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Full-Text Articles in Physics
Calculating The Shear And Divergence Of Light Rays, Matthew Witherell
Calculating The Shear And Divergence Of Light Rays, Matthew Witherell
Honors Program Theses and Projects
The purpose of this research was to calculate the shear and divergence of light rays bundles as they pass black holes. We defined a Lagrangian using the Schwarzchild metric then used the Euler-Lagrangian equation to create 6 first order OED’s for the light rays path. Next we found tangent vectors to the light ray so we could calculate Ψ0. In order to calculate the shear and divergence the method of calculation required simultaneously solving 16 ordinary differential equations. We used Mathematica to calculate how these light rays act but first we had to use calculus and algebra to derive these …
Analysis And Dynamics Of Laser Models, Kassaundra Przelomski
Analysis And Dynamics Of Laser Models, Kassaundra Przelomski
Honors Program Theses and Projects
Lasers produce a strong focused ray of light that is useful in many industries, including medicine and technology. For example, they can be used for guiding surgical instruments or playing compact discs. In this thesis I characterize the dynamics of a fundamental laser model. A mathematical goal is to determine the number of photons in the laser cavity as time evolves. Different choices of parameter values produce qualitatively different behaviors of the system. I perform a bifurcation analysis in order to capture the different physical situations, identifying equilibrium solutions and their stability properties. I sketch representative solutions using the bifurcation …