Georgia Tech Theses and Dissertations
http://hdl.handle.net/1853/3739
Electronic Theses and Dissertations2016-04-16T13:56:07ZDesign of Diffractive Optical Elements Through Low-dimensional Optimization
http://hdl.handle.net/1853/54614
Design of Diffractive Optical Elements Through Low-dimensional Optimization
Peters, David W.
The simulation of diffractive optical structures allows for the efficient testing of a large number of structures without having to actually fabricate these devices. Various forms of analysis of these structures have been done through computer programs in the past. However, programs that can actually design a structure to perform a given task are
very limited in scope. Optimization of a structure can be a task that is very processor time intensive, particularly if the optimization space has many dimensions. This thesis describes the creation of a computer program that is able to find an optimal structure while maintaining a low-dimensional search space, thus greatly reducing the processor time required to find the solution. The program can design the optimal structure for a wide variety of planar optical devices that conform to the weakly-guiding approximation with an efficient code that incorporates the low-dimensional search space concept. This
work is the first use of an electromagnetic field solver inside of an optimization loop for the design of an optimized diffractive-optic structure.
2001-07-01T00:00:00ZPeters, David W.The simulation of diffractive optical structures allows for the efficient testing of a large number of structures without having to actually fabricate these devices. Various forms of analysis of these structures have been done through computer programs in the past. However, programs that can actually design a structure to perform a given task are
very limited in scope. Optimization of a structure can be a task that is very processor time intensive, particularly if the optimization space has many dimensions. This thesis describes the creation of a computer program that is able to find an optimal structure while maintaining a low-dimensional search space, thus greatly reducing the processor time required to find the solution. The program can design the optimal structure for a wide variety of planar optical devices that conform to the weakly-guiding approximation with an efficient code that incorporates the low-dimensional search space concept. This
work is the first use of an electromagnetic field solver inside of an optimization loop for the design of an optimized diffractive-optic structure.First principles approach to understanding stability and phase transitions of metal A(II)B(IV)hexafluorides
http://hdl.handle.net/1853/54484
First principles approach to understanding stability and phase transitions of metal A(II)B(IV)hexafluorides
Pueschel, Charles A.
2015-11-24T00:00:00ZPueschel, Charles A.Combinatorial problems for graphs and partially ordered sets
http://hdl.handle.net/1853/54483
Combinatorial problems for graphs and partially ordered sets
Wang, Ruidong
This dissertation has three principal components. The first component is about the connections between the dimension of posets and the size of matchings in comparability and incomparability graphs. In 1951, Hiraguchi proved that for any finite poset P, the dimension of P is at most half of the number of points in P. We develop some new inequalities for the dimension of finite posets. These inequalities are then used to bound dimension in terms of the maximum size of matchings. We prove that if the dimension of P is d and d is at least 3, then there is a matching of size d in the comparability graph of P, and a matching of size d in the incomparability graph of P. The bounds in above theorems are best possible, and either result has Hiraguchi's theorem as an immediate corollary. In the second component, we focus on an extremal graph theory problem whose solution relied on the construction of a special kind of posets. In 1959, Paul Erdos, in a landmark paper, proved the existence of graphs with arbitrarily large girth and arbitrarily large chromatic number using probabilistic method. In a 1991 paper of Kriz and Nesetril, they introduced a new graph parameter eye(G). They show that there are graphs with large girth and large chromatic number among the class of graphs having eye parameter at most three. Answering a question of Kriz and Nesetril, we were able to strengthen their results and show that there are graphs with large girth and large chromatic number among the class of graphs having eye parameter at most two. The last component is about random posets--the poset version of the Erdos-Renyi random graphs. In 1991, Erdos, Kierstead and Trotter (EKT) investigated random height 2 posets and obtained several upper and lower bounds on the dimension of the random posets. Motivated by some extremal problems involving conditions which force a poset to contain a large standard example, we were compelled to revisit this subject. Our sharpened analysis allows us to conclude that as p approaches 1, the expected value of dimension first increases and then decreases, a subtlety not identified in EKT. Along the way, we establish connections with classical topics in analysis as well as with latin rectangles. Also, using structural insights drawn from this research, we are able to make progress on the motivating extremal problem with an application of the asymmetric form of the Lovasz Local Lemma.
2015-11-13T00:00:00ZWang, RuidongThis dissertation has three principal components. The first component is about the connections between the dimension of posets and the size of matchings in comparability and incomparability graphs. In 1951, Hiraguchi proved that for any finite poset P, the dimension of P is at most half of the number of points in P. We develop some new inequalities for the dimension of finite posets. These inequalities are then used to bound dimension in terms of the maximum size of matchings. We prove that if the dimension of P is d and d is at least 3, then there is a matching of size d in the comparability graph of P, and a matching of size d in the incomparability graph of P. The bounds in above theorems are best possible, and either result has Hiraguchi's theorem as an immediate corollary. In the second component, we focus on an extremal graph theory problem whose solution relied on the construction of a special kind of posets. In 1959, Paul Erdos, in a landmark paper, proved the existence of graphs with arbitrarily large girth and arbitrarily large chromatic number using probabilistic method. In a 1991 paper of Kriz and Nesetril, they introduced a new graph parameter eye(G). They show that there are graphs with large girth and large chromatic number among the class of graphs having eye parameter at most three. Answering a question of Kriz and Nesetril, we were able to strengthen their results and show that there are graphs with large girth and large chromatic number among the class of graphs having eye parameter at most two. The last component is about random posets--the poset version of the Erdos-Renyi random graphs. In 1991, Erdos, Kierstead and Trotter (EKT) investigated random height 2 posets and obtained several upper and lower bounds on the dimension of the random posets. Motivated by some extremal problems involving conditions which force a poset to contain a large standard example, we were compelled to revisit this subject. Our sharpened analysis allows us to conclude that as p approaches 1, the expected value of dimension first increases and then decreases, a subtlety not identified in EKT. Along the way, we establish connections with classical topics in analysis as well as with latin rectangles. Also, using structural insights drawn from this research, we are able to make progress on the motivating extremal problem with an application of the asymmetric form of the Lovasz Local Lemma.Additive manufacture of tissue engineering scaffolds for bone and cartilage
http://hdl.handle.net/1853/54482
Additive manufacture of tissue engineering scaffolds for bone and cartilage
Eshraghi, Shaun
Bone and cartilage constructs are often plagued with mechanical failure, poor nutrient transport, poor tissue ingrowth, and necrosis of embedded cells. However, advances in computer aided design (CAD) and computational modeling enable the design of scaffolds with complex internal michroarchitectures and the a priori prediction of their transport and mechanical properties, such that the design of constructs satisfying the needs of the tissue environment can be optimized. The goal of this research is to investigate the capability of additive manufacturing technologies to create designed microarchitectured tissue engineering scaffolds for bone and cartilage regeneration. This goal will be achieved by pursuing the following two objectives: (1) the manufacture of bioresorbable thermoplastic scaffolds by selective laser sintering (SLS) (2) and the manufacture of hydrogel scaffolds by large area maskless photopolymerization (LAMP). SLS is a laser based additive manufacturing method in which an object is built layer-by-layer by fusing powdered material using a computer-controlled scanning laser. LAMP is a massively parallel ultraviolet curing-based process that can be used to create hydrogels from a photomonomer on a large-scale (558x558mm) while maintaining extremely high feature resolution (20µm). In this research, SLS is used to process polycaprolactone (PCL) and composites of PCL with hydroxyapatite (HA) for bone tissue engineering applications while LAMP is used to process polyethylene glycol diacrylate (PEGDA) which can be used for hard and soft tissue applications.
2015-11-05T00:00:00ZEshraghi, ShaunBone and cartilage constructs are often plagued with mechanical failure, poor nutrient transport, poor tissue ingrowth, and necrosis of embedded cells. However, advances in computer aided design (CAD) and computational modeling enable the design of scaffolds with complex internal michroarchitectures and the a priori prediction of their transport and mechanical properties, such that the design of constructs satisfying the needs of the tissue environment can be optimized. The goal of this research is to investigate the capability of additive manufacturing technologies to create designed microarchitectured tissue engineering scaffolds for bone and cartilage regeneration. This goal will be achieved by pursuing the following two objectives: (1) the manufacture of bioresorbable thermoplastic scaffolds by selective laser sintering (SLS) (2) and the manufacture of hydrogel scaffolds by large area maskless photopolymerization (LAMP). SLS is a laser based additive manufacturing method in which an object is built layer-by-layer by fusing powdered material using a computer-controlled scanning laser. LAMP is a massively parallel ultraviolet curing-based process that can be used to create hydrogels from a photomonomer on a large-scale (558x558mm) while maintaining extremely high feature resolution (20µm). In this research, SLS is used to process polycaprolactone (PCL) and composites of PCL with hydroxyapatite (HA) for bone tissue engineering applications while LAMP is used to process polyethylene glycol diacrylate (PEGDA) which can be used for hard and soft tissue applications.