subject:(Homotopy Continuation)

NSYSU

1. Chang, Hen-wen. The End Game Problem in Solving Algebraic Eigenvalue Problems by Homotopy Continuation Method.

Degree: Master, Applied Mathematics, 2013, NSYSU

URL: http://etd.lib.nsysu.edu.tw/ETD-db/ETD-search/view_etd?URN=etd-0612113-133039

► The homotopy continuation method is considered to solve polynomial systems. If the number of solutions of the starting system is much more than that of… (more)

Subjects/Keywords: end game problem; eigenvalue problems; homotopy continuation

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APA · Chicago · MLA · Vancouver · CSE | Export to Zotero / EndNote / Reference Manager

APA (6^th Edition):

Chang, H. (2013). The End Game Problem in Solving Algebraic Eigenvalue Problems by Homotopy Continuation Method. (Thesis). NSYSU. Retrieved from http://etd.lib.nsysu.edu.tw/ETD-db/ETD-search/view_etd?URN=etd-0612113-133039

Note: this citation may be lacking information needed for this citation format:
Not specified: Masters Thesis or Doctoral Dissertation

Chicago Manual of Style (16^th Edition):

Chang, Hen-wen. “The End Game Problem in Solving Algebraic Eigenvalue Problems by Homotopy Continuation Method.” 2013. Thesis, NSYSU. Accessed April 22, 2021. http://etd.lib.nsysu.edu.tw/ETD-db/ETD-search/view_etd?URN=etd-0612113-133039.

Note: this citation may be lacking information needed for this citation format:
Not specified: Masters Thesis or Doctoral Dissertation

MLA Handbook (7^th Edition):

Chang, Hen-wen. “The End Game Problem in Solving Algebraic Eigenvalue Problems by Homotopy Continuation Method.” 2013. Web. 22 Apr 2021.

Vancouver:

Chang H. The End Game Problem in Solving Algebraic Eigenvalue Problems by Homotopy Continuation Method. [Internet] [Thesis]. NSYSU; 2013. [cited 2021 Apr 22]. Available from: http://etd.lib.nsysu.edu.tw/ETD-db/ETD-search/view_etd?URN=etd-0612113-133039.

Note: this citation may be lacking information needed for this citation format:
Not specified: Masters Thesis or Doctoral Dissertation

Council of Science Editors:

Chang H. The End Game Problem in Solving Algebraic Eigenvalue Problems by Homotopy Continuation Method. [Thesis]. NSYSU; 2013. Available from: http://etd.lib.nsysu.edu.tw/ETD-db/ETD-search/view_etd?URN=etd-0612113-133039

Note: this citation may be lacking information needed for this citation format:
Not specified: Masters Thesis or Doctoral Dissertation

University of New Mexico

2. Myers, Nicholas. An Sn Application of Homotopy Continuation in Neutral Particle Transport.

Degree: Nuclear Engineering, 2014, University of New Mexico

URL: http://hdl.handle.net/1928/24581

► The objective of this dissertation is to investigate the usefulness of homotopy continuation applied in the context of neutral particle transport where traditional methods of… (more)

Subjects/Keywords: Homotopy; Sn; Continuation; Transport; Eigenvalue; Diffusive

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APA (6^th Edition):

Myers, N. (2014). An Sn Application of Homotopy Continuation in Neutral Particle Transport. (Doctoral Dissertation). University of New Mexico. Retrieved from http://hdl.handle.net/1928/24581

Chicago Manual of Style (16^th Edition):

Myers, Nicholas. “An Sn Application of Homotopy Continuation in Neutral Particle Transport.” 2014. Doctoral Dissertation, University of New Mexico. Accessed April 22, 2021. http://hdl.handle.net/1928/24581.

MLA Handbook (7^th Edition):

Myers, Nicholas. “An Sn Application of Homotopy Continuation in Neutral Particle Transport.” 2014. Web. 22 Apr 2021.

Vancouver:

Myers N. An Sn Application of Homotopy Continuation in Neutral Particle Transport. [Internet] [Doctoral dissertation]. University of New Mexico; 2014. [cited 2021 Apr 22]. Available from: http://hdl.handle.net/1928/24581.

Council of Science Editors:

Myers N. An Sn Application of Homotopy Continuation in Neutral Particle Transport. [Doctoral Dissertation]. University of New Mexico; 2014. Available from: http://hdl.handle.net/1928/24581

University of Arkansas

3. Hutchison, Brandon. A Restarted Homotopy Method for the Nonsymmetric Eigenvalue Problem.

Degree: PhD, 2011, University of Arkansas

URL: https://scholarworks.uark.edu/etd/74

► The eigenvalues and eigenvectors of a Hessenberg matrix, H, are computed with a combination of homotopy increments and the Arnoldi method. Given a set,… (more)

Subjects/Keywords: Arnoldi; Continuation; Eigenvalue; Homotopy; Applied Mathematics

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APA (6^th Edition):

Hutchison, B. (2011). A Restarted Homotopy Method for the Nonsymmetric Eigenvalue Problem. (Doctoral Dissertation). University of Arkansas. Retrieved from https://scholarworks.uark.edu/etd/74

Chicago Manual of Style (16^th Edition):

Hutchison, Brandon. “A Restarted Homotopy Method for the Nonsymmetric Eigenvalue Problem.” 2011. Doctoral Dissertation, University of Arkansas. Accessed April 22, 2021. https://scholarworks.uark.edu/etd/74.

MLA Handbook (7^th Edition):

Hutchison, Brandon. “A Restarted Homotopy Method for the Nonsymmetric Eigenvalue Problem.” 2011. Web. 22 Apr 2021.

Vancouver:

Hutchison B. A Restarted Homotopy Method for the Nonsymmetric Eigenvalue Problem. [Internet] [Doctoral dissertation]. University of Arkansas; 2011. [cited 2021 Apr 22]. Available from: https://scholarworks.uark.edu/etd/74.

Council of Science Editors:

Hutchison B. A Restarted Homotopy Method for the Nonsymmetric Eigenvalue Problem. [Doctoral Dissertation]. University of Arkansas; 2011. Available from: https://scholarworks.uark.edu/etd/74

University of Toronto

4. Brown, David Anthony. Efficient Homotopy Continuation Algorithms with Application to Computational Fluid Dynamics.

Degree: PhD, 2016, University of Toronto

URL: http://hdl.handle.net/1807/71729

► New homotopy continuation algorithms are developed and applied to a parallel implicit finite-difference Newton-Krylov-Schur external aerodynamic flow solver for the compressible Euler, Navier-Stokes, and Reynolds-averaged… (more)

▼ New homotopy continuation algorithms are developed and applied to a parallel implicit finite-difference Newton-Krylov-Schur external aerodynamic flow solver for the compressible Euler, Navier-Stokes, and Reynolds-averaged Navier-Stokes equations with the Spalart-Allmaras one-equation turbulence model. Many new analysis tools, calculations, and numerical algorithms are presented for the study and design of efficient and robust homotopy continuation algorithms applicable to solving very large and sparse nonlinear systems of equations. Several specific homotopies are presented and studied and a methodology is presented for assessing the suitability of specific homotopies for homotopy continuation.\\ A new class of homotopy continuation algorithms, referred to as monolithic homotopy continuation algorithms, is developed. These algorithms differ from classical predictor-corrector algorithms by combining the predictor and corrector stages into a single update, significantly reducing the amount of computation and avoiding wasted computational effort resulting from over-solving in the corrector phase. The new algorithms are also simpler from a user perspective, with fewer input parameters, which also improves the user's ability to choose effective parameters on the first flow solve attempt. Conditional convergence is proved analytically and studied numerically for the new algorithms. The performance of a fully-implicit monolithic homotopy continuation algorithm is evaluated for several inviscid, laminar, and turbulent flows over NACA 0012 airfoils and ONERA M6 wings. The monolithic algorithm is demonstrated to be more efficient than the predictor-corrector algorithm for all applications investigated. It is also demonstrated to be more efficient than the widely-used pseudo-transient continuation algorithm for all inviscid and laminar cases investigated, and good performance scaling with grid refinement is demonstrated for the inviscid cases. Performance is also demonstrated to be better or comparable to the pseudo-transient continuation algorithm for all turbulent cases investigated. Stability of the new algorithms is also investigated. Advisors/Committee Members: Zingg, David W, Aerospace Science and Engineering.

Subjects/Keywords: computational aerodynamics; continuation; globalization; homotopy; predictor-corrector; pseudo-transient continuation; 0538

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APA · Chicago · MLA · Vancouver · CSE | Export to Zotero / EndNote / Reference Manager

APA (6^th Edition):

Brown, D. A. (2016). Efficient Homotopy Continuation Algorithms with Application to Computational Fluid Dynamics. (Doctoral Dissertation). University of Toronto. Retrieved from http://hdl.handle.net/1807/71729

Chicago Manual of Style (16^th Edition):

Brown, David Anthony. “Efficient Homotopy Continuation Algorithms with Application to Computational Fluid Dynamics.” 2016. Doctoral Dissertation, University of Toronto. Accessed April 22, 2021. http://hdl.handle.net/1807/71729.

MLA Handbook (7^th Edition):

Brown, David Anthony. “Efficient Homotopy Continuation Algorithms with Application to Computational Fluid Dynamics.” 2016. Web. 22 Apr 2021.

Vancouver:

Brown DA. Efficient Homotopy Continuation Algorithms with Application to Computational Fluid Dynamics. [Internet] [Doctoral dissertation]. University of Toronto; 2016. [cited 2021 Apr 22]. Available from: http://hdl.handle.net/1807/71729.

Council of Science Editors:

Brown DA. Efficient Homotopy Continuation Algorithms with Application to Computational Fluid Dynamics. [Doctoral Dissertation]. University of Toronto; 2016. Available from: http://hdl.handle.net/1807/71729

5. Viquerat, Andrew David. Polynomial continuation in the design of deployable structures.

Degree: PhD, 2012, University of Cambridge

URL: http://www.dspace.cam.ac.uk/handle/1810/241496https://www.repository.cam.ac.uk/bitstream/1810/241496/2/license.txt ; https://www.repository.cam.ac.uk/bitstream/1810/241496/3/license_url ; https://www.repository.cam.ac.uk/bitstream/1810/241496/4/license_text ; https://www.repository.cam.ac.uk/bitstream/1810/241496/5/license_rdf ; https://www.repository.cam.ac.uk/bitstream/1810/241496/8/ThesisDSpace.pdf.txt ; https://www.repository.cam.ac.uk/bitstream/1810/241496/9/ThesisDSpace.pdf.jpg

► Polynomial continuation, a branch of numerical continuation, has been applied to several primary problems in kinematic geometry. The objective of the research presented in this… (more)

▼ Polynomial continuation, a branch of numerical continuation, has been applied to several primary problems in kinematic geometry. The objective of the research presented in this document was to explore the possible extensions of the application of polynomial continuation, especially in the field of deployable structure design. The power of polynomial continuation as a design tool lies in its ability to find all solutions of a system of polynomial equations (even positive dimensional solution sets). A linkage design problem posed in polynomial form can be made to yield every possible feasible outcome, many of which may never otherwise have been found. Methods of polynomial continuation based design are illustrated here by way of various examples. In particular, the types of deployable structures which form planar rings, or frames, in their deployed configurations are used as design cases. Polynomial continuation is shown to be a powerful component of an equation-based design process. A polyhedral homotopy method, particularly suited to solving problems in kinematics, was synthesised from several researchers’ published continuation techniques, and augmented with modern, freely available mathematical computing algorithms. Special adaptations were made in the areas of level-k subface identification, lifting value balancing, and path-following. Techniques of forming closure/compatibility equations by direct use of symmetry, or by use of transfer matrices to enforce loop closure, were developed as appropriate for each example. The geometry of a plane symmetric (rectangular) 6R foldable frame was examined and classified in terms of Denavit-Hartenberg Parameters. Its design parameters were then grouped into feasible and non-feasible regions, before continuation was used as a design tool; generating the design parameters required to build a foldable frame which meets certain configurational specifications. iv Two further deployable ring/frame classes were then used as design cases: (a) rings which form (planar) regular polygons when deployed, and (b) rings which are doubly plane symmetric and planar when deployed. The governing equations used in the continuation design process are based on symmetry compatibility and transfer matrices respectively. Finally, the 6, 7 and 8-link versions of N-loops were subjected to a witness set analysis, illustrating the way in which continuation can reveal the nature of the mobility of an unknown linkage. Key features of the results are that polynomial continuation was able to provide complete sets of feasible options to a number of practical design problems, and also to reveal the nature of the mobility of a real overconstrained linkage.

Subjects/Keywords: 6R Linkage; Deployable ring; Deployable structures; Numerical continuation; Overconstrained mechanism; Polyhedral homotopy; Polynomial continuation

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APA (6^th Edition):

Viquerat, A. D. (2012). Polynomial continuation in the design of deployable structures. (Doctoral Dissertation). University of Cambridge. Retrieved from http://www.dspace.cam.ac.uk/handle/1810/241496https://www.repository.cam.ac.uk/bitstream/1810/241496/2/license.txt ; https://www.repository.cam.ac.uk/bitstream/1810/241496/3/license_url ; https://www.repository.cam.ac.uk/bitstream/1810/241496/4/license_text ; https://www.repository.cam.ac.uk/bitstream/1810/241496/5/license_rdf ; https://www.repository.cam.ac.uk/bitstream/1810/241496/8/ThesisDSpace.pdf.txt ; https://www.repository.cam.ac.uk/bitstream/1810/241496/9/ThesisDSpace.pdf.jpg

Chicago Manual of Style (16^th Edition):

Viquerat, Andrew David. “Polynomial continuation in the design of deployable structures.” 2012. Doctoral Dissertation, University of Cambridge. Accessed April 22, 2021. http://www.dspace.cam.ac.uk/handle/1810/241496https://www.repository.cam.ac.uk/bitstream/1810/241496/2/license.txt ; https://www.repository.cam.ac.uk/bitstream/1810/241496/3/license_url ; https://www.repository.cam.ac.uk/bitstream/1810/241496/4/license_text ; https://www.repository.cam.ac.uk/bitstream/1810/241496/5/license_rdf ; https://www.repository.cam.ac.uk/bitstream/1810/241496/8/ThesisDSpace.pdf.txt ; https://www.repository.cam.ac.uk/bitstream/1810/241496/9/ThesisDSpace.pdf.jpg.

MLA Handbook (7^th Edition):

Viquerat, Andrew David. “Polynomial continuation in the design of deployable structures.” 2012. Web. 22 Apr 2021.

Vancouver:

Viquerat AD. Polynomial continuation in the design of deployable structures. [Internet] [Doctoral dissertation]. University of Cambridge; 2012. [cited 2021 Apr 22]. Available from: http://www.dspace.cam.ac.uk/handle/1810/241496https://www.repository.cam.ac.uk/bitstream/1810/241496/2/license.txt ; https://www.repository.cam.ac.uk/bitstream/1810/241496/3/license_url ; https://www.repository.cam.ac.uk/bitstream/1810/241496/4/license_text ; https://www.repository.cam.ac.uk/bitstream/1810/241496/5/license_rdf ; https://www.repository.cam.ac.uk/bitstream/1810/241496/8/ThesisDSpace.pdf.txt ; https://www.repository.cam.ac.uk/bitstream/1810/241496/9/ThesisDSpace.pdf.jpg.

Council of Science Editors:

Viquerat AD. Polynomial continuation in the design of deployable structures. [Doctoral Dissertation]. University of Cambridge; 2012. Available from: http://www.dspace.cam.ac.uk/handle/1810/241496https://www.repository.cam.ac.uk/bitstream/1810/241496/2/license.txt ; https://www.repository.cam.ac.uk/bitstream/1810/241496/3/license_url ; https://www.repository.cam.ac.uk/bitstream/1810/241496/4/license_text ; https://www.repository.cam.ac.uk/bitstream/1810/241496/5/license_rdf ; https://www.repository.cam.ac.uk/bitstream/1810/241496/8/ThesisDSpace.pdf.txt ; https://www.repository.cam.ac.uk/bitstream/1810/241496/9/ThesisDSpace.pdf.jpg

University of Cambridge

6. Viquerat, Andrew David. Polynomial continuation in the design of deployable structures.

Degree: PhD, 2012, University of Cambridge

URL: https://doi.org/10.17863/CAM.14012 ; https://ethos.bl.uk/OrderDetails.do?uin=uk.bl.ethos.545890

► Polynomial continuation, a branch of numerical continuation, has been applied to several primary problems in kinematic geometry. The objective of the research presented in this… (more)

▼ Polynomial continuation, a branch of numerical continuation, has been applied to several primary problems in kinematic geometry. The objective of the research presented in this document was to explore the possible extensions of the application of polynomial continuation, especially in the field of deployable structure design. The power of polynomial continuation as a design tool lies in its ability to find all solutions of a system of polynomial equations (even positive dimensional solution sets). A linkage design problem posed in polynomial form can be made to yield every possible feasible outcome, many of which may never otherwise have been found. Methods of polynomial continuation based design are illustrated here by way of various examples. In particular, the types of deployable structures which form planar rings, or frames, in their deployed configurations are used as design cases. Polynomial continuation is shown to be a powerful component of an equation-based design process. A polyhedral homotopy method, particularly suited to solving problems in kinematics, was synthesised from several researchers' published continuation techniques, and augmented with modern, freely available mathematical computing algorithms. Special adaptations were made in the areas of level-k subface identification, lifting value balancing, and path-following. Techniques of forming closure/compatibility equations by direct use of symmetry, or by use of transfer matrices to enforce loop closure, were developed as appropriate for each example. The geometry of a plane symmetric (rectangular) 6R foldable frame was examined and classified in terms of Denavit-Hartenberg Parameters. Its design parameters were then grouped into feasible and non-feasible regions, before continuation was used as a design tool; generating the design parameters required to build a foldable frame which meets certain configurational specifications. Two further deployable ring/frame classes were then used as design cases: (a) rings which form (planar) regular polygons when deployed, and (b) rings which are doubly plane symmetric and planar when deployed. The governing equations used in the continuation design process are based on symmetry compatibility and transfer matrices respectively. Finally, the 6, 7 and 8-link versions of N-loops were subjected to a witness set analysis, illustrating the way in which continuation can reveal the nature of the mobility of an unknown linkage. Key features of the results are that polynomial continuation was able to provide complete sets of feasible options to a number of practical design problems, and also to reveal the nature of the mobility of a real overconstrained linkage.

Subjects/Keywords: 624.1; 6R Linkage; Deployable ring; Deployable structures; Numerical continuation; Overconstrained mechanism; Polyhedral homotopy; Polynomial continuation

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APA · Chicago · MLA · Vancouver · CSE | Export to Zotero / EndNote / Reference Manager

APA (6^th Edition):

Viquerat, A. D. (2012). Polynomial continuation in the design of deployable structures. (Doctoral Dissertation). University of Cambridge. Retrieved from https://doi.org/10.17863/CAM.14012 ; https://ethos.bl.uk/OrderDetails.do?uin=uk.bl.ethos.545890

Chicago Manual of Style (16^th Edition):

Viquerat, Andrew David. “Polynomial continuation in the design of deployable structures.” 2012. Doctoral Dissertation, University of Cambridge. Accessed April 22, 2021. https://doi.org/10.17863/CAM.14012 ; https://ethos.bl.uk/OrderDetails.do?uin=uk.bl.ethos.545890.

MLA Handbook (7^th Edition):

Viquerat, Andrew David. “Polynomial continuation in the design of deployable structures.” 2012. Web. 22 Apr 2021.

Vancouver:

Viquerat AD. Polynomial continuation in the design of deployable structures. [Internet] [Doctoral dissertation]. University of Cambridge; 2012. [cited 2021 Apr 22]. Available from: https://doi.org/10.17863/CAM.14012 ; https://ethos.bl.uk/OrderDetails.do?uin=uk.bl.ethos.545890.

Council of Science Editors:

Viquerat AD. Polynomial continuation in the design of deployable structures. [Doctoral Dissertation]. University of Cambridge; 2012. Available from: https://doi.org/10.17863/CAM.14012 ; https://ethos.bl.uk/OrderDetails.do?uin=uk.bl.ethos.545890

University of Alberta

7. Bondy, Ronald William. Distillation simulation using physical homotopies.

Degree: MS, Department of Chemical Engineering, 1988, University of Alberta

URL: https://era.library.ualberta.ca/files/2z10ws57g

Subjects/Keywords: Analytic continuation.; Homotopy theory.; Distillation.

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APA · Chicago · MLA · Vancouver · CSE | Export to Zotero / EndNote / Reference Manager

APA (6^th Edition):

Bondy, R. W. (1988). Distillation simulation using physical homotopies. (Masters Thesis). University of Alberta. Retrieved from https://era.library.ualberta.ca/files/2z10ws57g

Chicago Manual of Style (16^th Edition):

Bondy, Ronald William. “Distillation simulation using physical homotopies.” 1988. Masters Thesis, University of Alberta. Accessed April 22, 2021. https://era.library.ualberta.ca/files/2z10ws57g.

MLA Handbook (7^th Edition):

Bondy, Ronald William. “Distillation simulation using physical homotopies.” 1988. Web. 22 Apr 2021.

Vancouver:

Bondy RW. Distillation simulation using physical homotopies. [Internet] [Masters thesis]. University of Alberta; 1988. [cited 2021 Apr 22]. Available from: https://era.library.ualberta.ca/files/2z10ws57g.

Council of Science Editors:

Bondy RW. Distillation simulation using physical homotopies. [Masters Thesis]. University of Alberta; 1988. Available from: https://era.library.ualberta.ca/files/2z10ws57g

NSYSU

8. Chen, Ying-ren. Parallel Computing for Solving the Power Flow Equations.

Degree: Master, Applied Mathematics, 2017, NSYSU

URL: http://etd.lib.nsysu.edu.tw/ETD-db/ETD-search/view_etd?URN=etd-0707117-160535

► The power flow equations are an important part of the power system analysis. It describes the status of nodes in an electrical grid. A grid… (more)

Subjects/Keywords: Power flow equations; homotopy continuation method; parallel computing; Newtonâs iteration method

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APA (6^th Edition):

Chen, Y. (2017). Parallel Computing for Solving the Power Flow Equations. (Thesis). NSYSU. Retrieved from http://etd.lib.nsysu.edu.tw/ETD-db/ETD-search/view_etd?URN=etd-0707117-160535

Note: this citation may be lacking information needed for this citation format:
Not specified: Masters Thesis or Doctoral Dissertation

Chicago Manual of Style (16^th Edition):

Chen, Ying-ren. “Parallel Computing for Solving the Power Flow Equations.” 2017. Thesis, NSYSU. Accessed April 22, 2021. http://etd.lib.nsysu.edu.tw/ETD-db/ETD-search/view_etd?URN=etd-0707117-160535.

Note: this citation may be lacking information needed for this citation format:
Not specified: Masters Thesis or Doctoral Dissertation

MLA Handbook (7^th Edition):

Chen, Ying-ren. “Parallel Computing for Solving the Power Flow Equations.” 2017. Web. 22 Apr 2021.

Vancouver:

Chen Y. Parallel Computing for Solving the Power Flow Equations. [Internet] [Thesis]. NSYSU; 2017. [cited 2021 Apr 22]. Available from: http://etd.lib.nsysu.edu.tw/ETD-db/ETD-search/view_etd?URN=etd-0707117-160535.

Note: this citation may be lacking information needed for this citation format:
Not specified: Masters Thesis or Doctoral Dissertation

Council of Science Editors:

Chen Y. Parallel Computing for Solving the Power Flow Equations. [Thesis]. NSYSU; 2017. Available from: http://etd.lib.nsysu.edu.tw/ETD-db/ETD-search/view_etd?URN=etd-0707117-160535

Note: this citation may be lacking information needed for this citation format:
Not specified: Masters Thesis or Doctoral Dissertation

Colorado State University

9. Brake, Daniel Abram. Homotopy continuation methods, intrinsic localized modes, and cooperative robotic workspaces.

Degree: PhD, Mathematics, 2012, Colorado State University

URL: http://hdl.handle.net/10217/71548

► This dissertation considers three topics that are united by the theme of application of geometric and nonlinear mechanics to practical problems. Firstly we consider the… (more)

▼ This dissertation considers three topics that are united by the theme of application of geometric and nonlinear mechanics to practical problems. Firstly we consider the parallel implementation of numerical solution of nonlinear polynomial systems depending on parameters. The program written to do this is called Paramotopy, and uses the Message Passing Interface to distribute homotopy continuation solves in another program called Bertini across a supercomputer. Paramotopy manages writing of Bertini input files, allows automatic re-solution of the system at points at which paths failed, and makes data management easy. Furthermore, parameter homotopy nets huge performance gains over fresh homotopy continuation runs. Superlinear speedup was achieved, up to hard drive throughput capacity. Various internal settings are demonstrated and explored, and the User's Manual is included. Second, we apply nonlinear theory and simulation to nanomechanical sensor arrays. Using vibrating GaAs pillars, we model Intrinsic Localized Modes (ILMs), and investigate ILM-defect pinning, formation, lifetime, travel and movement, and parameter dependence. Intrinsic Localized Modes have been analyzed on arrays of nonlinear oscillators. So far, these oscillators have had a single direction of vibration. In current experiments for single molecule detection, arrays made of Gallium Arsenide will be innately bidirectional, forced, dissipative. We expand previous full models to bidirectionality, and simulate using ODE solvers. We show that small regions of a very large parameter space permit strong ILM formation. Additionally, we use Hamiltonian mechanics to derive new simplified models for the monodirectional ILM travel on an infinite array. This monodirectional ILMs of constant amplitude have unrealistic behavior. Permitting the amplitude of the ILM to vary in time produces much more realistic behavior, including wandering and intermittent pinning. The final set of problems concerns the application of numerical algebraic geometric methods to untangle the phase space of cooperating robots, and optimize configuration for fault tolerance. Given two robots in proximity to each other, if one experiences joint failure, the other may be able to assist, restoring lost workspace. We define a new multiplicity-weighted workspace measure, and use it to solve the optimization problem of finding the best location for an assistance socket and separation distance for the two robots, showing that the solution depends on robot geometry, which link is being grasped, and the choice of objective function. Advisors/Committee Members: Putkaradze, Vakhtang (advisor), Maciejewski, Tony (advisor), Marconi, Mario (committee member), Bates, Dan (committee member), Shipman, Patrick (committee member).

Subjects/Keywords: sensors; homotopy continuation; intrinsic localized mode; kinematics; parallel computing; robotics

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APA · Chicago · MLA · Vancouver · CSE | Export to Zotero / EndNote / Reference Manager

APA (6^th Edition):

Brake, D. A. (2012). Homotopy continuation methods, intrinsic localized modes, and cooperative robotic workspaces. (Doctoral Dissertation). Colorado State University. Retrieved from http://hdl.handle.net/10217/71548

Chicago Manual of Style (16^th Edition):

Brake, Daniel Abram. “Homotopy continuation methods, intrinsic localized modes, and cooperative robotic workspaces.” 2012. Doctoral Dissertation, Colorado State University. Accessed April 22, 2021. http://hdl.handle.net/10217/71548.

MLA Handbook (7^th Edition):

Brake, Daniel Abram. “Homotopy continuation methods, intrinsic localized modes, and cooperative robotic workspaces.” 2012. Web. 22 Apr 2021.

Vancouver:

Brake DA. Homotopy continuation methods, intrinsic localized modes, and cooperative robotic workspaces. [Internet] [Doctoral dissertation]. Colorado State University; 2012. [cited 2021 Apr 22]. Available from: http://hdl.handle.net/10217/71548.

Council of Science Editors:

Brake DA. Homotopy continuation methods, intrinsic localized modes, and cooperative robotic workspaces. [Doctoral Dissertation]. Colorado State University; 2012. Available from: http://hdl.handle.net/10217/71548

Colorado State University

10. Ihde, Steven L. Preconditioning polynomial systems for homotopy continuation.

Degree: MS(M.S.), Mathematics, 2011, Colorado State University

URL: http://hdl.handle.net/10217/51875

► Polynomial systems are ubiquitous in today's scientific world. These systems need to be solved quickly and efficiently. One key solution method comes from Numerical Algebraic… (more)

Subjects/Keywords: dual basis; polynomial systems; numerical algebraic geometry; homotopy continuation; H-basis

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APA · Chicago · MLA · Vancouver · CSE | Export to Zotero / EndNote / Reference Manager

APA (6^th Edition):

Ihde, S. L. (2011). Preconditioning polynomial systems for homotopy continuation. (Masters Thesis). Colorado State University. Retrieved from http://hdl.handle.net/10217/51875

Chicago Manual of Style (16^th Edition):

Ihde, Steven L. “Preconditioning polynomial systems for homotopy continuation.” 2011. Masters Thesis, Colorado State University. Accessed April 22, 2021. http://hdl.handle.net/10217/51875.

MLA Handbook (7^th Edition):

Ihde, Steven L. “Preconditioning polynomial systems for homotopy continuation.” 2011. Web. 22 Apr 2021.

Vancouver:

Ihde SL. Preconditioning polynomial systems for homotopy continuation. [Internet] [Masters thesis]. Colorado State University; 2011. [cited 2021 Apr 22]. Available from: http://hdl.handle.net/10217/51875.

Council of Science Editors:

Ihde SL. Preconditioning polynomial systems for homotopy continuation. [Masters Thesis]. Colorado State University; 2011. Available from: http://hdl.handle.net/10217/51875

Missouri University of Science and Technology

11. Mills, Thomas Karl. Identifying multiple steady states in the design of reactive distillation processes.

Degree: PhD, Chemical Engineering, Missouri University of Science and Technology

URL: https://scholarsmine.mst.edu/doctoral_dissertations/2190

► "Global homotopy continuation is used to identify multiple steady states in ideal reactive flash and reactive distillation systems involving a reaction of the form A+B… (more)

Subjects/Keywords: Global homotopy continuation; Chemical Engineering

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APA (6^th Edition):

Mills, T. K. (n.d.). Identifying multiple steady states in the design of reactive distillation processes. (Doctoral Dissertation). Missouri University of Science and Technology. Retrieved from https://scholarsmine.mst.edu/doctoral_dissertations/2190

Note: this citation may be lacking information needed for this citation format:
No year of publication.

Chicago Manual of Style (16^th Edition):

Mills, Thomas Karl. “Identifying multiple steady states in the design of reactive distillation processes.” Doctoral Dissertation, Missouri University of Science and Technology. Accessed April 22, 2021. https://scholarsmine.mst.edu/doctoral_dissertations/2190.

Note: this citation may be lacking information needed for this citation format:
No year of publication.

MLA Handbook (7^th Edition):

Mills, Thomas Karl. “Identifying multiple steady states in the design of reactive distillation processes.” Web. 22 Apr 2021.

Note: this citation may be lacking information needed for this citation format:
No year of publication.

Vancouver:

Mills TK. Identifying multiple steady states in the design of reactive distillation processes. [Internet] [Doctoral dissertation]. Missouri University of Science and Technology; [cited 2021 Apr 22]. Available from: https://scholarsmine.mst.edu/doctoral_dissertations/2190.

Note: this citation may be lacking information needed for this citation format:
No year of publication.

Council of Science Editors:

Mills TK. Identifying multiple steady states in the design of reactive distillation processes. [Doctoral Dissertation]. Missouri University of Science and Technology; Available from: https://scholarsmine.mst.edu/doctoral_dissertations/2190

Note: this citation may be lacking information needed for this citation format:
No year of publication.

University of Oulu

12. Tanskanen, J. P. (Juha P.). Phenomenon driven process design:focus on multicomponent reactive and ordinary distillation.

Degree: 1999, University of Oulu

URL: http://urn.fi/urn:isbn:9514251458

► Abstract This thesis describes part of the work that has been done in the Chemical Process Engineering Laboratory of the University of Oulu to systematize… (more)

▼ Abstract This thesis describes part of the work that has been done in the Chemical Process Engineering Laboratory of the University of Oulu to systematize conceptual process design. The aim has been to develop a design methodology, i.e. how process design is done, based on a carefully elaborated concept analysis. The starting point has been that all the knowledge related to process design, i.e. not only the procedural knowledge related to the design activity itself, but also the declarative knowledge related to the design target (process) and the environment (project) in which the design is done, should be systematized. The process design methodology can be represented within a single formalism by treating the activity, target and resources as structural parts of the project object. In that case, each design decision becomes properly constrained by the goal and the resources available, and is also stored together with the domain knowledge on which the decision was based. This holistic approach was adopted when the phenomenon driven process design methodology was built to systematize chemical process development while simultaneously supporting creativity. This thesis concentrates on knowledge generation activity as part of the phenomenon driven process design methodology. A brief description of the generic chemical process object model is presented, after which the focus is on the design activity and the strategy of design. The phenomenon driven process design of an MTBE production process is described as an illustration of the methodology. It is shown how combinations of reaction and separation, such as reactive distillation, evolve naturally during a design project. For the evaluation of attainable state distributions, which is an important design task implied by the methodology, a robust method was developed to solve the modified MESH equations of reactive distillation. The method was also applied when developing a rigorous calculation method for the determination of minimum energy demand of multicomponent distillation.

Subjects/Keywords: design methodology; homotopy continuation; minimum reflux

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APA (6^th Edition):

Tanskanen, J. P. (. P. ). (1999). Phenomenon driven process design:focus on multicomponent reactive and ordinary distillation. (Doctoral Dissertation). University of Oulu. Retrieved from http://urn.fi/urn:isbn:9514251458

Chicago Manual of Style (16^th Edition):

Tanskanen, J P (Juha P ). “Phenomenon driven process design:focus on multicomponent reactive and ordinary distillation.” 1999. Doctoral Dissertation, University of Oulu. Accessed April 22, 2021. http://urn.fi/urn:isbn:9514251458.

MLA Handbook (7^th Edition):

Tanskanen, J P (Juha P ). “Phenomenon driven process design:focus on multicomponent reactive and ordinary distillation.” 1999. Web. 22 Apr 2021.

Vancouver:

Tanskanen JP(P). Phenomenon driven process design:focus on multicomponent reactive and ordinary distillation. [Internet] [Doctoral dissertation]. University of Oulu; 1999. [cited 2021 Apr 22]. Available from: http://urn.fi/urn:isbn:9514251458.

Council of Science Editors:

Tanskanen JP(P). Phenomenon driven process design:focus on multicomponent reactive and ordinary distillation. [Doctoral Dissertation]. University of Oulu; 1999. Available from: http://urn.fi/urn:isbn:9514251458

University of Illinois – Chicago

13. Bliss, Nathan R. Computing Series Expansions of Algebraic Space Curves.

Degree: 2018, University of Illinois – Chicago

URL: http://hdl.handle.net/10027/22682

► We work towards a series-based computational approach for polynomial systems having positive-dimensional solution sets. The tropical variety gives information on the exponents of the leading… (more)

Subjects/Keywords: computational algebraic geometry; puiseux series; gauss-newton algorithm; tropical geometry; polynomial systems; homotopy continuation

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APA (6^th Edition):

Bliss, N. R. (2018). Computing Series Expansions of Algebraic Space Curves. (Thesis). University of Illinois – Chicago. Retrieved from http://hdl.handle.net/10027/22682

Note: this citation may be lacking information needed for this citation format:
Not specified: Masters Thesis or Doctoral Dissertation

Chicago Manual of Style (16^th Edition):

Bliss, Nathan R. “Computing Series Expansions of Algebraic Space Curves.” 2018. Thesis, University of Illinois – Chicago. Accessed April 22, 2021. http://hdl.handle.net/10027/22682.

Note: this citation may be lacking information needed for this citation format:
Not specified: Masters Thesis or Doctoral Dissertation

MLA Handbook (7^th Edition):

Bliss, Nathan R. “Computing Series Expansions of Algebraic Space Curves.” 2018. Web. 22 Apr 2021.

Vancouver:

Bliss NR. Computing Series Expansions of Algebraic Space Curves. [Internet] [Thesis]. University of Illinois – Chicago; 2018. [cited 2021 Apr 22]. Available from: http://hdl.handle.net/10027/22682.

Note: this citation may be lacking information needed for this citation format:
Not specified: Masters Thesis or Doctoral Dissertation

Council of Science Editors:

Bliss NR. Computing Series Expansions of Algebraic Space Curves. [Thesis]. University of Illinois – Chicago; 2018. Available from: http://hdl.handle.net/10027/22682

Note: this citation may be lacking information needed for this citation format:
Not specified: Masters Thesis or Doctoral Dissertation

University of Notre Dame

14. Timothy M McCoy. Mesh-Expanding Homotopies and Numerical Irreducible Decomposition Over a Number Field</h1>.

Degree: Applied and Computational Mathematics and Statistics, 2014, University of Notre Dame

URL: https://curate.nd.edu/show/6395w66528z

► Algorithms from the field of numerical algebraic geometry provide robust means to compute all isolated solutions of arbitrary systems of polynomials and to give… (more)

Subjects/Keywords: algebraic computation; numerical algebraic geometry; homotopy continuation; computational mathematics; polynomial systems; boundary value problems

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APA (6^th Edition):

McCoy, T. M. (2014). Mesh-Expanding Homotopies and Numerical Irreducible Decomposition Over a Number Field</h1>. (Thesis). University of Notre Dame. Retrieved from https://curate.nd.edu/show/6395w66528z

Note: this citation may be lacking information needed for this citation format:
Not specified: Masters Thesis or Doctoral Dissertation

Chicago Manual of Style (16^th Edition):

McCoy, Timothy M. “Mesh-Expanding Homotopies and Numerical Irreducible Decomposition Over a Number Field</h1>.” 2014. Thesis, University of Notre Dame. Accessed April 22, 2021. https://curate.nd.edu/show/6395w66528z.

Note: this citation may be lacking information needed for this citation format:
Not specified: Masters Thesis or Doctoral Dissertation

MLA Handbook (7^th Edition):

McCoy, Timothy M. “Mesh-Expanding Homotopies and Numerical Irreducible Decomposition Over a Number Field</h1>.” 2014. Web. 22 Apr 2021.

Vancouver:

McCoy TM. Mesh-Expanding Homotopies and Numerical Irreducible Decomposition Over a Number Field</h1>. [Internet] [Thesis]. University of Notre Dame; 2014. [cited 2021 Apr 22]. Available from: https://curate.nd.edu/show/6395w66528z.

Note: this citation may be lacking information needed for this citation format:
Not specified: Masters Thesis or Doctoral Dissertation

Council of Science Editors:

McCoy TM. Mesh-Expanding Homotopies and Numerical Irreducible Decomposition Over a Number Field</h1>. [Thesis]. University of Notre Dame; 2014. Available from: https://curate.nd.edu/show/6395w66528z

Note: this citation may be lacking information needed for this citation format:
Not specified: Masters Thesis or Doctoral Dissertation

University of Waterloo

15. Vu, Thi Xuan. Homotopy algorithms for solving structured determinantal systems.

Degree: 2020, University of Waterloo

URL: http://hdl.handle.net/10012/16566

► Multivariate polynomial systems arising in numerous applications have special structures. In particular, determinantal structures and invariant systems appear in a wide range of applications such… (more)

Subjects/Keywords: symbolic computation; polynomial systems solving; symbolic homotopy continuation; determinantal systems; invariant algebraic systems

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APA (6^th Edition):

Vu, T. X. (2020). Homotopy algorithms for solving structured determinantal systems. (Thesis). University of Waterloo. Retrieved from http://hdl.handle.net/10012/16566

Note: this citation may be lacking information needed for this citation format:
Not specified: Masters Thesis or Doctoral Dissertation

Chicago Manual of Style (16^th Edition):

Vu, Thi Xuan. “Homotopy algorithms for solving structured determinantal systems.” 2020. Thesis, University of Waterloo. Accessed April 22, 2021. http://hdl.handle.net/10012/16566.

Note: this citation may be lacking information needed for this citation format:
Not specified: Masters Thesis or Doctoral Dissertation

MLA Handbook (7^th Edition):

Vu, Thi Xuan. “Homotopy algorithms for solving structured determinantal systems.” 2020. Web. 22 Apr 2021.

Vancouver:

Vu TX. Homotopy algorithms for solving structured determinantal systems. [Internet] [Thesis]. University of Waterloo; 2020. [cited 2021 Apr 22]. Available from: http://hdl.handle.net/10012/16566.

Note: this citation may be lacking information needed for this citation format:
Not specified: Masters Thesis or Doctoral Dissertation

Council of Science Editors:

Vu TX. Homotopy algorithms for solving structured determinantal systems. [Thesis]. University of Waterloo; 2020. Available from: http://hdl.handle.net/10012/16566

Note: this citation may be lacking information needed for this citation format:
Not specified: Masters Thesis or Doctoral Dissertation

University of Texas – Austin

16. Gulino, Marco. A homotopic approach to solve the fuel optimal spacecraft proximity operations problem.

Degree: MSin Engineering, Aerospace Engineering, 2017, University of Texas – Austin

URL: http://hdl.handle.net/2152/60385

► This report focuses on finding the low-thrust fuel optimal solution to a class of spacecraft proximity operations subject to path constraints. The mission is for… (more)

Subjects/Keywords: Fuel optimal; Proximity operations; Clohessy-Wiltshire; Guidance; Optimal control; Homotopy; Stabilized continuation

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APA (6^th Edition):

Gulino, M. (2017). A homotopic approach to solve the fuel optimal spacecraft proximity operations problem. (Masters Thesis). University of Texas – Austin. Retrieved from http://hdl.handle.net/2152/60385

Chicago Manual of Style (16^th Edition):

Gulino, Marco. “A homotopic approach to solve the fuel optimal spacecraft proximity operations problem.” 2017. Masters Thesis, University of Texas – Austin. Accessed April 22, 2021. http://hdl.handle.net/2152/60385.

MLA Handbook (7^th Edition):

Gulino, Marco. “A homotopic approach to solve the fuel optimal spacecraft proximity operations problem.” 2017. Web. 22 Apr 2021.

Vancouver:

Gulino M. A homotopic approach to solve the fuel optimal spacecraft proximity operations problem. [Internet] [Masters thesis]. University of Texas – Austin; 2017. [cited 2021 Apr 22]. Available from: http://hdl.handle.net/2152/60385.

Council of Science Editors:

Gulino M. A homotopic approach to solve the fuel optimal spacecraft proximity operations problem. [Masters Thesis]. University of Texas – Austin; 2017. Available from: http://hdl.handle.net/2152/60385

Michigan State University

17. Chen, Tianran. Projective path tracking for homotopy continuation method.

Degree: 2012, Michigan State University

URL: http://etd.lib.msu.edu/islandora/object/etd:126

►

Thesis Ph. D. Michigan State University, Applied Mathematics 2012.

Solving systems of polynomial equations is an important problem in mathematics with a wide range of… (more)

Subjects/Keywords: Homotopy theory; Analytic functions; Analytic continuation; Polynomials; Equations – Numerical solutions; Geometry, Riemannian; Applied mathematics

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APA (6^th Edition):

Chen, T. (2012). Projective path tracking for homotopy continuation method. (Thesis). Michigan State University. Retrieved from http://etd.lib.msu.edu/islandora/object/etd:126

Note: this citation may be lacking information needed for this citation format:
Not specified: Masters Thesis or Doctoral Dissertation

Chicago Manual of Style (16^th Edition):

Chen, Tianran. “Projective path tracking for homotopy continuation method.” 2012. Thesis, Michigan State University. Accessed April 22, 2021. http://etd.lib.msu.edu/islandora/object/etd:126.

Note: this citation may be lacking information needed for this citation format:
Not specified: Masters Thesis or Doctoral Dissertation

MLA Handbook (7^th Edition):

Chen, Tianran. “Projective path tracking for homotopy continuation method.” 2012. Web. 22 Apr 2021.

Vancouver:

Chen T. Projective path tracking for homotopy continuation method. [Internet] [Thesis]. Michigan State University; 2012. [cited 2021 Apr 22]. Available from: http://etd.lib.msu.edu/islandora/object/etd:126.

Note: this citation may be lacking information needed for this citation format:
Not specified: Masters Thesis or Doctoral Dissertation

Council of Science Editors:

Chen T. Projective path tracking for homotopy continuation method. [Thesis]. Michigan State University; 2012. Available from: http://etd.lib.msu.edu/islandora/object/etd:126

Note: this citation may be lacking information needed for this citation format:
Not specified: Masters Thesis or Doctoral Dissertation

18. Imbach, Rémi. Résolution de contraintes géométriques en guidant une méthode homotopique par la géométrie : Solving geometric constraints by a continuation method led by geometry.

Degree: Docteur es, Informatique, 2013, Université de Strasbourg

URL: http://www.theses.fr/2013STRAD033

►

Suivant le domaine où on les sollicite, les solutions d’un système de contraintes géométriques (SCG) peuvent être : – formelles et exactes : elles prennent… (more)

▼

Suivant le domaine où on les sollicite, les solutions d’un système de contraintes géométriques (SCG) peuvent être : – formelles et exactes : elles prennent par exemple la forme d’un plan de construction produisant toutes les solutions, obtenu en appliquant des règles dérivées de lemmes de géométrie. Beaucoup de SCG, surtout en 3D, résistent à cette approche ; – numériques et approchées : elles sont les solutions d’un système d’équations construit à partir des contraintes et trouvées grâce à des méthodes numériques efficaces quand elles ne recherchent qu’une solution. De par la nature des problèmes traités, chercher toutes les solutions conduit à une complexité exponentielle. Les méthodes par continuation, ou homotopie, permettent d’obtenir toutes les solutions d’un système d’équations polynomiales. Leur application à des SCG est coûteuse et difficilement sujette aux raisonnements permis par l’origine géométrique du problème car elles opèrent hors de l’espace des figures géométriques. Notre travail a pour objet la spécialisation d’une méthode par continuation à des SCG. La géométrie simplifie et justifie sa mise en œuvre dans l’espace des figures, ou des raisonnements géométriques sont possibles. On aborde également les cas ou l’ensemble de solutions d’un problème contient des éléments isolés et des continuums. Des solutions proches d’une esquisse fournie par un utilisateur sont d’abord trouvées. La recherche d’autres solutions, malgré sa complexité exponentielle, est rendue envisageable par une approche itérative. Une nouvelle méthode de décomposition est proposée pour maîtriser le coût de la résolution.

Depending on the required application field, the solutions of a geometric constraints system (GCS) are either : – symbolic and exact such as construction plans, providing all the solutions, obtained by applying geometric rules. Many problems, mostly in a 3D context, resist to this approach ; – or numerical and approximated : they are the solutions of a system of equations built from the constraints, provided by generical numerical methods that are efficient when only one solution is sought. However, searching all the solutions leads to an exponential computation cost, due to the nature of problems. Continuation methods, also called homotopic methods, find all the solutions of a polynomial system. Using them to solve systems of equations associated to systems of constraints is nevertheless costly. Moreover, combining them with geometric reasoning is a challenge, because they act in a projective complex space and not in the realizations space. The aim of this work is to specialize a continuation method to GCS. Geometry is exploited to simplify and justify its adaptation in the space of realizations, so allowing geometric reasoning. Cases where the connected components of the solution space of a problem have heterogeneous dimensions are addressed. The method discussed here provides in a first step solutions that are similar to a sketch drawn by the user. Then a procedure is proposed to search new solutions. Its…

Advisors/Committee Members: Schreck, Pascal (thesis director).

Subjects/Keywords: Résolution de contraintes géométriques; Méthodes par continuation; Homotopie; Méthodes Hybrides; Modélisation géométrique; Geometric constraints solving; Continuation methods; Homotopy; Hybrid methods; Geometric modeling; 514.2

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APA (6^th Edition):

Imbach, R. (2013). Résolution de contraintes géométriques en guidant une méthode homotopique par la géométrie : Solving geometric constraints by a continuation method led by geometry. (Doctoral Dissertation). Université de Strasbourg. Retrieved from http://www.theses.fr/2013STRAD033

Chicago Manual of Style (16^th Edition):

Imbach, Rémi. “Résolution de contraintes géométriques en guidant une méthode homotopique par la géométrie : Solving geometric constraints by a continuation method led by geometry.” 2013. Doctoral Dissertation, Université de Strasbourg. Accessed April 22, 2021. http://www.theses.fr/2013STRAD033.

MLA Handbook (7^th Edition):

Imbach, Rémi. “Résolution de contraintes géométriques en guidant une méthode homotopique par la géométrie : Solving geometric constraints by a continuation method led by geometry.” 2013. Web. 22 Apr 2021.

Vancouver:

Imbach R. Résolution de contraintes géométriques en guidant une méthode homotopique par la géométrie : Solving geometric constraints by a continuation method led by geometry. [Internet] [Doctoral dissertation]. Université de Strasbourg; 2013. [cited 2021 Apr 22]. Available from: http://www.theses.fr/2013STRAD033.

Council of Science Editors:

Imbach R. Résolution de contraintes géométriques en guidant une méthode homotopique par la géométrie : Solving geometric constraints by a continuation method led by geometry. [Doctoral Dissertation]. Université de Strasbourg; 2013. Available from: http://www.theses.fr/2013STRAD033

University of Notre Dame

19. Daniel James Bates. Theory and Applications in Numerical Algebraic Geometry</h1>.

Degree: Mathematics, 2006, University of Notre Dame

URL: https://curate.nd.edu/show/sj13902265k

► Homotopy continuation techniques may be used to approximate all isolated solutions of a polynomial system. More recent methods which form the crux of the… (more)

Subjects/Keywords: path tracking; numerical algebraic geometry; Bertini; homotopy continuation

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APA (6^th Edition):

Bates, D. J. (2006). Theory and Applications in Numerical Algebraic Geometry</h1>. (Thesis). University of Notre Dame. Retrieved from https://curate.nd.edu/show/sj13902265k

Note: this citation may be lacking information needed for this citation format:
Not specified: Masters Thesis or Doctoral Dissertation

Chicago Manual of Style (16^th Edition):

Bates, Daniel James. “Theory and Applications in Numerical Algebraic Geometry</h1>.” 2006. Thesis, University of Notre Dame. Accessed April 22, 2021. https://curate.nd.edu/show/sj13902265k.

Note: this citation may be lacking information needed for this citation format:
Not specified: Masters Thesis or Doctoral Dissertation

MLA Handbook (7^th Edition):

Bates, Daniel James. “Theory and Applications in Numerical Algebraic Geometry</h1>.” 2006. Web. 22 Apr 2021.

Vancouver:

Bates DJ. Theory and Applications in Numerical Algebraic Geometry</h1>. [Internet] [Thesis]. University of Notre Dame; 2006. [cited 2021 Apr 22]. Available from: https://curate.nd.edu/show/sj13902265k.

Note: this citation may be lacking information needed for this citation format:
Not specified: Masters Thesis or Doctoral Dissertation

Council of Science Editors:

Bates DJ. Theory and Applications in Numerical Algebraic Geometry</h1>. [Thesis]. University of Notre Dame; 2006. Available from: https://curate.nd.edu/show/sj13902265k

Note: this citation may be lacking information needed for this citation format:
Not specified: Masters Thesis or Doctoral Dissertation

20. Bradley, Nicholas Ethan. Initial guess and optimization strategies for multi-body space trajectories with application to free return trajectories to near-Earth asteroids.

Degree: PhD, Aerospace Engineering, 2014, University of Texas – Austin

URL: http://hdl.handle.net/2152/26858

► This concept of calculating, optimizing, and utilizing a trajectory known as a ``Free Return Trajectory" to facilitate spacecraft rendezvous with Near-Earth Asteroids is presented in… (more)

▼ This concept of calculating, optimizing, and utilizing a trajectory known as a ``Free Return Trajectory" to facilitate spacecraft rendezvous with Near-Earth Asteroids is presented in this dissertation. A Free Return Trajectory may be defined as a trajectory that begins and ends near the same point, relative to some central body, without performing any deterministic velocity maneuvers (i.e., no maneuvers are planned in a theoretical sense for the nominal mission to proceed). Free Return Trajectories have been utilized previously for other purposes in astrodynamics, but they have not been previously applied to the problem of Near-Earth Asteroid rendezvous. Presented here is a series of descriptions, algorithms, and results related to trajectory initial guess calculation and optimal trajectory convergence. First, Earth-centered Free Return Trajectories are described in a general manner, and these trajectories are classified into several families based on common characteristics. Next, these trajectories are used to automatically generate initial conditions in the three-body problem for the purpose of Near-Earth Asteroid rendezvous. For several bodies of interest, example initial conditions are automatically generated, and are subsequently converged, resulting in feasible, locally-optimal, round-trip trajectories to Near-Earth Asteroids utilizing Free Return Trajectories. Subsequently, a study is performed on using an unpowered flyby of the Moon to lower the overall DV cost for a nominal round-trip voyage to a Near-Earth Asteroid. Using the Moon is shown to appreciably decrease the overall mission cost. In creating the formulation and algorithms for the Lunar flyby problem, an initial guess routine for generic planetary and lunar flyby tours was developed. This continuation algorithm is presented next, and details a novel process by which ballistic trajectories in a simplistic two-body force model may be iteratively converged in progressively more realistic dynamical models until a final converged ballistic trajectory is found in a full-ephemeris, full-dynamics model. This procedure is useful for constructing interplanetary transfers and moon tours in a realistic dynamical framework; an interplanetary and an inter-moon example are both shown. To summarize, the material in this dissertation consists of: novel algorithms to compute Free Return Trajectories, and application of the concept to Near-Earth Asteroid rendezvous; demonstration of cost-savings by using a Lunar flyby; and a novel routine to transfer trajectories from a simplistic model to a more realistic dynamical representation. Advisors/Committee Members: Russell, Ryan Paul, 1976- (advisor), Ocampo, Cesar (advisor).

Subjects/Keywords: Free return; Trajectory; Asteroid; Near-Earth asteroid; NEA; Continuation; Homotopy; optimization; Initial guess; FRT; Interplanetary; Tour; Rendezvous; Abort; Orbit; CRTBP; Resonance

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APA (6^th Edition):

Bradley, N. E. (2014). Initial guess and optimization strategies for multi-body space trajectories with application to free return trajectories to near-Earth asteroids. (Doctoral Dissertation). University of Texas – Austin. Retrieved from http://hdl.handle.net/2152/26858

Chicago Manual of Style (16^th Edition):

Bradley, Nicholas Ethan. “Initial guess and optimization strategies for multi-body space trajectories with application to free return trajectories to near-Earth asteroids.” 2014. Doctoral Dissertation, University of Texas – Austin. Accessed April 22, 2021. http://hdl.handle.net/2152/26858.

MLA Handbook (7^th Edition):

Bradley, Nicholas Ethan. “Initial guess and optimization strategies for multi-body space trajectories with application to free return trajectories to near-Earth asteroids.” 2014. Web. 22 Apr 2021.

Vancouver:

Bradley NE. Initial guess and optimization strategies for multi-body space trajectories with application to free return trajectories to near-Earth asteroids. [Internet] [Doctoral dissertation]. University of Texas – Austin; 2014. [cited 2021 Apr 22]. Available from: http://hdl.handle.net/2152/26858.

Council of Science Editors:

Bradley NE. Initial guess and optimization strategies for multi-body space trajectories with application to free return trajectories to near-Earth asteroids. [Doctoral Dissertation]. University of Texas – Austin; 2014. Available from: http://hdl.handle.net/2152/26858

Michigan State University

21. Mohseni Moghadam, Mahmoud. Homotopy continuation method for nonlinear equations.

Degree: PhD, Department of Mathematics, 1984, Michigan State University

URL: http://etd.lib.msu.edu/islandora/object/etd:41285

Subjects/Keywords: Homotopy theory; Analytic functions; Analytic continuation; Differential equations, Nonlinear – Numerical solutions

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APA · Chicago · MLA · Vancouver · CSE | Export to Zotero / EndNote / Reference Manager

APA (6^th Edition):

Mohseni Moghadam, M. (1984). Homotopy continuation method for nonlinear equations. (Doctoral Dissertation). Michigan State University. Retrieved from http://etd.lib.msu.edu/islandora/object/etd:41285

Chicago Manual of Style (16^th Edition):

Mohseni Moghadam, Mahmoud. “Homotopy continuation method for nonlinear equations.” 1984. Doctoral Dissertation, Michigan State University. Accessed April 22, 2021. http://etd.lib.msu.edu/islandora/object/etd:41285.

MLA Handbook (7^th Edition):

Mohseni Moghadam, Mahmoud. “Homotopy continuation method for nonlinear equations.” 1984. Web. 22 Apr 2021.

Vancouver:

Mohseni Moghadam M. Homotopy continuation method for nonlinear equations. [Internet] [Doctoral dissertation]. Michigan State University; 1984. [cited 2021 Apr 22]. Available from: http://etd.lib.msu.edu/islandora/object/etd:41285.

Council of Science Editors:

Mohseni Moghadam M. Homotopy continuation method for nonlinear equations. [Doctoral Dissertation]. Michigan State University; 1984. Available from: http://etd.lib.msu.edu/islandora/object/etd:41285

University of Southern California

22. Kobilarov, Marin. Discrete geometric motion control of autonomous vehicles.

Degree: PhD, Computer Science (Robotics & Automation), 2008, University of Southern California

URL: http://digitallibrary.usc.edu/cdm/compoundobject/collection/p15799coll127/id/109355/rec/2035

► The goal of this work is to develop methods to optimally control autonomous robotic vehicles in natural environments. The main contribution is the derivation of… (more)

▼ The goal of this work is to develop methods to optimally control autonomous robotic vehicles in natural environments. The main contribution is the derivation of state-space structure respecting integration and optimization schemes for mechanical systems with symmetries, controllable shape dynamics, and nonholonomic constraints based on the theory of discrete mechanics. At the core of this approach lies the discretization of variational principles of mechanics that results in various numerical benefits previously unexplored in the area. The resulting framework is then used as a basis for developing optimal control methods applicable to various systems. Developed examples include simplified models of a car, a helicopter, a snakeboard, and a boat. The resulting algorithms are numerically stable, preserve the mechanical geometric structure, and are numerically competitive to existing methods. In addition, two important extensions with view towards practical applications are proposed. First, complex constraints are handled morerobustly using homotopy continuation – the process of relaxing nontrivial motion constraints arising either from complicated dynamics or from obstacles in the environment and then smoothly transforming the solution of such easier problem into the original one by deforming the constraints back to their original shape. Second, the optimality and computational efficiency of solution trajectories is addressed by combining discrete mechanics and optimal control (DMOC) with sampling-based roadmaps – a motion planning method focused on global exploration of the state-space. This allows the composition of simple locally optimal DMOC solution trajectories into near globally optimal motions that can handle complex, cluttered environments. Advisors/Committee Members: Sukhatme, Gaurav S. (Committee Chair), Newton, Paul K. (Committee Member), Schaal, Stefan (Committee Member), Marsden, Jerrold (Committee Member), Desbrun, Mathieu (Committee Member).

Subjects/Keywords: robotics; motion planning; discrete mechanics; optimal control; probabilistic roadmap; homotopy; continuation

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APA (6^th Edition):

Kobilarov, M. (2008). Discrete geometric motion control of autonomous vehicles. (Doctoral Dissertation). University of Southern California. Retrieved from http://digitallibrary.usc.edu/cdm/compoundobject/collection/p15799coll127/id/109355/rec/2035

Chicago Manual of Style (16^th Edition):

Kobilarov, Marin. “Discrete geometric motion control of autonomous vehicles.” 2008. Doctoral Dissertation, University of Southern California. Accessed April 22, 2021. http://digitallibrary.usc.edu/cdm/compoundobject/collection/p15799coll127/id/109355/rec/2035.

MLA Handbook (7^th Edition):

Kobilarov, Marin. “Discrete geometric motion control of autonomous vehicles.” 2008. Web. 22 Apr 2021.

Vancouver:

Kobilarov M. Discrete geometric motion control of autonomous vehicles. [Internet] [Doctoral dissertation]. University of Southern California; 2008. [cited 2021 Apr 22]. Available from: http://digitallibrary.usc.edu/cdm/compoundobject/collection/p15799coll127/id/109355/rec/2035.

Council of Science Editors:

Kobilarov M. Discrete geometric motion control of autonomous vehicles. [Doctoral Dissertation]. University of Southern California; 2008. Available from: http://digitallibrary.usc.edu/cdm/compoundobject/collection/p15799coll127/id/109355/rec/2035

23. Mobahi, Hossein. Optimization by Gaussian smoothing with application to geometric alignment.

Degree: PhD, 0112, 2013, University of Illinois – Urbana-Champaign

URL: http://hdl.handle.net/2142/42330

► It is well-known that global optimization of a nonconvex function, in general, is computationally intractable. Nevertheless, many objective functions that we need to optimize may… (more)

▼ It is well-known that global optimization of a nonconvex function, in general, is computationally intractable. Nevertheless, many objective functions that we need to optimize may be nonconvex. In practice, when working with such a nonconvex function, a very natural heuristic is to employ a coarse-to-fine search for the global optimum. A popular deterministic procedure that exemplifies this idea can be summarized briefly as follows. Consider an unconstrained optimization task of minimizing some nonconvex function. One starts from a highly smoothed version of the objective function and hopes that the smoothing eliminates most spurious local minima. More ideally, one hopes that the highly smoothed function would be a convex function, whose global minimum can be found efficiently. Once the minimum of the smoothed function is found, one could gradually reduce the smoothing effect and follow the continuous path of the minimizer, eventually towards a minimum of the objective function. Empirically, people have observed that the minimum found this way has high chance to be the global minimum. Despite its empirical success, there has been little theoretical understanding about the effect of smoothing on optimization. This work rigorously studies some of the fundamental properties of the smoothing technique. In particular, we present a formal definition for the functions that can eventually become convex by smoothing. We present extremely simple sufficient condition for asymptotic convexity as well as a very simple form for an asymptotic minimizer. Our sufficient conditions hold when the objective function satisfies certain decay conditions. Our initial interest for studying this topic arise from its well-known use in geometric image alignment. The alignment problem can be formulated as an optimization task that minimizes the visual difference between the images by searching the space of transformations. Unfortunately, the cost function associated to this problem usually contains many local minima. Thus, unless very good initialization is provided, simple greedy optimization may lead to poor results. To improve the attained solution for the alignment task, we propose smoothing the objective function of the alignment task. In particular, we derive the theoretically correct image blur kernels that arise from (Gaussian) smoothing an alignment objective function. We show that, for smoothing the objective of common motion models, such as affine and homography, there exists a corresponding integral operator on the image space. We refer to the kernels of such integral operators as transformation kernels. Thus, instead of convolving the objective function with a Gaussian kernel in transformation space, we can equivalently compute an integral transform in the image space, which is much cheaper to compute. Advisors/Committee Members: Ma, Yi (advisor), Ma, Yi (Committee Chair), Huang, Thomas S. (committee member), Forsyth, David A. (committee member), Hoiem, Derek W. (committee member), Soatto, Stefano (committee member).

Subjects/Keywords: Nonconvex Optimization; Homotopy Continuation; Image Alignment; Point Cloud Alignment; Coarse-to-fine Optimization

…INTRODUCTION 1.1 Nonconvex Optimization . 1.2 Homotopy Continuation . 1.3 Smoothing… …continuation or homotopy continuation method. The idea is to somehow simplify the original… …reviewed in the rest of this chapter. 1.2 Homotopy Continuation Continuation is a well… …problem that involves a function f : X → Y. Homotopy continuation method embeds f (x)… …x5B;9], optimization by homotopy continuation [10], deterministic annealing…

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APA · Chicago · MLA · Vancouver · CSE | Export to Zotero / EndNote / Reference Manager

APA (6^th Edition):

Mobahi, H. (2013). Optimization by Gaussian smoothing with application to geometric alignment. (Doctoral Dissertation). University of Illinois – Urbana-Champaign. Retrieved from http://hdl.handle.net/2142/42330

Chicago Manual of Style (16^th Edition):

Mobahi, Hossein. “Optimization by Gaussian smoothing with application to geometric alignment.” 2013. Doctoral Dissertation, University of Illinois – Urbana-Champaign. Accessed April 22, 2021. http://hdl.handle.net/2142/42330.

MLA Handbook (7^th Edition):

Mobahi, Hossein. “Optimization by Gaussian smoothing with application to geometric alignment.” 2013. Web. 22 Apr 2021.

Vancouver:

Mobahi H. Optimization by Gaussian smoothing with application to geometric alignment. [Internet] [Doctoral dissertation]. University of Illinois – Urbana-Champaign; 2013. [cited 2021 Apr 22]. Available from: http://hdl.handle.net/2142/42330.

Council of Science Editors:

Mobahi H. Optimization by Gaussian smoothing with application to geometric alignment. [Doctoral Dissertation]. University of Illinois – Urbana-Champaign; 2013. Available from: http://hdl.handle.net/2142/42330

24. Kileel, Joseph David. Algebraic Geometry for Computer Vision.

Degree: Mathematics, 2017, University of California – Berkeley

URL: http://www.escholarship.org/uc/item/1mj041cc

► This thesis uses tools from algebraic geometry to solve problems about three-dimensional scene reconstruction. 3D reconstruction is a fundamental task in multiview geometry, a field… (more)

▼ This thesis uses tools from algebraic geometry to solve problems about three-dimensional scene reconstruction. 3D reconstruction is a fundamental task in multiview geometry, a field of computer vision. Given images of a world scene, taken by cameras in unknown positions, how can we best build a 3D model for the scene? Novel results are obtained for various challenging minimal problems, which are important algorithmic routines in Random Sampling Consensus pipelines for reconstruction. These routines reduce overfitting when outliers are present in image data.Our approach throughout is to formulate inverse problems as structured systems of polynomial equations, and then to exploit underlying geometry. We apply numerical algebraic geometry, commutative algebra and tropical geometry, and we derive new mathematical results in these fields. We present simulations on image data as well as an implementation of general-purpose homotopy-continuation software for implicitization in computational algebraic geometry.Chapter 1 introduces some relevant computer vision. Chapters 2 and 3 are devoted to the recovery of camera positions from images. We resolve an open problem concerning two calibrated cameras raised by Sameer Agarwal, a vision expert at Google Research, by using the algebraic theory of Ulrich sheaves. This gives a robust test for identifying outliers in terms of spectral gaps. Next, we quantify the algebraic complexity for notorious poorly understood cases for three calibrated cameras. This is achieved by formulating in terms of structured linear sections of an explicit moduli space and then computing via homotopy-continuation. In Chapter 4, a new framework for modeling image distortion is proposed, based on lifting algebraic varieties in projective space to varieties in other toric varieties. We check that our formulation leads to faster and more stable solvers than the state of the art. Lastly, Chapter 5 concludes by studying possible pictures of simple objects, as varieties inside products of projective planes. In particular, this dissertation exhibits that algebro-geometric methods can actually be useful in practical settings.

Subjects/Keywords: Mathematics; Algebraic geometry; Chow form; Commutative algebra; Computer vision; Homotopy continuation; Minimal problems

…geometry [11]. • We contribute general-purpose homotopy-continuation software for…

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APA (6^th Edition):

Kileel, J. D. (2017). Algebraic Geometry for Computer Vision. (Thesis). University of California – Berkeley. Retrieved from http://www.escholarship.org/uc/item/1mj041cc

Note: this citation may be lacking information needed for this citation format:
Not specified: Masters Thesis or Doctoral Dissertation

Chicago Manual of Style (16^th Edition):

Kileel, Joseph David. “Algebraic Geometry for Computer Vision.” 2017. Thesis, University of California – Berkeley. Accessed April 22, 2021. http://www.escholarship.org/uc/item/1mj041cc.

Note: this citation may be lacking information needed for this citation format:
Not specified: Masters Thesis or Doctoral Dissertation

MLA Handbook (7^th Edition):

Kileel, Joseph David. “Algebraic Geometry for Computer Vision.” 2017. Web. 22 Apr 2021.

Vancouver:

Kileel JD. Algebraic Geometry for Computer Vision. [Internet] [Thesis]. University of California – Berkeley; 2017. [cited 2021 Apr 22]. Available from: http://www.escholarship.org/uc/item/1mj041cc.

Note: this citation may be lacking information needed for this citation format:
Not specified: Masters Thesis or Doctoral Dissertation

Council of Science Editors:

Kileel JD. Algebraic Geometry for Computer Vision. [Thesis]. University of California – Berkeley; 2017. Available from: http://www.escholarship.org/uc/item/1mj041cc

Note: this citation may be lacking information needed for this citation format:
Not specified: Masters Thesis or Doctoral Dissertation

University of South Florida

25. Patel, Keyurkumar S. Automatic generation of global phase equilibrium diagram from equation of state.

Degree: 2007, University of South Florida

URL: https://scholarcommons.usf.edu/etd/2318

► A computational tool that uses an automated and reliable procedure for systematic generation of global phase equilibrium diagram (GPED) is developed for binary system using… (more)

Subjects/Keywords: Automatic differentiation; Homotopy continuation; Critical point; Phase stability; Mathematical modeling; American Studies; Arts and Humanities

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APA · Chicago · MLA · Vancouver · CSE | Export to Zotero / EndNote / Reference Manager

APA (6^th Edition):

Patel, K. S. (2007). Automatic generation of global phase equilibrium diagram from equation of state. (Thesis). University of South Florida. Retrieved from https://scholarcommons.usf.edu/etd/2318

Note: this citation may be lacking information needed for this citation format:
Not specified: Masters Thesis or Doctoral Dissertation

Chicago Manual of Style (16^th Edition):

Patel, Keyurkumar S. “Automatic generation of global phase equilibrium diagram from equation of state.” 2007. Thesis, University of South Florida. Accessed April 22, 2021. https://scholarcommons.usf.edu/etd/2318.

Note: this citation may be lacking information needed for this citation format:
Not specified: Masters Thesis or Doctoral Dissertation

MLA Handbook (7^th Edition):

Patel, Keyurkumar S. “Automatic generation of global phase equilibrium diagram from equation of state.” 2007. Web. 22 Apr 2021.

Vancouver:

Patel KS. Automatic generation of global phase equilibrium diagram from equation of state. [Internet] [Thesis]. University of South Florida; 2007. [cited 2021 Apr 22]. Available from: https://scholarcommons.usf.edu/etd/2318.

Note: this citation may be lacking information needed for this citation format:
Not specified: Masters Thesis or Doctoral Dissertation

Council of Science Editors:

Patel KS. Automatic generation of global phase equilibrium diagram from equation of state. [Thesis]. University of South Florida; 2007. Available from: https://scholarcommons.usf.edu/etd/2318

Note: this citation may be lacking information needed for this citation format:
Not specified: Masters Thesis or Doctoral Dissertation

26. Hodges, Timothy E. Avoiding singularities during homotopy continuation.

Degree: PhD, Mathematics, 2017, Colorado State University

URL: http://hdl.handle.net/10217/181397

► In numerical algebraic geometry, the goal is to find solutions to a polynomial system F(x1,x2,...xn). This is done through a process called homotopy continuation. During… (more)

Subjects/Keywords: branch points; numerical algebraic geometry; software development; homotopy continuation; Bertini; ramification points

…moving to a modern geometric method, homotopy continuation. We reduce the notation of z1 , z2… …continuation. 1.3. HOMOTOPY CONTINUATION Homotopy continuation is a technique for approximating… …are the solutions the start system, F(z; p0 ) = 0 In basic homotopy continuation… …continuation, see [10, 34]. What can go wrong during homotopy continuation? There may be… …encounter a singularity. 0 t 1 Figure 1.2. A 3-D depiction of homotopy continuation. The…

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APA (6^th Edition):

Hodges, T. E. (2017). Avoiding singularities during homotopy continuation. (Doctoral Dissertation). Colorado State University. Retrieved from http://hdl.handle.net/10217/181397

Chicago Manual of Style (16^th Edition):

Hodges, Timothy E. “Avoiding singularities during homotopy continuation.” 2017. Doctoral Dissertation, Colorado State University. Accessed April 22, 2021. http://hdl.handle.net/10217/181397.

MLA Handbook (7^th Edition):

Hodges, Timothy E. “Avoiding singularities during homotopy continuation.” 2017. Web. 22 Apr 2021.

Vancouver:

Hodges TE. Avoiding singularities during homotopy continuation. [Internet] [Doctoral dissertation]. Colorado State University; 2017. [cited 2021 Apr 22]. Available from: http://hdl.handle.net/10217/181397.

Council of Science Editors:

Hodges TE. Avoiding singularities during homotopy continuation. [Doctoral Dissertation]. Colorado State University; 2017. Available from: http://hdl.handle.net/10217/181397

27. Elgohary, Tarek A. Novel Computational and Analytic Techniques for Nonlinear Systems Applied to Structural and Celestial Mechanics.

Degree: PhD, Aerospace Engineering, 2015, Texas A&M University

URL: http://hdl.handle.net/1969.1/155254

► In this Dissertation, computational and analytic methods are presented to address nonlinear systems with applications in structural and celestial mechanics. Scalar Homotopy Methods (SHM) are… (more)

▼ In this Dissertation, computational and analytic methods are presented to address nonlinear systems with applications in structural and celestial mechanics. Scalar Homotopy Methods (SHM) are first introduced for the solution of general systems of nonlinear algebraic equations. The methods are applied to the solution of postbuckling and limit load problems of solids and structures as exemplified by simple plane elastic frames, considering only geometrical nonlinearities. In many problems, instead of simply adopting a root solving method, it is useful to study the particular problem in more detail in order to establish an especially efficient and robust method. Such a problem arises in satellite geodesy coordinate transformation where a new highly efficient solution, providing global accuracy with a non-iterative sequence of calculations, is developed. Simulation results are presented to compare the solution accuracy and algorithm performance for applications spanning the LEOtoGEO range of missions. Analytic methods are introduced to address problems in structural mechanics and astrodynamics. Analytic transfer functions are developed to address the frequency domain control problem of flexible rotating aerospace structures. The transfer functions are used to design a Lyapunov stable controller that drives the spacecraft to a target position while suppressing vibrations in the flexible appendages. In astrodynamics, a Taylor series based analytic continuation technique is developed to address the classical two-body problem. A key algorithmic innovation for the trajectory propagation is that the classical averaged approximation strategy is replaced with a rigorous series based solution for exactly computing the acceleration derivatives. Evidence is provided to demonstrate that high precision solutions are easily obtained with the analytic continuation approach. For general nonlinear initial value problems (IVPs), the method of Radial Basis Functions time domain collocation (RBF-Coll ) is used to address strongly nonlinear dynamical systems and to analyze short as well as long-term responses. The algorithm is compared against, the second order central difference, the classical Runge-Kutta, the adaptive Runge-Kutta-Fehlberg, the Newmark-β, the Hilber-Hughes-Taylor and the modified Chebyshev-Picard iteration methods in terms of accuracy and computational cost for three types of problems; (1) the unforced highly nonlinear Duffing oscillator, (2) the Duffing oscillator with impact loading and (3) a nonlinear three degrees of freedom (3-DOF) dynamical system. The RBF-Collmethod is further extended for time domain inverse problems addressing fixed time optimal control problems and Lamberts orbital transfer problem. It is shown that this method is very simple, efficient and very accurate in obtaining the solutions. The proposed algorithm is advantageous and has promising applications in solving general nonlinear dynamical systems, optimal control problems and high accuracy orbit propagation in celestial mechanics. Advisors/Committee Members: Junkins, John L (advisor), Turner, James D (advisor), Vadali, Srinivas R (committee member), Bhattacharyya, Shankar P (committee member).

Subjects/Keywords: Nonlinear Algebraic Equations; Post-Buckling; Scalar Homotopy Method; Satellite Geodesy; Hybrid Systems Structural Dynamics; Analytic Transfer Functions; Leibniz Rule; Analytic Continuation; Optimal Control; Collocation; Radial Basis Functions; Implicit Methods; Explicit Methods; Numerical Integration

…9 2.2 Homotopy Path Turning Points . . . . . . . . . . . . . . . . . . . . . 12 2.3… …22 Vertical Deflection vs. No. Iterations, l sin β = 0.32, Scalar Fixedpoint Homotopy… …23 2.11 Vertical Deflection vs. No. Iterations, l sin β = 0.44, Scalar Fixedpoint Homotopy… …32 2.17 Residual Error in Scalar Fixed-point Homotopy Method, [29] . . . . . 33… …2.9 ix 2.18 Residual Error in Scalar Newton Homotopy Method, [29]…

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APA · Chicago · MLA · Vancouver · CSE | Export to Zotero / EndNote / Reference Manager

APA (6^th Edition):

Elgohary, T. A. (2015). Novel Computational and Analytic Techniques for Nonlinear Systems Applied to Structural and Celestial Mechanics. (Doctoral Dissertation). Texas A&M University. Retrieved from http://hdl.handle.net/1969.1/155254

Chicago Manual of Style (16^th Edition):

Elgohary, Tarek A. “Novel Computational and Analytic Techniques for Nonlinear Systems Applied to Structural and Celestial Mechanics.” 2015. Doctoral Dissertation, Texas A&M University. Accessed April 22, 2021. http://hdl.handle.net/1969.1/155254.

MLA Handbook (7^th Edition):

Elgohary, Tarek A. “Novel Computational and Analytic Techniques for Nonlinear Systems Applied to Structural and Celestial Mechanics.” 2015. Web. 22 Apr 2021.

Vancouver:

Elgohary TA. Novel Computational and Analytic Techniques for Nonlinear Systems Applied to Structural and Celestial Mechanics. [Internet] [Doctoral dissertation]. Texas A&M University; 2015. [cited 2021 Apr 22]. Available from: http://hdl.handle.net/1969.1/155254.

Council of Science Editors:

Elgohary TA. Novel Computational and Analytic Techniques for Nonlinear Systems Applied to Structural and Celestial Mechanics. [Doctoral Dissertation]. Texas A&M University; 2015. Available from: http://hdl.handle.net/1969.1/155254

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