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You searched for +publisher:"Syracuse University" +contributor:("Claudia Miller"). Showing records 1 – 2 of 2 total matches.

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Syracuse University

1. Ottman, Eric Jeffrey. Homology over a Complete Intersection Ring via the Generic Hypersurface.

Degree: PhD, Mathematics, 2019, Syracuse University

We study homological properties and constructions for modules over a complete intersection ring Q/(f1,…,fc) by way of the related generic hypersurface ring Q[T1,…,Tc]/(f1T1+∙s+fcTc). The advantage of this approach is that over a hypersurface ring, free resolutions are eventually 2-periodic, given by matrix factorizations, and are thus relatively easy to understand. We approach this relationship in two ways. First, we give a correspondence between the two rings in the graded setting, where existing results are insufficient for preserving graded structures. As an application, we use this correspondence to move a functor appearing in a theorem of Orlov to the generic hypersurface setting. Second, we shift out of the graded setting to discuss the relationship between Tor groups over these rings, inspired by recent work of Bergh and Jorgensen, and building on cohomological results of Burke and Walker. This second part takes place in a scheme-theoretic context, so we develop some machinery that provides a sort of ``global Tor" for complexes of sheaves that can be compared to the usual Tor for modules. Advisors/Committee Members: Claudia Miller.

Subjects/Keywords: Algebraic Geometry; Commutative Algebra; Homological Algebra; Physical Sciences and Mathematics

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

APA (6th Edition):

Ottman, E. J. (2019). Homology over a Complete Intersection Ring via the Generic Hypersurface. (Doctoral Dissertation). Syracuse University. Retrieved from https://surface.syr.edu/etd/1131

Chicago Manual of Style (16th Edition):

Ottman, Eric Jeffrey. “Homology over a Complete Intersection Ring via the Generic Hypersurface.” 2019. Doctoral Dissertation, Syracuse University. Accessed July 04, 2020. https://surface.syr.edu/etd/1131.

MLA Handbook (7th Edition):

Ottman, Eric Jeffrey. “Homology over a Complete Intersection Ring via the Generic Hypersurface.” 2019. Web. 04 Jul 2020.

Vancouver:

Ottman EJ. Homology over a Complete Intersection Ring via the Generic Hypersurface. [Internet] [Doctoral dissertation]. Syracuse University; 2019. [cited 2020 Jul 04]. Available from: https://surface.syr.edu/etd/1131.

Council of Science Editors:

Ottman EJ. Homology over a Complete Intersection Ring via the Generic Hypersurface. [Doctoral Dissertation]. Syracuse University; 2019. Available from: https://surface.syr.edu/etd/1131


Syracuse University

2. Wijtmans, Sven. Defects and Rearrangements in Disordered Solids.

Degree: PhD, Physics, 2017, Syracuse University

In this thesis, I will investigate the properties of disordered materials under strain. Disordered materials encompass a large variety of materials, including glasses, polymers, granular matter, dense colloids, and gels. There is currently no constitutive equation based on microscopic observables that describes these materials. Given the prevalence and usefulness of these materials, we derive tools to aid our understanding of them. We develop a new method to isolate localized defects from extended vibrational modes in disordered solids. This method augments particle interactions with an artificial potential that acts as a high-pass filter: it preserves small-scale structures while pushing extended vibrational modes to higher frequencies. The low-frequency modes that remain are ``bare" defects; they are exponentially localized without the quadrupolar tails associated with elastic interactions. We demonstrate that these localized excitations are excellent predictors of plastic rearrangements in the solid. We characterize several of the properties of these defects that appear in mesoscopic theories of plasticity, including their distribution of energy barriers, number density, and size, which is a first step in testing and revising continuum models for plasticity in disordered solids. We additionally study the properties of rearrangement types in 2D disordered packings of particles with a harmonic potential at a range of packing fractions above jamming. We develop a generalizable procedure that classifies events by stress drop, energy drop, and reversibility under two protocols. Somewhat surprisingly, we find a large population of contact change events that have no associated stress drop. Reversible events become more common at high pressures above a packing fraction of φ=0.865, at which point line reversible events are more common than loop reversible events. At low pressures, irreversible events are associated with spatially extended events, while at high pressures reversible events are much more spatially localized. Advisors/Committee Members: Mary E. Manning, Claudia Miller.

Subjects/Keywords: disorder; jammed; vibration; Physical Sciences and Mathematics

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

APA (6th Edition):

Wijtmans, S. (2017). Defects and Rearrangements in Disordered Solids. (Doctoral Dissertation). Syracuse University. Retrieved from https://surface.syr.edu/etd/733

Chicago Manual of Style (16th Edition):

Wijtmans, Sven. “Defects and Rearrangements in Disordered Solids.” 2017. Doctoral Dissertation, Syracuse University. Accessed July 04, 2020. https://surface.syr.edu/etd/733.

MLA Handbook (7th Edition):

Wijtmans, Sven. “Defects and Rearrangements in Disordered Solids.” 2017. Web. 04 Jul 2020.

Vancouver:

Wijtmans S. Defects and Rearrangements in Disordered Solids. [Internet] [Doctoral dissertation]. Syracuse University; 2017. [cited 2020 Jul 04]. Available from: https://surface.syr.edu/etd/733.

Council of Science Editors:

Wijtmans S. Defects and Rearrangements in Disordered Solids. [Doctoral Dissertation]. Syracuse University; 2017. Available from: https://surface.syr.edu/etd/733

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