Information Geometry For Nonlinear Least-Squares Data Fitting And Calculation Of The Superconducting Superheating Field
| dc.contributor.author | Transtrum, Mark | en_US |
| dc.contributor.chair | Sethna, James Patarasp | en_US |
| dc.contributor.committeeMember | Hoffstaetter, Georg Heinz | en_US |
| dc.contributor.committeeMember | Teukolsky, Saul A | en_US |
| dc.date.accessioned | 2012-12-17T13:50:57Z | |
| dc.date.available | 2016-12-30T06:47:00Z | |
| dc.date.issued | 2011-08-31 | en_US |
| 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. | en_US |
| dc.identifier.other | bibid: 7955506 | |
| dc.identifier.uri | https://hdl.handle.net/1813/30694 | |
| dc.language.iso | en_US | en_US |
| dc.subject | nonlinear regression | en_US |
| dc.subject | superconductivity | en_US |
| dc.subject | information geometry | en_US |
| dc.title | Information Geometry For Nonlinear Least-Squares Data Fitting And Calculation Of The Superconducting Superheating Field | en_US |
| dc.type | dissertation or thesis | en_US |
| thesis.degree.discipline | Physics | |
| thesis.degree.grantor | Cornell University | en_US |
| thesis.degree.level | Doctor of Philosophy | |
| thesis.degree.name | Ph. D., Physics |
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