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### Current Faculty Research

Research interests of some members of the department include

- Dr. Bryant Wyatt - Particle Modeling
- Dr. Keith Emmert - Mathematical Biology
- Dr. Kathy Horak Smith- Mathematics education
- Dr. Jesse Crawford - Mathematical Statistics and Data Mining
- Dr. Javier Garza - Mathematical Models of Biology, Optimization,

Optimal Control Theory, and College Mathematics Education

### Dr. Jesse Crawford - Mathematical Statistics and Data Mining

Most of my research has involved the study of multivariate normal distributions with covariance matrices determined by group symmetries and acyclic mixed graphs, including the generalization of canonical correlations to group symmetry models, and developing a likelihood ratio test for testing equality of natural parameters for generalized Riesz distributions.

My current focus is applications of statistical models and data mining techniques to problems such as placement of college students, prediction of nitrate contamination in water wells, and detection of anomalous crop insurance claims using satellite data.

### Dr. Keith Emmert - Mathematical Biology

To date, my research has focused on the development of new deterministic and stochastic epidemic models for the spread of disease in a structured host population. Past models have been included difference as well as differential equations with both fixed or periodic coefficients. I use theory as well as simulations to investigate the richness of the models.

Future directions in research include investigating the robustness of stability results, improved visualization techniques for bifurcations in higher dimensions, animal movement models, epidemic models that incorporate a spatial component, and population genetics. Parallel algorithms and genetic algorithms will most likely be of great use in exploring these new topics.

### Dr. Javier Garza - Mathematical Models of Biology, Optimization,

Optimal Control Theory, and College Mathematics Education

My early career research interests included constrained optimization and related numerical methods. More recently, my research efforts have focused on mathematical models of biology, optimal control theory and sensitivity analysis of related models. Student research projects have focused on sensitivity analysis of transmission models and optimal intervention protocols for cholera in human populations and mastitis in dairy cow populations. I have also been engaged in the Scholarship of Teaching and Learning (SoTL), and faculty development designed to encourage SoTL. Future research efforts will focus on analytics and predictive modeling, in particular related to application in higher educational enrollment management.

### Dr. Bryant Wyatt - Particle Modeling

Dr. Wyatt. Kepler Trek, New Zealand

My students and I work in our high performance computing lab doing Particle Modeling research. In the old days to run large N-body simulations you needed a CRAY supercomputer which cost tens of millions of dollars. Today with the advances Graphics Processing Units (GPUs) supercomputing can be done in your living room. Our lab was built with a grant from Tarleton State University and donations from Mellanox Technology and NVIDIA. We are grateful for their support.

#### N-body Simulations of Late Lunar Forming Impacts

Brett Hokr (left) and Justin Highland (right)

The Giant Impact Hypothesis is currently the most widely accepted explanation for the formation of the Earth-Moon system. Though this mode of formation is stated in text books it has never been modeled. Dr. Robin Canup (Associate Vice President at the Southwest Research Institute) made the problem popular when she was featured on the history channel. Researchers have been able to create impact models that produce a disk of debris around the earth with enough mass to create the moon. They have also created models that can start with a disk of debris around the earth and coalesce into a moon. But no one to date has been able to produce both from a single model. Brett and Justin were able to produce models using only a single GPU with very similar results to Dr. Canup's. Some snapshots of their simulations are shown below.

Run Time 96 Hours |
Number of Particles 9286 |
Length of Collision 50 simulated hours |

Image results from same size impactor 2D run

Run Time 12 Hours |
Number of Particles 15210 |
Length of Collision 50 simulated hours |

Image results from Mars-sized impactor 3D run

Run Time 8 Hours |
Number of Particles 9286 |
Length of Collision 50 simulated hours |

Image results from same sized impactor 3D run

Run Time 30 minutes |
Number of Particles 2000 |
Length of Collision 20 simulated hours |
Damping Constant b 0.2 Me/Hr |

Image results from accretion disks run

Brett Hokr graduated from Tarleton in May 2011 and moved on to Texas A&M to work on his Ph.D. in Quantum Optics studying under Dr. Marlan Scully.

Brett at Old Faithful, Yellowstone National park.

Justin Highland graduated from Tarleton December 2011 and will be joining the team down at Texas A&M in the fall of 2012.

Justin trekking up Granite peak Montana

We are still trying to create a single model that will produce the accretion disk from an impact that will then coalesce into a moon.

#### N-body Study of the Thermodynamic Properties of Water

Student: Travis Salzillo

Travis is working on a model of the water molecule and trying to check the validity of the model to known thermodynamic properties of water. Once we have an understanding of the models temperature we will study the phase changes of water using the model.

Snapshots of Travis' Simulations

Travis talking with Maran Scully and Nobel Lariats David Lee and Dudley Herschbach in Wyoming.

Travis is scheduled to graduate in May 2013 and hopes to continue his studies toward his Ph.D.

#### Particle Based Simulation of Oscillating String

Student:Robert Pierce

Robert is working on comparing a particle based model to a continuum based model. He is building a physical vibrating string apparatus that he can set the amount of tension. He can also find the mass per unit length of the string. Using these two parameters he will build a continuous model that he solves using partial differential equations and a discrete case which he will solve using particle modeling. He will then compare both back to the physical vibrating string.

#### Particle Modeling Optimization on a CUDA-enabled High-performance Cluster

Student: David Gibson

David is working on ways of optimizing different N-body problems to run most efficiently on a CUDA cluster.

Super Dave and the cluster "Camden County with head node Earl"

Supper Computing 11 (SC11) in Seattle, Washington

Student: Eli Symm

Eli has just joined our group and is working on finding a problem to study.

Graduation parties on the Paluxy River at Wyatt's in Glen Rose.

If you would like more information on our group drop us a line at wyatt@tarleton.edu.

### Dr. Kathy Horak Smith- Mathematics education

My research mission is two-fold. I want to learn as much as I can about how students learn mathematics and how they acquire the academic vocabulary to communicate the mathematical concepts they have learned. I have two areas where my research occurs: public school classrooms and the college classroom.

Each summer, I work with two professors from Texas Christian University (TCU). We spend three weeks teaching summer school to rising fourth-sixth grade students in Fort Worth ISD’s Language Learning Centers (LLC) classroom teachers. The mathematics/science/language curriculum is not considered remedial, but an extension to the curriculum. The students enrolled in the summer school program have been in the United States less than three years and come from all over the world. This past year, our students claimed 21 different languages as their first language. We also involve classroom teachers, undergraduate and graduate students in the experience. This research group is involved in researching the acquisition of academic language in mathematics and science.

Specific areas that Tarleton State Undergraduate students are involved in include: use of word walls to teach academic language; use of graphic organizers to assess students’ problem solving ability; and the teaching scaling (scaling, ratio, and proportions) to fourth through sixth graders.