Matching Items (17)
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- All Subjects: Sustainability
- Creators: School of Mathematical and Statistical Sciences
- Member of: Barrett, The Honors College Thesis/Creative Project Collection
- Resource Type: Text
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
In this paper, I analyze representations of nature in popular film, using the feminist / deconstructionist concept of a dualism to structure my critique. Using Val Plumwood’s analysis of the logical structure of dualism and the 5 ‘features of a dualism’ that she identifies, I critique 5 popular movies – Star Wars, Lord of the Rings, Brave, Grizzly Man, and Planet Earth – by locating within each of them one of the 5 features and explaining how the movie functions to reinforce the Nature/Culture dualism . By showing how the Nature/Culture dualism shapes and is shaped by popular cinema, I show how “Nature” is a social construct, created as part of this very dualism, and reified through popular culture. I conclude with the introduction of a number of ‘subversive’ pieces of visual art that undermine and actively deconstruct the Nature/Culture dualism and show to the viewer a more honest presentation of the non-human world.
ContributorsBarton, Christopher Joseph (Author) / Broglio, Ron (Thesis director) / Minteer, Ben (Committee member) / Barrett, The Honors College (Contributor) / School of Sustainability (Contributor) / School of Mathematical and Statistical Sciences (Contributor) / School of Geographical Sciences and Urban Planning (Contributor)
Created2015-05
Description
From 2007 to 2017, the state of California experienced two major droughts that required significant governmental action to decrease urban water demand. The purpose of this project is to isolate and explore the effects of these policy changes on water use during and after these droughts, and to see how these policies interact with hydroclimatic variability. As explanatory variables in multiple linear regression (MLR) models, water use policies were found to be significant at both the zip code and city levels. Policies that specifically target behavioral changes were significant mathematical drivers of water use in city-level models. Policy data was aggregated into a timeline and coded based on categories including user type, whether the policy was voluntary or mandatory, the targeted water use type, and whether the change in question concerns active or passive conservation. The analyzed policies include but are not limited to state drought declarations, regulatory municipal ordinances, and incentive programs for household appliances. Spatial averages of available hydroclimatic data have been computed and validated using inverse distance weighting methods. The data was aggregated at the zip code level to be comparable to the available water use data for use in MLR models. Factors already known to affect water use, such as temperature, precipitation, income, and water stress, were brought into the MLR models as explanatory variables. After controlling for these factors, the timeline policies were brought into the model as coded variables to test their effect on water demand during the years 2000-2017. Clearly identifying which policy traits are effective will inform future policymaking in cities aiming to conserve water. The findings suggest that drought-related policies impact per capita urban water use. The results of the city level MLR models indicate that implementation of mandatory policies that target water use behaviors effectively reduce water use. Temperature, income, unemployment, and the WaSSI were also observed to be mathematical drivers of water use. Interaction effects between policies and the WaSSI were statistically significant at both model scales.
ContributorsHjelmstad, Annika Margaret (Author) / Garcia, Margaret (Thesis director) / Larson, Kelli (Committee member) / Civil, Environmental and Sustainable Eng Program (Contributor, Contributor) / School of Mathematical and Statistical Sciences (Contributor) / Barrett, The Honors College (Contributor)
Created2018-12
Description
As society's energy crisis continues to become more imminent many industries and niches are seeking a new, sustainable and renewable source of electricity production. Similar to solar, wind and tidal energy, kinetic energy has the potential to generate electricity as an extremely renewable source of energy generation. While stationary bicycles can generate small amounts of electricity, the idea behind this project was to expand energy generation into the more common weight lifting side of exercising. The method for solving this problem was to find the average amount of power generated per user on a Smith machine and determine how much power was available from an accompanying energy generator. The generator consists of three phases: a copper coil and magnet generator, a full wave bridge rectifying circuit and a rheostat. These three phases working together formed a fully functioning controllable generator. The resulting issue with the kinetic energy generator was that the system was too inefficient to serve as a viable system for electricity generation. The electrical production of the generator only saved about 2 cents per year based on current Arizona electricity rates. In the end it was determined that the project was not a sustainable energy generation system and did not warrant further experimentation.
ContributorsO'Halloran, Ryan James (Author) / Middleton, James (Thesis director) / Hinrichs, Richard (Committee member) / Barrett, The Honors College (Contributor) / Mechanical and Aerospace Engineering Program (Contributor) / The Design School (Contributor) / School of Mathematical and Statistical Sciences (Contributor)
Created2014-05
Description
Using object-oriented programming in MATLAB, a collection of functions, named Fourfun, has been created to allow quick and accurate approximations of periodic functions with Fourier expansions. To increase efficiency and reduce the number of computations of the Fourier transform, Fourfun automatically determines the number of nodes necessary for representations that are accurate to close to machine precision. Common MATLAB functions have been overloaded to keep the syntax of the Fourfun class as consistent as possible with the general MATLAB syntax. We show that the system can be used to efficiently solve several differential equations. Comparisons with Chebfun, a similar system based on Chebyshev polynomial approximations, are provided.
ContributorsMcleod, Kristyn Noelle (Author) / Platte, Rodrigo (Thesis director) / Gelb, Anne (Committee member) / Barrett, The Honors College (Contributor) / School of Mathematical and Statistical Sciences (Contributor) / School of International Letters and Cultures (Contributor)
Created2014-05
Description
Plastics continue to benefit society in innumerable ways, even though recent public focus on plastics has centered mostly on human health and environmental concerns, including their endocrine-disrupting properties and the long-term pollution they represent. The benefits of plastics are particularly apparent in medicine and public health. Plastics are versatile, cost-effective, require less energy to produce than alternative materials like metal or glass, and can be manufactured to have many different properties. Due to these characteristics, polymers are used in diverse health applications like disposable syringes and intravenous bags, sterile packaging for medical instruments as well as in joint replacements, tissue engineering, etc. However, not all current uses of plastics are prudent and sustainable, as illustrated by the widespread, unwanted human exposure to endocrine-disrupting bisphenol A (BPA) and di-(2-ethylhexyl) phthalate (DEHP), problems arising from the large quantities of plastic being disposed of, and depletion of non-renewable petroleum resources as a result of the ever-increasing mass production of plastic consumer articles. Using the health-care sector as example, this review concentrates on the benefits and downsides of plastics and identifies opportunities to change the composition and disposal practices of these invaluable polymers for a more sustainable future consumption. It highlights ongoing efforts to phase out DEHP and BPA in the health-care and food industry and discusses biodegradable options for plastic packaging, opportunities for reducing plastic medical waste, and recycling in medical facilities in the quest to reap a maximum of benefits from polymers without compromising human health or the environment in the process.
ContributorsNorth, Emily Jean (Co-author) / Halden, Rolf (Co-author, Thesis director) / Mikhail, Chester (Committee member) / Hurlbut, Ben (Committee member) / Barrett, The Honors College (Contributor) / School of Mathematical and Statistical Sciences (Contributor) / Chemical Engineering Program (Contributor)
Created2013-05
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 thesis attempts to explain Everettian quantum mechanics from the ground up, such that those with little to no experience in quantum physics can understand it. First, we introduce the history of quantum theory, and some concepts that make up the framework of quantum physics. Through these concepts, we reveal why interpretations are necessary to map the quantum world onto our classical world. We then introduce the Copenhagen interpretation, and how many-worlds differs from it. From there, we dive into the concepts of entanglement and decoherence, explaining how worlds branch in an Everettian universe, and how an Everettian universe can appear as our classical observed world. From there, we attempt to answer common questions about many-worlds and discuss whether there are philosophical ramifications to believing such a theory. Finally, we look at whether the many-worlds interpretation can be proven, and why one might choose to believe it.
ContributorsSecrest, Micah (Author) / Foy, Joseph (Thesis director) / Hines, Taylor (Committee member) / Computer Science and Engineering Program (Contributor) / Barrett, The Honors College (Contributor)
Created2021-05
Description
The purpose of this paper is to provide an analysis of entanglement and the particular problems it poses for some physicists. In addition to looking at the history of entanglement and non-locality, this paper will use the Bell Test as a means for demonstrating how entanglement works, which measures the behavior of electrons whose combined internal angular momentum is zero. This paper will go over Dr. Bell's famous inequality, which shows why the process of entanglement cannot be explained by traditional means of local processes. Entanglement will be viewed initially through the Copenhagen Interpretation, but this paper will also look at two particular models of quantum mechanics, de-Broglie Bohm theory and Everett's Many-Worlds Interpretation, and observe how they explain the behavior of spin and entangled particles compared to the Copenhagen Interpretation.
ContributorsWood, Keaten Lawrence (Author) / Foy, Joseph (Thesis director) / Hines, Taylor (Committee member) / Department of Physics (Contributor) / School of Mathematical and Statistical Sciences (Contributor) / Barrett, The Honors College (Contributor)
Created2021-05
Description
With the rise of fast fashion and its now apparent effects on climate change, there is an evident need for change in terms of how we as individuals use our clothing and footwear. Our team has created Ray Fashion Inc., a sustainable footwear company that focuses on implementing the circular economy to reduce the amount of waste generated in shoe creation. We have designed a sandal that accommodates the rapid consumption element of fast fashion with a business model that promotes sustainability through a buy-back method to upcycle and retain our materials.
ContributorsLiao, Yuxin (Co-author) / Yang, Andrea (Co-author) / Suresh Kumar, Roshni (Co-author) / Byrne, Jared (Thesis director) / Marseille, Alicia (Committee member) / Jordan, Amanda (Committee member) / Department of Finance (Contributor) / School of Mathematical and Statistical Sciences (Contributor) / Barrett, The Honors College (Contributor)
Created2021-05