Category Archives: Spring 2014

Project Proposal: Modeling Optical Filters

When analyzing the brightness of a star, or a mode of a laser beam we observe the effects of that object. In this case we gather photons, and we use tools to gather as much radiation as possible. This data is then transmitted onto a screen to see a representation of what is actually going on. When an electric signal is sent to an oscilloscope, are we actually seeing the signal? A spectrum of light must enter through a series of optical and electrical things before being displayed, and those things can and do distort the image. These are optical filters. Sometimes this is done intentionally to block out certain frequencies, but other times the distortion is unavoidable. By understanding the convolution of electromagnetic waves one can isolate the desired data from the signal presented. I will model using Mathematica different spectra and examine how convolution and deconvolution work as means of setting up usable data.

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Project Proposal: Electric & Magnetic Field Modeling

For my project, I will work with Peter Florio to model the electric and magnetic fields of a bar magnet, sphere and cylinder. I will be looking at the magnetic fields of these distributions in 3-space and modeling their vector fields using Mathematica and Maxwell’s Equations. Problems given in David Griffiths’ Introduction to Electrodynamics will be used as specific examples of these kinds of charge distributions. My results will then be compared to the electric fields of the same distributions found by Peter.

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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.

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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.

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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.

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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.

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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.

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