Two Bachelor´s Degree Project Presentations: Qie Kuang and Muhammad Mustafa

"Fractal dimension: introduction, example, and application"

• Student: Qie Kuang
• Time: 11:15-12:00
  

Abstract: Self-similarity and near perfect self-similarity objects exist everywhere, from the universal to the generated samples in pure mathematics. An indicator, called fractal dimension, can be used to study the complexity of them. This thesis addresses the question of relevant definitions of dimensions and gives ample but detailed examples showing how to calculate different dimensions. This work not only aids readers in the natural sciences to grasp these concepts more effectively but also demonstrates practical applications, making them accessible to wider audiences.

"The N-body problem"

• Student: Muhammad Mustafa
• Time: 13:15-14:00
  

Abstract: To simulate the orbits of a planetary system or a binary star are examples of the n-body problem. The goal of this project is to examine numerical methods for ordinary differential equations and how well they can simulate the orbits of heavenly bodies. Two models are simulated: The two- and the three-body problem, which both are special cases of the n-body problem. The two-body problem is used for obtaining the orbit of an exoplanet (a planet outside of the solar system) called 51 Pegasi b around its host star 51 Pegasi (a sun-like star), and the elliptical orbits of a binary star called Albireo (two stars orbiting their common center of mass). The three-body problem is used for simulating the orbits of two exoplanets around their only host star called HD 83443. The star’s two planets have distinct orbital characteristics: HD 83443 b follows an almost circular orbit (low eccentricity) while HD 83443 c has a highly eccentric orbit.

The orbits of heavenly bodies are simulated using two numerical methods: forward Euler and Runge-Kutta 4. The simulations are based on fundamental equations derived from Newton’s laws of motion and Kepler’s laws of planetary motion. The results of all the simulations indicate that Runge-Kutta 4 provides significantly higher accuracy compared to forward Euler method for obtaining the orbits of heavenly bodies over both short and long-time durations.