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- Creators: School of Mathematical and Statistical Sciences
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Description
In this thesis I introduce a new direction to computing using nonlinear chaotic dynamics. The main idea is rich dynamics of a chaotic system enables us to (1) build better computers that have a flexible instruction set, and (2) carry out computation that conventional computers are not good at it. Here I start from the theory, explaining how one can build a computing logic block using a chaotic system, and then I introduce a new theoretical analysis for chaos computing. Specifically, I demonstrate how unstable periodic orbits and a model based on them explains and predicts how and how well a chaotic system can do computation. Furthermore, since unstable periodic orbits and their stability measures in terms of eigenvalues are extractable from experimental times series, I develop a time series technique for modeling and predicting chaos computing from a given time series of a chaotic system. After building a theoretical framework for chaos computing I proceed to architecture of these chaos-computing blocks to build a sophisticated computing system out of them. I describe how one can arrange and organize these chaos-based blocks to build a computer. I propose a brand new computer architecture using chaos computing, which shifts the limits of conventional computers by introducing flexible instruction set. Our new chaos based computer has a flexible instruction set, meaning that the user can load its desired instruction set to the computer to reconfigure the computer to be an implementation for the desired instruction set. Apart from direct application of chaos theory in generic computation, the application of chaos theory to speech processing is explained and a novel application for chaos theory in speech coding and synthesizing is introduced. More specifically it is demonstrated how a chaotic system can model the natural turbulent flow of the air in the human speech production system and how chaotic orbits can be used to excite a vocal tract model. Also as another approach to build computing system based on nonlinear system, the idea of Logical Stochastic Resonance is studied and adapted to an autoregulatory gene network in the bacteriophage λ.
ContributorsKia, Behnam (Author) / Ditto, William (Thesis advisor) / Huang, Liang (Committee member) / Lai, Ying-Cheng (Committee member) / Helms Tillery, Stephen (Committee member) / Arizona State University (Publisher)
Created2011
Description
What can classical chaos do to quantum systems is a fundamental issue highly relevant to a number of branches in physics. The field of quantum chaos has been active for three decades, where the focus was on non-relativistic quantumsystems described by the Schr¨odinger equation. By developing an efficient method to solve the Dirac equation in the setting where relativistic particles can tunnel between two symmetric cavities through a potential barrier, chaotic cavities are found to suppress the spread in the tunneling rate. Tunneling rate for any given energy assumes a wide range that increases with the energy for integrable classical dynamics. However, for chaotic underlying dynamics, the spread is greatly reduced. A remarkable feature, which is a consequence of Klein tunneling, arise only in relativistc quantum systems that substantial tunneling exists even for particle energy approaching zero. Similar results are found in graphene tunneling devices, implying high relevance of relativistic quantum chaos to the development of such devices. Wave propagation through random media occurs in many physical systems, where interesting phenomena such as branched, fracal-like wave patterns can arise. The generic origin of these wave structures is currently a matter of active debate. It is of fundamental interest to develop a minimal, paradigmaticmodel that can generate robust branched wave structures. In so doing, a general observation in all situations where branched structures emerge is non-Gaussian statistics of wave intensity with an algebraic tail in the probability density function. Thus, a universal algebraic wave-intensity distribution becomes the criterion for the validity of any minimal model of branched wave patterns. Coexistence of competing species in spatially extended ecosystems is key to biodiversity in nature. Understanding the dynamical mechanisms of coexistence is a fundamental problem of continuous interest not only in evolutionary biology but also in nonlinear science. A continuous model is proposed for cyclically competing species and the effect of the interplay between the interaction range and mobility on coexistence is investigated. A transition from coexistence to extinction is uncovered with a non-monotonic behavior in the coexistence probability and switches between spiral and plane-wave patterns arise. Strong mobility can either promote or hamper coexistence, while absent in lattice-based models, can be explained in terms of nonlinear partial differential equations.
ContributorsNi, Xuan (Author) / Lai, Ying-Cheng (Thesis advisor) / Huang, Liang (Committee member) / Yu, Hongbin (Committee member) / Akis, Richard (Committee member) / Arizona State University (Publisher)
Created2012
Description
Complex dynamical systems consisting interacting dynamical units are ubiquitous in nature and society. Predicting and reconstructing nonlinear dynamics of units and the complex interacting networks among them serves the base for the understanding of a variety of collective dynamical phenomena. I present a general method to address the two outstanding problems as a whole based solely on time-series measurements. The method is implemented by incorporating compressive sensing approach that enables an accurate reconstruction of complex dynamical systems in terms of both nodal equations that determines the self-dynamics of units and detailed coupling patterns among units. The representative advantages of the approach are (i) the sparse data requirement which allows for a successful reconstruction from limited measurements, and (ii) general applicability to identical and nonidentical nodal dynamics, and to networks with arbitrary interacting structure, strength and sizes. Another two challenging problem of significant interest in nonlinear dynamics: (i) predicting catastrophes in nonlinear dynamical systems in advance of their occurrences and (ii) predicting the future state for time-varying nonlinear dynamical systems, can be formulated and solved in the framework of compressive sensing using only limited measurements. Once the network structure can be inferred, the dynamics behavior on them can be investigated, for example optimize information spreading dynamics, suppress cascading dynamics and traffic congestion, enhance synchronization, game dynamics, etc. The results can yield insights to control strategies design in the real-world social and natural systems. Since 2004, there has been a tremendous amount of interest in graphene. The most amazing feature of graphene is that there exists linear energy-momentum relationship when energy is low. The quasi-particles inside the system can be treated as chiral, massless Dirac fermions obeying relativistic quantum mechanics. Therefore, the graphene provides one perfect test bed to investigate relativistic quantum phenomena, such as relativistic quantum chaotic scattering and abnormal electron paths induced by klein tunneling. This phenomenon has profound implications to the development of graphene based devices that require stable electronic properties.
ContributorsYang, Rui (Author) / Lai, Ying-Cheng (Thesis advisor) / Duman, Tolga M. (Committee member) / Akis, Richard (Committee member) / Huang, Liang (Committee member) / Arizona State University (Publisher)
Created2012
Description
This research compares shifts in a SuperSpec titanium nitride (TiN) kinetic inductance detector's (KID's) resonant frequency with accepted models for other KIDs. SuperSpec, which is being developed at the University of Colorado Boulder, is an on-chip spectrometer designed with a multiplexed readout with multiple KIDs that is set up for a broadband transmission of these measurements. It is useful for detecting radiation in the mm and sub mm wavelengths which is significant since absorption and reemission of photons by dust causes radiation from distant objects to reach us in infrared and far-infrared bands. In preparation for testing, our team installed stages designed previously by Paul Abers and his group into our cryostat and designed and installed other parts necessary for the cryostat to be able to test devices on the 250 mK stage. This work included the design and construction of additional parts, a new setup for the wiring in the cryostat, the assembly, testing, and installation of several stainless steel coaxial cables for the measurements through the devices, and other cryogenic and low pressure considerations. The SuperSpec KID was successfully tested on this 250 mK stage thus confirming that the new setup is functional. Our results are in agreement with existing models which suggest that the breaking of cooper pairs in the detector's superconductor which occurs in response to temperature, optical load, and readout power will decrease the resonant frequencies. A negative linear relationship in our results appears, as expected, since the parameters are varied only slightly so that a linear approximation is appropriate. We compared the rate at which the resonant frequency responded to temperature and found it to be close to the expected value.
ContributorsDiaz, Heriberto Chacon (Author) / Mauskopf, Philip (Thesis director) / McCartney, Martha (Committee member) / Department of Physics (Contributor) / School of Mathematical and Statistical Sciences (Contributor) / Barrett, The Honors College (Contributor)
Created2018-05
Description
This study estimates the capitalization effect of golf courses in Maricopa County using the hedonic pricing method. It draws upon a dataset of 574,989 residential transactions from 2000 to 2006 to examine how the aesthetic, non-golf benefits of golf courses capitalize across a gradient of proximity measures. The measures for amenity value extend beyond home adjacency and include considerations for homes within a range of discrete walkability buffers of golf courses. The models also distinguish between public and private golf courses as a proxy for the level of golf course access perceived by non-golfers. Unobserved spatial characteristics of the neighborhoods around golf courses are controlled for by increasing the extent of spatial fixed effects from city, to census tract, and finally to 2000 meter golf course ‘neighborhoods.’ The estimation results support two primary conclusions. First, golf course proximity is found to be highly valued for adjacent homes and homes up to 50 meters way from a course, still evident but minimal between 50 and 150 meters, and insignificant at all other distance ranges. Second, private golf courses do not command a higher proximity premia compared to public courses with the exception of homes within 25 to 50 meters of a course, indicating that the non-golf benefits of courses capitalize similarly, regardless of course type. The results of this study motivate further investigation into golf course features that signal access or add value to homes in the range of capitalization, particularly for near-adjacent homes between 50 and 150 meters thought previously not to capitalize.
ContributorsJoiner, Emily (Author) / Abbott, Joshua (Thesis director) / Smith, Kerry (Committee member) / Economics Program in CLAS (Contributor) / School of Sustainability (Contributor) / School of Mathematical and Statistical Sciences (Contributor) / Barrett, The Honors College (Contributor)
Created2018-05
Description
The objective of this paper is to provide an educational diagnostic into the technology of blockchain and its application for the supply chain. Education on the topic is important to prevent misinformation on the capabilities of blockchain. Blockchain as a new technology can be confusing to grasp given the wide possibilities it can provide. This can convolute the topic by being too broad when defined. Instead, the focus will be maintained on explaining the technical details about how and why this technology works in improving the supply chain. The scope of explanation will not be limited to the solutions, but will also detail current problems. Both public and private blockchain networks will be explained and solutions they provide in supply chains. In addition, other non-blockchain systems will be described that provide important pieces in supply chain operations that blockchain cannot provide. Blockchain when applied to the supply chain provides improved consumer transparency, management of resources, logistics, trade finance, and liquidity.
ContributorsKrukar, Joel Michael (Author) / Oke, Adegoke (Thesis director) / Duarte, Brett (Committee member) / Hahn, Richard (Committee member) / School of Mathematical and Statistical Sciences (Contributor) / Department of Economics (Contributor) / Barrett, The Honors College (Contributor)
Created2018-05
Description
The Super Catalan numbers are a known set of numbers which have so far eluded a combinatorial interpretation. Several weighted interpretations have appeared since their discovery, one of which was discovered by William Kuszmaul in 2017. In this paper, we connect the weighted Super Catalan structure created previously by Kuszmaul and a natural $q$-analogue of the Super Catalan numbers. We do this by creating a statistic $\sigma$ for which the $q$ Super Catalan numbers, $S_q(m,n)=\sum_X (-1)^{\mu(X)} q^{\sigma(X)}$. In doing so, we take a step towards finding a strict combinatorial interpretation for the Super Catalan numbers.
ContributorsHouse, John Douglas (Author) / Fishel, Susanna (Thesis director) / Childress, Nancy (Committee member) / School of Mathematical and Statistical Sciences (Contributor) / Barrett, The Honors College (Contributor)
Created2018-05
Description
Construction is a defining characteristic of geometry classes. In a traditional classroom, teachers and students use physical tools (i.e. a compass and straight-edge) in their constructions. However, with modern technology, construction is possible through the use of digital applications such as GeoGebra and Geometer’s SketchPad.
Many other studies have researched the benefits of digital manipulatives and digital environments through student completion of tasks and testing. This study intends to research students’ use of the digital tools and manipulatives, along with the students’ interactions with the digital environment. To this end, I conducted exploratory teaching experiments with two calculus I students.
In the exploratory teaching experiments, students were introduced to a GeoGebra application developed by Fischer (2019), which includes instructional videos and corresponding quizzes, as well as exercises and interactive notepads, where students could use digital tools to construct line segments and circles (corresponding to the physical straight-edge and compass). The application built up the students’ foundational knowledge, culminating in the construction and verbal proof of Euclid’s Elements, Proposition 1 (Euclid, 1733).
The central findings of this thesis are the students’ interactions with the digital environment, with observed changes in their conceptions of radii and circles, and in their use of tools. The students were observed to have conceptions of radii as a process, a geometric shape, and a geometric object. I observed the students’ conceptions of a circle change from a geometric shape to a geometric object, and with that change, observed the students’ use of tools change from a measuring focus to a property focus.
I report a summary of the students’ work and classify their reasoning and actions into the above categories, and an analysis of how the digital environment impacts the students’ conceptions. I also briefly discuss the impact of the findings on pedagogy and future research.
Many other studies have researched the benefits of digital manipulatives and digital environments through student completion of tasks and testing. This study intends to research students’ use of the digital tools and manipulatives, along with the students’ interactions with the digital environment. To this end, I conducted exploratory teaching experiments with two calculus I students.
In the exploratory teaching experiments, students were introduced to a GeoGebra application developed by Fischer (2019), which includes instructional videos and corresponding quizzes, as well as exercises and interactive notepads, where students could use digital tools to construct line segments and circles (corresponding to the physical straight-edge and compass). The application built up the students’ foundational knowledge, culminating in the construction and verbal proof of Euclid’s Elements, Proposition 1 (Euclid, 1733).
The central findings of this thesis are the students’ interactions with the digital environment, with observed changes in their conceptions of radii and circles, and in their use of tools. The students were observed to have conceptions of radii as a process, a geometric shape, and a geometric object. I observed the students’ conceptions of a circle change from a geometric shape to a geometric object, and with that change, observed the students’ use of tools change from a measuring focus to a property focus.
I report a summary of the students’ work and classify their reasoning and actions into the above categories, and an analysis of how the digital environment impacts the students’ conceptions. I also briefly discuss the impact of the findings on pedagogy and future research.
ContributorsSakauye, Noelle Marie (Author) / Roh, Kyeong Hah (Thesis director) / Zandieh, Michelle (Committee member) / School of Mathematical and Statistical Sciences (Contributor) / School of International Letters and Cultures (Contributor) / Barrett, The Honors College (Contributor)
Created2020-05
Description
The original version of Helix, the one I pitched when first deciding to make a video game
for my thesis, is an action-platformer, with the intent of metroidvania-style progression
and an interconnected world map.
The current version of Helix is a turn based role-playing game, with the intent of roguelike
gameplay and a dark fantasy theme. We will first be exploring the challenges that came
with programming my own game - not quite from scratch, but also without a prebuilt
engine - then transition into game design and how Helix has evolved from its original form
to what we see today.
for my thesis, is an action-platformer, with the intent of metroidvania-style progression
and an interconnected world map.
The current version of Helix is a turn based role-playing game, with the intent of roguelike
gameplay and a dark fantasy theme. We will first be exploring the challenges that came
with programming my own game - not quite from scratch, but also without a prebuilt
engine - then transition into game design and how Helix has evolved from its original form
to what we see today.
ContributorsDiscipulo, Isaiah K (Author) / Meuth, Ryan (Thesis director) / Kobayashi, Yoshihiro (Committee member) / School of Mathematical and Statistical Sciences (Contributor) / Computer Science and Engineering Program (Contributor) / Barrett, The Honors College (Contributor)
Created2020-05
Description
This thesis evaluates the viability of an original design for a cost-effective wheel-mounted dynamometer for road vehicles. The goal is to show whether or not a device that generates torque and horsepower curves by processing accelerometer data collected at the edge of a wheel can yield results that are comparable to results obtained using a conventional chassis dynamometer. Torque curves were generated via the experimental method under a variety of circumstances and also obtained professionally by a precision engine testing company. Metrics were created to measure the precision of the experimental device's ability to consistently generate torque curves and also to compare the similarity of these curves to the professionally obtained torque curves. The results revealed that although the test device does not quite provide the same level of precision as the professional chassis dynamometer, it does create torque curves that closely resemble the chassis dynamometer torque curves and exhibit a consistency between trials comparable to the professional results, even on rough road surfaces. The results suggest that the test device provides enough accuracy and precision to satisfy the needs of most consumers interested in measuring their vehicle's engine performance but probably lacks the level of accuracy and precision needed to appeal to professionals.
ContributorsKing, Michael (Author) / Ren, Yi (Thesis director) / Spanias, Andreas (Committee member) / School of Mathematical and Statistical Sciences (Contributor) / Mechanical and Aerospace Engineering Program (Contributor) / Barrett, The Honors College (Contributor)
Created2018-05