## Abstract

# TSU Particle Modeling Group

Tarleton’s Particle Modeling Group, led by Dr. Bryant Wyatt, focuses on creating discrete dynamical models for solving a large array of problems. This method results in large n-body simulations that must be propagated through time numerically. Because the total force on each particle (body) can be accumulated independently, this work can be paralyzed and offloaded to NVIDIA GPUs for acceleration. Over the last ten years, the group has worked on nonlinear dynamical systems ranging from late lunar forming impacts simulations to novel techniques for optimizing the traveling salesman problem. The group has given hundreds of presentations across the country and won numerous awards for the work they have done utilizing the power of NVIDIA graphics cards. Dr. Wyatt’s true mission in life is to show the world that math talks do not have to be boring and the source of all interesting research imitates at the crossroads of mathematics, physics, and computer science. As a result of this mission, Dr. Wyatt was the MAA’s Distinguished Teacher of Mathematics for Texas in 2018. A link to his acceptance presentation “Thor onto Democritus: A Topological Isomorphism on Atoms and the Void” is given here.

Dr. Wyatt’s personal favorite talk “Circumplanetarydisk-o” is given here.

For more information, contact Dr. Wyatt at wyatt@tarleton.edu

## Supraventricular Tachycardia (SVT)

We were contacted by a medical group from the Dallas Fort Worth metroplex to see if we could model a heart that could be used to perform simulated ablations on. Irregular rhythms above the right ventricle, Supraventricular Tachycardia (SVT), though not in itself deadly, is the leading cause of strokes, heart attacks, and heart failure. Therefore, one could argue that SVT is indirectly the leading global killer. Hence, the success of this project could greatly affect thousands of lives annually. We have just started work on this project but our preliminary results have been very positive.

## Late Lunar Forming Impacts

The Earth-Moon system is unique in our solar system and possesses several features that are not easy to explain. For instance, the isotopic signature of soil samples from the Moon is strikingly similar to the soil here on Earth. This suggests that the Earth and Moon were both created from the same parent material. Earth being a rocky planet contains a large iron core but the Moon though large enough to be a rocky planet contains very little iron. This suggests that the Moon formed differently than all the other rocky planets. The leading theory as to how the Moon was formed is the giant impact hypothesis, where two rocky planets collided to form the Earth-Moon system. Researchers studying the giant impact hypothesis have been successful in creating simulations that answer many questions about the origin of the Earth-Moon system but have trouble getting the correct angular momentum of the system and Moon’s off equatorial orbit. Here we demonstrate that straight forward initial conditions can produce a correct Earth-Moon system solely from a single giant impact.

## Mass Transfer in Multiple Stars Systems

This is a project that the particle modeling group has been working on for several years with Dr. Shaukat Godarya from the physics department. Most stars in our university do not live alone but are born, mature, and eventually die in groups. Stars within these systems can exchange mass which affects the life cycles of all stars involved. This exchange of mass is not well understood and is what we are studying here.

## Lattice Tower Optimization

Here we optimize free standing lattice towers using muscle growth and atrophy for inspiration. If a muscle is asked to perform past its correct development it grows, if a muscle is not asked to perform up to its correct development for a period of time it atrophies. We apply this process to members of a lattice tower. If a member is stretched or compressed past a given upper limit its cross-sectional area is increased. If a member is not asked to perform past a given lower limit its cross-sectional area is decreased. This method is applied to the entire structure until the structure stops adjusting. We have gotten exceptional results compared to static structure optimization models and in addition, this method also works on dynamic structures which other optimization techniques can not do.

## Matter and GPUs: Should the Focus of Our Modeling Classes be Adjusted?

A Simple Oscillating String Example

We did this project to demonstrate the basics of particle modeling. We wanted to use something that everyone had an intuition about from their everyday life. Something that they could actually see and feel. We also wanted this to be something that could easily be modeled with continuum mathematics. This would allow us to do a direct comparison between discrete particle modeling and traditional continuum modeling and let the reader conclude which method produced a better outcome.

## N-Body Art on Nvidia GPUS

The Tarleton State University Particle Modeling Group specializes in modeling Math, science, and engineering problems using N-body techniques accelerated on NVIDIA GPUs. Through the years, the group has been amazed at how beautiful many of the simulations they created can be. In fact, some of the most interesting and visually appealing runs have come from simulations gone awry. The group has always wanted to share how unique and intriguing N-body simulation can be. Hence, this year we have created a simulation not to advance the STEM fields, but solely to advance the humanities and make known the true beauty behind mathematical simulations.

## Orbital Resonance

This project grew out of the lunar forming impact project. We wanted to get a general idea of the velocity of impact of two planets with close orbits around the Sun. Our thought was that gravity between the planets would slow the leading planet and they would eventually collide. We would use this velocity of impact to give us a starting point for the velocity of impact in our lunar forming collisions. What we learned was that the planets never collide but perform a strange dance as they travel around the Sun.

## Fractal Performance Analysis

Here we wanted a problem that demonstrated the power of modern NVIDIA GPUs. Fractal generation is embarrassingly parallel and we show how fast it can be generated on the GPU.

## Traveling Salesman Problem

The Traveling Salesman Problem (TSP) is a classical problem in mathematics and has a wide range of applications across engineering and business. The task is to have a set of cities that you must visit and return home with the shortest path. With a set of five cities, there are 12 possible routes. Calculate the length of all 12 routes and choose the shortest. Hence, the method of finding the exact solution is straightforward and easily understood. The difficulty lies in the fact that the total number of routes grows factorially as the number of cities grows. Total routes = ((n-1)1)/2. If a salesman must visit 25 cities that gives 310,224,200,900,000,000,000,000 possible routes. If you had a computer that could run through a billion routes a second it would still take you 9.8 million years to run through them all. Fruit forcing the solution is just not feasible therefore good approximation techniques are needed. Here we turn the TSP into a physics problem and push the cities into a minimal energy path.

## Self-Assembly

We got this project from a 2010 Science article “The Free-Energy Landscape of Clusters of Attractive Hard Spheres” by Vinothan N. Manoharan. If you have 1,2,3,4 or 5 hard spheres they can only form a single structure but when you increase this to 6 spheres there are two structures that can form. The interesting thing about this is that one structure will form 24 times more frequently than the other. At Harvard, they were physically looking at hard spheres suspended in a fluid through a microscope. We thought we could just simulate the forces and kick-off thousands of simultaneous simulations on the GPU and sort the results. When we did this we got identical results. We did not pursue this project very intensely but it was interesting to see that our model tracked so well with the results in the Science article. Another interesting turn on this project was that I was giving a talk on GPU computing at The 2012 TAMU Casper College Summer School on Quantum Science and Engineering in Wyoming and a colleague of Vinothan N. Manoharan was in the audience and got my students in touch with Vinothan.

## Fish Schools

This was just a class project but that turned out really well and won a couple of awards. We got the idea from Steven Stogatz’s Ted talk on The Science of Sync. The basic idea is that the mechanism that allows animals to move as a group is governed by a few simple rules.

## Miscellaneous Projects

These are all the miscellaneous projects that may have been class projects that were good enough to present at a regional or local conference or larger projects that didn’t get fully developed.