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Articles 1 - 5 of 5
Full-Text Articles in Physical Sciences and Mathematics
Nonlinear Dynamics Of Filaments In Free Space And Fluids, Victoria Kelley
Nonlinear Dynamics Of Filaments In Free Space And Fluids, Victoria Kelley
Senior Honors Projects, 2010-2019
The purpose of this paper is to study a straight rod, held at both ends, with a known twist and tension or compression. We study the stability of this steady state when the system is dominated either by inertia or drag. In order to do this, we first replicate the work of Goriely and Tabor to look at the case with inertia, without drag. After conducting the analysis for that case, we then apply their framework to perform a linear stability analysis of a model that is without inertia, but with hydrodynamic drag. Our motivation is the study of locomotion …
Mathematical Models For Infectious Disease Transmission With Stochastic Simulation Of Measles Outbreaks, Valerie Welty
Mathematical Models For Infectious Disease Transmission With Stochastic Simulation Of Measles Outbreaks, Valerie Welty
Honors College Theses
As they are the leading cause of death among children and adolescents worldwide, it is of extreme importance to control the spread of infectious diseases. Information gained from mathematical modeling of these events often proves quite useful in establishing policy decisions to accomplish this goal. Human behavior, however, is quite difficult to recreate when using equations with pre-determined results, such as deterministic differential equations often used with epidemic models. Because of this, the focus of the research was to create a simulation of an outbreak, specifically of measles, by using an imaginary population experiencing simulated stochastic events on a discrete …
Yeast For Mathematicians - A Ferment Of Discovery, Matthew Lewis, James A. Powell
Yeast For Mathematicians - A Ferment Of Discovery, Matthew Lewis, James A. Powell
Mathematics and Statistics Faculty Publications
In addition to the memorization, algorithmic skills and vocabulary which are the default focus in many mathematics classrooms, professional mathematicians are expected to creatively apply known techniques, construct new mathematical approaches and communicate with and about mathematics. We propose that students can learn these professional, higher-level skills through Laboratory Experiences in Mathematical Biology which put students in the role of mathematics researcher creating mathematics to describe and understand biological data. Here we introduce a laboratory experience centered on yeast (Saccharomyces cerevisiae) growing in a small capped flask with a jar to collect carbon dioxide created during yeast growth …
Modeling Lotic Organism Populations With Partial Differential Equations, Chase Viss, Tom Clark, Eric Eager
Modeling Lotic Organism Populations With Partial Differential Equations, Chase Viss, Tom Clark, Eric Eager
Faculty Work Comprehensive List
We present in this paper a mathematical model for a population of caddisfly larvae in the Upper Mississippi River, which can either live in the current of the water or fix themselves to large wood debris submerged throughout the river. The model consists of a system of partial differential equations which captures these coupled dynamics. After introducing the model, we give a qualitative analysis of the dynamics, which includes a steady state solution followed by a numerical solution to the system using a finite difference scheme implemented in R. Finally, we extend the model to a competitive system with the …
Parts Of The Whole: Teaching Quantitative Reasoning In The Predator-Prey Model, Dorothy Wallace
Parts Of The Whole: Teaching Quantitative Reasoning In The Predator-Prey Model, Dorothy Wallace
Numeracy
The classical predator-prey equations are in nearly every differential equations text and mathematical biology text. Usually they are presented fait accompli, leaving the student to analyze them or play with a computer program. Here we show that the process of fully understanding where these equations come from and how they are derived provides numerous opportunities to teach or reinforce quantitative reasoning skills necessary to future scientists. This example is used to invoke logic, systems thinking, causal reasoning, understanding functions of one or more variables, quantities versus rates of change, proportional reasoning, unit analysis, and comparison to data.