Matching Items (127)
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
A novel concept for integration of flame-assisted fuel cells (FFC) with a gas turbine is analyzed in this paper. Six different fuels (CH4, C3H8, JP-4, JP-5, JP-10(L), and H2) are investigated for the analytical model of the FFC integrated gas turbine hybrid system. As equivalence ratio increases, the efficiency of the hybrid system increases initially then decreases because the decreasing flow rate of air begins to outweigh the increasing hydrogen concentration. This occurs at an equivalence ratio of 2 for CH4. The thermodynamic cycle is analyzed using a temperature entropy diagram and a pressure volume diagram. These thermodynamic diagrams show as equivalence ratio increases, the power generated by the turbine in the hybrid setup decreases. Thermodynamic analysis was performed to verify that energy is conserved and the total chemical energy going into the system was equal to the heat rejected by the system plus the power generated by the system. Of the six fuels, the hybrid system performs best with H2 as the fuel. The electrical efficiency with H2 is predicted to be 27%, CH4 is 24%, C3H8 is 22%, JP-4 is 21%, JP-5 is 20%, and JP-10(L) is 20%. When H2 fuel is used, the overall integrated system is predicted to be 24.5% more efficient than the standard gas turbine system. The integrated system is predicted to be 23.0% more efficient with CH4, 21.9% more efficient with C3H8, 22.7% more efficient with JP-4, 21.3% more efficient with JP-5, and 20.8% more efficient with JP-10(L). The sensitivity of the model is investigated using various fuel utilizations. When CH4 fuel is used, the integrated system is predicted to be 22.7% more efficient with a fuel utilization efficiency of 90% compared to that of 30%.
ContributorsRupiper, Lauren Nicole (Author) / Milcarek, Ryan (Thesis director) / Wang, Liping (Committee member) / Mechanical and Aerospace Engineering Program (Contributor) / School for Engineering of Matter,Transport & Enrgy (Contributor) / Barrett, The Honors College (Contributor)
Created2021-05
Description
Production from a high pressure gas well at a high production-rate encounters the risk of operating near the choking condition for a compressible flow in porous media. The unbounded gas pressure gradient near the point of choking, which is located near the wellbore, generates an effective tensile stress on the porous rock frame. This tensile stress almost always exceeds the tensile strength of the rock and it causes a tensile failure of the rock, leading to wellbore instability. In a porous rock, not all pores are choked at the same flow rate, and when just one pore is choked, the flow through the entire porous medium should be considered choked as the gas pressure gradient at the point of choking becomes singular. This thesis investigates the choking condition for compressible gas flow in a single microscopic pore. Quasi-one-dimensional analysis and axisymmetric numerical simulations of compressible gas flow in a pore scale varicose tube with a number of bumps are carried out, and the local Mach number and pressure along the tube are computed for the flow near choking condition. The effects of tube length, inlet-to-outlet pressure ratio, the number of bumps and the amplitude of the bumps on the choking condition are obtained. These critical values provide guidance for avoiding the choking condition in practice.
ContributorsYuan, Jing (Author) / Chen, Kangping (Thesis advisor) / Wang, Liping (Committee member) / Huang, Huei-Ping (Committee member) / Arizona State University (Publisher)
Created2013
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
Tesla turbo-machinery offers a robust, easily manufactured, extremely versatile prime mover with inherent capabilities making it perhaps the best, if not the only, solution for certain niche applications. The goal of this thesis is not to optimize the performance of the Tesla turbine, but to compare its performance with various working fluids. Theoretical and experimental analyses of a turbine-generator assembly utilizing compressed air, saturated steam and water as the working fluids were performed and are presented in this work. A brief background and explanation of the technology is provided along with potential applications. A theoretical thermodynamic analysis is outlined, resulting in turbine and rotor efficiencies, power outputs and Reynolds numbers calculated for the turbine for various combinations of working fluids and inlet nozzles. The results indicate the turbine is capable of achieving a turbine efficiency of 31.17 ± 3.61% and an estimated rotor efficiency 95 ± 9.32%. These efficiencies are promising considering the numerous losses still present in the current design. Calculation of the Reynolds number provided some capability to determine the flow behavior and how that behavior impacts the performance and efficiency of the Tesla turbine. It was determined that turbulence in the flow is essential to achieving high power outputs and high efficiency. Although the efficiency, after peaking, begins to slightly taper off as the flow becomes increasingly turbulent, the power output maintains a steady linear increase.
ContributorsPeshlakai, Aaron (Author) / Phelan, Patrick (Thesis advisor) / Trimble, Steve (Committee member) / Wang, Liping (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
This work summarizes the development of a dynamic measurement platform in a cryostat to measure sample temperature response to space-like conditions and the creation a MATLAB theoretical model to predict sample temperature responses in the platform itself. An interesting variable-emittance sample called a Fabry-Perot emitter was studied for its thermal homeostasis behavior using the two developments. Using the measurement platform, it was shown that there was no thermal homeostatic behavior demonstrated by the sample at steady state temperatures. Theoretical calculations show other ways to demonstrate the cooling homeostasis behavior through time-varying heat inputs. Factors within the system such as heat loss and thermal mass contributed to an inhibited sample performance in the platform. Future work will have to be conducted, not only to verify the findings of the initial experiments but also to improve the measurement platform and the theoretical model.
ContributorsBoman, Neal D (Author) / Wang, Liping (Thesis director) / Taylor, Syndey (Committee member) / Mechanical and Aerospace Engineering Program (Contributor, Contributor) / Barrett, The Honors College (Contributor)
Created2021-05
Description
A thermochromic mid-infrared filter is designed, where a spectrally-selective transmittance peak exists while vanadium dioxide layers are below their transition temperature but broad opaqueness is observed below the transition temperature. This filter takes advantage of interference effects between a silicon spacer and insulating vanadium dioxide to create the transmittance peak and the drastic optical property change between insulating and metallic vanadium dioxide. The theoretical performance of the filter in energy dissipation and thermal camouflaging applications is analyzed and can be optimized by tuning the thicknesses of the thin-film layers.
ContributorsChao, Jeremy (Author) / Wang, Liping (Thesis director) / Taylor, Sydney (Committee member) / Mechanical and Aerospace Engineering Program (Contributor, Contributor) / Barrett, The Honors College (Contributor)
Created2021-05
Description
Students across the United States lack the necessary skills to be successful college students in Science, Technology and Math (STEM) majors and as a result post-secondary institutions are developing summer bridge programs to aid in their transition. As they develop these programs, effective theory and approach are critical to developing successful programs. Though there are a multitude of theories on successful student development, a focus on self-efficacy is critical. Summer Bridge programs across the country as well as the Bio Bridge summer program at Arizona State University were studied alone and through the lens of Cognitive Self-Efficacy Theory as mentioned in Albert Bandura's "Perceived Self-Efficacy in Cognitive Development and Functioning." Cognitive Self-Efficacy Theory provides a framework for self-efficacy development in academic settings. An analysis of fifteen bridge programs found that a large majority focused on developing academic capabilities and often overlooked development of community and social efficacy. An even larger number failed to focus on personal psychology in managing self-debilitating thought patterns based on published goals. Further, Arizona State University's Bio Bridge program could not be considered successful at developing cognitive self-efficacy or increasing retention as data was inconclusive. However, Bio Bridge was tremendously successful at developing social efficacy and community among participants and faculty. Further research and better evaluative techniques need to be developed to understand the program's effectiveness in cognitive self-efficacy development and retention.
ContributorsTummala, Sailesh Vardhan (Author) / Orchinik, Miles (Thesis director) / Brownell, Sara (Committee member) / Shortlidge, Erin (Committee member) / Barrett, The Honors College (Contributor) / School of Life Sciences (Contributor)
Created2015-05
Description
Zeolitic Imidazolate Frameworks (ZIFs) are a promising technology for the separation of gases. ZIFs represent a type of hybrid material that is a subset of metal organic frameworks while displaying zeolite properties. ZIFs have tunable pore metrics, high thermal stability, and large surface areas giving them advantages over traditional zeolites. The experiment sought to determine the flux of hexane vapor through ZIF-68 with Fourier Transform Infrared Spectroscopy (FTIR) mapping. FTIR mapping was used to obtain three spectra per crystal and the concentration gradient was analyzed to determine the flux. ZIF-68 was completely stable when loaded with hexane and exposed to the atmosphere. There was no hexane diffusion out of the crystal. As a result, ZIF-68 was heated to 50°C to increase diffusion and calculate the flux. ZIF-68 adhered to Knudsen Diffusion, and the flux was calculated to be 2.00*10-5 kg mol/s*m2. The small flux occurred because almost no concentration gradient was obtained through the crystal. It was hypothesized that the resistance in the crystal was substantially lower than the resistance at the boundary layer, which would have caused a small concentration gradient. Using film mass transfer theory, the resistance inside the crystal was found to be 1200 times lower than the resistance at the boundary layer confirming the hypothesis.
ContributorsSigrist, Dallas Dale (Author) / Lin, Jerry (Thesis director) / Wang, Liping (Committee member) / Chemical Engineering Program (Contributor) / Barrett, The Honors College (Contributor)
Created2016-05