Matching Items (4)
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- All Subjects: MATLAB
- Creators: Kostelich, Eric
- Creators: Trichopoulos, Georgios
Description
Chebfun is a collection of algorithms and an open-source software system in object-oriented Matlab that extends familiar powerful methods of numerical computation involving numbers to continuous or piecewise-continuous functions. The success of this strategy is based on the mathematical fact that smooth functions can be represented very efficiently by polynomial interpolation at Chebyshev points or by trigonometric interpolation at equispaced points for periodic functions. More recently, the system has been extended to handle bivariate functions and vector fields. These two new classes of objects are called Chebfun2 and Chebfun2v, respectively. We will show that Chebfun2 and Chebfun2v, and can be used to accurately and efficiently perform various computations on parametric surfaces in two or three dimensions, including path trajectories and mean and Gaussian curvatures. More advanced surface computations such as mean curvature flows are also explored. This is also the first work to use the newly implemented trigonometric representation, namely Trigfun, for computations on surfaces.
ContributorsPage-Bottorff, Courtney Michelle (Author) / Platte, Rodrigo (Thesis director) / Kostelich, Eric (Committee member) / School of Mathematical and Statistical Sciences (Contributor) / Barrett, The Honors College (Contributor)
Created2016-05
Description
Dividing the plane in half leaves every border point of one region a border point of both regions. Can we divide up the plane into three or more regions such that any point on the boundary of at least one region is on the border of all the regions? In fact, it is possible to design a dynamical system for which the basins of attractions have this Wada property. In certain circumstances, both the Hénon map, a simple system, and the forced damped pendulum, a physical model, produce Wada basins.
ContributorsWhitehurst, Ryan David (Author) / Kostelich, Eric (Thesis director) / Jones, Donald (Committee member) / Armbruster, Dieter (Committee member) / Barrett, The Honors College (Contributor) / School of Mathematical and Statistical Sciences (Contributor) / Department of Chemistry and Biochemistry (Contributor)
Created2013-05
Description
This Creative Project was carried out in coordination with the capstone project, Around the Corner Imaging with Terahertz Waves. This capstone project deals with a system designed to implement Around the Corner, or Non Line-of-Sight (NLoS) Imaging. This document discusses the creation of a GUI using MATLAB to control the Terahertz Imaging system. The GUI was developed in response to a need for synchronization, ease of operation, easy parameter modification, and data management. Along the way, many design decisions were made ranging from choosing a software platform to determining how variables should be passed. These decisions and considerations are discussed in this document. The resulting GUI has measured up to the design criteria and will be able to be used by anyone wishing to use the Terahertz Imaging System for further research in the field of Around the Corner or NLoS Imaging.
ContributorsWood, Jacob Cannon (Author) / Trichopoulos, Georgios (Thesis director) / Aberle, James (Committee member) / Electrical Engineering Program (Contributor) / School of Mathematical and Statistical Sciences (Contributor) / Barrett, The Honors College (Contributor)
Created2019-05
Description
The purpose of this project is to analyze the MIT OpenCourseWare coffee can radar design and modify it to be better suited for drone based synthetic aperture radar (SAR) applications while maintaining the low-cost aspect of the original design. The MIT coffee can radar can function as a ranged radar, a Doppler radar, or as SAR. Through simulations and research, the suggestions for how to modify the radar resulted in swapping the coffee can monopole antennas for patch antenna arrays or helical ordinary end-fire antennas, adding an Arduino for automatic recording of output pulses, and switching from a breadboard construction to a PCB to shrink form factor and keep costs and construction time low.
ContributorsRivera, Danielle (Author) / Trichopoulos, Georgios (Thesis director) / Aberle, James (Committee member) / Department of Information Systems (Contributor) / Electrical Engineering Program (Contributor) / Barrett, The Honors College (Contributor)
Created2020-12