Matching Items (293)
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Description
Nonlinear dispersive equations model nonlinear waves in a wide range of physical and mathematics contexts. They reinforce or dissipate effects of linear dispersion and nonlinear interactions, and thus, may be of a focusing or defocusing nature. The nonlinear Schrödinger equation or NLS is an example of such equations. It appears

Nonlinear dispersive equations model nonlinear waves in a wide range of physical and mathematics contexts. They reinforce or dissipate effects of linear dispersion and nonlinear interactions, and thus, may be of a focusing or defocusing nature. The nonlinear Schrödinger equation or NLS is an example of such equations. It appears as a model in hydrodynamics, nonlinear optics, quantum condensates, heat pulses in solids and various other nonlinear instability phenomena. In mathematics, one of the interests is to look at the wave interaction: waves propagation with different speeds and/or different directions produces either small perturbations comparable with linear behavior, or creates solitary waves, or even leads to singular solutions. This dissertation studies the global behavior of finite energy solutions to the $d$-dimensional focusing NLS equation, $i partial _t u+Delta u+ |u|^{p-1}u=0, $ with initial data $u_0in H^1,; x in Rn$; the nonlinearity power $p$ and the dimension $d$ are chosen so that the scaling index $s=frac{d}{2}-frac{2}{p-1}$ is between 0 and 1, thus, the NLS is mass-supercritical $(s>0)$ and energy-subcritical $(s<1).$ For solutions with $ME[u_0]<1$ ($ME[u_0]$ stands for an invariant and conserved quantity in terms of the mass and energy of $u_0$), a sharp threshold for scattering and blowup is given. Namely, if the renormalized gradient $g_u$ of a solution $u$ to NLS is initially less than 1, i.e., $g_u(0)<1,$ then the solution exists globally in time and scatters in $H^1$ (approaches some linear Schr"odinger evolution as $ttopminfty$); if the renormalized gradient $g_u(0)>1,$ then the solution exhibits a blowup behavior, that is, either a finite time blowup occurs, or there is a divergence of $H^1$ norm in infinite time. This work generalizes the results for the 3d cubic NLS obtained in a series of papers by Holmer-Roudenko and Duyckaerts-Holmer-Roudenko with the key ingredients, the concentration compactness and localized variance, developed in the context of the energy-critical NLS and Nonlinear Wave equations by Kenig and Merle. One of the difficulties is fractional powers of nonlinearities which are overcome by considering Besov-Strichartz estimates and various fractional differentiation rules.
ContributorsGuevara, Cristi Darley (Author) / Roudenko, Svetlana (Thesis advisor) / Castillo_Chavez, Carlos (Committee member) / Jones, Donald (Committee member) / Mahalov, Alex (Committee member) / Suslov, Sergei (Committee member) / Arizona State University (Publisher)
Created2011
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Description

Analyzing Incident Rates of COVID-19 Before and After Stay-At-Home Orders Throughout the Southwestern U.S. with Respect to Limited Mobility Models

ContributorsTilleman, Karl Benson (Author) / Albuquerque, Fabio Suzart de (Thesis director) / Powers, Brian (Committee member) / College of Integrative Sciences and Arts (Contributor) / Barrett, The Honors College (Contributor)
Created2021-05
Description

This thesis worked towards the development of a parameterized 3D model off a cover that could go over any specific prosthesis depending on the parameters that had been entered. It also focused on gathering user inputs, which was done with the aid of the Amputee Coalition, that could be used

This thesis worked towards the development of a parameterized 3D model off a cover that could go over any specific prosthesis depending on the parameters that had been entered. It also focused on gathering user inputs, which was done with the aid of the Amputee Coalition, that could be used to create an aesthetic design on this cover. The Amputee Coalition helped to recruit participants through its website and social media platforms. Finally, multiple methods of creating a design were developed to increase the amount of customization that a user could have for their cover.

ContributorsFusaro, Gerard Anthony (Co-author) / Riley, Nicholas (Co-author) / Sugar, Thomas (Thesis director) / Redkar, Sangram (Committee member) / College of Integrative Sciences and Arts (Contributor) / Engineering Programs (Contributor, Contributor) / Barrett, The Honors College (Contributor)
Created2021-05
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Mathematical and analytical approach at the floor and diffuser of a Formula 1 vehicle and how they produce downforce. Reaches a conclusion about how engineers and aerodynamicists creates the desired effects underneath the vehicle to produce substantial downforce.

ContributorsMarcantonio, Nicholas Joseph (Author) / Rajadas, John (Thesis director) / Hillery, Scott (Committee member) / College of Integrative Sciences and Arts (Contributor) / Engineering Programs (Contributor, Contributor) / Barrett, The Honors College (Contributor)
Created2021-05
Description

This podcast explores the life of Cendraini, growing up in the developing country of Indonesia as well as her eventual immigration to America. It delves into prominent topics and history of Indonesia in regards to Cen's life. The podcast focuses on family, and how no matter the challenges that life

This podcast explores the life of Cendraini, growing up in the developing country of Indonesia as well as her eventual immigration to America. It delves into prominent topics and history of Indonesia in regards to Cen's life. The podcast focuses on family, and how no matter the challenges that life may bring, family will be there for you.

ContributorsGoldstein, Rachel (Author) / Schmidt, Peter (Thesis director) / Levin, Irina (Committee member) / School of International Letters and Cultures (Contributor) / College of Integrative Sciences and Arts (Contributor) / Barrett, The Honors College (Contributor)
Created2021-05
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Preeclampsia is a disease that occurs during pregnancy and affects upwards of 10% of pregnancies around the world (Osungbade & Ige, 2011). African American pregnant women are particularly vulnerable and die at a disproportionate rate compared to other races. In this literature review, three research studies were analyzed to determine

Preeclampsia is a disease that occurs during pregnancy and affects upwards of 10% of pregnancies around the world (Osungbade & Ige, 2011). African American pregnant women are particularly vulnerable and die at a disproportionate rate compared to other races. In this literature review, three research studies were analyzed to determine if African American pregnant women were included in preeclampsia Studies. Only one of the studies included in this review met all criteria by including African American pregnant women. One research study met half of the criteria; however, the authors noted that there was not enough evidence for Black Americans. The third research article also only met half of the criteria. We conclude that further studies are needed that include African American women in studies on preeclampsia.

ContributorsCheeks, Maiya (Author) / Lateef, Dalya (Thesis director) / Briggs, Georgette (Committee member) / College of Integrative Sciences and Arts (Contributor) / Barrett, The Honors College (Contributor)
Created2021-05
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A research project turned creative project focusing on the narrative of the student's perspective in the Next Generation Service Corps scholarship program. Using survey results from the program members, narratives of their experiences were compiled to offer insight and direction for the growth of the program.<br/><br/>A video of the defense

A research project turned creative project focusing on the narrative of the student's perspective in the Next Generation Service Corps scholarship program. Using survey results from the program members, narratives of their experiences were compiled to offer insight and direction for the growth of the program.<br/><br/>A video of the defense can be found at this link: https://youtu.be/O63NRz0z1Ys

ContributorsJanezic, John Henry (Author) / Hunt, Brett (Thesis director) / Smith, Jacqueline (Committee member) / College of Integrative Sciences and Arts (Contributor) / School of International Letters and Cultures (Contributor) / Barrett, The Honors College (Contributor)
Created2021-05
Description

The purpose of this creative project was to create a stereo sound system in a unique medium. As a team, we decided to integrate a Tesla Coil with a bluetooth audio source. These high frequency, high voltage systems can be configured to emit their electrical discharge in a manner that

The purpose of this creative project was to create a stereo sound system in a unique medium. As a team, we decided to integrate a Tesla Coil with a bluetooth audio source. These high frequency, high voltage systems can be configured to emit their electrical discharge in a manner that resembles playing tunes. Originally the idea was to split the audio into left and right, then to further segregate the signals to have a treble, mid, and base emitter for each side. Due to time, budget, and scope constraints, we decided to complete the project with only two coils.<br/><br/>For this project, the team decided to use a solid-state coil kit. This kit was purchased from OneTelsa and would help ensure everyone’s safety and the project’s success. The team developed our own interrupting or driving circuit through reverse-engineering the interrupter provided by oneTesla and discussing with other engineers. The custom interpreter was controlled by the PSoC5 LP and communicated with an audio source through the DFRobot Bluetooth module. Utilizing the left and right audio signals it can drive the two Tesla Coils in stereo to play the music.

ContributorsPinkowski, Olivia N (Co-author) / Hutcherson, Cree (Co-author) / Jordan, Shawn (Thesis director) / Sugar, Thomas (Committee member) / Engineering Programs (Contributor, Contributor) / College of Integrative Sciences and Arts (Contributor) / Barrett, The Honors College (Contributor)
Created2021-05
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An X class solar flare has the potential to remove our satellites from orbit, permanently deactivate our main forms of communication and bring humanity into a technology-free age. By using Geant4, it is possible to simulate several layers of the Earth's atmosphere and send a simulated solar flare and coronal

An X class solar flare has the potential to remove our satellites from orbit, permanently deactivate our main forms of communication and bring humanity into a technology-free age. By using Geant4, it is possible to simulate several layers of the Earth's atmosphere and send a simulated solar flare and coronal mass ejection. This thesis will show the interaction of photons and protons of various energies with several kilometers of atmosphere.

ContributorsDolghier, Kristian Adrian (Author) / Shovkovy, Igor (Thesis director) / Steinkamp, Brian (Committee member) / Economics Program in CLAS (Contributor) / College of Integrative Sciences and Arts (Contributor, Contributor) / Barrett, The Honors College (Contributor)
Created2021-05
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Description

The Founders lab is a year-long program that gives its students an opportunity to participate in a unique team-based, experiential Barrett honors thesis project to design and apply marketing and sales strategies, as well as business and financial models to start up and launch a new business. This honors thesis

The Founders lab is a year-long program that gives its students an opportunity to participate in a unique team-based, experiential Barrett honors thesis project to design and apply marketing and sales strategies, as well as business and financial models to start up and launch a new business. This honors thesis project focuses on increasing the rate of vaccination outcomes in a country where people are increasingly busy (less time) and unwilling to get a needle through a new business venture that provides a service that brings vaccinations straight to businesses, making them available for their employees. Through our work with the Founders Lab, our team was able to create this pitch deck.

ContributorsGomez, Isaias Abraham (Co-author) / Hanzlick, Emily (Co-author) / Zatonskiy, Albert (Co-author) / Byrne, Jared (Thesis director) / Hall, Rick (Committee member) / Silverstein, Taylor (Committee member) / College of Integrative Sciences and Arts (Contributor, Contributor) / Barrett, The Honors College (Contributor)
Created2021-05