Physical Sciences and Mathematics Commons^™

Geometry, Growth And Pattern Formation In Thin Elastic Structures, Salem Al-Mosleh

Doctoral Dissertations

Thin shells are abundant in nature and industry, from atomic to planetary scales. The mechanical behavior of a thin shell depends crucially on its geometry and embedding in 3 dimensions (3D). In fact, the behavior of extremely thin shells becomes scale independent and only depends on geometry. That is why the crumpling of graphene will have similarities to the crumpling of paper. In this thesis, we start by discussing the static behavior of thin shells, highlighting the role of asymptotic curves (curves with zero normal curvature) in determining the possible deformations and in controlling the folding patterns. In particular, we …

Relations Between Theta Functions Of Genus One And Two From Geometry, Thomas Hill

Undergraduate Honors Capstone Projects

Genus-two curves with special symmetries are related to pairs of genus-one curves by two and three-sheeted ramified coverings. This classical work dates back to early 20th century and is known as Jacobi and Hermite reduction. Jacobians of genus-two curves can be used to construct complex two-dimensional complex projective manifolds known as Kummer surfaces. On the other hand, the defining coordinates and parameters of both elliptic curves and Kummer surfaces can be related to Riemann Theta functions and Siegel Theta functions, respectively. This result goes back to the seminal work of Mumford in the 1980s. We use the geometric relation between …

Generalized Characteristics Of A Generic Polytope, Tommy Naugle

Electronic Theses and Dissertations

For a smooth hypersurface S ⊂ R 2n given by the level set of a Hamiltonian function H, a symplectic form ω on R2n induces a vector field XH which flows tangent to S. By the nondegeneracy of ω, there exists a distinguished line bundle LS whose characteristics are the integral curves of XH. When S is the boundary of a smooth convex domain K˜ ⊂ R 2n, then the least action among closed characteristics of LS is equal to the Ekeland-Hofer-Zehnder capacity, a symplectic invariant. From a result due to Artstein-Avidan and Ostrover, there exists a continuous extension of …

Geometry Of Derived Categories On Noncommutative Projective Schemes, Blake Alexander Farman

Theses and Dissertations

Noncommutative Projective Schemes were introduced by Michael Artin and J.J. Zhang in their 1994 paper of the same name as a generalization of projective schemes to the setting of not necessarily commutative algebras over a commutative ring. In this work, we study the derived category of quasi-coherent sheaves associated to a noncommutative projective scheme with a primary emphasis on the triangulated equivalences between two such categories.

We adapt Artin and Zhang’s noncommutative projective schemes for the language of differential graded categories and work in Ho (dgcatk), the homotopy category of differential graded categories, making extensive use of Bertrand Toën’s Derived …

An Autothermal, Representative Scale Test Of Compost Heat Potential Using Geostatistical Analysis, William J. Mccune-Sanders

Graduate College Dissertations and Theses

Composting has been practiced for thousands of years as a way of stabilizing and recycling organic matter into useful soil amendments. Thermophilic compost releases significant amounts of heat at temperatures (~140 °F) that are useful for environmental heating or process water. This heat has been taken advantage of in various ways throughout history, but development of a widely adopted technology remains elusive.

The biggest barrier to adoption of compost heat recovery (CHR) systems is projecting accurate, attractive economic returns. The cost of transfer equipment is significant, and with variability in composting substrates and methods, it is difficult to predict the …

Advanced Enrichment Topics In An Honors Geometry Course, Kayla Woods

Masters Essays

No abstract provided.

Using Geogebra To Explore Properties Of Circles In Euclidean Geometry, Erin Hanna

Masters Essays

No abstract provided.