Project Proposal – Scattering and the Interstellar Medium (ISM)

For my project, I will be studying Mie scattering and it’s relevance to the study of the interstellar medium. The ISM, the space between stars and galaxies, is filled with gas (atomic and molecular), dust, and is permeated by radiation – starlight. Observations of various astrophysical phenomena show that along a given line of sight, their is “extinction” of this radiation. Scattering and absorption account for these observations and occur due to the presence of various dust grains within the ISM. I will model Mie scattering and look at the asymmetry parameter g, a measure of the fraction of light scattered in the forward direction, in an effort to model the relationship between this value and dust grain properties  such as size, composition, etc.

Project Proposal: Diffraction Symmetries of C. elegans

The C. elegans nematode is a common subject of biological studies, and has become more and more popular in physics research. I intend to find the diffraction patterns generated by the worms’ shape and log the findings into a Symmetries Library (with the eventual goal of using Group Theory to get the worm shape directly from a diffraction image).

The shape of the worm (photos to be taken with a microscope) will correspond to a particular diffraction pattern. I will model the Fraunhoufer diffraction patterns (Far-Field diffraction) of the electromagnetic waves (light waves) by generating images with Mathematica using the Fourier Transforms. The idea is that $\left | Fourier Transform | \right ^2 $ = the diffraction pattern. This project is a study of the behaviors of light waves.

I will eventually be keeping a log of my findings on the already existing website, the Diffraction Symmetries Library.

Project Proposal: Modeling of EM Fields for Spheres in Mathematica

For my project, I propose the modeling of electromagnetic fields for spheres. I will use Mathematica to start, and possibly attempt to use other software products as well, such as OriginLab or MatLab. I will begin with the simplest case of a hollow sphere with radius approaching zero, or a point charge. I will then model electric fields for conducting spheres of different radii. From there, I will attempt other cases as well, potentially including: concentric spheres, spherical dielectrics, and systems of multiple spheres. Additionally, I will attempt to model magnetic fields for currents traveling in a spherical conductor, and magnetic fields within and surrounding spherical dielectrics. 

Project Proposal: Modeling E and B Fields of a Toroidal Conductor to Explore Tokamak Plasmas

I am interested in trying to determine why existing tokamaks (toroidal magnetic fusion reactors) use tori with the aspect ratios that they do.  To determine this, I intend to model the electric and magnetic fields (and D and H) of a solid toroidal conductor with a current flowing through it, and to examine how these fields change when the aspect ratio is varied.  I will chose the material properties of the conductor based on fusion plasmas in operating reactors.  Modeling the plasma as a solid seems reasonable due to the fact that tokamak plasmas do not change shape significantly during operation, and, other than some fluid dynamics disturbances, the plasma is relatively stable.

E & M 341 spring project: Modeling Railguns with John Loree and Elias Kim

Railguns are some of the most powerful weapons currently in production. However, along with being incredibly powerful, they are ideal for civilian use in aerospace engineering, or transportation. Elias Kim and I plan to build, model, and explore the physics behind these impressive devices, modeling the system with Mathematica. We plan to split the project into two parts, one individual modeling the circuitry of the railgun, and the other modeling the inductance and forces upon the railgun in matter, then combining our work to produce equations of motion. Additionally, we intend to build a small scale railgun, test-fire it, and compare its actual efficiency to the model generated earlier in the project.

E and M Spring Project

Our project for this course is Modeling electric and magnetic fields of a bar magnet, a cylinder, and a sphere using mathematica. I will be modeling the electric and magnetic fields for a cylinder. After developing a model for a general cylinder, I plan on modeling the electric and magnetic fields for different types of cylindrically shaped matter. This includes conductors and dielectrics. I would also like to do this for items with different current levels and to also model the magnetic field for different magnets (paramagnets, diamagnets, and ferromagnets). With this, I want to create a model for more complex systems, such as solenoids.

Developing Models of RLC Circuits

For my project, I will study RLC circuits. RLC circuits have three main components; resistors, inductors, and capacitors. These circuits are important because of their prevalence in radios and televison (among other things). Specifically, I will develop a few different configurations of these circuits and measure characteristics such as voltage, current, resonance, and most importantly, damping. The physics that governs RLC circuits relies heavily on the mathematics of differential equations. For this reason, Mathematica, due to its strong capabilities in regards to differential equations, is the ideal program to use to model and study these systems.

Project Proposal – Modeling the Magnetic Field of Magnetic Dipoles using Mathematica

For my project, I will work with Tewa Kpulun and Ramy Abbady on modeling vector fields of different geometries using Mathematica software. I plan on modeling the magnetic field $\vec{B}$ of a magnetic dipole with the eventual goal of modeling large scale magnet shapes.  I will begin by modeling a single magnetic dipole with a set magnetic moment $\vec{m}$ before modeling more complicated systems.  Eventually, I plan to superimpose many magnetic dipoles to create more complex magnetic geometries, such as a bar magnet or classic horseshoe magnet, possibly with regions where different internal currents create individual, unique magnetic dipoles.

Elias Kim Spring Project

Project Proposal:

Electrodynamics provides for some frighteningly fascinating applications. John Loree and I plan on investigating the physics of rail guns, powerful machines that fire slugs at high velocities using electromagnetic forces. We plan to build a functioning gun and analyze its motion with LoggerPro. Furthermore, I hope to use Mathematica to model the physics involved in the circuitry of the gun. This analysis will include finding current as a function of resistance, charging capacitors in the system, and the induced EMF. John and I will combine our results to produce general equations of motion for the rail gun.