributed storage systems (DSS) have
been scaled to contain hundreds to thousands of nodes that are connected through a networking
infrastructure. Such data-centers are usually built out of commodity components,
which make failures the norm rather than the exception.
In order to combat node failures, data is typically stored in a redundant fashion. Due to
the exponential data growth rate, many DSS are beginning to resort to error control coding
over conventional replication methods, as coding offers high storage space efficiency. This
paradigm shift from replication to coding, along with the need to guarantee reliability, efficiency,
and security in DSS, has created a new set of challenges and opportunities, opening
up a new area of research. This thesis addresses several of these challenges and opportunities
by broadly making the following contributions. (i) We design practically amenable,
low-complexity coding schemes that guarantee security of cloud systems, ensure quick
recovery from failures, and provide high availability for retrieving partial information; and
(ii) We analyze fundamental performance limits and optimal trade-offs between the key
performance metrics of these coding schemes.
More specifically, we first consider the problem of achieving information-theoretic
security in DSS against an eavesdropper that can observe a limited number of nodes. We
present a framework that enables design of secure repair-efficient codes through a joint
construction of inner and outer codes. Then, we consider a practically appealing notion
of weakly secure coding, and construct coset codes that can weakly secure a wide class of regenerating codes that reduce the amount of data downloaded during node repair.
Second, we consider the problem of meeting repair locality constraints, which specify
the number of nodes participating in the repair process. We propose a notion of unequal
locality, which enables different locality values for different nodes, ensuring quick recovery
for nodes storing important data. We establish tight upper bounds on the minimum
distance of linear codes with unequal locality, and present optimal code constructions.
Next, we extend the notion of locality from the Hamming metric to the rank and subspace
metrics, with the goal of designing codes for efficient data recovery from special types of
correlated failures in DSS.We construct a family of locally recoverable rank-metric codes
with optimal data recovery properties.
Finally, we consider the problem of providing high availability, which is ensured by
enabling node repair from multiple disjoint subsets of nodes of small size. We study
codes with availability from a queuing-theoretical perspective by analyzing the average
time necessary to download a…
Advisors/Committee Members: Sprintson, Alex (advisor), Kumar, P. R. (committee member), Narayanan, Krishna (committee member), Rojas, J. Maurice (committee member).
Subjects/Keywords: Coding for Distributed Storage; Information-Theoretic Security; Locally Recoverable Codes; Regenerating Codes; Availability; Rank-Metric Codes; Subspace Codes; Secret Sharing; Fork-Join Queues
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APA ·
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APA (6th Edition):
Kadhe, S. R. (2017). Coding for the Clouds: Coding Techniques for Enabling Security, Locality, and Availability in Distributed Storage Systems. (Doctoral Dissertation). Texas A&M University. Retrieved from http://hdl.handle.net/1969.1/173263
Chicago Manual of Style (16th Edition):
Kadhe, Swanand Ravindra. “Coding for the Clouds: Coding Techniques for Enabling Security, Locality, and Availability in Distributed Storage Systems.” 2017. Doctoral Dissertation, Texas A&M University. Accessed March 07, 2021.
http://hdl.handle.net/1969.1/173263.
MLA Handbook (7th Edition):
Kadhe, Swanand Ravindra. “Coding for the Clouds: Coding Techniques for Enabling Security, Locality, and Availability in Distributed Storage Systems.” 2017. Web. 07 Mar 2021.
Vancouver:
Kadhe SR. Coding for the Clouds: Coding Techniques for Enabling Security, Locality, and Availability in Distributed Storage Systems. [Internet] [Doctoral dissertation]. Texas A&M University; 2017. [cited 2021 Mar 07].
Available from: http://hdl.handle.net/1969.1/173263.
Council of Science Editors:
Kadhe SR. Coding for the Clouds: Coding Techniques for Enabling Security, Locality, and Availability in Distributed Storage Systems. [Doctoral Dissertation]. Texas A&M University; 2017. Available from: http://hdl.handle.net/1969.1/173263
10.
Eser, Zekiye.
Primary Components of Binomial Ideals.
Degree: PhD, Mathematics, 2014, Texas A&M University
URL: http://hdl.handle.net/1969.1/153345
► Binomials are polynomials with at most two terms. A binomial ideal is an ideal generated by binomials. Primary components and associated primes of a binomial…
(more)
▼ Binomials are polynomials with at most two terms. A binomial ideal is an ideal generated by binomials. Primary components and associated primes of a binomial ideal are still binomial over algebraically closed fields. Primary components of general binomial ideals over algebraically closed fields with characteristic zero can be described combinatorially by translating the operations on binomial ideals to operations on exponent vectors. In this dissertation, we obtain more explicit descriptions for primary components of special binomial ideals. A feature of this work is that our
results are independent of the characteristic of the field.
First of all, we analyze the primary decomposition of a special class of binomial ideals, lattice ideals, in which every variable is a nonzerodivisor modulo the ideal. Then we provide a description for primary decomposition of lattice ideals in fields with positive characteristic.
In addition, we study the codimension two lattice basis ideals and we compute their primary components explicitly.
An ideal I ⊆ k[x_(1),….x_(n) ] is cellular if every variable is either a nonzerodivisor modulo I or is nilpotent modulo I. We characterize the minimal primary components of cellular binomial ideals explicitly. Another significant result is a computation of the Hull of a cellular binomial ideal, that is the intersection of all of its minimal primary components.
Lastly, we focus on commutative monoids and their congruences. We study properties of monoids that have counterparts in the study of binomial ideals. We provide a characterization of primary ideals in positive characteristic, in terms of the congruences they induce.
Advisors/Committee Members: Matusevich, Laura F (advisor), Sottile, Frank (committee member), Rojas, J Maurice (committee member), Keyser, John (committee member).
Subjects/Keywords: primary decomposition; binomial ideals
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APA (6th Edition):
Eser, Z. (2014). Primary Components of Binomial Ideals. (Doctoral Dissertation). Texas A&M University. Retrieved from http://hdl.handle.net/1969.1/153345
Chicago Manual of Style (16th Edition):
Eser, Zekiye. “Primary Components of Binomial Ideals.” 2014. Doctoral Dissertation, Texas A&M University. Accessed March 07, 2021.
http://hdl.handle.net/1969.1/153345.
MLA Handbook (7th Edition):
Eser, Zekiye. “Primary Components of Binomial Ideals.” 2014. Web. 07 Mar 2021.
Vancouver:
Eser Z. Primary Components of Binomial Ideals. [Internet] [Doctoral dissertation]. Texas A&M University; 2014. [cited 2021 Mar 07].
Available from: http://hdl.handle.net/1969.1/153345.
Council of Science Editors:
Eser Z. Primary Components of Binomial Ideals. [Doctoral Dissertation]. Texas A&M University; 2014. Available from: http://hdl.handle.net/1969.1/153345
11.
Bruccoleri, Christian.
Flower constellation optimization and implementation.
Degree: PhD, Aerospace Engineering, 2009, Texas A&M University
URL: http://hdl.handle.net/1969.1/ETD-TAMU-2404
► Satellite constellations provide the infrastructure to implement some of the most important global services of our times both in civilian and military applications, ranging from…
(more)
▼ Satellite constellations provide the infrastructure to implement some of the most important
global services of our times both in civilian and military applications, ranging
from telecommunications to global positioning, and to observation systems. Flower
Constellations constitute a set of satellite constellations characterized by periodic
dynamics. They have been introduced while trying to augment the existing design
methodologies for satellite constellations. The dynamics of a Flower Constellation
identify a set of implicit rotating reference frames on which the satellites follow the
same closed-loop relative trajectory. In particular, when one of these rotating reference
frames is “Planet Centered, Planet Fixed”, then all the orbits become compatible
(or resonant) with the planet; consequently, the projection of the relative path on the
planet results in a repeating ground track.
The satellite constellations design methodology currently most utilized is the
Walker Delta Pattern or, more generally, Walker Constellations. The set of orbital
planes and initial spacecraft positions are represented by a set of only three integers
and two real parameters rather than by all the orbital elements; Flower Constellations
provide a more general framework in which most of the former restrictions are
removed, by allowing the use of resonant elliptical orbits. Flower Constellations can
represent hundreds of spacecraft with a set of 6 integers and 5 real parameters only
and existing constellations can be easily reproduced.
How to design a Flower Constellation to satisfy specific mission requirements is an important problem for promoting the acceptance of this novel concept by the
space community. Therefore one of the main goals of this work is that of proposing
design techniques that can be applied to satisfy practical mission requirements.
The results obtained by applying Global optimization techniques, such as Genetic
Algorithms, to some relevant navigation and Earth observation space-based systems
show that the Flower Constellations not only are as effective asWalker Constellations,
but can also be applied to non-traditional constellation problem domains, such as
regional coverage and reconnaissance.
Advisors/Committee Members: Mortari, Daniele (advisor), Junkins, J. L. (committee member), Pollock, Thomas C. (committee member), Rojas, J. Maurice (committee member).
Subjects/Keywords: Satellite Constellations; Reconnaissance; Coverage
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APA (6th Edition):
Bruccoleri, C. (2009). Flower constellation optimization and implementation. (Doctoral Dissertation). Texas A&M University. Retrieved from http://hdl.handle.net/1969.1/ETD-TAMU-2404
Chicago Manual of Style (16th Edition):
Bruccoleri, Christian. “Flower constellation optimization and implementation.” 2009. Doctoral Dissertation, Texas A&M University. Accessed March 07, 2021.
http://hdl.handle.net/1969.1/ETD-TAMU-2404.
MLA Handbook (7th Edition):
Bruccoleri, Christian. “Flower constellation optimization and implementation.” 2009. Web. 07 Mar 2021.
Vancouver:
Bruccoleri C. Flower constellation optimization and implementation. [Internet] [Doctoral dissertation]. Texas A&M University; 2009. [cited 2021 Mar 07].
Available from: http://hdl.handle.net/1969.1/ETD-TAMU-2404.
Council of Science Editors:
Bruccoleri C. Flower constellation optimization and implementation. [Doctoral Dissertation]. Texas A&M University; 2009. Available from: http://hdl.handle.net/1969.1/ETD-TAMU-2404
12.
El Rouayheb, Salim Y.
Network and Index Coding with Application to Robust and Secure Communications.
Degree: PhD, Electrical Engineering, 2011, Texas A&M University
URL: http://hdl.handle.net/1969.1/ETD-TAMU-2009-12-7364
► Since its introduction in the year 2000 by Ahlswede et al., the network coding paradigm has revolutionized the way we understand information flows in networks.…
(more)
▼ Since its introduction in the year 2000 by Ahlswede et al., the network coding paradigm has revolutionized the way we understand information flows in networks.
Traditionally, information transmitted in a communication network was treated as a commodity in a transportation network, much like cars on highways or fluids in pipes.
This approach, however, fails to capture the very nature of information, which in contrast to material goods, can be coded and decoded. The network coding techniques
take full advantage of the inherent properties of information, and allow the nodes in a network, not only to store and forward, but also to "mix", i.e., encode, their received data. This approach was shown to result in a substantial throughput gain over the traditional routing and tree packing techniques.
In this dissertation, we study applications of network coding for guarantying reliable and secure information transmission in networks with compromised edges.
First, we investigate the construction of robust network codes for achieving network resilience against link failures. We focus on the practical important case of unicast networks with non-uniform edge capacities where a single link can fail at a time. We demonstrate that these networks exhibit unique structural properties when they are minimal, i.e., when they do not contain redundant edges. Based on this structure, we prove that robust linear network codes exist for these networks over GF(2), and devise an efficient algorithm to construct them.
Second, we consider the problem of securing a multicast network against an eavesdropper that can intercept the packets on a limited number of network links.
We recast this problem as a network generalization of the classical wiretap channel
of Type II introduced by Ozarow and Wyner in 1984. In particular, we demonstrate that perfect secrecy can be achieved by using the Ozarow-Wyner scheme of coset
coding at the source, on top of the implemented network code. Consequently, we transparently recover important results available in the literature on secure network
coding. We also derive new bounds on the required secure code alphabet size and an algorithm for code construction.
In the last part of this dissertation, we study the connection between index coding, network coding, and matroid linear representation. We devise a reduction from the index coding problem to the network coding problem, implying that in the linear case these two problems are equivalent. We also present a second reduction from the
matroid linear representability problem to index coding, and therefore, to network coding. The latter reduction establishes a strong connection between matroid theory
and network coding theory. These two reductions are then used to construct special instances of the index coding problem where vector linear codes outperform scalar
linear ones, and where non-linear encoding is needed to achieve the optimal number of transmission. Thereby, we provide a counterexample to a related conjecture in the
literature and demonstrate the benefits…
Advisors/Committee Members: Georghiades, Costas N. (advisor), Sprintson, Alexander (advisor), Datta, Aniruddha (committee member), Chamberland, Jean-Francois (committee member), Rojas, J. Maurice (committee member).
Subjects/Keywords: Network Coding; Index Coding; Matroid Theory; Communications
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Manager
APA (6th Edition):
El Rouayheb, S. Y. (2011). Network and Index Coding with Application to Robust and Secure Communications. (Doctoral Dissertation). Texas A&M University. Retrieved from http://hdl.handle.net/1969.1/ETD-TAMU-2009-12-7364
Chicago Manual of Style (16th Edition):
El Rouayheb, Salim Y. “Network and Index Coding with Application to Robust and Secure Communications.” 2011. Doctoral Dissertation, Texas A&M University. Accessed March 07, 2021.
http://hdl.handle.net/1969.1/ETD-TAMU-2009-12-7364.
MLA Handbook (7th Edition):
El Rouayheb, Salim Y. “Network and Index Coding with Application to Robust and Secure Communications.” 2011. Web. 07 Mar 2021.
Vancouver:
El Rouayheb SY. Network and Index Coding with Application to Robust and Secure Communications. [Internet] [Doctoral dissertation]. Texas A&M University; 2011. [cited 2021 Mar 07].
Available from: http://hdl.handle.net/1969.1/ETD-TAMU-2009-12-7364.
Council of Science Editors:
El Rouayheb SY. Network and Index Coding with Application to Robust and Secure Communications. [Doctoral Dissertation]. Texas A&M University; 2011. Available from: http://hdl.handle.net/1969.1/ETD-TAMU-2009-12-7364
Texas A&M University
13.
Abdelkhalik, Osama Mohamed Omar.
Orbit design and estimation for surveillance missions using genetic algorithms.
Degree: PhD, Aerospace Engineering, 2006, Texas A&M University
URL: http://hdl.handle.net/1969.1/3126
► The problem of observing a given set of Earth target sites within an assigned time frame is examined. Attention is given mainly to visiting these…
(more)
▼ The problem of observing a given set of Earth target sites within an assigned time
frame is examined. Attention is given mainly to visiting these sites as sub-satellite
nadir points. Solutions to this problem in the literature require thrusters to continuously
maneuver the satellite from one site to another. A natural solution is proposed.
A natural solution is a gravitational orbit that enables the spacecraft to satisfy the
mission requirements without maneuvering. Optimization of a penalty function is
performed to find natural solutions for satellite orbit configurations. This penalty
function depends on the mission objectives. Two mission objectives are considered:
maximum observation time and maximum resolution. The penalty function poses
multi minima and a genetic algorithm technique is used to solve this problem. In
the case that there is no one orbit satisfying the mission requirements, a multi-orbit
solution is proposed. In a multi-orbit solution, the set of target sites is split into
two groups. Then the developed algorithm is used to search for a natural solution
for each group. The satellite has to be maneuvered between the two solution orbits.
Genetic algorithms are used to find the optimal orbit transfer between the two orbits
using impulsive thrusters. A new formulation for solving the orbit maneuver problem
using genetic algorithms is developed. The developed formulation searches for a mini mum fuel consumption maneuver and guarantees that the satellite will be transferred
exactly to the final orbit even if the solution is non-optimal. The results obtained
demonstrate the feasibility of finding natural solutions for many case studies.
The problem of the design of suitable satellite constellation for Earth observing
applications is addressed. Two cases are considered. The first is the remote sensing
missions for a particular region with high frequency and small swath width. The second
is the interferometry radar Earth observation missions. In satellite constellations
orbit's design, a new set of compatible orbits, called the "Two-way orbits",whose
ground track path is a closed-loop trajectory that intersects itself, in some points,
with tangent intersections is introduced. Conditions are derived on the orbital elements
such that these Two-way Orbits exist and satellites flying in these orbits pass
the tangent intersection points at the same time. Finally, the recently proposed concept
of observing a space object from onboard a spacecraft using a star tracker is
considered. The measurements of the star tracker provide directions to the target in
space and do not provide range measurements. Estimation for the orbit of the target
space object using the measurements of the star tracker is developed. An observability
analysis is performed to derive conditions on the observability of the system states.
The Gaussian Least Squares Differential Correction Technique is implemented. The
results obtained demonstrate the feasibility of using the measurements of the star
tracker to get a good estimate for the target…
Advisors/Committee Members: Mortari, Daniele (advisor), Junkins, John (committee member), Rojas, J. Maurice (committee member), Vadali, Srinivas (committee member).
Subjects/Keywords: Orbit design; Genetic Algorithms; Ground Surveillance; Optimization; Orbit Maneuver
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APA ·
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MLA ·
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APA (6th Edition):
Abdelkhalik, O. M. O. (2006). Orbit design and estimation for surveillance missions using genetic algorithms. (Doctoral Dissertation). Texas A&M University. Retrieved from http://hdl.handle.net/1969.1/3126
Chicago Manual of Style (16th Edition):
Abdelkhalik, Osama Mohamed Omar. “Orbit design and estimation for surveillance missions using genetic algorithms.” 2006. Doctoral Dissertation, Texas A&M University. Accessed March 07, 2021.
http://hdl.handle.net/1969.1/3126.
MLA Handbook (7th Edition):
Abdelkhalik, Osama Mohamed Omar. “Orbit design and estimation for surveillance missions using genetic algorithms.” 2006. Web. 07 Mar 2021.
Vancouver:
Abdelkhalik OMO. Orbit design and estimation for surveillance missions using genetic algorithms. [Internet] [Doctoral dissertation]. Texas A&M University; 2006. [cited 2021 Mar 07].
Available from: http://hdl.handle.net/1969.1/3126.
Council of Science Editors:
Abdelkhalik OMO. Orbit design and estimation for surveillance missions using genetic algorithms. [Doctoral Dissertation]. Texas A&M University; 2006. Available from: http://hdl.handle.net/1969.1/3126
Texas A&M University
14.
Ouchi, Koji.
Exact polynomial system solving for robust geometric computation.
Degree: PhD, Computer Science, 2007, Texas A&M University
URL: http://hdl.handle.net/1969.1/4805
► I describe an exact method for computing roots of a system of multivariate polynomials with rational coefficients, called the rational univariate reduction. This method enables…
(more)
▼ I describe an exact method for computing roots of a system of multivariate
polynomials with rational coefficients, called the rational univariate reduction. This
method enables performance of exact algebraic computation of coordinates of the
roots of polynomials. In computational geometry, curves, surfaces and points are described
as polynomials and their intersections. Thus, exact computation of the roots
of polynomials allows the development and implementation of robust geometric algorithms.
I describe applications in robust geometric modeling. In particular, I show
a new method, called numerical perturbation scheme, that can be used successfully
to detect and handle degenerate configurations appearing in boundary evaluation
problems. I develop a derandomized version of the algorithm for computing the rational
univariate reduction for a square system of multivariate polynomials and a
new algorithm for a non-square system. I show how to perform exact computation
over algebraic points obtained by the rational univariate reduction. I give a formal
description of numerical perturbation scheme and its implementation.
Advisors/Committee Members: Friesen, Donald (advisor), Keyser, John (advisor), Chen, Jianer (committee member), Rojas, J. Maurice (committee member).
Subjects/Keywords: exact computation; geometric computation
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APA (6th Edition):
Ouchi, K. (2007). Exact polynomial system solving for robust geometric computation. (Doctoral Dissertation). Texas A&M University. Retrieved from http://hdl.handle.net/1969.1/4805
Chicago Manual of Style (16th Edition):
Ouchi, Koji. “Exact polynomial system solving for robust geometric computation.” 2007. Doctoral Dissertation, Texas A&M University. Accessed March 07, 2021.
http://hdl.handle.net/1969.1/4805.
MLA Handbook (7th Edition):
Ouchi, Koji. “Exact polynomial system solving for robust geometric computation.” 2007. Web. 07 Mar 2021.
Vancouver:
Ouchi K. Exact polynomial system solving for robust geometric computation. [Internet] [Doctoral dissertation]. Texas A&M University; 2007. [cited 2021 Mar 07].
Available from: http://hdl.handle.net/1969.1/4805.
Council of Science Editors:
Ouchi K. Exact polynomial system solving for robust geometric computation. [Doctoral Dissertation]. Texas A&M University; 2007. Available from: http://hdl.handle.net/1969.1/4805
Texas A&M University
15.
Sethuraman, Swaminathan.
New measures and effects of stochastic resonance.
Degree: MS, Electrical Engineering, 2005, Texas A&M University
URL: http://hdl.handle.net/1969.1/2705
► In the case of wideband (aperiodic) signals, the classical signal and noise measures used to characterize stochastic resonance do not work because their way of…
(more)
▼ In the case of wideband (aperiodic) signals, the classical signal and noise measures used to characterize stochastic resonance do not work because their way of distinguishing signal from noise fails. In a study published earlier (L. B. Kish, 1996), a new way of measuring and identifying noise and aperiodic (wideband) signals during strongly nonlinear transfer was introduced. The method was based on using cross-spectra between the input and the output. According to the study, in the case of linear transfer and sinusoidal signals, the method gives the same results as the classical method and in the case of aperiodic signals it gives a sensible measure. In this paper we refine the theory and present detailed simulations which validate and refine the conclusions reached in that study. As neural and ion channel signal transfer are nonlinear and aperiodic, the new method has direct applicability in membrane biology and neural science (S.
M. Bezrukov and I. Vodyanoy, 1997).
Advisors/Committee Members: Kish, Laszlo B. (advisor), Su, Chin B. (committee member), Halverson, Don (committee member), Rojas, J. Maurice (committee member).
Subjects/Keywords: stochastic resonance; noise; SNR; neural signals; biological signals; cross spectral measure
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APA (6th Edition):
Sethuraman, S. (2005). New measures and effects of stochastic resonance. (Masters Thesis). Texas A&M University. Retrieved from http://hdl.handle.net/1969.1/2705
Chicago Manual of Style (16th Edition):
Sethuraman, Swaminathan. “New measures and effects of stochastic resonance.” 2005. Masters Thesis, Texas A&M University. Accessed March 07, 2021.
http://hdl.handle.net/1969.1/2705.
MLA Handbook (7th Edition):
Sethuraman, Swaminathan. “New measures and effects of stochastic resonance.” 2005. Web. 07 Mar 2021.
Vancouver:
Sethuraman S. New measures and effects of stochastic resonance. [Internet] [Masters thesis]. Texas A&M University; 2005. [cited 2021 Mar 07].
Available from: http://hdl.handle.net/1969.1/2705.
Council of Science Editors:
Sethuraman S. New measures and effects of stochastic resonance. [Masters Thesis]. Texas A&M University; 2005. Available from: http://hdl.handle.net/1969.1/2705
Texas A&M University
16.
Lutes, Brad Aubrey.
Special Values of the Goss L-function and Special Polynomials.
Degree: PhD, Mathematics, 2010, Texas A&M University
URL: http://hdl.handle.net/1969.1/ETD-TAMU-2010-08-8251
► Let K be the function field of an irreducible, smooth projective curve X defined over Fq. Let [lemniscate] be a fixed point on X and…
(more)
▼ Let K be the function field of an irreducible, smooth projective curve X defined over Fq. Let [lemniscate] be a fixed point on X and let A [a subset of or is equal to] K be the Dedekind domain of functions which are regular away from [lemniscate]. Following the work of Greg Anderson, we define special polynomials and explain how they are used to define an A-module (in the case where the class number of A and the degree of [lemniscate] are both one) known as the module of special points associated to the Drinfeld A-module [rho]. We show that this module is finitely generated and explicitly compute its rank. We also show that if K is a function field such that the degree of [lemniscate] is one, then the Goss L-function, evaluated at 1, is a finite linear combination of logarithms evaluated at algebraic points. We conclude with examples showing how to use special polynomials to compute special values of both the Goss L-function and the Goss zeta function.
Advisors/Committee Members: Papanikolas, Matthew (advisor), Rojas, J. Maurice (committee member), Tretkoff, Paula (committee member), Dahm, P. Fred (committee member).
Subjects/Keywords: Function Fields; Drinfeld Modules; L-functions
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Export
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APA (6th Edition):
Lutes, B. A. (2010). Special Values of the Goss L-function and Special Polynomials. (Doctoral Dissertation). Texas A&M University. Retrieved from http://hdl.handle.net/1969.1/ETD-TAMU-2010-08-8251
Chicago Manual of Style (16th Edition):
Lutes, Brad Aubrey. “Special Values of the Goss L-function and Special Polynomials.” 2010. Doctoral Dissertation, Texas A&M University. Accessed March 07, 2021.
http://hdl.handle.net/1969.1/ETD-TAMU-2010-08-8251.
MLA Handbook (7th Edition):
Lutes, Brad Aubrey. “Special Values of the Goss L-function and Special Polynomials.” 2010. Web. 07 Mar 2021.
Vancouver:
Lutes BA. Special Values of the Goss L-function and Special Polynomials. [Internet] [Doctoral dissertation]. Texas A&M University; 2010. [cited 2021 Mar 07].
Available from: http://hdl.handle.net/1969.1/ETD-TAMU-2010-08-8251.
Council of Science Editors:
Lutes BA. Special Values of the Goss L-function and Special Polynomials. [Doctoral Dissertation]. Texas A&M University; 2010. Available from: http://hdl.handle.net/1969.1/ETD-TAMU-2010-08-8251
Texas A&M University
17.
Wilkins, Matthew Paul.
The Flower Constellations - theory, design process, and applications.
Degree: PhD, Aerospace Engineering, 2006, Texas A&M University
URL: http://hdl.handle.net/1969.1/3053
► In this research, constellations of satellites all having orbits compatible with rotating reference frames are considered. That is to say, no matter how many satellites…
(more)
▼ In this research, constellations of satellites all having orbits compatible with rotating
reference frames are considered. That is to say, no matter how many satellites are considered
for the constellation, when viewed from an arbitrarily defined rotating reference frame
of interest, they all follow a single, identical relative trajectory. In this regard, one could
think of the relative trajectories as ?space trajectories on a rotating reference frame.?
In particular, this research concerns itself with reference frames constrained to rotate
with the planet under consideration (e.g. the Earth Centered Earth Fixed (ECEF) frame,
a frame rotating with the Earth). When the axis of symmetry of these constellations is
aligned with the spin axis of the planet, then the ground track as projected onto the planet
surface will be repeating.
Flower Constellations are identified by eight parameters. Five are integer parameters:
the number of petals (Np), the number of sidereal days to repeat the ground track (Nd), the
number of satellites (Ns), and two integers to govern the phasing (Fn and Fd). Three are
orbit parameters that are generally equal for all satellites: the argument of perigee (w), the
orbit inclination (i), and the perigee altitude (hp). Each of these parameters has a unique effect on the overall design of a Flower Constellation. Based upon specific choices of these parameters, some broad categories of constellation types are presented along with some unique cases. Often, a large number of satellites are used to completely visualize these constellations. While Flower Constellations lend themselves to micro- and nano-satellite constellations very easily, they are also readily scalable to any mission requirement. Also investigated are inverse design techniques where the governing equations are solved for the Flower Constellation parameters to achieve a desired final constellation or formation shape. Flower Constellations present beautiful and interesting dynamical features that allow us to explore a wide range of potential applications that include: telecommunications, Earth and deep space observation, global positioning systems, and new kinds of formation flying schemes among others. To demonstrate their potential, some specific Flower Constellations are described and discussed. Finally, the effect of perturbations such as the Earth?s oblateness are investigated and options for mitigating perturbations are discussed.
Advisors/Committee Members: Mortari, Daniele (advisor), Alfriend, Kyle T. (advisor), Rojas, J. Maurice (committee member), Junkins, John L. (committee member), Vadali, Srinivas R. (committee member).
Subjects/Keywords: Satellites; Constellations; Formations; Design
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APA ·
Chicago ·
MLA ·
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Export
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APA (6th Edition):
Wilkins, M. P. (2006). The Flower Constellations - theory, design process, and applications. (Doctoral Dissertation). Texas A&M University. Retrieved from http://hdl.handle.net/1969.1/3053
Chicago Manual of Style (16th Edition):
Wilkins, Matthew Paul. “The Flower Constellations - theory, design process, and applications.” 2006. Doctoral Dissertation, Texas A&M University. Accessed March 07, 2021.
http://hdl.handle.net/1969.1/3053.
MLA Handbook (7th Edition):
Wilkins, Matthew Paul. “The Flower Constellations - theory, design process, and applications.” 2006. Web. 07 Mar 2021.
Vancouver:
Wilkins MP. The Flower Constellations - theory, design process, and applications. [Internet] [Doctoral dissertation]. Texas A&M University; 2006. [cited 2021 Mar 07].
Available from: http://hdl.handle.net/1969.1/3053.
Council of Science Editors:
Wilkins MP. The Flower Constellations - theory, design process, and applications. [Doctoral Dissertation]. Texas A&M University; 2006. Available from: http://hdl.handle.net/1969.1/3053
. 
Open Access Theses and Dissertations
