PAPERS AND TALKS

A Tale of Two Stock Markets

with V. Piercey and S. Greene-Hunley
Mathematics Teaching in the Middle School, NCTM; May 2015

Real-world data bring economics to life by combining mathematics and language arts and promoting financial literacy.

Introducing the stock market to students during math class makes both economics and mathematics more meaningful, teaches mathematical concepts using real-world data, and fits in well with the Common Core State Standards for Mathematics (CCSSM) (CCSSI 2010b). Furthermore, fluctuations in the stock market can lead to valuable student insight about change in function values over time. Armstrong, Michelle Hine, Piercey, V.I., and Greene-Hunley, S. (2015). "A Tale of Two Stock Markets." Mathematics Teaching in the Middle School, 20(9), 522-530. (Link to NCTM)

Computational Growth and Remodeling

World Congress of Biomechanics, Boston, MA; July 10, 2014

Most growth models for soft tissue assume that soft tissue deforms as a purely elastic material. However, biological tissues are saturated with fluid that bears part of the load, reducing the amount of deformation in response to stress. Our previous research has modeled the complex response of soft tissue using a one-dimensional, large-strain mixed porohyperelastic transport and swelling (MPHETS) finite element model with mechanically-driven growth. The purpose of the current model is to build upon our previous work and incorporate chemically-driven growth into a simplified MPHETS growth model.

Abstract for Poster: MPHETS with Chemically-Driven Growth

Computational Growth and Remodeling

Graduate Brown Bag Seminar, Tucson, AZ; October 25, 2013

Growth is a fundamental driving process behind the long-term behavior of living tissues. One of the more popular methods is to decompose growth into two steps--a stress-free, possibly incompatible growth step followed by an elastic deformation to satisfy both material continuity and boundary conditions. Motivated by a simple example of a one-dimensional growing rod, I will cover the basic ideas behind growth and remodeling. At the end, I will discuss how growth may be computationally implemented in a three-dimensional problem.

Presentation: Computational Growth

Making Math Stick: Teaching Through Project Based Learning

G-TEAMS Summer Institute, Tucson, AZ; June 3, 2013
Heatwaves Summer Institute, Tucson, AZ; June 18, 2013

Explore three different projects that were implemented in 4th and 5th grade. Project based learning provides authentic student experiences that place math in context. These learner-driven, inquiry-based opportunities combine math, science, literacy, art, economics and more. Through Original Soda Flavors, Fourth Grade Design Project, and the Stock Market Project, students encountered sophisticated concepts and developed higher order thinking skills. Presented at the G-TEAMS Summer Institute with S. Hunley.

Presentation: Making Math Stick

Elasticity Theory and Finite Elements Using a Porous Media Formulation

Mathematics Brown Bag Seminar, Tucson, AZ; April 2, 2013

The theory of poroelasticity is used in applications as varied as soil mechanics and soft tissue deformation. Models for linear elasticity and linear poroelasticity in one dimension are introduced, as well as the the finite element method, which is a well-known computational tool used to solve boundary value problems.
This talk is geared to undergraduate students who have completed calculus.

Presentation: Elasticity Theory and Finite Elements

Collaboration with Project Based Learning: Recipe for an Engaged Classroom

ITSP Conference, Boston, MA; February 13, 2013

This session focused on the collaboration between a University of Arizona math graduate student and elementary school teachers in planning and implementing STEAM (STEM plus Arts)-focused Project Based Learning opportunities and problem solving parties for 4th/5th grade students. Learn how projects were developed and how connections between math, science, literacy, and the arts were created and sustained. Presented with S. Clements.

Presentation: Recipe for an Engaged Classroom

Fall 2011

I worked with Dr. Larry Winter from the Department of Hydrology and Water Resources, studying the contaminant transport problem over a random conductivity field.

	Solving the Contaminant Transport Problem Over a Random Conductivity Field
	Presentation: Solving the Contaminant Transport Problem Over a Random Conductivity Field

Spring 2011

Each student in the Program in Applied Mathematics writes a second semester term paper. I worked with Dr. Stepanov studying the exponential Rosenbrock-type method of order two. It is an explicit method that solves stiff ODEs. The method linearizes the equation with each step, then uses a matrix exponential to solve the linearized equation exactly. In this paper, I explore the stiffness capabilities of this second order method as stiffness increases toward infinity. The paper contains estimation-style analysis of the step size and order. I also test the exponential Rosenbrock-type method on two stiff equations: decay of a particle to a circle, and a partial differential equation on a circle with either a viscosity or a hyperviscosity term. Through numerical testing, it is evident that the exponential Rosenbrock-type method exhibits stiffness characteristics in the limit as stiffness tends towards infinity; however, for high stiffness, the method has order reduction to first order.

	The Stiff Limit of the Exponential Rosenbrock-Type Method
	Presentation: The Stiff Limit of the Exponential Rosenbrock-Type Method

Fall 2010

As part of Math 586, Case Studies in Applied Mathematics, I co-authored a paper with Yusuke Shimabukuro and Amy Veprauskas on fingering of both Newtonian and non-Newtonian fluids. We explored an adaptation of the power law time dependence of finger growth rate to describe the behavior of non-Newtonian fluids.

Power Law Model Adaptation to Fingering of Non-Newtonian Fluids