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Full-Text Articles in Physical Sciences and Mathematics
Colliding Wind Binaries With Orbital Motion: Line Wind Formulation, Brendan O'Connor
Colliding Wind Binaries With Orbital Motion: Line Wind Formulation, Brendan O'Connor
Honors Theses
Stars lose mass in the form of supersonic winds. In a binary star system, these winds collide to produce shockwaves. Such stellar wind collisions are observed in many binary star systems. Due to the orbital motion of the system, a trailing spiral structure is produced. We present a solution method in the co- rotating frame of the stars, which allow us to consider steady state solutions. This requires the inclusion of Coriolis and centrifugal forces, including their effects on the pre-shock winds, for which we were restricted to orbital speed slower than wind speeds. We assume efficient post-shock cooling, which …
General Relativity And Differential Geometry, Harry Hausner
Partial Differential Equations, Nathaniel James Onnen
Partial Differential Equations, Nathaniel James Onnen
Honors Theses
This paper will discuss methods for solving many different partial differential equations, as well as real world applications in physics. We are interested in finding solutions to the wave and heat equations in one dimension, the wave equation in two dimensions, as well as a solution to Schrodinger’s equation. In order to do this, we will study different methods including Fourier series, Bessel functions, and Hermite polynomials. I will use these methods to derive solutions for the mentioned problems, as well as to produce visualizations for many of them.
The Calculus Of Variations, Erin Whitney
The Calculus Of Variations, Erin Whitney
Honors Theses
The Calculus of Variations is a highly applicable and advancing field. My thesis has only scraped the top of the applications and theoretical work that is possible within this branch of mathematics. To summarize, we began by exploring a general problem common to this field, finding the geodesic be-tween two given points. We then went on to define and explore terms and concepts needed to further delve into the subject matter. In Chapter 2, we examined a special set of smooth functions, inspired by the Calabi extremal metric, and used some general theory of convex functions in order to de-termine …