Major:Physics & Math
Mentor:Dr. Joseph Iaia
Current Research Topic:Math Modeling in Physics
Abstract:The initial goal was to submerse myself in the study of partial differential equations as they pertain to physics, such as the Korteweg-de Vries equation in order to study self-reinforcing wave packets called solitons. However, in order to get to that level mathematically, one would have to obtain a Master’s degree in mathematics. The new goal is to bridge the gap of the undergraduate and graduate understanding of partial differential equations. The shortening of this gap can be done by producing mathematical models of physical systems. The models that describe the time evolution of such systems are called dynamical systems. When the state of the system is continuous, opposed to discrete, differential equations can be used to describe the system. I want to construct physical systems in which I can record and analyze how their states change as time increases. By comparing results obtained experimentally to those from theoretical models of the physical systems, I can adhere models to describe what happens to all systems of the same sort, given the same initial conditions and parameters. My results will be presented with simulations to show how differential equations can dictate future behavior of these systems.