The 7th
Annual
NC
Undergraduate
Summer Research Symposium
NC State REU in Modeling
and Industrial Applied Mathematics abstracts
Abstracts are listed in
alphabetical order by the last name of the corresponding author.
Arnold, Rachel F. Marous, Daniel
R. McLamb, April
J. Thompson, Karmethia
C. Woodruff, William R. 

Home Institution: 
Virginia Tech 
Program: 
NC State REU in Modeling and Industrial Applied
Mathematics 
College: 
PAMS 
Department(s): 
Mathematics 
Research 
Mansoor A. Haider/Mathematics Janine M. Haugh/Mathematics 
Title of Presentation: 
Your Hips Don't Lie:
Modeling Cartilage Regeneration 
With
an increasing life expectancy and a growing population participating in
athletic activities, the need for an eﬀective process for
cartilage repair is paramount. Cartilage is a dense connective tissue comprised
of specialized cells called chondrocytes. It is
primarily found on the articular surfaces of the
bones, e.g. the knees and hips. In particular, it serves as a protective covering
on bone endings in joints, preventing a painful sensation from boneonbone
contact. In a healthy environment, cartilage resides in a state of homeostasis,
repairing any minor damages that it may incur. However, an unhealthy aging
process or extensive injury can render the cartilage naturally irreparable.
Consequently, researchers are seeking techniques to encourage cartilage
regeneration. One such method involves injecting biocompatible scaﬀolding
materials seeded with chondrocytes into the defective
areas. Because of its similarities to natural tissue, a hydrogel
substance is a suitable selection for the material harboring these cells. With
an ample nutrient supply, the chondrocytes are
ideally able to restore the damaged cartilage to homeostasis. Researchers are
in need of a mathematical model that describes this biological process. With a
model at hand, they can better identify the characteristics of the hydrogel procedure that demand further investigation. In
our work, we present a mathematical model that illustrates the regeneration of
cartilage via a hydrogel substance. Our model is
comprised of ordinary diﬀerential
equations that describe the rates at which the nutrient, hydrogel,
and cartilage concentrations change throughout regeneration.
Boudreaux,
Brittany Foster, Krista Uttal, Cerena Vogel, Thomas 

Home Institution: 
Youngstown State
University 
Program: 
NC State REU in Modeling and Industrial Applied
Mathematics 
College: 
PAMS 
Department(s): 
Mathematics 
Research 
H.T. Banks/Center for
Research in Scientific Computation Amanda Criner/Mathematics 
Title of Presentation: 
Can Thermal Methods Detect
Structural Damage? 
Most modern aero and space structures are composed of
composite materials containing significant porosity. Although
nondestructive analysis techniques have been developed to detect damage in
homogeneous materials, little research has been done on heterogeneous
materials. This project uses the heat equation to simulate a thermal
interrogation method for identifying damage in a porous compartment. The
model first uses different probability schemes to randomly generate pores and
then flash heats the compartment along one of its boundaries. Temperature
data along the heated boundary is recorded and then analyzed to distinguish
differences between the undamaged and damaged materials. These results
indicate that it is possible to detect damage of a certain size within a porous
medium.
Cousins, William B. Deutsch, Steven R. Stroka, Amy M. Tessler, M.
Henry Washington, Janatta R. 

Home Institution: 
Keuka College 
Program: 
NC State REU in Modeling and Industrial Applied
Mathematics 
College: 
PAMS 
Department(s): 
Mathematics 
Research 
Pierre A. Gremaud/Mathematics 
Title of Presentation: 
Modeling of Traffic
Congestion and Mass Evacuations 
The
destructive nature of hurricane seasons makes efficient mass evacuation plans a
necessity. Mathematical modeling techniques were implemented in this project in
order to accurately represent large scale evacuations for areas in the North
Carolina coast. Traffic congestion was simulated through the use of a
microscopic model, which predicts individual driver behavior using systems of
Ordinary and Delay Differential Equations. In this model, the behavior of a car
was determined entirely by the behavior of the car immediately preceding it.
Another route taken utilized a macroscopic model derived from physical
applications of scalar conservation laws. This model examines the densities of
cars and velocity fields through the use of Partial Differential Equations. An
additional tool used was SUMO (Simulation of Urban MObility),
an open source traffic simulation software package developed by the Centre for
Applied Informatics (ZAIK) and the Institute of Transport Research at the
German Aerospace Centre. Simulations were created for the evacuations of Bird
Island and the coast of North Carolina through the use of SUMO and the
macroscopic model. These simulations were then compared and critically
analyzed.
Crompton, Kasey Davis, Andrew Ito, Satoru Morton, Gregory Olsen, Amanda 

Home Institution: 
LaGrange College 
Program: 
NC State REU in Modeling and Industrial Applied
Mathematics 
College: 
PAMS 
Department(s): 
Mathematics 
Research 
Mette S. Olufsen/Mathematics Daniela ValdezJasso/Mathematics 
Title of Presentation: 
Viscoelasticity of the Arterial Wall 
The
design of stents and grafts require knowledge of the
mechanical properties of the arterial wall, which can be hard to determine experimentally.
Difficulties arise, since the mechanics differ invivo and invitro, and
because the vessel wall displays viscoelastic
behavior. This study utilizes a 2parameter elastic model and a 4parameter
Kelvin viscoelastic model to predict elastic and viscoelastic properties of the arterial wall using invivo
measurements of vessel area and blood pressure. Data were measured in the
proximal ascending aorta in seven sheep at a number of different frequencies.
Mechanical properties were predicted by estimating model parameters by solving
the inverse problem, minimizing the least squares error between computed and
measured values of vessel area. Results showed that we were able to estimate
model parameters using only a portion of the data, and that parameter estimates
did not differ significantly even without prior filtering of the data. While
the vessel radius was not significantly impacted by changes in frequency,
differences were observed in both elastic and viscoelastic
parameters. Results of sensitivity analyses showed that all parameters were
sensitive, and since all model parameters are independent, we conclude that it
is possible to estimate all parameters. Moreover, results showed that the
Kelvin viscoelastic model was able to capture the
pressurearea hysteresis, which the elastic model
could not predict. Finally, we showed that the hysteresis
is significantly smaller invivo than invitro, a phenomenon, which may be a
result of smooth muscle cell regulation and support of the tunica adventitia.
Davis, Steven Gadson, Sean E.
Tallis, William J. 

Home Institution: 
NCSU 
Program: 
NC State REU in Modeling and Industrial Applied
Mathematics 
College: 
PAMS 
Department(s): 
Mathematics 
Research 
Hien Tran/Mathematics R. Lawrence Ives/Calabazas Creek Research, Inc. 
Title of Presentation: 
Computer Optimization of
Electron Beam Devices 
Electron
beams can be used as power sources for highfrequency, high energy radio and microwave
sources for a variety of applications including radar, communications,
electronic countermeasures, and many defense and homeland security systems.
Existing cylindrical beam designs cannot achieve the required beam power for
some applications. Sheet beam guns can deliver much more power; however, at
higher power levels the magnetic field containing the beam interacts with the
electric field of the electrons to generate a force that curls the beam at the
edges. Counteracting this curling requires adding components to alter the
magnetic field at the edges of the beam. The shape of the beam is very
sensitive to the location of these components, and the placement of components
cannot be optimized independently. Consequently, the performance of the beam depends
on too many parameters to be effectively optimized manually. Computer
optimization can dramatically reduce the costs and time to develop new electron
beam devices. Our research focused on an automated process for optimizing the
focusing of electron beams, using a sheet beam gun as a realworld problem. Two
optimization algorithms are being studied, including parallel implementations
of both algorithms.
Dodd, Val
L. Ritch, Ryan D. Huff, Kelly J. 

Home Institution: 
Asbury College 
Program: 
NC State REU in Modeling and Industrial Applied
Mathematics 
College: 
PAMS 
Department(s): 
Industrial Applied
Mathematics 
Research 
Laura Ellwein/Industrial
Applied Mathematics 
Title of Presentation: 
Analysis of Cardiovascular
Models to Examine the Potential Effects of Particulate Matter 
Recent studies have indicated an alarming connection
between the inhalation of particulate matter (PM) and increases in morbidity
and mortality. These tiny particles suspended in the air appear to be a
substantial causitory factor of harmful respiratory
and cardiovascular conditions. As cardiovascular events seem to compose the
largest number of PM related deaths, we sought to discover the means through
which PM affects the cardiovascular system. Because the exact composition of PM
can vary widely depending upon its source, we focused on PM resulting from
gasoline and diesel fumes. Previous studies indicate that some of the effects
of PM on the cardiovascular system include elevated heart rate, arrhythmias,
decreased compliance of the blood vessels, and increased blood viscosity. We
examined several models of the cardiovascular system in order to establish a
model that incorporates parameters that may be affected by PM. Investigation
into PM is still in its early stages, so data on the exact changes effected by
PM is limited. However, having discovered from previous studies how PM affects
certain parameters and outptus in our model such as
compliances and heart rate, we used a cadiovascular
model to hypothesize how PM brings about harmful effects. By observing how the
alterations of parameters change our model output, we may be able to determine
more specifically how PM exerts its detrimental effects. Commonly seen effects
of PM include changes in heart rate variation and the presence of abnormal
beats. Because of this, we found a pulsatile model of
the heart, incorporating fluctuations in blood volume and pressure associated
with the beating of the heart, to be helpful in observing these specific
effects of PM. Future collaboration with scientists would be useful in
obtaining more exact data on how those parameters common to most cardiovascular
models are affected by PM.
Durant, Ellen Sawyer, Megan Weissenstein, Eric 

Home Institution: 
NCSU 
Program: 
NC State REU in Modeling and Industrial Applied
Mathematics 
College: 
PAMS 
Department(s): 
Mathematics 
Research 
Sharon Lubkin/Mathematics 
Title of Presentation: 
Demonstration of Emergent
Properties of Tissues by Stochastic Modeling 
Cell
movement provides the foundation for the development of cysts, tissues, organs,
and, consequentially, entire organisms. Morphogenesis in animals is
mostly due to motion of individual cells and can be modeled using the relative
strength of surface energies of touching cells. By adjusting these energies in
a cluster of cells, we demonstrate different emergent properties of tissues.
We develop a modified cellular Potts algorithm in two and threedimensions
that preserves area and cell sorting under differential adhesion.
Furthermore, we extend this model to include cell division and secretion of
lumen, which, in combination with cell sorting, can model the creation of a
cyst.
Feldman, Jacob Morgante, Anna Pendeleton,
Terrance Reynolds, Doneshia 

Home Institution: 
Meredith College 
Program: 
NC State REU in Modeling and Industrial Applied Mathematics 
College: 
PAMS 
Department(s): 
Mathematics 
Research 
James Selgrade/Mathematics 
Title of Presentation: 
Modeling Hormonal
Regulation of the Menstrual Cycle 
The aim of this project was to improve and to make additions to a mathematical
model for regulation of the menstrual cycle of a normally cycling woman, which
accurately predicts levels of the essential reproductive hormones.
Exposure to environmental estrogens, such as dioxin, polychlorinated biphenyls
(PCBs), and oral contraceptives, in women today may have adverse effects on
hormone levels and the metabolism of the body. Elevated levels of
estrogen are a possible contributing factor to breast cancer in women.
Two primary sources of reproductive hormone synthesis within the body: the
pituitary gland located in the brain, and the ovaries. Follicle
stimulating hormone (FSH) and luteinizing hormone
(LH) are synthesized by the pituitary gland, while the ovary is the primary
producer of estradiol (E2), progesterone (P4), and inhibin (Ih). We
redeveloped an existing system of differential equations that models the rates
of change of these five hormones. Optimization techniques, as well as
informed adjustments of the parameters, allowed us to increase the accuracy of
the hormone models. Our models were compared to published data and were
found to portray the profile of each hormone accurately. As a result of
this project, these models can be used to predict the effects of changes in
hormone levels on the reproductive endocrine system.
Glover, Travious 

Home Institution: 
Virginia Tech 
Program: 
NC State REU in Modeling and Industrial Applied
Mathematics 
College: 
PAMS 
Department(s): 
Mathematics 
Research 
Ralph C. Smith/Mathematics 
Title of Presentation: 
Modeling Multifunctional
Materials 
Advanced aerospace, aeronautic, industrial, biomedical and nanotechnology applications increasingly rely
on multifunctional materials to achieve design specifications. These
materials exhibit the capability of coupling electrical, magnetic, thermal and
mechanical behavior, but do so at the cost of complex and nonlinear material
dynamics. This project focuses on the development of modeling, simulation
and statistical techniques for these advanced materials. We also consider
methods to make the implementation of these models more efficient while
maintaining enough accuracy so that the models remain applicable.
McCall, Pearlie 

Home Institution: 
Spelman College 
Program: 
NC State REU in Modeling and Industrial Applied Mathematics 
College: 
PAMS 
Department(s): 
Mathematics 
Research 
Sharon Lubkin/Mathematics 
Title of Presentation: 
Modeling Cellular Movement
in Tissues 
The movement of cells in tissues is an uncanny and intriguing phenomenon in the
scientific world. It is critical to understand the mechanisms of cellular
movement because they illuminate the connection between development of humans
and disease. In our research, we are creating mathematical models and using MatLab software to realistically mimic the movement of
cells in tissues.
Moran, Patrick A. Herwaldt, Bethany
A. Salter, Jeffrey 

Home Institution: 
College of Charleston 
Program: 
NC State REU in Modeling and Industrial Applied
Mathematics 
College: 
PAMS 
Department(s): 
Mathematics 
Research 
Carl D. Meyer/Mathematics 
Title of Presentation: 
Feature Extraction From
Textual Datasets 
The
Internet holds a wealth of new information, which is increasingly taking the
form of usergenerated content. Many are interested in knowing the
general opinions on a given topic without having to read thousands of reviews
and articles. Our goal is to find a technique that will allow us to
identify the topics discussed in a group of documents, then
determine the common opinion (positive or negative) of that topic. The first
step of finding the topics is to find a list words which should be characteristic
of the various topics. One way is through the nonnegative matrix factorization.
Another technique we can use to obtain characteristic words is to compare the
ratios of the frequencies of words in the document to the frequencies of those
words in some large corpus of general English.
Once found, these words must be grouped into topics. We create a graph
of the words, wherein the distance between two words is determined by WordNet similarity and word proximity. WordNet
similarity is a measure of how semantically related two words are, independent
of their context. Word proximity is based on the average number of words
between the two words in the document collection. These terms can then be
clustered with any traditional clustering algorithm. Topics are then scored for
positivity or negativity with natural language
programming. We attempt to detect associations between words characteristic of
a given topic and words known to be positive or negative. We then use this
information to try to score documents as having positive or negative opinions.
[ Participant Listing
 Abstracts ]
Last modified June 2008 by Sharon E. Hunt