Go With the Flow: Classifying the Asymptotic Behaviors of Semidiscrete Curve-Shortening Flows by Mitchell Eithun

Mathematics

A semidiscrete curve-shortening flow continuously deforms a polygon in the direction of an inward normal until it shrinks to a point. We are interested in the long-time behavior of polygons under such flows. Is there a semidiscrete flow under which all polygons become asymptotically regular? This is an open question, but we provide numerical evidence to suggest that the recent β-polygon flow of Glickenstein and Liang produces regular polygons. It is known that triangles become regular under the β-polygon flow. Using a rescaled flow in which a regular polygon is a fixed point, we note how side lengths and angles evolve under the β-polygon flow and conjecture that all quadrilaterals become rhombic and polygons with more than 5 vertices become regular.

Mitchell Eithun

Senior Showcase Oral Presentation

Ripon College

April 18, 2017

The author reserves all rights.

Majors: Mathematics and Computer Science

Minor: Music

Minor: Music

New London, Wisconsin

protein assumes its folded shape remains an open question and has intrigued biologist and chemists for decades. Mathematicians have joined forces with the natural scientists and brought with them the tools of differential geometry, which prove powerful for modeling proteins. We explore the method of [3] to model a small subset of proteins using polyhelical space curves. We successfully modeled three alpha-helical repeat proteins. The developed model has demonstrated possible uses in predicting theoretical tertiary structures of proteins given a set of secondary structures--a step in the right direction of solving the protein folding problem. Additionally, we provide insight into the relationship between clashes and the model's stability calculator, which may improve the viability of their model.]]>

Pondering Polyhelical Proteins: Mathematically Modeling Helical Repeat Proteins by Lincoln Wurtz

Mathematics

Proteins are the most abundant biological macromolecules and, based on their

three-dimensional shape, perform life-sustaining functions. The process by which a

protein assumes its folded shape remains an open question and has intrigued biologist and chemists for decades. Mathematicians have joined forces with the natural scientists and brought with them the tools of differential geometry, which prove powerful for modeling proteins. We explore the method of [3] to model a small subset of proteins using polyhelical space curves. We successfully modeled three alpha-helical repeat proteins. The developed model has demonstrated possible uses in predicting theoretical tertiary structures of proteins given a set of secondary structures--a step in the right direction of solving the protein folding problem. Additionally, we provide insight into the relationship between clashes and the model's stability calculator, which may improve the viability of their model.

three-dimensional shape, perform life-sustaining functions. The process by which a

protein assumes its folded shape remains an open question and has intrigued biologist and chemists for decades. Mathematicians have joined forces with the natural scientists and brought with them the tools of differential geometry, which prove powerful for modeling proteins. We explore the method of [3] to model a small subset of proteins using polyhelical space curves. We successfully modeled three alpha-helical repeat proteins. The developed model has demonstrated possible uses in predicting theoretical tertiary structures of proteins given a set of secondary structures--a step in the right direction of solving the protein folding problem. Additionally, we provide insight into the relationship between clashes and the model's stability calculator, which may improve the viability of their model.

Lincoln Wurtz

Senior Showcase Oral Presentation

Ripon College

April 18, 2017

The author reserves all rights.

Majors: Mathematics and Chemistry-Biology