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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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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
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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
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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
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Description

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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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
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Description
Bacteria are often regarded s pathogens, with deleterious impacts on the human body. However, it is known that the presence of trillions of bacteria on and in the human body impart beneficial effects on human health. Like a fingerprint, each individual’s microbiome is unique. The composition of bacteria in one

Bacteria are often regarded s pathogens, with deleterious impacts on the human body. However, it is known that the presence of trillions of bacteria on and in the human body impart beneficial effects on human health. Like a fingerprint, each individual’s microbiome is unique. The composition of bacteria in one person’s gut is different from the gut bacteria in another individual. Together, the human gut microbiome is a complex mix of organisms that is commonly referred to as “the second brain.� Its role in the human body goes beyond digestion and immune system function. The health of the microbiome factors into risk for illnesses as diverse as depression, obesity, bowel disorders and autism (Perlmutter et al., 2015). In context of the myriad of bacteria that live on and within the human body, the composition of bacteria in the gut may have the most significant impact on an individual’s well-being. This “superorganism� co-evolved with its host in order to provide essential and mutually beneficial functions (Ragonnaud et al., 2021).

Affecting millions of Americans, depression is one of the leading causes of the Global Burden of Disease (GBD), followed by anxiety (Gibson-Smith et al., 2018). Communication that occurs between the human brain and the gut microbiome has been found to be a major contributor towards mental health. The human gut microbiome is comprised of many microbes that can communicate with the brain through the gut-brain axis. However, factors such as stress and diets can interfere with this process, especially after increasing the permeability of the intestine (Khoshbin et al., 2020). Perturbation of the gut-brain axis has been implicated across a wide scale of neurodegenerative disorders, with respect to psychopathology (Bonaz et al., 2018). The environment of the gut, along with which species reside there, can help determine the link between gut function and disease. Therefore, it may be possible to prevent the degradation of an individual’s immune function and well-being through alteration of the gut microbiome. (abstract)
ContributorsPisarczyk, Nicole (Author) / Penton, Christopher (Thesis director) / Huffman, Holly (Committee member) / College of Integrative Sciences and Arts (Contributor) / Barrett, The Honors College (Contributor)
Created2021-05
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Description
This thesis outlines the development of a vector retrieval technique, based on data assimilation, for a coherent Doppler LIDAR (Light Detection and Ranging). A detailed analysis of the Optimal Interpolation (OI) technique for vector retrieval is presented. Through several modifications to the OI technique, it is shown that the modified

This thesis outlines the development of a vector retrieval technique, based on data assimilation, for a coherent Doppler LIDAR (Light Detection and Ranging). A detailed analysis of the Optimal Interpolation (OI) technique for vector retrieval is presented. Through several modifications to the OI technique, it is shown that the modified technique results in significant improvement in velocity retrieval accuracy. These modifications include changes to innovation covariance portioning, covariance binning, and analysis increment calculation. It is observed that the modified technique is able to make retrievals with better accuracy, preserves local information better, and compares well with tower measurements. In order to study the error of representativeness and vector retrieval error, a lidar simulator was constructed. Using the lidar simulator a thorough sensitivity analysis of the lidar measurement process and vector retrieval is carried out. The error of representativeness as a function of scales of motion and sensitivity of vector retrieval to look angle is quantified. Using the modified OI technique, study of nocturnal flow in Owens' Valley, CA was carried out to identify and understand uncharacteristic events on the night of March 27th 2006. Observations from 1030 UTC to 1230 UTC (0230 hr local time to 0430 hr local time) on March 27 2006 are presented. Lidar observations show complex and uncharacteristic flows such as sudden bursts of westerly cross-valley wind mixing with the dominant up-valley wind. Model results from Coupled Ocean/Atmosphere Mesoscale Prediction System (COAMPS®) and other in-situ instrumentations are used to corroborate and complement these observations. The modified OI technique is used to identify uncharacteristic and extreme flow events at a wind development site. Estimates of turbulence and shear from this technique are compared to tower measurements. A formulation for equivalent wind speed in the presence of variations in wind speed and direction, combined with shear is developed and used to determine wind energy content in presence of turbulence.
ContributorsChoukulkar, Aditya (Author) / Calhoun, Ronald (Thesis advisor) / Mahalov, Alex (Committee member) / Kostelich, Eric (Committee member) / Huang, Huei-Ping (Committee member) / Phelan, Patrick (Committee member) / Arizona State University (Publisher)
Created2013
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Description

This thesis looks at how Latinx communities in Wyoming, despite recognizing the impossibility of overcoming the traditional conservative autocracy, still utilize their identity as a political response to unify Latinx communities throughout the state. The project draws from oral histories conducted with Latinx/Chicanx community members in Wyoming, including professors, legislators,

This thesis looks at how Latinx communities in Wyoming, despite recognizing the impossibility of overcoming the traditional conservative autocracy, still utilize their identity as a political response to unify Latinx communities throughout the state. The project draws from oral histories conducted with Latinx/Chicanx community members in Wyoming, including professors, legislators, and everyday citizens.

ContributorsFranco, David (Author) / Fonseca-Chávez, Vanessa (Thesis director) / Martínez, Rafael (Committee member) / College of Integrative Sciences and Arts (Contributor, Contributor) / Barrett, The Honors College (Contributor)
Created2021-05