Matching Items (17)
Filtering by
- All Subjects: Sustainability
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
Mathematics is an increasingly critical subject and the achievement of students in mathematics has been the focus of many recent reports and studies. However, few studies exist that both observe and discuss the specific teaching and assessment techniques employed in the classrooms across multiple countries. The focus of this study is to look at classrooms and educators across six high achieving countries to identify and compare teaching strategies being used. In Finland, Hong Kong, Japan, New Zealand, Singapore, and Switzerland, twenty educators were interviewed and fourteen educators were observed teaching. Themes were first identified by comparing individual teacher responses within each country. These themes were then grouped together across countries and eight emerging patterns were identified. These strategies include students active involvement in the classroom, students given written feedback on assessments, students involvement in thoughtful discussion about mathematical concepts, students solving and explaining mathematics problems at the board, students exploring mathematical concepts either before or after being taught the material, students engagement in practical applications, students making connections between concepts, and students having confidence in their ability to understand mathematics. The strategies identified across these six high achieving countries can inform educators in their efforts of increasing student understanding of mathematical concepts and lead to an improvement in mathematics performance.
ContributorsAnglin, Julia Mae (Author) / Middleton, James (Thesis director) / Vicich, James (Committee member) / Barrett, The Honors College (Contributor) / School of Mathematical and Statistical Sciences (Contributor)
Created2014-12
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
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
Description
This thesis analyzed Canon GPR-30 Black Standard Yield Toner in hopes to gain better understanding of the additives and plastic used in a popular photocopier toner formulation. By analyzing the toner’s composition from the perspective of its recyclability and potential to be manufactured using recycled plastic, this thesis hoped to fill a gap in current literature regarding how toner fits into a circular economy. While the analysis of the selected toner was ultimately inconclusive, three hypotheses about the toner’s composition are put forth based upon data from differential scanning calorimetry (DSC), solubility analysis, and Fourier Transform Infrared (FTIR) spectroscopy experimentation. It is hypothesized that the toner is most likely composed of either polymethyl methacrylate (PMMA) or polyethylene terephthalate (PET). Both of these polymers have characteristic FTIR peaks that were exhibited in the toner spectra and both polymers exhibit similar solubility behavior to toner samples. However, the glass transition temperature and melting temperature of the toner sampled were 58℃ and 74.5℃ respectively, both of which are much lower than that of PMMA and PET. Thus, a third hypothesis that would better support DSC findings is that the toner is primarily composed of nylon 6,6. While DSC data best matches this polymer, FTIR data seems to rule out nylon 6,6 as an option because its characteristic peaks were not found in experimental data. Thus, the Canon GPR-30 Black Standard Yield Toner is probably made from either PMMA or PET. Both PMMA and PET are 100% recyclable plastics which are commonly repurposed at recycling facilities, however, unknowns regarding toner additives make it difficult to determine how this toner would be recycled. If the printing industry hopes to move towards a circular economy in which plastic can be recycled to use towards toner manufacturing and toner can be “unprinted” from paper to be recycled into new toner, it is likely that monetary incentives or government regulations will need to be introduced to promote the sharing of toner formulations for recycling purposes.
ContributorsChase, Jasmine (Author) / Green, Matthew (Thesis director) / Emady, Heather (Committee member) / Barrett, The Honors College (Contributor) / School of Mathematical and Statistical Sciences (Contributor) / Mechanical and Aerospace Engineering Program (Contributor)
Created2023-05