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 …

Generalized Branching In Circle Packing, James Russell Ashe

Doctoral Dissertations

Circle packings are configurations of circle with prescribed patterns of tangency. They relate to a surprisingly diverse array of topics. Connections to Riemann surfaces, Apollonian packings, random walks, Brownian motion, and many other topics have been discovered. Of these none has garnered more interest than circle packings' relationship to analytical functions. With a high degree of faithfulness, maps between circle packings exhibit essentially the same geometric properties as seen in classical analytical functions. With this as motivation, an entire theory of discrete analytic function theory has been developed. However limitations in this theory due to the discreteness of circle packings …

Surface And Subsurface Structures Of The Western Valley And Ridge In Tennessee And Geometry And Kinematics That Permit Reconstruction Of The Tennessee Salient, Southern Appalachians, Jennifer Kathleen Whisner

Doctoral Dissertations

The southern and central Appalachian foreland fold-thrust belt comprises a series of orogen -scale curves that extend from Alabama to New York. One of these is the Tennessee salient, a foreland-convex curve that extends from Cartersville, Georgia, to Roanoke, Virginia. Development of a kinematic model for deformation in the salient has been hindered by a paucity of penetrative deformation in this generally low temperature, low volume-loss portion of the orogen.

Industry seismic reflection lines provide greater resolution of subsurface geometry of both the basement surface and the overlying fold-thrust belt, confirming some previous interpretations and changing others. A series of …