{"id":{"repo_id":"cornell","oai_identifier":"oai:ecommons.cornell.edu:1813/30694"},"canonical_url":"https://search.dev.ndltd.org/etd/cornell/oai:ecommons.cornell.edu:1813/30694","repository":{"repo_id":"cornell","name":"Cornell University","base_url":"https://ecommons.cornell.edu/server/oai/request"},"display":{"title":"Information Geometry For Nonlinear Least-Squares Data Fitting And Calculation Of The Superconducting Superheating Field","abstract":"This thesis consist of two parts, each of which consist of two chapters. First we explore the information geometric properties of least squares data fitting, particularly for so-called \"sloppy\" models. Second we describe a calculation of the superconducting superheating field, relevant for advancing gradients in particle accelerator resonance cavities. Parameter estimation by nonlinear least squares minimization is a ubiquitous problem that has an elegant geometric interpretation: all possible parameter values induce a manifold embedded within the space of data. The minimization problem is then to find the point on the manifold closest to the data. By interpreting nonlinear models as a generalized interpolation scheme, we find that the manifolds of many models, known as sloppy models, have boundaries and that their widths form a hierarchy. We describe this universal structure as a hyper-ribbon. The hyper-ribbon structure explains many of the difficulties associated with fitting nonlinear models and suggests improvements to standard algorithms. We add a \"geodesic acceleration\" correction to the standard Levenberg-Marquardt algorithm and observe a dramatic increase in success rate and convergence speed on many fitting problems. We study the superheating field of a bulk superconductor within the GinzburgLandau, which is valid only near Tc , and Eilenberger theory, which is valid at all temperatures. We calculate as functions of both the Ginzburg-Landau parameter [kappa] and reduced temperature t = T /Tc the superheating field Hsh and the critical momentum kc describing the wavelength of the unstable perturbations to flux penetration. By mapping the two-dimensional linear stability theory into a one-dimensional eigenfunction problem for a linear operator, we solve the problem numerically. Within the Ginzburg-Landau theory, We demonstrate agreement between the numerics and analytics, and show convergence to the known results at both small and large [kappa]. Within the Eilenberger theory we demonstrate agreement with the results of Ginzburg-Landau theory near Tc , but find discrepancies with the temperature-dependent results for large [kappa]. We speculate that this discrepancy is due to a lack of convergence at low temperatures due to small length scales of the perturbations analogous to the small length scales associated with the vortex cores of the mixed state.","abstract_html":"This thesis consist of two parts, each of which consist of two chapters. First we explore the information geometric properties of least squares data fitting, particularly for so-called "sloppy" models. Second we describe a calculation of the superconducting superheating field, relevant for advancing gradients in particle accelerator resonance cavities. Parameter estimation by nonlinear least squares minimization is a ubiquitous problem that has an elegant geometric interpretation: all possible parameter values induce a manifold embedded within the space of data. The minimization problem is then to find the point on the manifold closest to the data. By interpreting nonlinear models as a generalized interpolation scheme, we find that the manifolds of many models, known as sloppy models, have boundaries and that their widths form a hierarchy. We describe this universal structure as a hyper-ribbon. The hyper-ribbon structure explains many of the difficulties associated with fitting nonlinear models and suggests improvements to standard algorithms. We add a "geodesic acceleration" correction to the standard Levenberg-Marquardt algorithm and observe a dramatic increase in success rate and convergence speed on many fitting problems. We study the superheating field of a bulk superconductor within the GinzburgLandau, which is valid only near Tc , and Eilenberger theory, which is valid at all temperatures. We calculate as functions of both the Ginzburg-Landau parameter [kappa] and reduced temperature t = T /Tc the superheating field Hsh and the critical momentum kc describing the wavelength of the unstable perturbations to flux penetration. By mapping the two-dimensional linear stability theory into a one-dimensional eigenfunction problem for a linear operator, we solve the problem numerically. Within the Ginzburg-Landau theory, We demonstrate agreement between the numerics and analytics, and show convergence to the known results at both small and large [kappa]. Within the Eilenberger theory we demonstrate agreement with the results of Ginzburg-Landau theory near Tc , but find discrepancies with the temperature-dependent results for large [kappa]. We speculate that this discrepancy is due to a lack of convergence at low temperatures due to small length scales of the perturbations analogous to the small length scales associated with the vortex cores of the mixed state.","abstract_has_math":false,"creators":["Transtrum, Mark"],"institution":"Cornell University","degree_name":"Ph. D., Physics","degree_level":"Doctor of Philosophy","degree_discipline":"Physics","degree_department":null,"school":null,"contributors":[],"advisors":[],"committee_chairs":[],"committee_members":["Hoffstaetter, Georg Heinz","Teukolsky, Saul A"],"year":2011,"date_issued":"2011-08-31","date_published":"2011-08-31","updated_at":"2026-07-24T01:48:56Z","subjects":["nonlinear regression","superconductivity","information geometry"],"languages":["en_US"],"rights":[],"rights_urls":[],"identifier_entries":[]},"links":{"outbound_url":"https://hdl.handle.net/1813/30694","outbound_label":"Handle","outbound_source":"dc:identifier.uri"},"metadata_groups":[{"id":"people","label":"People","entries":[{"key":"dc:contributor.committeemember","label":"Committee Member","values":["Hoffstaetter, Georg Heinz","Teukolsky, Saul A"]},{"key":"dc:creator","label":"Author","values":["Transtrum, Mark"]}]},{"id":"academic_context","label":"Academic Context","entries":[{"key":"dc:date.accessioned","label":"Dc Date Accessioned","values":["2012-12-17T13:50:57Z"]},{"key":"dc:date.available","label":"Dc Date Available","values":["2016-12-30T06:47:00Z"]},{"key":"dc:date.issued","label":"Date","values":["2011-08-31"]},{"key":"dc:type","label":"Dc Type","values":["dissertation or thesis"]},{"key":"thesis:degree_discipline","label":"Discipline","values":["Physics"]},{"key":"thesis:degree_level","label":"Degree Level","values":["Doctor of Philosophy"]},{"key":"thesis:degree_name","label":"Degree Name","values":["Ph. D., Physics"]},{"key":"thesis:institution_name","label":"Thesis Institution Name","values":["Cornell University"]}]},{"id":"subjects_keywords","label":"Subjects and Keywords","entries":[{"key":"dc:subject","label":"Dc Subject","values":["nonlinear regression","superconductivity","information geometry"]}]},{"id":"language_rights","label":"Language and Rights","entries":[{"key":"dc:language.iso","label":"Language (ISO)","values":["en_US"]}]},{"id":"identifiers","label":"Identifiers","entries":[{"key":"dc:identifier.uri","label":"Identifier URI","values":["https://hdl.handle.net/1813/30694"]}]},{"id":"additional","label":"Additional Metadata","entries":[{"key":"dc:description.abstract","label":"Abstract","values":["This thesis consist of two parts, each of which consist of two chapters. First we explore the information geometric properties of least squares data fitting, particularly for so-called \"sloppy\" models. Second we describe a calculation of the superconducting superheating field, relevant for advancing gradients in particle accelerator resonance cavities. Parameter estimation by nonlinear least squares minimization is a ubiquitous problem that has an elegant geometric interpretation: all possible parameter values induce a manifold embedded within the space of data. The minimization problem is then to find the point on the manifold closest to the data. By interpreting nonlinear models as a generalized interpolation scheme, we find that the manifolds of many models, known as sloppy models, have boundaries and that their widths form a hierarchy. We describe this universal structure as a hyper-ribbon. The hyper-ribbon structure explains many of the difficulties associated with fitting nonlinear models and suggests improvements to standard algorithms. We add a \"geodesic acceleration\" correction to the standard Levenberg-Marquardt algorithm and observe a dramatic increase in success rate and convergence speed on many fitting problems. We study the superheating field of a bulk superconductor within the GinzburgLandau, which is valid only near Tc , and Eilenberger theory, which is valid at all temperatures. We calculate as functions of both the Ginzburg-Landau parameter [kappa] and reduced temperature t = T /Tc the superheating field Hsh and the critical momentum kc describing the wavelength of the unstable perturbations to flux penetration. By mapping the two-dimensional linear stability theory into a one-dimensional eigenfunction problem for a linear operator, we solve the problem numerically. Within the Ginzburg-Landau theory, We demonstrate agreement between the numerics and analytics, and show convergence to the known results at both small and large [kappa]. Within the Eilenberger theory we demonstrate agreement with the results of Ginzburg-Landau theory near Tc , but find discrepancies with the temperature-dependent results for large [kappa]. We speculate that this discrepancy is due to a lack of convergence at low temperatures due to small length scales of the perturbations analogous to the small length scales associated with the vortex cores of the mixed state."]},{"key":"dc:format.mimetype","label":"Dc Format Mimetype","values":["application/pdf"]},{"key":"dc:title","label":"Title","values":["Information Geometry For Nonlinear Least-Squares Data Fitting And Calculation Of The Superconducting Superheating Field"]}]}],"canonical_facts":{"dc:contributor.committeemember":["Hoffstaetter, Georg Heinz","Teukolsky, Saul A"],"dc:creator":["Transtrum, Mark"],"dc:date.accessioned":["2012-12-17T13:50:57Z"],"dc:date.available":["2016-12-30T06:47:00Z"],"dc:date.issued":["2011-08-31"],"dc:description.abstract":["This thesis consist of two parts, each of which consist of two chapters. First we explore the information geometric properties of least squares data fitting, particularly for so-called \"sloppy\" models. Second we describe a calculation of the superconducting superheating field, relevant for advancing gradients in particle accelerator resonance cavities. Parameter estimation by nonlinear least squares minimization is a ubiquitous problem that has an elegant geometric interpretation: all possible parameter values induce a manifold embedded within the space of data. The minimization problem is then to find the point on the manifold closest to the data. By interpreting nonlinear models as a generalized interpolation scheme, we find that the manifolds of many models, known as sloppy models, have boundaries and that their widths form a hierarchy. We describe this universal structure as a hyper-ribbon. The hyper-ribbon structure explains many of the difficulties associated with fitting nonlinear models and suggests improvements to standard algorithms. We add a \"geodesic acceleration\" correction to the standard Levenberg-Marquardt algorithm and observe a dramatic increase in success rate and convergence speed on many fitting problems. We study the superheating field of a bulk superconductor within the GinzburgLandau, which is valid only near Tc , and Eilenberger theory, which is valid at all temperatures. We calculate as functions of both the Ginzburg-Landau parameter [kappa] and reduced temperature t = T /Tc the superheating field Hsh and the critical momentum kc describing the wavelength of the unstable perturbations to flux penetration. By mapping the two-dimensional linear stability theory into a one-dimensional eigenfunction problem for a linear operator, we solve the problem numerically. Within the Ginzburg-Landau theory, We demonstrate agreement between the numerics and analytics, and show convergence to the known results at both small and large [kappa]. Within the Eilenberger theory we demonstrate agreement with the results of Ginzburg-Landau theory near Tc , but find discrepancies with the temperature-dependent results for large [kappa]. We speculate that this discrepancy is due to a lack of convergence at low temperatures due to small length scales of the perturbations analogous to the small length scales associated with the vortex cores of the mixed state."],"dc:format.mimetype":["application/pdf"],"dc:identifier.uri":["https://hdl.handle.net/1813/30694"],"dc:language.iso":["en_US"],"dc:subject":["nonlinear regression","superconductivity","information geometry"],"dc:title":["Information Geometry For Nonlinear Least-Squares Data Fitting And Calculation Of The Superconducting Superheating Field"],"dc:type":["dissertation or thesis"],"thesis:degree_discipline":["Physics"],"thesis:degree_level":["Doctor of Philosophy"],"thesis:degree_name":["Ph. D., Physics"],"thesis:institution_name":["Cornell University"]},"updated_at":"2026-07-24T01:48:56Z"}