Papers

This is our growing collection of research and technical documentation. Each paper reflects our work in simulations, modeling, or applied design.

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Simplification of the Gaussian Integral

By Joseph Yazuardi

This paper presents a personal exploration of the Gaussian integral and its polar coordinate transformation. Written independently as an undergraduate, it walks through a full derivation and concludes with a graphical visualization of the bell curve. It was also Joseph’s first project using LaTeX.

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Pendulum Motion: Numerical Methods and Analysis

By Carl Somera

This paper explores the motion of a pendulum using Newtonian mechanics and numerical methods, specifically the Runge-Kutta 4 (RK4) algorithm. It compares results from small-angle approximations with full nonlinear numerical solutions, and even includes damping analysis for air resistance models.

📎 Download Python code (VectorRK4.py)

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String Theory Textbook

By Carl Somera

String theory textbook that will cover both bosonic and superstring theory. It is meant to provide a rigrous yet easy to understand introduction to the subject at a graduate level.

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Alpha-Induced X-ray Emission

By Joseph Yazuardi & Yufeng Chen

A lab report from the University of Michigan’s Advanced Physics Laboratory (P441), exploring X-ray spectroscopy using alpha particle excitation. The experiment validates Moseley’s Law and analyzes samples like aluminum, a U.S. quarter, and YBCO. Unknowns revealed tantalum, lead, and bismuth. Yufeng Chen was Joseph’s lab partner for this project.

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