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- Creators: Barrett, The Honors College
- Creators: Haydn, Joseph, 1732-1809
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
The theory of geometric quantum mechanics describes a quantum system as a Hamiltonian dynamical system, with a projective Hilbert space regarded as the phase space. This thesis extends the theory by including some aspects of the symplectic topology of the quantum phase space. It is shown that the quantum mechanical uncertainty principle is a special case of an inequality from J-holomorphic map theory, that is, J-holomorphic curves minimize the difference between the quantum covariance matrix determinant and a symplectic area. An immediate consequence is that a minimal determinant is a topological invariant, within a fixed homology class of the curve. Various choices of quantum operators are studied with reference to the implications of the J-holomorphic condition. The mean curvature vector field and Maslov class are calculated for a lagrangian torus of an integrable quantum system. The mean curvature one-form is simply related to the canonical connection which determines the geometric phases and polarization linear response. Adiabatic deformations of a quantum system are analyzed in terms of vector bundle classifying maps and related to the mean curvature flow of quantum states. The dielectric response function for a periodic solid is calculated to be the curvature of a connection on a vector bundle.
ContributorsSanborn, Barbara (Author) / Suslov, Sergei K (Thesis advisor) / Suslov, Sergei (Committee member) / Spielberg, John (Committee member) / Quigg, John (Committee member) / Menéndez, Jose (Committee member) / Jones, Donald (Committee member) / Arizona State University (Publisher)
Created2011
Description
Geology and its tangential studies, collectively known and referred to in this thesis as geosciences, have been paramount to the transformation and advancement of society, fundamentally changing the way we view, interact and live with the surrounding natural and built environment. It is important to recognize the value and importance of this interdisciplinary scientific field while reconciling its ties to imperial and colonizing extractive systems which have led to harmful and invasive endeavors. This intersection among geosciences, (environmental) justice studies, and decolonization is intended to promote inclusive pedagogical models through just and equitable methodologies and frameworks as to prevent further injustices and promote recognition and healing of old wounds. By utilizing decolonial frameworks and highlighting the voices of peoples from colonized and exploited landscapes, this annotated syllabus tackles the issues previously described while proposing solutions involving place-based education and the recentering of land within geoscience pedagogical models. (abstract)
ContributorsReed, Cameron E (Author) / Richter, Jennifer (Thesis director) / Semken, Steven (Committee member) / School of Earth and Space Exploration (Contributor, Contributor) / School of Sustainability (Contributor) / Barrett, The Honors College (Contributor)
Created2021-05
Description
The ASU COVID-19 testing lab process was developed to operate as the primary testing site for all ASU staff, students, and specified external individuals. Tests are collected at various collection sites, including a walk-in site at the SDFC and various drive-up sites on campus; analysis is conducted on ASU campus and results are distributed virtually to all patients via the Health Services patient portal. The following is a literature review on past implementations of various process improvement techniques and how they can be applied to the ABCTL testing process to achieve laboratory goals. (abstract)
ContributorsKrell, Abby Elizabeth (Co-author) / Bruner, Ashley (Co-author) / Ramesh, Frankincense (Co-author) / Lewis, Gabriel (Co-author) / Barwey, Ishna (Co-author) / Myers, Jack (Co-author) / Hymer, William (Co-author) / Reagan, Sage (Co-author) / Compton, Carolyn (Thesis director) / McCarville, Daniel R. (Committee member) / Industrial, Systems & Operations Engineering Prgm (Contributor) / Barrett, The Honors College (Contributor)
Created2021-05
ContributorsHaydn, Joseph, 1732-1809 (Composer)
ContributorsHaydn, Joseph, 1732-1809 (Composer)
Description
Factory production is stochastic in nature with time varying input and output processes that are non-stationary stochastic processes. Hence, the principle quantities of interest are random variables. Typical modeling of such behavior involves numerical simulation and statistical analysis. A deterministic closure model leading to a second order model for the product density and product speed has previously been proposed. The resulting partial differential equations (PDE) are compared to discrete event simulations (DES) that simulate factory production as a time dependent M/M/1 queuing system. Three fundamental scenarios for the time dependent influx are studied: An instant step up/down of the mean arrival rate; an exponential step up/down of the mean arrival rate; and periodic variation of the mean arrival rate. It is shown that the second order model, in general, yields significant improvement over current first order models. Specifically, the agreement between the DES and the PDE for the step up and for periodic forcing that is not too rapid is very good. Adding diffusion to the PDE further improves the agreement. The analysis also points to fundamental open issues regarding the deterministic modeling of low signal-to-noise ratio for some stochastic processes and the possibility of resonance in deterministic models that is not present in the original stochastic process.
ContributorsWienke, Matthew (Author) / Armbruster, Dieter (Thesis advisor) / Jones, Donald (Committee member) / Platte, Rodrigo (Committee member) / Gardner, Carl (Committee member) / Ringhofer, Christian (Committee member) / Arizona State University (Publisher)
Created2015
Description
Presented is a study on the chemotaxis reaction process and its relation with flow topology. The effect of coherent structures in turbulent flows is characterized by studying nutrient uptake and the advantage that is received from motile bacteria over other non-motile bacteria. Variability is found to be dependent on the initial location of scalar impurity and can be tied to Lagrangian coherent structures through recent advances in the identification of finite-time transport barriers. Advantage is relatively small for initial nutrient found within high stretching regions of the flow, and nutrient within elliptic structures provide the greatest advantage for motile species. How the flow field and the relevant flow topology lead to such a relation is analyzed.
ContributorsJones, Kimberly (Author) / Tang, Wenbo (Thesis advisor) / Kang, Yun (Committee member) / Jones, Donald (Committee member) / Arizona State University (Publisher)
Created2015
Description
A continuously and stably stratified fluid contained in a square cavity subjected to harmonic body forcing is studied numerically by solving the Navier-Stokes equations under the Boussinesq approximation. Complex dynamics are observed near the onset of instability of the basic state, which is a flow configuration that is always an exact analytical solution of the governing equations. The instability of the basic state to perturbations is first studied with linear stability analysis (Floquet analysis), revealing a multitude of intersecting synchronous and subharmonic resonance tongues in parameter space. A modal reduction method for determining the locus of basic state instability is also shown, greatly simplifying the computational overhead normally required by a Floquet study. Then, a study of the nonlinear governing equations determines the criticality of the basic state's instability, and ultimately characterizes the dynamics of the lowest order spatial mode by the three discovered codimension-two bifurcation points within the resonance tongue. The rich dynamics include a homoclinic doubling cascade that resembles the logistic map and a multitude of gluing bifurcations.
The numerical techniques and methodologies are first demonstrated on a homogeneous fluid contained within a three-dimensional lid-driven cavity. The edge state technique and linear stability analysis through Arnoldi iteration are used to resolve the complex dynamics of the canonical shear-driven benchmark problem. The techniques here lead to a dynamical description of an instability mechanism, and the work serves as a basis for the remainder of the dissertation.
The numerical techniques and methodologies are first demonstrated on a homogeneous fluid contained within a three-dimensional lid-driven cavity. The edge state technique and linear stability analysis through Arnoldi iteration are used to resolve the complex dynamics of the canonical shear-driven benchmark problem. The techniques here lead to a dynamical description of an instability mechanism, and the work serves as a basis for the remainder of the dissertation.
ContributorsYalim, Jason (Author) / Welfert, Bruno D. (Thesis advisor) / Lopez, Juan M. (Thesis advisor) / Jones, Donald (Committee member) / Tang, Wenbo (Committee member) / Platte, Rodrigo (Committee member) / Arizona State University (Publisher)
Created2019
Description
For as long as humans have been working, they have been looking for ways to get that work done better, faster, and more efficient. Over the course of human history, mankind has created innumerable spectacular inventions, all with the goal of making the economy and daily life more efficient. Today, innovations and technological advancements are happening at a pace like never seen before, and technology like automation and artificial intelligence are poised to once again fundamentally alter the way people live and work in society. Whether society is prepared or not, robots are coming to replace human labor, and they are coming fast. In many areas artificial intelligence has disrupted entire industries of the economy. As people continue to make advancements in artificial intelligence, more industries will be disturbed, more jobs will be lost, and entirely new industries and professions will be created in their wake. The future of the economy and society will be determined by how humans adapt to the rapid innovations that are taking place every single day. In this paper I will examine the extent to which automation will take the place of human labor in the future, project the potential effect of automation to future unemployment, and what individuals and society will need to do to adapt to keep pace with rapidly advancing technology. I will also look at the history of automation in the economy. For centuries humans have been advancing technology to make their everyday work more productive and efficient, and for centuries this has forced humans to adapt to the modern technology through things like training and education. The thesis will additionally examine the ways in which the U.S. education system will have to adapt to meet the demands of the advancing economy, and how job retraining programs must be modernized to prepare workers for the changing economy.
ContributorsCunningham, Reed P. (Author) / DeSerpa, Allan (Thesis director) / Haglin, Brett (Committee member) / School of International Letters and Cultures (Contributor) / Department of Finance (Contributor) / Barrett, The Honors College (Contributor)
Created2018-05