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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 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
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 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
Description
In this thesis, we present the study of several physical properties of relativistic mat- ters under extreme conditions. We start by deriving the rate of the nonleptonic weak processes and the bulk viscosity in several spin-one color superconducting phases of quark matter. We also calculate the bulk viscosity in the nonlinear and anharmonic regime in the normal phase of strange quark matter. We point out several qualitative effects due to the anharmonicity, although quantitatively they appear to be relatively small. In the corresponding study, we take into account the interplay between the non- leptonic and semileptonic weak processes. The results can be important in order to relate accessible observables of compact stars to their internal composition. We also use quantum field theoretical methods to study the transport properties in monolayer graphene in a strong magnetic field. The corresponding quasi-relativistic system re- veals an anomalous quantum Hall effect, whose features are directly connected with the spontaneous flavor symmetry breaking. We study the microscopic origin of Fara- day rotation and magneto-optical transmission in graphene and show that their main features are in agreement with the experimental data.
ContributorsWang, Xinyang, Ph.D (Author) / Shovkovy, Igor (Thesis advisor) / Belitsky, Andrei (Committee member) / Easson, Damien (Committee member) / Peng, Xihong (Committee member) / Vachaspati, Tanmay (Committee member) / Arizona State University (Publisher)
Created2013
Description
Numerical simulations are very helpful in understanding the physics of the formation of structure and galaxies. However, it is sometimes difficult to interpret model data with respect to observations, partly due to the difficulties and background noise inherent to observation. The goal, here, is to attempt to bridge this gap between simulation and observation by rendering the model output in image format which is then processed by tools commonly used in observational astronomy. Images are synthesized in various filters by folding the output of cosmological simulations of gasdynamics with star-formation and dark matter with the Bruzual- Charlot stellar population synthesis models. A variation of the Virgo-Gadget numerical simulation code is used with the hybrid gas and stellar formation models of Springel and Hernquist (2003). Outputs taken at various redshifts are stacked to create a synthetic view of the simulated star clusters. Source Extractor (SExtractor) is used to find groupings of stellar populations which are considered as galaxies or galaxy building blocks and photometry used to estimate the rest frame luminosities and distribution functions. With further refinements, this is expected to provide support for missions such as JWST, as well as to probe what additional physics are needed to model the data. The results show good agreement in many respects with observed properties of the galaxy luminosity function (LF) over a wide range of high redshifts. In particular, the slope (alpha) when fitted to the standard Schechter function shows excellent agreement both in value and evolution with redshift, when compared with observation. Discrepancies of other properties with observation are seen to be a result of limitations of the simulation and additional feedback mechanisms which are needed.
ContributorsMorgan, Robert (Author) / Windhorst, Rogier A (Thesis advisor) / Scannapieco, Evan (Committee member) / Rhoads, James (Committee member) / Gardner, Carl (Committee member) / Belitsky, Andrei (Committee member) / Arizona State University (Publisher)
Created2012
Description
Understanding the temperature structure of protoplanetary disks (PPDs) is paramount to modeling disk evolution and future planet formation. PPDs around T Tauri stars have two primary heating sources, protostellar irradiation, which depends on the flaring of the disk, and accretional heating as viscous coupling between annuli dissipate energy. I have written a "1.5-D" radiative transfer code to calculate disk temperatures assuming hydrostatic and radiative equilibrium. The model solves for the temperature at all locations simultaneously using Rybicki's method, converges rapidly at high optical depth, and retains full frequency dependence. The likely cause of accretional heating in PPDs is the magnetorotational instability (MRI), which acts where gas ionization is sufficiently high for gas to couple to the magnetic field. This will occur in surface layers of the disk, leaving the interior portions of the disk inactive ("dead zone"). I calculate temperatures in PPDs undergoing such "layered accretion." Since the accretional heating is concentrated far from the midplane, temperatures in the disk's interior are lower than in PPDs modeled with vertically uniform accretion. The method is used to study for the first time disks evolving via the magnetorotational instability, which operates primarily in surface layers. I find that temperatures in layered accretion disks do not significantly differ from those of "passive disks," where no accretional heating exists. Emergent spectra are insensitive to active layer thickness, making it difficult to observationally identify disks undergoing layered vs. uniform accretion. I also calculate the ionization chemistry in PPDs, using an ionization network including multiple charge states of dust grains. Combined with a criterion for the onset of the MRI, I calculate where the MRI can be initiated and the extent of dead zones in PPDs. After accounting for feedback between temperature and active layer thickness, I find the surface density of the actively accreting layers falls rapidly with distance from the protostar, leading to a net outward flow of mass from ~0.1 to 3 AU. The clearing out of the innermost zones is possibly consistent with the observed behavior of recently discovered "transition disks."
ContributorsLesniak, Michael V., III (Author) / Desch, Steven J. (Thesis advisor) / Scannapieco, Evan (Committee member) / Timmes, Francis (Committee member) / Starrfield, Sumner (Committee member) / Belitsky, Andrei (Committee member) / Arizona State University (Publisher)
Created2012
Description
This thesis deals with the first measurements done with a cold neutron beam at the Spallation Neutron Source at Oak Ridge National Laboratory. The experimental technique consisted of capturing polarized cold neutrons by nuclei to measure parity-violation in the angular distribution of the gamma rays following neutron capture. The measurements presented here for the nuclei Chlorine ( 35Cl) and Aluminum ( 27Al ) are part of a program with the ultimate goal of measuring the asymmetry in the angular distribution of gamma rays emitted in the capture of neutrons on protons, with a precision better than 10-8, in order to extract the weak hadronic coupling constant due to pion exchange interaction with isospin change equal with one ( hπ 1). Based on theoretical calculations asymmetry in the angular distribution of the gamma rays from neutron capture on protons has an estimated size of 5·10-8. This implies that the Al parity violation asymmetry and its uncertainty have to be known with a precision smaller than 4·10-8. The proton target is liquid Hydrogen (H2) contained in an Aluminum vessel. Results are presented for parity violation and parity-conserving asymmetries in Chlorine and Aluminum. The systematic and statistical uncertainties in the calculation of the parity-violating and parity-conserving asymmetries are discussed.
ContributorsBalascuta, Septimiu (Author) / Alarcon, Ricardo (Thesis advisor) / Belitsky, Andrei (Committee member) / Doak, Bruce (Committee member) / Comfort, Joseph (Committee member) / Schmidt, Kevin (Committee member) / Arizona State University (Publisher)
Created2012
Description
It is possible in a properly controlled environment, such as industrial metrology, to make significant headway into the non-industrial constraints on image-based position measurement using the techniques of image registration and achieve repeatable feature measurements on the order of 0.3% of a pixel, or about an order of magnitude improvement on conventional real-world performance. These measurements are then used as inputs for a model optimal, model agnostic, smoothing for calibration of a laser scribe and online tracking of velocimeter using video input. Using appropriate smooth interpolation to increase effective sample density can reduce uncertainty and improve estimates. Use of the proper negative offset of the template function has the result of creating a convolution with higher local curvature than either template of target function which allows improved center-finding. Using the Akaike Information Criterion with a smoothing spline function it is possible to perform a model-optimal smooth on scalar measurements without knowing the underlying model and to determine the function describing the uncertainty in that optimal smooth. An example of empiric derivation of the parameters for a rudimentary Kalman Filter from this is then provided, and tested. Using the techniques of Exploratory Data Analysis and the "Formulize" genetic algorithm tool to convert the spline models into more accessible analytic forms resulted in stable, properly generalized, KF with performance and simplicity that exceeds "textbook" implementations thereof. Validation of the measurement includes that, in analytic case, it led to arbitrary precision in measurement of feature; in reasonable test case using the methods proposed, a reasonable and consistent maximum error of around 0.3% the length of a pixel was achieved and in practice using pixels that were 700nm in size feature position was located to within ± 2 nm. Robust applicability is demonstrated by the measurement of indicator position for a King model 2-32-G-042 rotameter.
ContributorsMunroe, Michael R (Author) / Phelan, Patrick (Thesis advisor) / Kostelich, Eric (Committee member) / Mahalov, Alex (Committee member) / Arizona State University (Publisher)
Created2012
Description
Some of the most talented, innovative, and experimental artists are students, but they are often discouraged by the price of higher education and lack of scholarship or funding opportunities. Additionally, the art industry has become stagnant. Traditional brick-and-mortar galleries are not willing to represent young, unknown artists. Their overhead is simply too high for risky choices.
The Student Art Project is art patronage for the 21st century—a curated online gallery featuring exceptional student artists. The Student Art Project is a highly curated experience for buyers. Only five artists are featured each month. Buyers are not bombarded with thousands of different products and separate artists “shops”. They can read artists bios and find art they connect with.
Student artists apply through an online form. Once accepted to the program, artists receive a $200 materials stipend to create an exclusive collection of 5-10 pieces. Original artwork and limited edition prints are sold through our website. These collections can potentially fund an entire year of college tuition, a life-changing amount for many students.
Brick-and-mortar galleries typically take 40-60% of the retail price of artwork. The Student Art Project will only take 30%, which we will use to reinvest in future artists. Other art websites, like Etsy, require the artists to ship, invoice, and communicate with customers. For students, this means less time spent in the classroom and less time developing their craft. The Student Art Project handles all business functions for our artists, allowing them to concentrate on what really matters, their education.
The Student Art Project is art patronage for the 21st century—a curated online gallery featuring exceptional student artists. The Student Art Project is a highly curated experience for buyers. Only five artists are featured each month. Buyers are not bombarded with thousands of different products and separate artists “shops”. They can read artists bios and find art they connect with.
Student artists apply through an online form. Once accepted to the program, artists receive a $200 materials stipend to create an exclusive collection of 5-10 pieces. Original artwork and limited edition prints are sold through our website. These collections can potentially fund an entire year of college tuition, a life-changing amount for many students.
Brick-and-mortar galleries typically take 40-60% of the retail price of artwork. The Student Art Project will only take 30%, which we will use to reinvest in future artists. Other art websites, like Etsy, require the artists to ship, invoice, and communicate with customers. For students, this means less time spent in the classroom and less time developing their craft. The Student Art Project handles all business functions for our artists, allowing them to concentrate on what really matters, their education.
ContributorsDangler, Rebecca Leigh (Author) / Trujillo, Rhett (Thesis director) / Coleman, Sean (Committee member) / Barrett, The Honors College (Contributor) / Herberger Institute for Design and the Arts (Contributor) / Department of Management (Contributor)
Created2015-05
Description
Drought is one of the most pressing issues affecting the future of the standard of living here in Phoenix. With the threat of water rationing and steep price hikes looming on the horizon for water customers in California, the desert southwest, and in drought-stricken communities worldwide, industrial designers are in a prime position to help improve the experience of water conservation so that consumers are willing to start taking conscious steps toward rethinking their relationship with water usage.
In a research group, several designers sought to understand the depth and complexity of this highly politicized issue by interviewing a wide variety of stakeholders, including sustainability experts, landscapers, water company executives, small business owners, reservoir forest rangers, and many more. Data synthesis led to the conclusion that residential water use is a lifestyle issue, and the only real way to conserve involves a significant shift in the collective idea of an “ideal” home—lawns, pools, and overwatered landscaping contribute to 70% of all water use by residences in the Phoenix area. The only real way to conserve involves increasing population density and creating communal green spaces.
DR. DISH is a dishwashing device that is meant to fit into the high-density living spaces that are rapidly being built in the face of the massive exodus of people into the world’s cities. To help busy apartment and condominium dwellers conserve water and time, DR. DISH converts a standard kitchen sink into a small dishwasher, which uses significantly less water than hand-washing dishes or rinsing dishes before putting them into a conventional dishwasher. Using advanced filtration technology and a powerful rinse cycle, a load dishes can be cleaned with about 2 gallons of water. Fully automating the dishwashing process also saves the user time and minimizes unpleasant contact with food residue and grease.
This device is meant to have a significant impact upon the water use of households that do not have a dishwasher, or simply do not use their dishwasher. With a low target price point and myriad convenient features, DR. DISH is a high-tech solution that promises water savings at a time when every effort toward conservation is absolutely critical. As we move toward a new era in determining water rights and imposing mandatory restrictions upon each and every person living in affected areas, creating conservation solutions that will be relevant for the lifestyles of the future is especially important, and the agility of designers in coming up with products that quickly cut consumer water consumption will be a key factor in determining whether humanity will be able to adapt to a new era in our relationship with natural resources.
In a research group, several designers sought to understand the depth and complexity of this highly politicized issue by interviewing a wide variety of stakeholders, including sustainability experts, landscapers, water company executives, small business owners, reservoir forest rangers, and many more. Data synthesis led to the conclusion that residential water use is a lifestyle issue, and the only real way to conserve involves a significant shift in the collective idea of an “ideal” home—lawns, pools, and overwatered landscaping contribute to 70% of all water use by residences in the Phoenix area. The only real way to conserve involves increasing population density and creating communal green spaces.
DR. DISH is a dishwashing device that is meant to fit into the high-density living spaces that are rapidly being built in the face of the massive exodus of people into the world’s cities. To help busy apartment and condominium dwellers conserve water and time, DR. DISH converts a standard kitchen sink into a small dishwasher, which uses significantly less water than hand-washing dishes or rinsing dishes before putting them into a conventional dishwasher. Using advanced filtration technology and a powerful rinse cycle, a load dishes can be cleaned with about 2 gallons of water. Fully automating the dishwashing process also saves the user time and minimizes unpleasant contact with food residue and grease.
This device is meant to have a significant impact upon the water use of households that do not have a dishwasher, or simply do not use their dishwasher. With a low target price point and myriad convenient features, DR. DISH is a high-tech solution that promises water savings at a time when every effort toward conservation is absolutely critical. As we move toward a new era in determining water rights and imposing mandatory restrictions upon each and every person living in affected areas, creating conservation solutions that will be relevant for the lifestyles of the future is especially important, and the agility of designers in coming up with products that quickly cut consumer water consumption will be a key factor in determining whether humanity will be able to adapt to a new era in our relationship with natural resources.
ContributorsMarcinkowski, Margaret Nicole (Author) / Shin, Dosun (Thesis director) / McDermott, Lauren (Committee member) / Barrett, The Honors College (Contributor) / The Design School (Contributor) / Herberger Institute for Design and the Arts (Contributor)
Created2015-05
Description
Fire Shelter Foam Assist is meant as a firefighter's last effort of survival when a wildfire threatens their position. When deployed, it will cover the firefighter as the fire blows over. By reducing the time of deployment and simplifying the process, firefighters will have more time to ensure the area around them is cleared. The Fire Shelter Foam Assist has features that allow it to auto deploy around the firefighter through the use of fire foam retardant. The fire foam retardant inflates the shelter as well as provides an extra layer of protection against the wildfire.
ContributorsSmith, Tori Elizabeth (Author) / Shin, Dosun (Thesis director) / McDermott, Lauren (Committee member) / Barrett, The Honors College (Contributor) / Herberger Institute for Design and the Arts (Contributor) / The Design School (Contributor)
Created2015-05