# SSRD 2023 Schedule

## Room 6 Schedule: Collins 318

ZOOM link for off-campus community members
• 9:00 a.m. | JACQUELINE ANDERSON | Has the S-STEM Program Made a Difference at Willamette University?

In 2017, Willamette University received a National Science Foundation grant to implement the S-STEM program on campus. The main focus of this program is to increase retention of students with high financial need who are interested in Science, Technology, Engineering, and Mathematics by providing scholarships and mentoring support. To determine the program's effectiveness, Python can be used to perform a statistical analysis of the students who were part of the S-STEM program by utilizing the free OpenPyXL module. Effectiveness is being measured by comparing graduation rates and academic performance of STEM students in, and outside, the program.

Discipline: Physics

• 9:20 a.m. | JACK RANDALL | Titanium Coloration

When titanium is exposed to heat, colorful titanium-oxide layers form on the surface. With the help of a pulsed laser and the motors from a 3D printer, we can create these layers: The laser allows for the heating of a small area of titanium, and the 3D printer allows for precise control over what part of the sample the laser beam is hitting and how fast the laser beam is traveling over the sample. With this setup we were able to catalog the different colors that we created. Applications range from the arts to improving monetary security.

Discipline: Physics

• 9:40 a.m. | COLLIN JAMES BRADFORD | A Detailed Study of Galaxy Motion Estimates using the CosmicFlows-4 Catalog

Galaxy motion due to gravity is important to understand the matter distribution in the Universe. One measure of galaxy motions is the bulk flow: the average velocity of galaxies within a spherical volume centered around Earth. The Cosmicflows 4 (CF4) database is the most extensive collection of galaxy velocities and has been used to estimate the bulk flow using the Minimum Variance (MV) method, a mathematical process that optimally weights galaxies to achieve the most accurate estimate possible. This research deeply analyzes the weighting scheme of this analysis in order to develop better intuition for how the MV method operates.

Discipline: Physics

• 10:00 a.m. | JADE HODGES | Using a Pulsed Laser to Simulate the Wavefield of Bouncing Droplets

We can make a small liquid droplet bounce on the surface of a dish of that same liquid. As the drop bounces, it creates waves that travel outwards and can push and pull on other droplets. By pulsing a laser onto the surface of the liquid, we can generate waves similar to those caused by the droplets. We can use this laser-driven wave to move the bouncing droplets around. To determine how similar the laser-driven waves are to the droplet-generated waves, we create a 3D reconstruction of the liquid’s surface.

Discipline: Physics

• 10:30 a.m. | GABE HOLLIDAY | Analog Implementation Of Chaotic Systems to Encrypt Signals

A chaotic system is a system of equations that is highly sensitive to initial conditions. Because of this sensitivity, chaotic systems can appear random and be difficult to predict. The Lorentz System is a chaotic system that models atmospheric convection. In this talk we discuss how one may implement the Lorentz System using analog electronics. We show that two such circuits can be synchronized when coupled. The ability of chaotic systems to synchronize allows us to mask a transmitted message and then decode it.

Discipline: Physics

• 10:50 a.m. | CHRIS CHANG | Developing a Model of a Myofibril Using the Markov Chain Monte Carlo Method

This project aims to model the complex force generating behavior of muscles by considering a
phenomenon known as residual force enhancement (RFE). This occurs when a contracting muscle is stretched which results in more force generated than if a contracting muscle were not stretched. Starting from the fundamental force generating molecule called myosin, we created a model of the structure that comprises out muscles called a myofibril. We then fit our model to experimental RFE data using the Markov Chain Monte Carlo method. From this we determined the most important model parameters for describing RFE.

Discipline: Physics

• 2:00 p.m. | TYLER PRZBYLSKI, AUGUST BERGQUIST | Homology, Building the Hole Picture

In the field of algebraic topology, homology offers a way of associating a topological space, like the sphere or the donut, with algebraic groups which measure the number of “holes” an object has. While the technicality of homology can seem intimidating, beautiful insights can be gained by transferring between the two separate worlds of topology and algebra. This presentation will show the concepts of homology in 5 different difficulty levels starting with a beginner and math-phobic friendly approach. Emphasis will be placed on the process of building the mathematical theory as well as a strong intuitive understanding with pictures.

Discipline: Mathematics

• 2:20 p.m. | AUGUST BERGQUIST | Invariance of Dimension: A Story of Mathematical Structure

N-dimensional Euclidean space is one of the most widely known and loved mathematical structures. From Group Theory to Linear Algebra, Euclidean space can be understood from many angles and it is clear that dimension plays a fundamental role. On the other hand, the fact that dimension is a topological invariant requires significant structural buildup. Using the power and properties of homology, a tool for turning topology into algebra, we will outline a proof of Invariance of Dimension.

Discipline: Mathematics

• 2:40 p.m. | SETH BELL | Topological Stability

Topological Data Analysis (TDA) is a relatively novel field of applied mathematics in which topology is used to detect the underlying shape of data. In order for the techniques of TDA to be usable, they must be "stable;" if our dataset is disturbed by a small amount, our results should only be disturbed by a small amount. We present a statistical TDA method called the "persistence landscape" and explore the justification and implications for its stability. We describe an application in economic finance.

Discipline: Mathematics

• 3:10 p.m. | MITCHELL EVERETTS, YIZE SMITH-ROCKNE | Proof of Frieze's Limit Theorem Using Random Coalescent Theory

In 1985, Frieze proved the asymptotic result for mean minimal spanning trees on the complete graph. In this talk, we will present an alternative proof to Frieze’s result using the theory of  multiplicative coalescence. This alternative approach demonstrates the connection between the multiplicative coalescent processes and the Erdos-Reyni random graphs.