# Research by New Projects

Below is a list of our new research projects. For more information click on the title of the project.

## Power laws and Tornadogenesis

**Advisor(s):** Doug Dokken

**Abstract:** Students will need to familiarize ourselves with the visualization software “VisIt” as well as CM1 on Linux and Unix operating systems. Then we will collect data on the weather of past tornadoes in order to generate a tornado on in the computer simulated storm. We will analyze this data to determine exactly why some storms result in tornadoes and why others do not.

**Number of students needed:** 2

**Research Description:** Run numerical simulations, modify code and learn how to use filtering tools to analyze radar data.

**Student qualifications:** Linear algebra and multivariable calculus and some programming experience.

Hours per week (up to 25) and start/stop dates (must be between May 27 and August 29 inclusive).

## Radian Measure: Practical Application and Introduction in the 5-12 Classroom

**Title: **Radian Measure: Practical Application and Introduction in the 5-12 Classroom

**Advisor(s):** Lisa Rezac

**Abstract:** This project will examine the importance of radian measure in mathematics, a practical application of radian measure in use today, and activities that will help students understand radian measure more deeply.

**Number of students needed:** 2

**Names of students you have already identified to work on the project:** Michael Driscoll (dris8896@stthomas.edu) and Will Abbott (abbo3254@stthomas.edu)

**Student duties:**

- Search “Mathematics Teacher” Journal and related resources (NCMT Illuminations) for Radian Measure Activities, and historical explanations and uses of radian measure
- Examine the practical application of Radian measure in military mapping
- Compare and contrast the introduction of radian measure in typical textbooks
- Produce an “Illuminations”- type lesson plan or “Mathematics Teacher”- type article summarizing work and incorporating practical applications of radian measure.

**Student qualifications:** Math 325 or equivalent; interest in math education, knowledge of practical application of radian measure

Hours per week (up to 25) and start/stop dates (must be between May 27 and August 29 inclusive).

**Project Start/Stop Date:**May 27 to August 29.

Max hours per week: 25

## Guaranteed Options in Variable Annuity Products

**Title: **Guaranteed Options in Variable Annuity Products**Advisor(s):** Thorsten Moening, Heekyung Youn**Abstract: **In recent years, variable annuity products have become a popular investment vehicle, in part due to their favorable tax treatment. A policyholder of a variable annuity often directs the insurer to invest his/her money in the equity market and hence faces an uncertainty that the investment might lose value. To offset this risk, at least partially, the policyholder can purchase (for an additional fee) a guarantee such as a Guaranteed Minimum Death Benefit (GMDB) that guarantees a certain level of payout at the time of the policy holder’s death if that happens before the policy maturity. Similarly, a Guaranteed Minimum Accumulation Benefit (GMAB) ensures that the policyholder will be paid a certain minimum amount at maturity if the policy holder survives till then, even if the fund value drops below the minimum level. In this project, we will investigate whether the fees charged by the insurance companies reflect the benefits provided. In particular, we want to consider whether the fee should depend on the policyholder’s age at inception of the variable annuity, and to what extent insurers account for that in practice.

**Number of students needed:** 2**Names of students you have already identified to work on the project:** None

**Student duties: **

**Student qualifications:** Students who would have completed at least one of MATH 313 and ACSC 264 by the end of this semester, and are willing to learn and work hard.

Hours per week (up to 25) and start/stop dates (must be between May 27 and August 29 inclusive).

**Project Start/Stop Date:**May 27 to August 29.

Max hours per week: 25

## Bank Data Analysis

**Tile: **Bank Data Analysis

**Advisor(s):** Heekyung Youn, Arkady Shemyakin

**Abstract: **Banks lend money to consumers. One of such types of loans is home mortgage. These loans have the underlying house (property) as collateral, and often the terms of the loans are very long: 10, 15 or 30 years.

**Number of students needed:** 2

**Names of students you have already identified to work on the project:** Michael Driscoll (dris8896@stthomas.edu) and Will Abbott (abbo3254@stthomas.edu)

**Student duties: **See advisor for this porject.

**Student qualifications:** Completed at least MATH 313, preferably STAT 314, by the end of this semester.

Hours per week (up to 25) and start/stop dates (must be between May 27 and August 29 inclusive).

**Project Start/Stop Date: **May 27 to August 29. Max hours per week: 25

## 3D Rapid Prototyping of Ruled Surfaces in Architecture

**Advisor(s): **Dr. Michael P. Hennessey (School of Engineering), Dr. Cheri Shakiban (Department of Mathematics )

**Abstract:** Ruled surfaces have been used by famous architects throughout the ages, such as Gaudi in his masterpiece, La Sagrada Familia. As another example, the Vatican has several impressive ruled surfaces that St. Thomas students have seen in a J-Term course that focused on geometry and mechanics of architecture. The student researchers will learn about the mathematical theory of ruled surfaces and using appropriate software, will create files of well-known geometrical structures that are printed out in plastic on a 3D printer, also known as rapid prototyping in mechanical engineering.

**Number of students needed:** 2

**Research Description:** Focus is on two fundamentally different approaches based on either using *Mathematica* or MATLAB (and/or SolidWorks). For the *Mathematica* approach, there are several steps envisioned, specifically: (a) characterizing the ruled surface mathematically with the appropriate equations, (b) either creating a so-called STL file that can be input directly to a rapid prototyping machine or employing SolidWorks to further process the numerical surface data from which the STL file can be created. In the case of the MATLAB approach, given the fundamental surface equations, there are 3 different ideas on how best to create ruled surface part models: (a) create surfaces in MATLAB using specialty commands and then proceeding on to SolidWorks if necessary and the 3D printer, (b) exporting coordinate data, such as for grid points, to SolidWorks, and then using surface tools to further process prior to generating the printable STL file, and (c) just use SolidWorks directly to create the model. We have several specific surfaces that we would like to have modeled. Upon completion, we will evaluate the capabilities and tradeoffs associated with each approach.

**Student qualifications:**

**Mathematics Course Requirements (Minimum):** Ideally, the calculus sequence, linear algebra, and differential equations (prefer above 3.5 GPA in those mathematics courses).

**Student Interests/Skills:** Generally, the students would have an interest in both applied mathematics and mechanical engineering. Someone who is at least a sophomore and double majoring or major/minoring in a combination of mathematics and mechanical engineering would be ideal. It is also a requirement that the student either know some MATLAB^{TM} and/or *Mathematica* basics or have an interest in learning. Knowing something about SolidWorks and 3D printing is beneficial as well.

**Hours per week:** (up to 25) and start/stop dates (must be between May 27 and August 29 inclusive).

May 27- August 29 (20 hours per week maximum) with possible follow-on activity such as a research conference paper (e.g. ASME and/or Bridges of Mathematics Conference).

## Hyundai Car Repair Analysis

**Advisor(s):** Arkady Shemyakin, Heekyung Youn

**Abstract:** Hyundai cars carry 100,000 miles/10 year warranty. Repair records of the cars are closely tracked in terms of types of repair and the times of repair. We will study joint distributions of lifetimes of different vehicle components. In particular, we will single out a principal component, and try to see if the other components’ failures may trigger the failure of the principal component.

The project will utilize linear and non-linear regression, copula modeling, and possibly Markov Chain Monte Carlo methods to help predict future failures of the principal component.

**Number of students needed:** 2

**Research Description:** See advisor for this project.

**Student qualifications:** Completed at least MATH 313, preferably STAT 314, by the end of this semester

Hours per week (up to 25) and start/stop dates (must be between May 27 and August 29 inclusive).

## Graphs and Rings

**Advisor(s):** Mike Axtell

**Abstract:** Abstract: We will seek to apply the techniques and ideas of graph theory to gain algebraic knowledge about commutative rings. Topics such as factoring and zero-divisors will be our primary focus.

**Number of students needed:** 2

**Names of students you have already identified to work on the project:** Emily Punyko

**Student duties: **Research, present ideas both orally and in written form. Attend conferences to rpesent results.

**Student qualifications:** Math 301 required

Hours per week (up to 25) and start/stop dates (must be between May 27 and August 29 inclusive).: 20-25 hours/week from 6/2 - 8/29

## Reverse Mortgage Strategies

**Advisor(s):** Heekyung Youn, John Kemper

**Abstract:** Reverse mortgages (RMs) are experiencing a resurgence as the U.S. economic recovery becomes more evident. The aims of this project include the following parts:

--understanding the terms of a typical RM

--recognizing the risks and rewards of a RM from the point of view of each of the three

primary participants: the lender, the borrower and the insurer

--modeling housing values

--modeling RM termination probabilities

--modeling the financial risks and rewards for the RM participants

--seeking to identify optimal termination strategies for the borrower and the related impact on insurers

--identifying, if possible, hedging strategies for the insurer

**Number of students needed: **One or two students are needed for this project. Students must, by June 1 (2014), have completed ACSC 264. To apply, send an email to Professor Kemper ( jtkemper@stthomas.edu ) that includes

-a list of the mathematics, actuarial science and business courses taken through spring ‘14

-names two faculty members who are familiar with your coursework or research

-a paragraph describing your interest in this project

Students chosen to participate in the project will be expected to agree to and follow CAM regulations for summer research projects.

**Names of students you have already identified to work on the project:** Jake Damiani

**Student duties: **Research, present ideas both orally and in written form. Attend conferences to rpesent results.

**Student qualifications:** Completed ACSC 264

Hours per week: 20 hours per week for 8-10 weeks.

## The Selfish Herd Hypothesis with small groups

**Advisor(s): **Paul Ohmann

**Abstract:** The Selfish Herd Hypothesis asserts that certain animals congregate because of the protective quality that this grouping confers – i.e. individuals are less exposed to predators. This is often modeled by defining a “degree of danger” around each individual and showing that clumping together helps minimize this value. Typically, these simulations start with a sizable collection of individuals, but what happens when the density of individuals is sparse? Can we determine when it is in the best interest of individuals to congregate when there isn’t already a sizable group to follow? Is there a tipping point beyond which groupings will tend to be large, and below which groupings are either disfavored or else otherwise constrained to be small? This project will attempt to investigate these questions.

**Number of students needed:** 1**Names of students you have already identified to work on the project:** Nick Ose

**Research Description:**

- Background reading and synthesis of the historical papers on this subject (e.g. Hamilton, W.D. (1971), “Geometry for the Selfish Herd”,
*Journal of Theoretical Biology***31**:295-311.) - Build Matlab predator-prey models with various small numbers of prey. We will need to define and keep track of relevant quantities, such as prey lifetimes and distances between individuals. We will also need to carefully analyze these simulations in order to interpret the results.
- Write a final report summarizing the project, following CAM’s guidelines for final reports.
- Present your results at the Inquiry at UST Poster Session in September.

**Student qualifications: **Students should have completed Phys 112 as well as CISC 130 (or have Matlab experience), along with a good GPA and an ability to work independently with faculty guidance.

Hours per week (up to 25) and start/stop dates (must be between May 27 and August 29, 2014).

## Mathematical Modeling of Craniosynostosis

**Advisor(s):** Magdalena Stolarska

**Abstract:** Craniosynostosis is a condition in infants where skull plates fuse prematurely leading to abnormal skull and brain growth. Due to the fact that abnormal brain growth can increase intracranial pressures, which can have adverse affects on development, the aim of this project is to develop a model and run simulations of the growing brain/skull system and quantify the intracranial pressures that occur when particular skull plates are fused. To develop the model, students will use mathematical methods based on continuum mechanics and use the finite element method for simulations.

**Number of students needed:** 2

**Names of students you have already identified to work on the project:** Jackson Penning (penn5708@stthomas.edu) and Madeline Anderson (ande2354@stthomas.edu)

**Student duties:**

**Student qualifications:**May 27 to August 29. Max hours per week: 25

**Project Start/Stop Date:**